analysis of astronomical spectroscopy

Analysis and Interpretation of Astronomical Spectra 1

Analysis and Interpretation of

Astronomical Spectra

Theoretical Background and

Practical Applications for

Amateur Astronomers

Richard Walker

Version 8.7 07/2013


Table of Contents

1 Introduction .................................................................................................................. 7

2 Photons – Messengers from the Universe ............................................................... 8

2.1 Photons transport Information and Energy ..................................................................................... 8 2.2 The Duality of Waves and Particles ................................................................................................. 8 2.3 The Quantisation of the Electromagnetic Radiation....................................................................... 8 2.4 Properties of the Photons ................................................................................................................. 9

3 The Continuum ........................................................................................................... 10

3.1 Black Body Radiation and the Course of the Continuum Level .................................................. 10 3.2 Wien's Displacement Law ............................................................................................................. 10 3.3 The Pseudo Continuum .................................................................................................................. 11

4 Spectroscopic Wavelength Domains ....................................................................... 13

4.1 The Usable Spectral Range for Amateurs .................................................................................... 13 4.2 The Selection of the Spectral Range ............................................................................................ 13 4.3 Terminology of the Spectroscopic Wavelength Domains ........................................................... 14

5 Typology of the Spectra ............................................................................................ 15

5.1 Continuous Spectrum .................................................................................................................... 15 5.2 Absorption Spectrum ..................................................................................................................... 15 5.3 Emission Spectrum......................................................................................................................... 15 5.4 Absorption Band Spectrum............................................................................................................ 16 5.5 Band Spectrum with Inversely Running Intensity Gradient ........................................................ 16 5.6 Mixed Emission- and Absorption Spectrum ................................................................................. 17 5.7 Composite Spectrum...................................................................................................................... 17 5.8 Reflection Spectrum....................................................................................................................... 18 5.9 Cometary Spectrum ....................................................................................................................... 18

6 Form and Intensity of the Spectral Lines ................................................................ 19

6.1 The Form of the Spectral Line ....................................................................................................... 19 6.2 The Information Content of the Line Shape ................................................................................. 19 6.3 Blends .............................................................................................................................................. 19 6.4 The Saturation of Absorption Line in the Spectral Diagram ....................................................... 19 6.5 The Oversaturated Emission Line in the Spectral Diagram ........................................................ 20

7 The Measurement of the Spectral Lines ................................................................. 21

7.1 Methods and Reference Values of the Intensity Measurement ................................................. 21 7.2 Metrological Differences between Absorption and Emission Lines .......................................... 21 7.3 The Peak Intensity P ....................................................................................................................... 22 7.4 Full Width at Half Maximum Height ............................................................................... 22 7.5 , Equivalent Width .................................................................................................................... 23 7.6 Normalised Equivalent Width ................................................................................................. 24 7.7 FWZI Full Width at Zero Intensity ............................................................................................. 24 7.8 Influence of the Spectrograph Resolution on the FWHM- and EW Values ............................... 24 7.9 Practical Consequences for the FWHM and EW Measurements ............................................... 26 7.10 The Measurement of the Wavelength .......................................................................................... 26 7.11 Additional Measurement Options ................................................................................................. 26

8 Calibration and Normalisation of Spectra ............................................................... 27

8.1 The Calibration of the Wavelength ............................................................................................... 27


8.2 The Selective Attenuation of the Continuum Intensity ............................................................... 27 8.3 Relationship Between Original-Continuum and Pseudo-Continuum ...................... 28 8.4 The Importance of the Pseudo-Continuum .................................................................................. 29 8.5 Rectification of the Pseudo-Continuum ....................................................................................... 29 8.6 The Relative Radiometric Profile Correction with a Synthetic Continuum ................................ 31 8.7 The Relative Radiometric Profile Correction with Recorded Standard Stars ............................ 33 8.8 The Absolute Flux Calibration ....................................................................................................... 35 8.9 The Intensity Comparison between Different Spectral Lines ..................................................... 35

9 Visible Effects of Quantum Mechanics.................................................................... 36

9.1 Textbook Example Hydrogen Atom and Balmer Series ............................................................... 36 9.2 The Balmer Series .......................................................................................................................... 37 9.3 Spectral Lines of Other Atoms ...................................................................................................... 38

10 Wavelength and Energy ............................................................................................ 39

10.1 Planck’s Energy Equation .............................................................................................................. 39 10.2 Units for Energy and Wavelength ................................................................................................. 39 10.3 The Photon Energy of the Balmer Series ...................................................................................... 40 10.4 Balmer- Paschen- and Bracket Continuum .................................................................................. 41

11 Ionisation Stage and Degree of Ionisation .............................................................. 42

11.1 The Lyman Limit of Hydrogen ........................................................................................................ 42 11.2 Ionisation Stage versus Degree of Ionisation .............................................................................. 42 11.3 Astrophysical Form of Notation for the Ionisation Stage ............................................................ 42

12 Forbidden Lines or –Transitions .............................................................................. 43

13 The Spectral Classes ................................................................................................. 44

13.1 Preliminary Remarks ...................................................................................................................... 44 13.2 The Fraunhofer Lines ..................................................................................................................... 44 13.3 Further Development Steps ........................................................................................................... 45 13.4 The Harvard System ....................................................................................................................... 46 13.5 “Early” and “Late” Spectral Types ................................................................................................. 47 13.6 The MK (Morgan Keenan) or Yerkes System ............................................................................... 47 13.7 Further Adaptations up to the Present ......................................................................................... 47 13.8 The Rough Determination of the Spectral Class ......................................................................... 49 13.9 Effect of the Luminosity Class on the Line Width ........................................................................ 53

14 The Hertzsprung - Russell Diagram (HRD) .............................................................. 54

14.1 Introduction to the Basic Version .................................................................................................. 54 14.2 The Absolute Magnitude and Photospheric Temperature of the Star ....................................... 55 14.3 The Evolution of the Sun in the HRD ............................................................................................ 56 14.4 The Evolution of Massive Stars ..................................................................................................... 57 14.5 The Relation between Stellar Mass and Life Expectancy ........................................................... 57 14.6 Age Determination of Star Clusters .............................................................................................. 58

15 The Measurement of the Radial Velocity ................................................................ 59

15.1 The Doppler Effect.......................................................................................................................... 59 15.2 The Measurement of the Doppler Shift ........................................................................................ 60 15.3 Radial Velocities of nearby Stars .................................................................................................. 60 15.4 Relative Displacement within a Spectrum caused by the Doppler Effect ................................. 60 15.5 Radial Velocities of Galaxies ......................................................................................................... 60 15.6 Short Excursus on "Hubble time" tH .............................................................................................. 61 15.7 Radial- and Cosmological Recess Velocities of the Messier Galaxies ...................................... 62


15.8 Recess Velocity of the Quasar 3C273 ......................................................................................... 64

16 The Measurement of the Rotation Velocity ............................................................ 65

16.1 Terms and Definitions .................................................................................................................... 65 16.2 The Rotation Velocity of the Large Planets .................................................................................. 65 16.3 The Rotation Velocity of the Sun ................................................................................................... 66 16.4 The Rotation Velocity of Galaxies ................................................................................................. 66 16.5 Calculation of the Value with the Velocity Difference ................................................. 66 16.6 The Rotation Velocity of the Stars ................................................................................................ 67 16.7 The Rotation Velocity of the Circumstellar Disks around Be Stars ............................................ 69

17 The Measurement of the Expansion Velocity ......................................................... 73

17.1 P Cygni Profiles .............................................................................................................................. 73 17.2 Inverse P Cygni Profiles ................................................................................................................. 73 17.3 Broadening of the Emission Lines ................................................................................................. 74 17.4 Splitting of the Emission Lines ...................................................................................................... 74

18 The Measurement of the Stellar Photosphere Temperature ................................ 75

18.1 Introduction .................................................................................................................................... 75 18.2 Temperature Estimation of the Spectral Class ............................................................................ 75 18.3 Temperature Estimation Applying Wien’s Displacement Law.................................................... 76 18.4 Temperature Determination Based on Individual Lines .............................................................. 79 18.5 The “Balmer-Thermometer“........................................................................................................... 79 18.6 Precision Temperature Measurements by Analysis of Individual Lines .................................... 80

19 Spectroscopic Binary Stars ....................................................................................... 81

19.1 Terms and Definitions .................................................................................................................... 81 19.2 Effects of the Binary Orbit on the Spectrum ................................................................................ 82 19.3 The Perspectivic Influence from the Spatial Orbit-Orientation .................................................. 84 19.4 The Estimation of some Orbital Parameters ................................................................................ 85

20 Balmer–Decrement ................................................................................................... 87

20.1 Introduction .................................................................................................................................... 87 20.2 Qualitative Analysis ........................................................................................................................ 87 20.3 Quantitative Analysis ..................................................................................................................... 88 20.4 Quantitative Definition of the Balmer-Decrement ....................................................................... 88 20.5 Experiments with the Balmer Decrement .................................................................................... 89

21 Spectroscopic Determination of Interstellar Extinction ........................................ 90

21.1 Spectroscopic Definition of the Interstellar Extinction ............................................................... 90 21.2 Extinction Correction with the Measured Balmer Decrement .................................................... 90 21.3 Balmer Decrement and Color Excess ........................................................................................... 91 21.4 Balmer-Decrement and Extinction Correction in the Amateur Sector ....................................... 91

22 Plasma Diagnostics for Emission Nebulae ............................................................. 92

22.1 Preliminary Remarks ...................................................................................................................... 92 22.2 Overview of the Phenomenon “Emission Nebulae” .................................................................... 92 22.3 Common Spectral Characteristics of Emission Nebulae ............................................................ 92 22.4 Ionisation Processes in H II Emission Nebulae ............................................................................ 92 22.5 Recombination Process ................................................................................................................. 93 22.6 Line Emission by Electron Transition ............................................................................................ 93 22.7 Line Emission by Collision Excitation ........................................................................................... 94 22.8 Line Emission by Permitted Transitions (Direct absorption) ...................................................... 94 22.9 Line Emission by Forbidden Transitions ....................................................................................... 94


22.10 Scheme of the Photon Conversion Process in Emission Nebulae ......................................... 96 22.11 Practical Aspects of Plasma Diagnostics ................................................................................. 97 22.12 Determination of the Excitation Class .................................................................................. 97 22.13 The Excitation Class as an Indicator for Plasma Diagnostics ................................................. 98 22.14 Estimation of Te and Ne with the O III and N II Method ......................................................... 99 22.15 Estimation of the Electron Density from the S II and O II Ratio ............................................. 99 22.16 Distinguishing Characteristics in the Spectra of Emission Nebulae .................................... 100

23 Analysis of the Chemical Composition ................................................................. 101

23.1 Astrophysical Definition of Element Abundance ....................................................................... 101 23.2 Astrophysical Definition of Metal Abundance Z (Metallicity) ................................................... 101 23.3 Quantitative Determination of the Chemical Composition ....................................................... 101 23.4 Relative Abundance-Comparison at Stars of Similar Spectral Class ....................................... 102

24 Spectroscopic Parallax ........................................................................................... 103

24.1 Spectroscopic Possibilities of Distance Measurement ............................................................. 103 24.2 Term and Principle of Spectroscopic Parallax ........................................................................... 103 24.3 Spectral Class and Absolute Magnitude .................................................................................... 103 24.4 Distance Modulus......................................................................................................................... 105 24.5 Calculation of the Distance with the Distance Modulus ........................................................... 105 24.6 Examples for Main Sequence Stars (with Literature Values) ................................................... 105

25 Identification of Spectral Lines ............................................................................. 106

25.1 Task and Requirements ............................................................................................................... 106 25.2 Practical Problems and Solving Strategies ................................................................................ 106 25.3 Tools for the Identification of Spectral Lines ............................................................................. 107

26 Literature and Internet ........................................................................................... 108


Change log of the Document Versions

Version 6.0:

General: Correction of several typing errors Sect. 4.2: Supplement of the Spectro Tool Program by Peter Schlatter Sect. 7: General revision “The Measurement of the Spectral Lines” Sect. 8: General revision “Calibration and Normalisation of Spectra” Sect. 15.8: General revision “Recess Velocity of the Quasar 3C273”, Sect. 16.5: Correction of errors concerning formulas {24} and {25} and related variables Sect. 19.4: Supplement Sect. 20: Several supplements. New: formula {54a} and {54b}

Version 7.0:

Table of content: Inserting of an additional subtitle level Sect. 3.0: Some minor addenda Sect. 5.4: New: „Graph of the high-resolution O2 band spectrum of the Fraunhofer A line“ Sect. 5.5: New: „Band spectra with inversely running intensity gradient“ Sect. 6.0: Some addenda: “Form and Intensity of the Spectral Lines” Sect. 7: General revision “The Measurement of the Spectral Lines” Sect. 8: General revision “Calibration and Normalisation of Spectra“ Sect. 10: Introduction of the unit “Wavenumber” and “Effective Temperature” Teff Sect. 19: General revision “Tests with the Balmer Decrement Sect. 20: General revision “Application of Extinction Correction in the Amateur Sector“ Sect. 22: Practical Tips for Identifying Spectral Lines Entire Document: Additional formulas, therefore partially renumbering.

Version 8.0:

Sect. 5.9: New: “Cometary Spectra“ Sect. 6.4: Supplement Sect. 10.4: New: “Balmer- Paschen- and Bracket Continuum” Sect. 18: New: “The Measurement of the Stellar Photosphere Temperature“ Sect. 23: New: “Chemical Composition Analysis“ Sect. 24: New: “Spectroscopic Parallax”

Versions 8.5 and 8.6:

Sect. 8: General revision “Calibration and Normalisation of Spectra” in consideration of re-cent test results on "correction curves”.

Version 8.7:

Sect. 15.7: Review and corrections in the table of Messier galaxies and appropriate ad-justments in the text.


1 Introduction

Technological advances like CCD cameras, but also affordable spectrographs on the market cause a significant upturn of spectroscopy within the community of amateur astronomers. Further freeware programs and detailed instructions are available to enable the processing, calibrating and normalising of the spectra. Several publications explain the function and even the self-construction of spectrographs and further many papers can be found on spe-cific monitoring projects. The numerous possibilities however for analysis and interpreta-tion of the spectral profiles, still suffer from a considerable deficit of suitable literature.

This publication presents as a supplement practical applications and the appropriate astro-physical backgrounds. Further the Spectroscopic Atlas for Amateur Astronomers [33] is available, which covers all relevant spectral classes by commenting most of the lines, visi-ble in medium resolved spectral profiles. It is primarily intended to be used as a tool for the line identification. Each spectral class, relevant for amateurs, is presented with their main characteristics and typical features.

Further, a detailed tutorial [30] (German only) on the processing of the spectra with the Vspec and IRIS software is downloadable. Since all documents should remain independent, some text and graphics are included redundantly.

Spectroscopy is the real key to astrophysics. Without them, our current picture of the uni-verse would be unthinkable. The photons, which have been several million years “on the road” to our CCD cameras, provide an amazing wealth of information about the origin ob-ject. This may be fascinating, even without the ambition to strive for academic laurels. Fur-ther there is no need for a degree in physics with, specialisation in mathematics, for a re-warding deal with this matter. Required is some basic knowledge in physics, the ability to calculate simple formulas with given numbers on a technical calculator and finally a healthy dose of enthusiasm.

Also the necessary chemical knowledge remains very limited. In the hot stellar atmos-pheres and excited nebulae the individual elements can hardly undergo any chemical com-pounds. Only in the outermost layers of relatively "cool" stars, some very simple molecules can survive. More complex chemical compounds are found only in really cold dust clouds of the interstellar space and in planetary atmospheres – a typical domain of radio astronomy. Moreover in stellar astronomy, all elements, except hydrogen and helium, are simplistically called as "metals".

The share of hydrogen and helium of the visible matter in the universe is still about 99%. The most "metals", have been formed long time after the Big Bang within the first genera-tion of massive stars, which distributed it at the end of their live in to the surrounding space by Supernova explosions or repelled by Planetary Nebulae.

Much more complex, however, is the quantum-mechanically induced behavior of the ex-cited atoms in stellar atmospheres. These effects are directly responsible for the formation and shape of the spectral lines. Anyway for the practical work of the "average amateur" some basic knowledge is sufficient.

Richard Walker, CH 8911-Rifferswil © [email protected]

mailto:[email protected]


2 Photons – Messengers from the Universe

2.1 Photons transport Information and Energy

Photons are generated in stars, carrying valuable information over immense periods of time and unimaginable distances, and finally end in the pixel field of our CCD cameras. By their “destruction” they deposit the valuable information, contributing electrons to the selective saturation of individual pixels – in fact trivial, but somehow still fascinating. By switching a spectrograph between the telescope and camera the photons will provide a wealth of in-formation which surpasses by far the simple photographic image of the object. It is there-fore worthwhile to make some considerations about this absolutely most important link in the chain of transmission.

It was on the threshold of the 20th Century, when it caused tremendous "headaches" to the entire community of former top physicists. This intellectual "show of strength" finally cul-minated in the development of quantum mechanics. The list of participants reads substan-tially like the Who's Who of physics at the beginning of the 20th century: Werner Heisen-berg, Albert Einstein, Erwin Schrödinger, Max Born, Wolfgang Pauli, Niels Bohr, just to name a few. Quantum mechanics became, besides the theory of relativity, the second revo-lutionary theory of the 20th Century. For the rough understanding about the formation of the photons and finally of the spectra, the necessary knowledge is reduced to some key points of this theory.

2.2 The Duality of Waves and Particles

Electromagnetic radiation has both wave and particle nature. This principle applies to the entire spectrum. Starting with the long radio waves, it remains valid on the domains of in-frared radiation, visible light, up to the extremely short-wave ultraviolet, X-rays and gamma rays.

Source: Wikipedia For our present technical applications, both properties are indispensable. For the entire telecommunications, radio, TV, mobile telephony, as well as the radar and the microwave grill it's the wave character. The CCD photography, light meter of cameras, gas discharge lamps (eg energy saving light bulbs and street lighting), and last but not least, the spectros-copy would not work without the particle nature.

2.3 The Quantisation of the Electromagnetic Radiation

It was one of the pioneering discoveries of quantum mechanics that electromagnetic radia-tion is not emitted continuously but rather quantised (or quasi "clocked"). Simplified ex-


plained a minimum "dose" of electromagnetic radiation is generated, called “photon”, which belongs to the Bosons within the "zoo" of elementary particles.

2.4 Properties of the Photons

– Without external influence photons have an infinitely long life

– Their production and “destruction” takes place in a variety of physical processes. Rele-vant for the spectroscopy are electron transitions between different atomic orbital (de-tails see later).

– A photon always moves with light speed. According to the Special Relativity Theory (SRT) it can therefore possess no rest mass.

– Each photon has a specific frequency (or wavelength), which determines its energy – the higher the frequency, the higher the energy of the photon (details see sect. 10).


3 The Continuum

3.1 Black Body Radiation and the Course of the Continuum Level

The red curve, hereafter referred to as continuum level corresponds to the course of the radiation intensity or flux density, plotted over the wavelength (increasing from left to right). As a fit to the blue continuum it is cleaned by any existing absorption or emission lines (blue curve). The entire area between the horizontal wavelength axis and the contin-uum level is called continuum [5].

Most important physical basis for the origin and course of the continuum is the so-called black body radiation. The blackbody is a theoretical working model which, in that perfec-tion, doesn’t exist in nature.

For most amateurs it is sufficient to know, that:

– The blackbody is an ideal absorber which absorbs broadband electromagnetic radiation, regardless of the wavelength, completely and uniformly.

– The ideal black body represents a thermal radiation source, which emits a broad-band electromagnetic radiation, according to the Planck's radiation law, with an exclusively temperature-dependent intensity profile.

– Stars in most cases may simplified be considered as black-body radiators.

3.2 Wien's Displacement Law

This theory has practical relevance for us because the intensity profile of the spectrum pro-vides information about the temperature of the radiator! The radiation distribution of differ-ent stars shows bell-shaped curves, whose peak intensity shifts to shorter wavelength, re-spectively higher frequency with increasing temperature (Planck's radiation law).

Continuum Level Ic

C o n t i n u u m

Inten-sity

Wavelength [Å]

0 5000 10‘000 15‘000 20‘000

T=12‘000 Kλmax=2415 Å

T=6000 Kλmax=4830 Å

T=3000 Kλmax=9660 Å


With Wien's displacement law (German physicist Wilhelm Wien 1864-1928) and the given wavelength

[Å] of the maximum radiation intensity it is theoretically possible to

calculate the atmosphere temperature [K] of a star. This is also called “Effective tempera-ture” or “Photosphere temperature”.

[Å]: Angström, 1 Å = 10-10m [K]: Kelvin K ≈ °Celsius + 273°

Examples: Alnitak = ca. 25‘000 K

= 1‘160 Å (Ultraviolet)

Sun = ca. 5‘800 K = 4‘996 Å (Green)

Betelgeuse = ca. 3‘450 K = 8‘400 Å (Infrared)

3.3 The Pseudo Continuum

By all stellar spectra, the course of the unprocessed continuum differs strongly from the theoretical shape of reference curves, regardless if recorded with professional or amateur equipments. The reasons are primarily interstellar, atmospheric and instrument-specific ef-fects (telescope, spectrograph, camera), which distort the original intensity course of the spectral profile to a so called pseudo continuum . Therefore, the Wien’s displacement law, on the basis of the maximum profile intensity, can be observed only qualitatively. The following chart shows the superimposed spectral profiles (pseudo continua) of all bright Orion stars, obtained with a simple transmission grating (200L/mm), a Canon compact camera (Powershot S 60) and processed with the Vspec software. Denoted are here the spectral classes, as well as some identified absorption lines.

Here it is obvious, that the profile shapes and their maximum intensities of the late O- and early B-classes (sect. 13) are nearly identical. As expected, this intensity is by Rigel, a slightly lesser hot, late-B giant (green profile), and in stark extent by the cool M-giant Betel-geuse (orange profile), shifted to the right towards larger wavelengths. Theoretically and according to sect. 3.2, the maximum intensities of the O and B stars would be located far left, outside of the diagram in the UV range, for the cold Betelgeuse far right and also outside the diagram in the IR range. Main causes for this error are the spec-tral selectivity of the CCD chip and the IR filter in the compact camera, pretending that all

Alnilam B0Ia

Alnitak O9.7Ib

Relative

Intensity

Wavelength [Angström]

Hβ

4861 A

Hγ 4

340 A

Hδ

4102 A

Bellatrix B2III

Mintaka O9.5II

Rigel B8Ia

Saiph B0.5Ia

Beteigeuze M1-2Ia-Iab

He I 4

471 A

OII

4638/-

49 A

TiO

TiOTiO

TiO

TiO

TiOTiO

Na I 5

890 A


the peaks would be located within the diagram. Here is also clearly visible, that the absorp-tion lines (sect. 5.2) are quasi "imprinted" on the continuum profile, similar to the modula-tion on a carrier wave. These lines carry the information about the object, the course of the continuum reveals only the temperature of the radiator. The profile of Betelgeuse shows impressively, that the spectra of cool stars are dominated by broad molecular titanium ox-ide (TiO) bands (sect. 5.4). The example also shows the dramatic influence of the spectral characteristics of the camera. In the blue wavelength range, the sensitivity of most cameras drops quickly. Astronomical cameras usually have easy removable/upgradable IR filters, ex-clusively used for the astrophotography and without them spectra can be recorded well in to the IR range.


4 Spectroscopic Wavelength Domains

4.1 The Usable Spectral Range for Amateurs

The professional astronomers nowadays study the objects in nearly the entire electro-magnetic spectrum – including also radio astronomy. Also space telescopes are used, which are increasingly optimised for the infrared region in order to record the extremely red-shifted spectra of objects from the early days of the universe (sect.15.5–15.8). For the ground-based amateur, equipped with standard telescopes and spectrographs only a mod-est fraction of this domain is available. The usable range for us is, in addition to the specific design features of the spectrograph, limited mainly by the spectral characteristics of the camera including any filters. The Meade DSI III or Atik 314L+ e.g. achieves with the DADOS spectrograph useful results in the range of approximately 3800 – 8000 Å, i.e. throughout the visible domain and the near infrared part of the spectrum. Here also the best known and best documented lines are located, such as the hydrogen lines of H-Balmer series and the Fraunhofer lines (see later).

4.2 The Selection of the Spectral Range

For high-resolution spectra, the choice of the range is normally determined by a specific monitoring project or the interest in particular lines. Perhaps also the calibration lamp emission lines have to be considered in the planning of the recorded section.

For low-resolution, broadband spectra mostly the range of the H-Balmer series is preferred (sect. 9). Hot O- and B- stars can be taken rather in the short-wave part, because their maximum radiation lies in the UV range. It usually makes little sense to record the area on the red side of Hα, except the emission lines of P Cygni, Be stars, as well as from emission line nebulae (sect. 22). Between approximately 6,200 – 7,700Å (see picture below), it lit-erally swarms of atmospheric related (telluric) H2O and O2 absorption bands.

Apart from their undeniable aesthetics they are interesting only for atmospheric physicist. For astronomers, they are usually only a hindrance, unless the fine water vapour lines are used to calibrate the spectra! They can partly be extracted with the Vspec software or nearly completely with the freeware program SpectroTools by Peter Schlatter. [413].

By the late spectral types of K, and the entire M-Class (sect. 13.5), however, it makes sense to record this range, since the radiation intensity of these stars is very strong in the IR range and shows here particularly interesting molecular absorption bands. Also, the reflec-tion spectra (sect. 5.7) of the large gas planets show mainly here the impressive gaps in the continuum.

Useful guidance for setting the wavelength range of the spectrograph are eg the microme-ter scale, the calibration lamp spectrum or the daylight (solar) spectrum, respectively. At night the reflected solar spectrum is available from the moon and the planets. A good marker on the blue side of the spectrum is the impressive double line of the Fraunhofer H- and K-Absorption (sect. 13.2.).

FraunhoferA Band O2

Hα H2O AbsorptionFraunhoferB Band O2


4.3 Terminology of the Spectroscopic Wavelength Domains

Terminology for wavelength domains is used inconsistently in astrophysics [4] and depends on the context. Furthermore many fields of astronomy, various satellite projects etc. often use different definitions.

Here follows a summary according to [4] and Wikipedia (Infrared Astronomy). Given are ei-ther the center wavelength λ of the corresponding photometric band filters, or their ap-proximate passband.

Optical range UBVRI λλ 3,300 – 10,000 (Johnson/Bessel/Cousins)

Center wavelength Astrophysical wavelength

domain

Required instruments

λ [μm] λ [Å]

0.35 3,500 U – Band (UV) Most optical telescopes

0.44 4,400 B – Band (blue)

0.55 5,500 V – Band (green)

0.65 6,500 R – Band (red)

0.80 8,000 I – Band (infrared)

Further in use is also the Z–Band, some λλ 8,000 – 9,000 and the Y–Band, some λλ 9,500 – 11,000 (ASAHI Filters).

Infrared range according to Wikipedia (Infrared Astronomy)

Center wavelength Astrophysical wave-

length domain

Required instruments

λ [μm] λ [Å]

1.25 10,250 J – Band Most optical- and dedicated

infrared telescopes 1.65 16,500 H – Band

2.20 22,000 K – Band

3.45 34,500 L – Band Some optical- and dedicated

infrared telescopes 4.7 47,000 M – Band

10 100,000 N – Band

20 200,000 Q – Band

200 2,000,000 Submilimeter Submilimeter telescopes

For ground based telescopes mostly the following terminology is in use [Å]:

– Far Ultraviolet (FUV): λ <3000 – Near Ultra Violet (NUV): λ 3000 – 3900 – Optical (VIS): λ 3900 – 7000 – Near Infrared (NIR): λ 6563 (Hα) – 10,000 – Infrared or Mid-Infrared: λ 10,000 – 40,000 (J, H, K, L – Band 1 – 4 μm) – Thermal Infrared: λ 40,000 – 200,000 (M, N, Q – Band 4 - 20μm) – Submilimeter: λ >200,000 (200 μm)


5 Typology of the Spectra

5.1 Continuous Spectrum

Incandescent solid or liquid light sources emit, similar to a black body radiator, a continu-ous spectrum, eg Bulbs. The maximum intensity and the course of the continuum obey the Plank's radiation law.

5.2 Absorption Spectrum

An absorption spectrum is produced when radiated broadband light has to pass a low pres-sure and rather cool gas layer on its way to the observer. Astronomically, the radiation source is in the majority of cases a star and the comparatively "cooler" gas layer to be trav-ersed, its own atmosphere. Depending on the chemical composition of the gas it will ab-sorb photons of specific wavelengths by exciting the atoms, ie single electrons are momen-tarily lifted to a higher level. The absorbed photons are ultimately lacking at these wave-lengths, leaving characteristic dark gaps in the spectrum, the so-called absorption lines. This process is described in more detail in sect. 9.1. The example shows absorption lines in the green region of the solar spectrum (DADOS 900L/mm).

Hβ Fe Fe Fe Mg Fe

5.3 Emission Spectrum

An emission spectrum is generated when the atoms of a thin gas are heated or excited so that photons with certain discrete wavelengths are emitted, eg neon glow lamps, energy saving lamps, sodium vapor lamps of the street lighting, etc. Depending on the chemical composition of the gas, the electrons are first raised to a higher level by thermal excitation or photons of exactly matching wavelengths – or even completely released, where the atom becomes ionised. The emission takes place after the recombination or when the ex-cited electron falls back from higher to lower levels, while a photon of specific wavelength is emitted (sect. 9.1). Astronomically, this type of spectral line comes mostly from ionised nebulae (sect. 22) in the vicinity of very hot stars, planetary nebulae, or extremely hot stars, pushing off their gaseous envelops (eg, P Cygni). ). The following picture (DADOS 200L/mm) shows the emission spectrum (Hα, Hβ, Hγ, He, [O III]), of the Planetary Nebula NGC6210, which is ionised by the very hot central star (some 58‘000K), [33].

Hγ Hβ [O III] He Hα


5.4 Absorption Band Spectrum

Band spectra are generated by highly complex rotational and vibrational processes, caused by heated molecules. This takes place in the relatively cool atmospheres of red giants. The following spectrum originates from Betelgeuse (DADOS 200L/mm). At this resolution it shows only a few discrete lines. The majority is dominated by absorption bands, which are here mainly caused by titanium oxide (TiO) and to a lesser extent by magnesium hydride (MgH). In this case, these asymmetric structures reach the greatest intensity on the left, short-wave band end (called bandhead), and then slowly weaken to the right. The wave-length of absorption bands always refers to the point of greatest intensity ("most distinct edge").

But also several of the prominent Fraunhofer lines in the solar spectrum are caused by mo-lecular absorption. The following picture, taken with the SQUES echelle spectrograph [400], shows a high-resolution O2 band spectrum of the Fraunhofer A line (sect. 4.2 and 13.2).

5.5 Band Spectrum with Inversely Running Intensity Gradient

The following picture (DADOS 200L/mm) shows C2 carbon molecular absorption bands in the blue-green region of the spectrum of the carbon star Z Piscium [33]. Generally at some carbon molecules (eg CO, C2), the intensity gradient of the absorption bands runs in the op-posite direction as with titanium oxide (TiO) or O2.

Already in the middle of the 19th Century this effect has been recognised by Father Angelo Secchi (Sect. 13.3). For such spectra, he introduced the “Spectral type IV”.


5.6 Mixed Emission- and Absorption Spectrum

There are many cases where absorption and emission lines appear together in the same spectrum. The best known example is P Cygni, a textbook object for amateurs. To this un-stable and variable supergiant of the spectral type B2 Ia numerous publications exist. In the 17th Century, it appeared for 6 years as a star of the third magnitude, and then "disap-peared" again. In the 18th Century it gained again luminosity until it reached its current, slightly variable value of approximately +4.7m to +4.9m. The distance of P Cygni is esti-mated to ca. 5000 – 7000 ly (Karkoschka 5000 ly).

The picture below shows the expanding shell, taken with the Hubble Space Telescope (HST). The star in the center is fully covered. The diagram right shows the typical formation of the so-called P Cygni profiles, which are shown here in the violet region of the spectrum (DADOS 900L/mm).

In the area of the blue arrow a small section of the shell, consisting of thin gas, is moving exactly toward Earth and generating blue-shifted absorption lines (Doppler Effect). The red arrows symbolise the light, emitted by sections of the shell, expanding sideward, producing emission lines. In the combination results a broad emission line and a generally less intense blue-shifted absorption line. P Cygni profiles are present in almost all spectral types and are a reliable sign of a massive radial motion of matter ejected from the star.

Based on the wavelength difference between the absorption and emission part of the line, the expansion velocity of the envelope can be estimated using the Doppler formula (sect. 15). This object is further described in sect. 17, where also the estimation of the expansion velocity is demonstrated.

5.7 Composite Spectrum

Superimposed spectra of several light sources are also called “composite”- sometimes also “integrated spectra”. The English term “composite” was coined in 1891 by Pickering for composite spectra in binary systems. Today it is often used also for integrated spectra of stellar clusters, galaxies and quasars, which consist from hundreds of thousands up to sev-eral hundred billions superposed individual spectra.

Direction towardearth


5.8 Reflection Spectrum

The objects of our solar system are not self-luminous, but only visible thanks to reflected sunlight. Therefore, these spectra always contain the absorption lines of the solar spec-trum. The continuum course is however coined, because certain molecules in the atmos-pheres of the large gas planets, eg CH4 (methane), absorb and/or reflect the light differ-ently strong at specific wavelengths.

The following chart shows the reflection spectrum of Jupiter (red), recorded with the DA-DOS spectrograph and the 200L/mm grating. Superimposed (green) is generated by dawn light, previously captured in the daylight- (solar) spectrum. Before rectifying, both profiles have been normalised on the same continuum section [30]. In this wavelength range, the most striking intensity differences are observed between 6100 and 7400 Å.

5.9 Cometary Spectrum

Such can be considered as a special case of the reflection spectra. Comets, like all other objects in the solar system, reflect the sunlight. However on its course into the inner solar system core material increasingly evaporates, flowing out into the coma, and subsequently into the mostly separated plasma- and dust tails. The increasing solar wind, containing highly ionised particles (mainly protons and helium cores), excites the molecules of the comet. Thus the reflected solar spectrum gets more or less strongly overprinted with mo-lecular emission bands, – chiefly due to vaporised carbon compounds of the cometary’s material. The most striking features are the C2 Swan bands Further frequently occurring emissions are CN (cyan), NH2 (Amidogen Radicals), and C3. Sometimes also Na I lines can be detected. Only slightly modified appears the solar spectrum, recorded from sunlight, which has exclusively been reflected by the dust tail. All these facts and the associated ef-fects, create complex composite spectra. The influence of the possible components de-pends primarily on the current intensity of the core eruptions, as well as on our specific perspective, regarding the coma, as well as the plasma- and dust tail. Further details see [33].


Wavelength λ

Inte

nsi

tyI

Core

Blue Wing Red Wing

Continuum Level

saturated

λ

Continuum

6 Form and Intensity of the Spectral Lines

6.1 The Form of the Spectral Line

The chart on the right shows several absorption lines with the same wavelength, showing an ideal Gaussian-like intensity dis-tribution but with different width and inten-sity. According to their degree of saturation, they penetrate differently deep into the con-tinuum, maximally down to the wavelength axis. The red profiles are both unsaturated. The green one, which just touches the deep-est point on the wavelength axis, is saturated and the blue one even oversaturated [5]. The lower part of the profile is called "Core", which passes in the upper part over the "Wings" in to the continuum level. The short-wavelength wing is called "Blue Wing", the long-wave- "Red Wing" [5].

Emission line profiles, in contrast to the presented absorption lines, always rise upwards from the continuum level.

6.2 The Information Content of the Line Shape

There hardly exists any stellar spectral line, which shows this ideal shape. But in the devia-tion from this form a wealth of information is hidden about the object. Here are some ex-amples of physical processes which have a characteristic influence on the profile shape and become therefore measurable:

– The rotational speed of a star, caused by the Doppler Effect, flattens and broadens the line (rotational broadening), see sect. 16.

– The temperature and density/pressure of the stellar atmosphere broaden the line (tem-perature/pressure-/collision broadening), see sect. 13.9.

– Macro turbulences in the Stellar Atmosphere, caused by the Doppler Effect, broaden the line, see sect. 16.6.

– Instrumental responses broaden the line (instrumental broadening)

– In strong magnetic fields (eg sunspots) a splitting and shifting of the spectral line occurs due to the so-called Zeeman Effect.

– Electric fields produce a similar phenomenon, the so-called Stark Effect.

The combined effects of pressure- and Doppler broadening result in the so-called Voigt pro-files.

6.3 Blends

Stellar spectral lines are usually more or less strongly deformed by closely neighbouring lines - causing this way so-called "blends". The lower the resolutions of the spectrograph, the more lines appearing combined into blends.

6.4 The Saturation of Absorption Line in the Spectral Diagram

The following spectral profile is generated with Vspec, based on the course of an 11-step gray-scale chart, running parallel to the wavelength axis. The maximum possible range from


black to white, covered by Vspec, comprises 256 gray levels [411]. The Profile section in the black area is here, as expected, saturated to 100% and runs therefore on the lowest level, ie congruent with the wavelength axis. The saturation of the remaining gray values decreases staircase-like upward, until on the continuum level, it finally becomes white. If an underexposed spectral stripe was prepared in advance with IRIS [410] [30], the gray scale is stretched, so that the highest point on the chart becomes white. Thus, a maximum con-trast is achieved.

So far remains the theory, covering the electronic recording and the data reduction level. According to [11] however, in astronomical spectra, an absorption line reaches already full saturation before it touches the wavelength axis. In fact the "Wings" in the upper part of an oversaturated line profile, appear massively broadened, without penetrating much further into the continuum (sketch according to [11]).

6.5 The Oversaturated Emission Line in the Spectral Diagram

No tricks are required for the presentation of an oversaturated emission line. This just needs to overexpose the calibration lamp spectrum. Such oversaturated Neon lines appear flattened on the top. Such an unsuccessful neon spectrum must never be used for calibration purposes!

Continuum Level = white

saturated = black

Gray-scale chart

Wavelength axis = black

Gray-values

[Å]

I/Ic

λ

saturated

oversaturated


7 The Measurement of the Spectral Lines

7.1 Methods and Reference Values of the Intensity Measurement

Depending on the specific task, the line intensity is determined either by simple relative measurement, or quite complexly and time consuming, with absolutely calibrated dimen-sions. Here we focus exclusively on the relative measurement which is sufficient for most amateur purposes, and is supported by the analysis software (eg Vspec). As a reference or dimension unit usually serves the local or normalised continuum level (sect. 8.5) but possibly also values of a linear, but otherwise arbitrary scaling of the intensity axis.

7.2 Metrological Differences between Absorption and Emission Lines

For measurements of spectral lines the following differences must be noted.

The absorption lines can simplified be considered as the product of a "filtering process". The photons of a specific wavelength λ, which are mostly absorbed in the stellar photosphere, cause a gap in the continuum of defined area, shape and penetration depth. Therefore, the parameters of the absorption remain always relatively connected to the continuum intensity .

The emission lines are generated independently of the continuum by recombination and/or electron transitions (sect. 9). Because this process is also excited by the stellar radiation, it results a certain strongly object-dependent, time related degree of coupling to the con-tinuum radiation. For instance at P Cygni these lines are generated directly in the turbulent expanding gas envelope – at the Be stars (sect. 16) mostly in the circumstellar gas disk – and in the cases of the H II regions or Planetary Nebulae PN, even some ly away, where almost regular laboratory conditions exist!

The combination of emission lines and continuum radiation results in a superposition of the two intensities:

Due to the physically and locally different generation, as well as may fluctuate independently of each other. The continuum-level is dependent on the radiation density, which the star generates at the wavelength . To this level, is adding up independently.

The combination of emission lines and absorption lines results also in a superposition of the two intensities.

At Be-stars, the slim hydrogen emission line is produced in the cir-cumstellar disk or -shell, and appears superimposed to the rotation- and pressure-broadened H-absorption of the stellar photosphere. The resulting spectral feature is therefore called “Shell Core” [4]. The H-absorption of such a spectral feature may also originate from the pho-tosphere of a hot O-star and the emission line from the surrounding H II region, see eg the Hβ line of Θ1Ori C / M42 [33].

λ

I IC λ)

IA λ)

λ

IIE λ)

λ

I

IE λ)

IC λ)

I C λ

) +

IE λ

)

λ

IIE λ

IA λ


FWHM

½ Imax

Imax

I = 0

7.3 The Peak Intensity P

The Line Intensity

The intensity offers the easiest way to measure a spectral line. However this measure is only significant in a radiomet-rically corrected or absolutely calibrated profile as described in section 8.6, 8.7, 8.8.

The Peak intensity

In a pseudo-continuum, but also in a just rectified profile ac-cording to sect. 8.5, the intensity gets only comparable with other lines if related to its local continuum level . This is expressed as the dimensionless Peak intensity .

The Peak intensity at absorption lines

is here also called for “Line Depth”. Related to the continuum level , the peak inten-sity of the absorption line, corresponds to the maximum intensity or flux density , which is removed from the continuum radiation by the absorption process. This further cor-responds to the photon energy per time, area, the considered wavelength interval and re-lated on the level (units see sect. 8.8). In addition, it qualitatively shows the degree of absorption, or the share of photons, which is absorbed in the peak of the absorption line with the penetration depth .

The Peak intensity at emission lines

If the upwards striving and independently generated emission lines are superimposed on a continuum {3}, they are also related to the Level {4}, eg for investigations of individual lines. Related to the continuum level , the peak intensity of the emission line corre-sponds to the maximum intensity or flux density . This further corresponds to the pho-ton energy per time, area, the considered wavelength interval and related on the level .

7.4 Full Width at Half Maximum Height

The FWHM value is the line width in [Å] at half height of the maximum intensity. It can be correctly measured even in non-normalised spectral profiles. The width of a spec-tral line is inter alia depending on temperature, pressure, density, and turbulence effects in stellar atmospheres. It allows therefore important conclusions and is often used as a variable in equations, eg to determine the rotational velocity of stars (sect. 16.6).

This line width is specified in most cases as wavelength-difference . For the measurement of rotational and ex-pansion velocities is also expressed as a velocity value according to the Doppler principle. For this purpose [Å] is converted with the Doppler formula {15} to a speed value [km/s] (sect. 15).

The FWHM value, obtained from the spectrum [30] has now to be corrected from the in-strumental broadening.

corresponds to the theoretical maximum resolution [Å] of the spectrograph, ie the smallest dimension of a line detail, which can be resolved.

IcI

IcI

P=I/Ic


The resolution is limited on one side by the optical design of the spectrograph (dispersion of the grating, collimator optics, slit width, etc.). It can normally be found in the manual of the spectrograph as so-called -Value which is valid for a defined wavelength range ( = considered wavelength) [302].

This value is determined by measurements at thinnest possible spectral lines, eg atmospheric H2O absorptions or somewhat less accurate, at emission lines of calibration light sources [11], [123], [302]. In the laboratories for example emissionlines, generated by microwave excited mercury lamps are used, in order to minimise temperature broadening. Such profiles are called "instrumental profile" or "δ-function response" [11]. The resolution may further be limited by the pixel grid of the connected camera [Å/pixel], if this value is greater than of the spectrograph. For a wavelength-calibrated profile, this value is shown in the head panel of the Vspec screen. Compared to monochrome-, with color CCD cameras, a significant loss of resolution must be accepted.

7.5 , Equivalent Width

The EW-value or Equivalent Width is always based on the continuum level and is a relative measure for the area of a spectral line.

Definition

The profile area between the continuum level and the profile of the spectral line has the same size as the rectangular area with the fully saturated depth (here ) and the equivalent width [Å].

The -value must therefore be measured in a spec-trum, normalised to ([30], sect. 10). This is the mathematically correct expression for :

In simple terms the red area above the spectral curve is calculated by summing up an infinite number of vertical, infinitely narrow rectangular strips with the width and the variable heights , within the entire range from to . To get finally the equivalent width , these values are still to divide by the entire height of the continuum-, resp. of the saturated square.

The integral sign ∫ is derived from the letter S, and stands here for "sum". is the continuum intensity, the variable intensity of the spectral line depending on (or a function of) the wavelength .

Inte

nsi

tyI

0

1 Ic = 1

Wavelength λ

Ic

Iλ

Ic - Iλ

λ1 λ2

EW

Inte

nsi

tyI

0

1 Continuum level Ic = 1

Wavelength λ

Profilearea =


The EW value at absorption lines

As sketched above and related to the continuum level , corresponds to the measure of the total radiation flux , which the entire absorption line removes from the continuum radiation. This further corresponds to the photon energy per time, area and re-lated on the level (common units see sect. 8.8).

The EW value at emission lines

Related to the continuum level , the value of the upwards striving emission line corre-sponds to the measure of their entire radiation flux . This further corresponds to the photon energy per time, area, and related on the level .

Signs and measurement of the EW values

values of absorption lines are by definition always positive (+), those of emission lines negative ( ).

Since the value is always measured at a continuum level, normalized to , it is neither influenced by the course of the continuum, nor by the absolute radiation flux. Should be measured in a non rectified profile, the continuum must be normalised immediately at the base of the spectral line to !

In scientific publications is also designated with the capital . designates the equivalent width of the Hα Line.

Somewhat confusing: In some publications I have also found the FWHM value expressed in . The conclusion: One must always simply check which value is really meant.

7.6 Normalised Equivalent Width

Rather rarely the normalised value is used [128]:

This allows the comparison of -values of different lines at different wavelengths , tak-ing into consideration the linearly increasing photon energy towards decreasing wave-length λ, according to formula {8}. Anyway, in astrophysics this is not applied for most of the mainly empirical formulas and procedures.

7.7 FWZI Full Width at Zero Intensity

Rather rarely the FWZI value of a spectral line is applied. The Full With at Zero Intensity cor-responds to the integration range of the definite integral according to formula and chart {6a}:

7.8 Influence of the Spectrograph Resolution on the FWHM- and EW Values

The above outlined theories about FWHM- and EW must realistically be relativated. This need is dramatically illustrated by the following spectral profiles of the Sun, taken with different highly resolving spectrographs (M. Huwiler/R. Walker). The R-values are here within a range of approximately 800 – 80,000.


The comparison of these graphs shows the following:

If the resolution (R) is increased it becomes clearly evident that in stellar spectra practi-cally no "pure" lines exist. Apparent single lines almost turn out as a "blend" of several sub lines, if considered at higher resolutions.

Sun Spectrum λ 5256 – 5287 ÅComparison Prototype Echelle- with Cerny Turner Spectrograph

Echelle R ≈ 20‘000

Cerny Turner R ≈ 80‘000

Sun Spectrum λ 5160 – 5270 ÅComparison Prototyp Echelle- with DADOS Spectrograph 900- and 200 L mm-1

Echelle R ≈ 20‘000

DADOS 900L mm-1 R ≈ 4‘000

DADOS 200L mm-1 R ≈ 800

Magnesium Triplet: λ 5167, 5173, 5183 Å

Richard Walker 2011/03


Striking is also the so-called "Instrumental Broadening" effect. Even relatively well-insulated seeming lines broaden dramatically with decreasing resolution (R), due to the instrumental influences. This affects the measured FWHM or the half-width of a line.

The EW value, related to the profile area, remains theoretically independent of the reso-lution. At higher resolutions, the area of the slimmer line profile is compensated by a higher peak-value .

7.9 Practical Consequences for the FWHM and EW Measurements

FWHM values must always be corrected in respect of the "Instrumental Broadening", applying the formulas {5} to {5b}.

The comparability of the EW values, obtained with different resolutions, remains purely theoretical and is limited to discrete and well isolated single lines. Assuming the case of a blended absorption line, a high-resolution spectrograph measures, in an ideal case, the EW value of only one, well-defined single line. However, at low resolution and the same wavelength, a substantially larger value is measured due to a blend of several insepara-ble lines. In this case, only EW-values are seriously comparable, if they have been ob-tained from profiles with similar resolution. This necessarily requires a declaration of the R-value.

According to formula {6a}, the EW-value is clearly defined. However to determine this value e.g. for strongly deformed, broad emission lines, possibly even with a double peak, remains a serious problem. With Gaussian fits in such cases reasonably reproducible, al-beit relatively imprecise results may result. The profile fit with Spline filter, or similar al-gorithms is perhaps more accurate, but the result is subjectively influenced by the inves-tigator.

For amateur monitoring projects it is important, that all participants work with similarly high resolutions and the recording and processing of the spectra is clearly standardised. A problem with the EW values poses the standardisation of the integration area (FWZI) of formula {6a}, since the width of the line base may change significantly with varying intensity. Further the section of the continuum must be specified, on which the profile is to normalise. This is unavoidable at least for the later spectral classes, which exhibit a rather diffuse continuum. When monitoring emission lines one must always keep in mind that the measured EW values are related to a possibly independently fluc-tuating continuum level (sect. 7.2).

7.10 The Measurement of the Wavelength

The wavelength of a spectral line (Nanometer [nm] or Angström [Å]) can be obtained in a wavelength calibrated spectrum directly via Gaussian fit (Vspec) or by positioning of the cursor at the peak of the line. Which method is better, depends upon whether a strongly asymmetric blend or an isolated single-line is present.

7.11 Additional Measurement Options

Depending on the applied analysis software, further information can be obtained from the calibrated spectral profile. In Vspec these are, among other, e.g. the signal to noise ratio SNR and the dispersion in Å/pixel, etc. For details see the respective manuals.


8 Calibration and Normalisation of Spectra

8.1 The Calibration of the Wavelength

Usually spectra are plotted as course of the radiation intensity over the wavelength. In prin-ciple, both dimensions can be calibrated. For most applications, only the calibration of the wavelength is required. This can be done relatively easy with lines of known wavelength within the spectrum, or absolutely with appropriate spectral calibration lamps. These pro-cedures are well documented in literature eg [30], [411]. For further information refer also to sect. 15.

8.2 The Selective Attenuation of the Continuum Intensity

The intensity profile of the undisturbed stellar original spectrum is determined mainly by the black body radiation characteristics of the star and its effective temperature

(sect. 3.2). On the long way to the unprocessed raw spectrum the continuum of be-comes deformed by the following damping influences into a so called pseudo-continuum (sect. 3.3).

1. The Attenuation by the Interstellar Matter is mainly caused by scattering effects of dust grains and gas. Thereby the intensity is selectively much stronger dampened in the blue short wave part of the spectrum. Thus the maximum of the continuum radiation is shifted in the red long-wavelength range, which is called "Interstellar reddening" (sect. 21). The extent of this effect depends on the object distance, the direction of the line of sight and is, as expected, most intensive within the galactic plane. It can roughly be estimated with a corresponding 3D model by F. Arenou et al. [209], [201].

2. The Attenuation in the Earth's Atmosphere acts similarly. Well known effects are the reddish sunsets. The modelling of the atmospheric transmission is mainly applied in the professional sector. It is rather complex and depends inter alia on the zenith-distance (or the complementary elevation angle) of the observed object, the altitude of the observa-tion site and the meteorological conditions [303].

3. The Attenuation by Instrumental Influences of the system telescope-spectrograph-camera follows at the very end of the transmission chain. This could be de-termined relatively precisely, eg by comparison with the well known continuum radiation distribution of a halogen incandescent lamp, or by the known intensities of several emis-sion lines [300], [313], [480]. A discussion of further possibilities and the difficulties in-volved, see [315], [316].

The resulting dampening effect does:

The empirical function provides to any wavelength the correction factor between the continuum intensities of and .

This empirical scaling or "correction function" can be determined as a rough ap-proximation only. The intensity profile of the original stellar spectrum can be simulated just on a theoretical basis and the individual factors can only approximately be estimated. Simi-lar approaches with empirical functions can be found in [300] and [303]. The practical cal-culation with profiles is enabled – including all basic operations – by the software of the analysis tools. At Vspec this feature is to find under Operations/Divide-, Multiply-, Add-, Subtract profiles by a profile.


8.3 Relationship Between Original-Continuum and Pseudo-Continuum

The following diagram shows two identical sections of the same spectrum: on the left the undisturbed original profile and on the right the recorded raw spectrum with the pseudo-continuum It shows each an absorption and an emission line. Within this fic-tional spectral section, the course of , and is assumed to run horizon-tally.

The following relationships and its consequences can be derived:

Due to the attenuation, at a certain wavelength , the continuum-intensity of the re-corded profile appears reduced by , compared with the original-spectrum .

The continuum intensity , the superimposed emission line and the penetration depth of the absorption line , are attenuated proportionally equal.

For reasons of proportionality the Peak intensity of the emission line , as well as of the absorption line , remain unaffected by the attenuation factor .

Thus the original ratio of the absorption- and emission intensities, related to the contin-uum level, is maintained. This is in contrast to the directly and independently of the con-tinuum measured intensities and , which are attenuated by according to and .

Since follows . Therefore, the initial in-tensity ratio in the original profile, between any two emissions or absorptions at the wavelengths and , is modified by the attenuation:

ΔIC

Ps λ

IE

IC IA

λ

IAO

Or λ

IEO

ICO

λ

I

OriginalProfile

RecordedProfile


Summary of the consequences:

In contrast to the independently measured intensity values , and , the peak inten-sities and , which are related to the continuum level , are not attenuated .

The original ratio of the absorption and emission intensities, related to the original-continuum level, is maintained also in the pseudo-continuum

On the other hand, the original intensity ratio between any two emissions ap-pears attenuated in the pseudo-continuum .

The following graph of the Sirius spectrum finally demonstrates that, considered the -related measures, not only the peak intensity but even the equivalent width , are not affected by the attenuating effects. This applies to both, the absorption- and emis-sion lines (not shown here). The value is always measured relative to hence the integrated profile area, according to {6a}, always remains the same.

Anyway the example of the Hγ line also shows that the relative line intensities , measured either at or and independently of the continuum-level, are very different. At they correspond very roughly to those in the original profile . Further here can be seen that, caused by the higher local radiation intensity, the Hγ line absorbs the greater energy flux as Hα. Such considerations apply analogously to the emission lines , which are generated independently of the continuum.

8.4 The Importance of the Pseudo-Continuum

If the damping function is approximately known, the pseudo continuum con-tains the information, to enable the approximate reconstruction of the original profile , applying formula . Further, according to sect. 3.2 and 3.3, the wavelength of the maxi-mum intensity is, even in the strongly dampened pseudo-continuum, a very rough indicator at least for the order of magnitude of the effective temperature .

Otherwise in most other cases the course of the recorded profile, with the pseudo-continuum , is useless. Depending on the wavelength, just shows the amount of electrons, which has been read out of the individual pixels, amplified by the camera elec-tronics and finally averaged by the spectral processing software over a defined height of the vertical pixel rows. Thus it reflects roughly proportional the recorded photon flux which however is loaded with all the mentioned attenuating influences. As intensity unit for raw profiles therefore often ADU (Analog – Digital Units) is used.

8.5 Rectification of the Pseudo-Continuum

The pseudo-continuum can be rectified by dividing it by its own “smoothed” or fitted intensity course . This way the continuum-intensity is unified or "normalised"

I

Ic

IIc

I / Ic = I / Ic

EW = EW

Rc(λ)

Ps(λ)

Hα

Hβ

Hγ


through the entire range, and usually set to . The resulting profile is called „Residual Intensity“

Due to this division, the profile runs now horizontally and the intensity of the emissions - and absorptions is related to the unified continuum intensity . This process proportion-ally scales the intensities of all spectral lines from their individual -values in the pseudo-continuum, up to the level . This corresponds now to the original profile of a virtual star which shows a horizontally running, but physically impossible radiation characteristic.

Consequences and benefits of Rectifying the Pseudo-Continuum

Useful for certain applications – the profile normalisation allows the elimination, of the often irrelevant, or even hindering, wavelength-dependent distribution, of the stellar radiation intensity. It generates a "quasi neutralisation", but not a real correction of the attenuating effects. Thus enables the direct comparison of the peak intensities be-tween individual absorption lines, according to .

At also the original ratio of the individual emission lines is maintained {7g}. This allows the intensity comparison of individual lines, eg of Hα in different profiles. It also enables the comparison of any emission intensities, relative to a unified radiation course (possible application see sect. 20, Balmer-Decrement).

However at , the intensities of the lines and , independently measured of the continuum, appear attenuated to different extents, depending on the wavelength {7h}.

The rectified profile, normalised to , allows the quick determination of the EW val-ues and facilitates the measurement of the FWHM at arbitrary lines.

By the rectification of the profile, the information gets lost, which allows, by means of the known damping function , to approximately reconstruct the original file .

Anyway for most amateur applications, the profile normalisation is clearly the best option [11].

The scaling effect of a rectified profile is impressively demonstrated at the absorptions in the solar spectrum by the two Fraunhofer H- and K- lines of ionised calcium (Ca II). The blue profile of the pseudo-continuum shows these lines only stunted at the short wavelength end of the spectrum (blue arrow). After rectifying of the continuum (red profile), the H- and K- lines appear now obviously as the strongest absorptions, which the sun generates itself (red arrow).


8.6 The Relative Radiometric Profile Correction with a Synthetic Continuum

The goal of this procedure is a rough approximation of the recorded profile with the pseudo-continuum , to the original- and therefore not reddened continuum . This procedure is described in the manual of the Vspec software. With dividing by correction curves, the spectral lines of the pseudo-continuum are directly transferred to the syn-thetically produced and fitted continuum course of a mostly virtual model star with the same spectral class and unreddened by interstellar dust. Similar to sect. 8.5, this proc-ess proportionally scales the intensities of all spectral lines from their individual -values in the pseudo-continuum, up to the level of . For specific applications this procedure is also applied in the professional field [301].

In the following chart the blue spectrum is the recorded profile with the pseudo-continuum of Sirius. The red profile is the aimed, fitted continuum course of the syn-thetic model star of the same spectral type, from the Vspec library (CDS Database). It ap-pears cleaned from all spectral lines and thus roughly corresponds to the black body radia-tion characteristics of this star .

On the following graph, the green correction curve is generated by the division of the fitted blue pseudo-continuum with the red synthetic reference profile . It is called by Vspec “Instrumental Response” and is here denoted hereinafter with correction function .

approximately corresponds here to the damping-function , according to .

Pseudo-continuum Ps(λ)

Smoothed reference profile ofthe model star

Ms Fit (λ)

Radiometrically correctedprofile

Rc(λ)

Instrumental responseIr(λ)

Ps(λ)


Finally the division of the blue recorded raw profile , by the green correction function , results in the radiometrically corrected profile (black). It shows now the same continuum course like the red smoothed reference profile , but now overprinted with the accordingly scaled lines of the recorded profile.

Remarks to the „Instrumental Response“

For a correction function , obtained according to , the term "instrumental re-sponse" is misleading. In professional fields, this term is used as "Instrumental System Re-sponse", which is clearly restricted to the erroneous recording characteristic of , considering just the system telescope – spectrograph – camera [305]. In contrast, the cor-rection curve , generated according to , is additionally loaded by the wavelength dependent damping effects of the Interstellar Matter and of the earth's atmosphere .

Experiments have shown that such correction curves , which are generated just with an unreddened virtual model spectrum of the same spectral class, are not universally appli-cable. They cannot generally be applied to any raw profiles, which have been recorded at different atmospheric conditions and zenith distances.

Deviation between and

The following figure shows for the spectral classes B, A, D, G, the ranges of the smallest deviation between (pink) and (blue), valid for the setup C8/DADOS/Atik 314L+. This information may be useful to estimate the rough size of error, when intensity ratios, as described in sect. 20 – 22, are measured approximately, ie without any radiomet-ric corrections. This applies also for the detailed analysis of the Hα line!

I I / Ic = I / Ic

Kr(λ)

Ps(λ)

HαHβ Hα

Hβ

ε Ori, Alnilam B0 Iab

α Cma, Sirius A1V

ζ Leo, Adhafera F0 III

Sun G2V


Consequences and benefits of a radiometric profile correction with a synthetic continuum

This procedure provides not a true correction of the attenuation influences , , . With the direct transformation of the intensity profile from to , the pseudo continuum is just scaled up to the level of the synthetic and therefore not reddened model star, and not to the original profile of the observed ject . Thus, the attenuating effects are simply bypassed and a “synthetic”, rough approximation to the original profile is reached this way. Therefore fluctuations of the continuum radiation cannot be measured in such a profile.

Since complies now very roughly to the original profile , also the relative line intensities correspond approximately with those in the original profile. This applies also to the continuum-independent emission lines . However it must be kept in mind that between different stars even of the very same spectral class, considerable differences in the continuum course may occur. This effect can be significantly enhanced by a strongly different metallicity and/or rotation velocity ( s ).

The original relative relationship between two line intensities and as well as and , which are measured directly and independently of the continuum level, can here be estimated.

This method does not yet allow any calibration of the intensity axis in physical units!

8.7 The Relative Radiometric Profile Correction with Recorded Standard Stars

Correction methods in amateur fields

With this somewhat time consuming procedure the recorded profile is corrected, similarly to section 8.6, with a correction function . However is obtained here, analogously to formula , by a recorded and real existing standard star , mostly of the spectral type A0V. The continuum course of is well known and corresponds to the profile, just reddened by interstellar dust, as it would have been recorded outside the Earth's atmosphere and without any instrument influences [300]. Such curves can eg be found in the ISIS software [410], in the MILES database [104], but also in the Pickles- or Jacobi Hunter-Christians-atlas [310] [311].

Standard stars must be recorded with a minimum of time difference and as close as possi-ble to the object under investigation. Subsequently, the obtained raw profile is divided by the specific reference spectrum of the same star from the catalogue. Thus, the atmospheric and instrumental influences can be corrected in a good approximation. Anyway the resulting spectrum remains here – star-dependent differently strong – red-dened by the interstellar matter , however in the "close range" of a few dozen light years, just very slightly [209] [11]. In contrast to the correction function is determined here only by and , which corresponds also to common practice in professional astronomy.

In contrast to sect. 8.6 such real standard star correction curves, which were recorded very promptly and with similar elevation angle to the investigated object, can be applied to any spectral classes. With the graphic below, Robin Leadbeater [481] shows, that for different spectral classes, very similar correction curves are obtained this way (many thanks Robin!).


Correction methods in professional fields

Anyway the professional astronomy applies significantly higher sophisticated and more ac-curate methods. For most of the large professional telescopes is well known. is usually determined separately by observations of standard stars with different zenith distances . This way not a correction curve is generated, but instead a model of the atmospheric extinction becomes parameterised, like MODTRAN [314]. Thus, finally the pro-file of the examined object will be corrected in function of the zenith distance [305]. Fur-ther methods are presented in [300] and [303].

The recording of standard stars consumes valuable telescope time. To relieve the main in-strument of this "annoying" task, the separate determination of with smaller “Photometric Monitoring Telescopes” was already proposed [314]. Further possibilities are based on the measurement of atmospheric Cherenkov radiation as well as on LIDAR [314].

In the infrared range the spectral class A0 shows just few and very faint stellar lines. There-fore, these more or less purely telluric influenced profiles are generally used to extract the atmospheric H20 and O2 lines in any stellar spectra [300].

Consequences and benefits of the Radiometric Correction with Recorded Standard Stars

The achievable accuracy of this rather delicate method is highly dependent on the quality of execution and tends to be rather overestimated. Numerous are the potential sources of er-rors and in addition, some of the reference profiles of the various databases show signifi-cant differences in their continuum courses. Anyway, if applied appropriately and accu-rately, this fairly time consuming method provides a reasonable approximation to the origi-nal theoretical spectral profile , which appears still reddened by the interstellar ter . This effect is unavoidable and allows – due to the selective elimination of the atmospheric and instrumental effects – the determination of the effective Balmer-decrement according to sect. 20 and thus also of the true interstellar extinction, according to sect. 21. This way, at least theoretically, also greater fluctuations in the continuum radia-tion are detectable and the effective temperature according to sect. 18.3 can be esti-

mated.


8.8 The Absolute Flux Calibration

As a final step of the radiometric correction, the intensity axis could be absolutely calibrated in physical units for the spectral flux density – normally [erg s-1 cm-2 Å-1]. This calibration is very challenging, time consuming and just needed by some special sectors of the professional astronomy. It is relatively common for spectra, recorded by space telescopes, which of course remain clean of any atmospheric influences [301].

For amateur applications an acceptable accuracy of the results is usually prevented already by the inadequate quality of the ob-servation site. Thus even in the professional sector, such abso-lutely flux-calibrated spectra can be found rather rarely.

The total flux of an emission line, here in a simplified form di-rectly drawn on the wavelength axis, corresponds to their area, [302]. The unit for the total flux of the line is [erg s-1 cm-2].

If the emission line is superimposed on a continuum, the continuum flux must be subtracted from formula .

This process is based on the comparison of the absolute calibrated radiation flux of a stan-dard star. However, many additional data are required for this correction procedure, such as the exposure time of the spectral recordings and even the slit width of the spectrograph.

8.9 The Intensity Comparison between Different Spectral Lines

The intensities of two different lines can be compared in normalised profiles with their equivalent widths . However if the widths of the lines are not too different, a rough comparison is also feasible with the peak intensities .

For most emission nebulae (sect. 22), which don’t show any evaluable continuum, formula {7t} can per definition, no longer be applied. Here just remains to compare the directly and independently of the continuum measured intensities , which have individually been cor-rected, based on the values of the undisturbed Balmer-Decrement (sect. 21.4, 22.11) or

with the absolute fluxes according to .

λ2λ1

λ

F

F λ

[erg

s-1cm

-2Å-1]

[erg s-1 cm-2]


9 Visible Effects of Quantum Mechanics

9.1 Textbook Example Hydrogen Atom and Balmer Series

The following energy level diagram shows for the simplest possible example, the hydrogen atom, the fixed grid of the energy levels (or "terms") , which a single electron can occupy in its orbit around the atomic nucleus. They are identical with the shells of the famous Bohr's atomic model and are also called principal quantum numbers. Which level the elec-tron currently occupies depends on its state of excitation. A stay between the orbits is ex-tremely unlikely. The lowest level is . It is closest to the nucleus and also called the ground state.

With increasing number (here from bottom to top):

– increases the distance to the nucleus – increases the total energy difference, in relation to – the distances between the levels and thus the required energy values to reach the next higher level, are getting smaller and smaller, and finally tend to zero on the Level

(or ).

The energy level E on the level is physically defined as [5] and also called Ionisation Limit. The level number is to consider as "theoretical", as a limited number of about 200 is expected, which a hydrogen atom in the interstellar space can really occupy [6]. By definition, with decreasing number the energy becomes increasingly negative. Above , ie outside of the atom, it becomes positive.

Absorption occurs only when the atom is hit by a photon whose energy matches exactly to a level difference by which the electron is then briefly raised at the higher level (resonance absorption).

Emission occurs when the electron falls back to a lower level and though a photon is emit-ted, which corresponds exactly to the energy level difference.

Hydrogene Series

Lyman(Ultra violet)

Balmer(visible)

Paschen(Infrared)

n = 1

n = 2

n = 3

n = 4n = 5n = 6n = ∞

Exci

tati

on

Leve

ls

Emis

sio

n

Ab

sorp

tio

n

Ion

izat

ion

Re

com

bin

atio

n

General Transitions

Ene

rgy

Leve

ls

E = 0 eV

E 4

E 2

E 3

E 1

Hα

Hβ

Hγ

Hδ

Hε

E 5


Ionisation of an atom occurs when the excitation energy is high enough so the negative electron is lifted over the level and leaves the atom. This can be triggered by a high-energy photon (photo ionisation), by heating (thermal ionisation) or a collision with ex-ternal electrons or ions (collision ionisation).

Recombination occurs if an ionised atom recaptures a free electron from the surrounding area and becomes "neutral” again.

9.2 The Balmer Series

A group of electron transitions between a fixed energy level and all higher levels is called “Transition Series”. For amateurs primarily the Balmer series (red arrow group) is important, because only their spec-tral lines are in the visible range of the spectrum. It contains the fa-mous H-lines and includes all the electron transitions, which start up-ward from the second-lowest energy level (absorption) or end here, “falling” down from an upper level (emission). The Balmer series was discovered and described by the Swiss mathematician and archi-tect (!) Johann Jakob Balmer (1825-1898). The lines of the adjacent Paschen series lie in the infrared, those of the Lyman series in the ul-traviolet range.

This sounds very theoretical, but has high practical relevance and can virtually be made "visible" using even the simplest slitless spectrograph! For this purpose the easiest way is to record the classical beginner object, a stellar spectrum of the class A (sect. 13.4). Most suitable is Sirius (A1) or Vega (A0). These stars have a surface temperature of about 10,000 K, which is best suited to generate impressively strong H-Balmer absorptions. The reason for this: Due to thermal excitation at this temperature, the portion of electrons reaches the maximum which occupy already the basic level of the Balmer series. With further increasing temperature, this portion decreases again, because it is shifted to even higher levels (Paschen series) and will finally be completely released, which results in the ionisation of the H atoms.

In the following Sirius spectrum six of the H-Balmer lines appear, labelled with the relevant electron transitions. These absorption lines are labelled consecutively with lowercase Greek letters, starting with Hα in the red region of the spectrum, which is generated by the lowest transition . From Hε upwards often the respective level number is used, eg Hζ = H8. Here is nice to see how the line spacing in the Blue area gets more and more closer – a direct reflection of the decreasing amounts of energy, which are required to reach the next higher level. In my feeling this is the aesthetically most pleasing, which the spectroscopy has optically to offer!

n2

–n

3

n2

–n

4

n2

–n

5

n2

–n

6

n2

–n

7n

2 –

n8

HαHβHγHδHεHζ

Triggering electron transitions

Denotation of the lines


9.3 Spectral Lines of Other Atoms

For all other atoms, i.e. with more than one electron, the description of line formation can be very complex. All atoms have different energy levels and are therefore distinguished by different wavelengths of the spectral lines. Another factor is the number of valence elec-trons on the outer shell, or how many of the inner levels are already fully occupied. Further the main levels are subdivided in a large number of so-called Sublevels and Sub-Sublevels, each of them with completely other implications in respect of quantum mechanics. The en-ergy differences between such sublevels must logically be very low. This explains why metals often appear in dense groups, a few with distances even <1Å! Typical examples are the sodium lines at 5896 Å and 5890 Å, and the famous Magnesium Triplet at 5184, 5173, 5169Å in the solar spectrum. By the hydrogen atoms these sublevels play no practical role, particularly for amateurs, because they are degenerated here [5]. The stay of the electrons within this complex level system is also subject to a set of rules. The best known is proba-bly the so called Pauli Exclusion Principle which demands that the various sublevels may be occupied by only one electron at the same time.

For most spectroscopic amateur activities, detailed knowledge of this complex matter is not really necessary. For those, deeper interested in quantum mechanics, [5] is recommended as a “first reading”, which provides a good overview on this matter and is relatively easy and understandable to read.


10 Wavelength and Energy

10.1 Planck’s Energy Equation

In the above wavelength-calibrated Sirius spectrum we want to calculate the corresponding photon energies of the hydrogen lines. This is possible with the familiar and simple equation of Max Planck (1858 – 1947):

Radiation Energy in Joule [J]

Planck’s Quantum of Action [6.626 10-34 J s]

(Greek: „nu“) Radiation frequency [s-1] of the spectral line.

The Radiation frequency of the spectral line is simply related to the wave-

length [m] ( = light speed 3 108 m/s):

Insert {9} into {8}:

The most important statement of formulas {8} and {10}: The radiation energy is propor-

tional to the radiation frequency and inversely proportional to the wavelength .

10.2 Units for Energy and Wavelength

To express such extremely low amounts of energy in Joules [J] is very impractical and not easy to interpret. Joule has been defined to be applied in traditional mechanics. In quantum mechanics and therefore also in spectroscopy, the units of electron volts [eV] is in use [5].

Further in the optical spectral domain also the wavelengths are extremely small and there-fore in astronomy usually measured in angstroms [Å] or nanometres [nm]. One should be aware that 1Å corresponds about to the diameter of an atom, including its electron shells! In the infrared range also [μm] is in use:

, , , ,

Rather rarely, the frequency is also expressed as “Wavenumber” . This is the reciprocal value of the wavelength , usually expressed somewhat “special” in number of waves within

In the optical spectral domain, the wavelength is usually based on the standard atmos-phere (atmospheric pressure 1013.25 hPa, temperature 15° C). The program SpectroTools [413] by Peter Schlatter, enables also to convert vacuum wavelengths to this atmospheric standard (or vice versa) and to demonstrate the temperature dependency of a measure-ment. So it becomes clear why the calibration spectrum should, as quick as possible, be re-corded immediately prior to, and/or after the object spectrum!

The following simple formulas, suitable for pocket calculators, allow to convert the wave-length [Å] into energy [eV] and vice versa,:


10.3 The Photon Energy of the Balmer Series

To the wavelengths of the hydrogen lines we can now calculate with formula the corresponding values of the photon energy .

In professional publications, spectra in the UV region are often calibrated in photon energy [eV], instead of the wavelength .

On the left side, the so-called Balmer Edge or Balmer Jump is marked with a red bar (also called Balmer Discontinuity). The Balmer series ends here at 3647 Å and the continuum suffers a dramatic drop in intensity. This takes place due to the huge phalanx of highly con-centrated and increasingly closer following absorption lines, acting here as a barrier to pho-tons at corresponding wavelengths (see sect. 10.4).

The Value of a spectral line corresponds to the energy difference between the initial and final level of the causal electron transition. It fits therefore also to the arrow lengths in the following energy level diagram. In the spectrum above e.g. 2.55eV corresponds to the tran-sition or Hβ. This relationship enables now to calculate the energy levels of the H-Balmer series.

65

63

Å

HβHγHδHεHζ

Wavelength [Å]

PhotonEnergies Ep [eV]

48

61

Å

43

40

Å

41

02

Å

39

70

Å

Hα

38

89

Å

1.8

9 e

V

2.5

5 e

V

3.0

2 e

V

2.8

6 e

V

3.1

2 e

V3

.19

eV

36

47

Å3

.40

eV

BalmerEdge

Electrontransition

n2

–n

3

n2

–n

4

n2

–n

5

n2

–n

6

n2

–n

7n

2 –

n8

n2

–B

alm

er-

Ed

ge

Lyman(Ultra violet)

Balmer(visible)

Paschen(Infrared)

n = 1

n = 2

n = 3

n = 4n = 5n = 6n = ∞

Exc

ita

tio

nle

vel

En

erg

yle

vel

E [

eV

]

0

-3.40

-1.51

-13.6

Hα

Hβ

Hγ

Hδ

Hε

-0.85-0.54


Since by definition the energy on the level is set to , we shift the value of

the Balmer edge 3.40 eV with negative sign to the initial level of the Balmer Series . 3.40 eV corresponds also to the energy difference between the initial level and the Balmer edge, as well as to the minimum required energy to ionise a hydrogen atom from the initial level . For the calculation of the other energy levels the values of the corresponding level differences must now be subtracted from 3.40 eV. For the energy level,

eg , the subtraction 3.40 eV – 1.89 eV = 1.51 eV is required (1.89 eV = EpHα). Per definition the values of the energy levels have here negative signs.

10.4 Balmer- Paschen- and Bracket Continuum

Hot stars, with main radiation intensity in the UV region of the spectrum, show a steeply rising continuum level toward shorter wavelengths. As already shown above, this tendency is abruptly stopped by the Balmer Jump at 3646 Å. After a dramatic drop in intensity, the continuum rises again in the UV range, until it reaches the final ionisation limit of hydrogen (also called the Lyman limit) at 912 Å. The following graph shows the Balmer Jump at a synthetic A0 I profile from the Vspec database.

A similar process occurs near the border to the infrared region at 8207 Å, the so-called Paschen Jump. Somewhat confusing is the designation of the intermediate continuum sec-tions which always bear the name of the preceding jumps or series. The Balmer Series

is therefore located within the so-called Paschen Continuum. On the shortwave (UV) side of the Balmer Jump, follows the Balmer Continuum with the Lyman Series

. In the infrared region, the Paschen Series is located within the Bracket Continuum. The dramatic influence of the hydrogen absorption on the continuum can be explained by the extremely high occurrence of this element in most of stellar photospheres.

[Å]

I

λ

Paschen Jump8207 Å


11 Ionisation Stage and Degree of Ionisation

11.1 The Lyman Limit of Hydrogen

In the second diagram of sect. 10.3 the energy for the lowest excitation level of the Lyman

Series results to . Converted with formula {10}, this gives the well-known Lyman limit or Lyman edge in the UV range with wavelength λ = 912 Å. It is func-tionally equivalent to the “Balmer edge” of the Balmer Series (sect. 10.4). This value is very important for astrophysics, because it defines the minimum required energy to ionise the H-atom from its ground state . This level is only achievable by very hot stars of the O- and early B-Class. [3]. The very high UV radiation of such stars ionises first the hydrogen clouds which are shining due to emitted photons by the subsequent recombination (H II re-gions, eg M42, Orion Nebula, sect. 22).

11.2 Ionisation Stage versus Degree of Ionisation

The term “Ionisation stage” refers here to the number of electrons, which an ionised atom has lost to the space (Si IV, Fe II, H II, etc.). This must not be confused with the term “De-gree of ionisation” in plasma physics. It defines for a gas mixture the ratio of atoms (of a certain element) that are ionised into charged particles, regarding the temperature, density and the required ionisation energy of the according element. This “Degree” is determined in astrophysics with the famous Saha equation.

11.3 Astrophysical Form of Notation for the Ionisation Stage

Unfortunately, in astrophysics the chemical form of notation is not in use but instead of it another somewhat misleading version. The neutral hydrogen is denoted by chemists with

H, and the ionised with H+, which is clear and unambiguous. On the other hand astrophysi-cists, denote already the neutral hydrogen with an additional Roman numeral as H I and the ionised with H II. The doubly ionised calcium is referred by chemists with Ca++, for astro-physicists this corresponds to Ca III. Si IV is for example triply ionised silicon Si+++. This sys-tem therefore works according to the “(n–1) principle”, ie in astrophysics the ionisation stage of an atom is always by 1 lower than the Roman numeral. A high ionisation stage of atoms always means that very high temperatures must be involved in the process.


12 Forbidden Lines or –Transitions

Based on the already presented theories this phenomenon can only roughly be explained. For a more comprehensive understanding, further quantum mechanical knowledge would be required. For practical amateur spectroscopy, this is anyway not really necessary.

Most amateurs certainly have an [O III] filter for the contrast enhancement of emission nebulae. It lets pass the two green emission lines of the doubly ionised oxygen [O III] at 4959Å und 5007Å. These lines are generated here by so-called "Forbidden Transitions" be-tween the energy levels (sect. 22). The initial levels of such transitions are called “metasta-ble”, because they are highly sensitive to impacts and an electron must remain her for a quite long time (several seconds to minutes) until it performs the forbidden “jump”. These circumstances increase drastically the likelihood that this state is destroyed before the transition happens.

"Forbidden" therefore means that in dense gases, such as on the earth's surface or in stel-lar atmospheres, these transitions are extremely unlikely, because they are prevented by frequent collisions with other particles. This disturbing effect occurs very rarely within the extremely thin gases of the interstellar space. Thus such transitions are possible here. Such forbidden lines are denoted within square brackets eg [O III], [N II], [Fe XIV].

In addition to nitrogen bands, the forbidden airglow line [OI] (5577.35Å) is the main cause for the formation of the usually greenish polar lights in the extremely thin upper layers of the atmosphere. For the generation of higher ionisation stages such as [O III] the required ionisation energy is missing here.

www.nww-web.at

http://www.nww-web.at/


13 The Spectral Classes

13.1 Preliminary Remarks

Basic knowledge of the spectral classes is an indispensable prerequisite for a reasonable spectroscopic activity. Combined with appropriate skills and tools, this classification sys-tem contains a considerable qualitative and quantitative information potential about the classified objects. The average-equipped amateur will hardly ever come into the embar-rassment, that he really must determine an unknown classification of a star, unless of cer-tainly recommendable didactic reasons. The spectral classes can nowadays be obtained from Internet sources [100], planetarium programs, etc. For a deeper understanding of the classification system, a rough knowledge of the historical development is very useful since from each development step something important remained until to date!

13.2 The Fraunhofer Lines

At the beginning of the 19th Century, the physicist and optician Joseph von Fraunhofer (1787-1826) investi-gated, based on the discovery of Wollaston, the sunlight with his home-built prism spectroscope. He discovered over 500 absorption lines in this very complex spectrum. The more intensive of them he denoted with the letters A – K, at that time still unaware of the physical context.

Picture below: Original drawing by Fraunhofer from Inter-net sources. This line names can frequently be found even in recent papers!

Fraunhofer has been studied the brighter stars with this spectroscope, and already recognised that in the spectrum of Sirius broad strong lines are dominating and Pollux shows a similar pattern as the spectrum of the sun! Further he observed the spectrum of Betelgeuse which shows barely discrete absorption lines but broad absorption bands.

The table on the right and the graphics below show how this system was expanded later on. (Source: NASA).

Line Element Wavelength Å

A – Band O2 7594 – 7621

B – Band O2 6867 – 6884

C H (α) 6563

a – Band O2 6276 – 6287

D 1, 2 Na 5896 & 5890

E Fe 5270

b 1, 2 Mg 5184 & 5173

F H (β) 4861

D Fe 4668

E Fe 4384

F H (γ) 4340

G – Band CH 4300 - 4310

G Ca 4227

H H (δ) 4102

H Ca II 3968

K Ca II 3934


Here are some of the identified Fraunhofer lines in the solar spectrum, obtained with the DADOS Spectrograph in the range of 4200 – 6700 Å (200L/mm).

Below left, the H and K lines of ionised calcium. Ca II are the most intense of the sun-grown absorption lines (3968/3934 Å). Below right is the beautiful so-called A-band (7594 – 7621 Å), caused by the O2 molecule in the earth’s atmosphere (DADOS and 900L/mm grat-ing).

13.3 Further Development Steps

In the further course of the 19th to the early 20th Century, the astronomy, and particularly the spectroscopy benefited from im-pressive advances in chemistry and physics. So it became in-creasingly possible to assign the spectral lines to chemical ele-ments - primarily the merit of Robert Bunsen (1811 - 1899) and Gustav Kirchhoff (1824 - 1887)

Father Angelo Secchi (1818 - 1878) from the Vatican Observa-tory decisively influenced the future path of the stellar spectral classification. He is therefore referred by many sources as the father of the modern astrophysics. He subdivided the stellar spectra into five groups according to specific characteristics (I-V “Secchi Classes”).

Type I Bluish-white stars with relatively simple spectra, which are dominated by small but very bold lines. These are distributed like thick rungs over the spectral stripe and turned out later as the hydrogen lines of the famous Balmer series. This simple characteristic allows even beginners, to roughly classify such stars into the currently used A- or late B-Class (Sir-ius, Vega, Castor).

Type II Yellow shining stars with complex spectra, dominated by numerous metal lines, like they exhibit the Sun, Capella, Arcturus, Pollux (now Classes ≈ F, G, K).


Type III Reddish-orange stars with complex band spectra and a few discrete lines. The ab-sorption bands get darker (more intense) towards the shortwave (blue) side. Such features show, e.g. Betelgeuse, Antares, and Mira. Not until 1904, it became clear that these ab-sorption bands are mainly caused by the titanium oxide molecule TiO (today's Class M).

Type IV Very rare reddish stars with absorptions bands getting darker (more intense) to the longwave (red) side. Angelo Secchi already recognised that it is generated by carbon (sect. 5.4)!

Type V Finally, stars with "bright lines" – emission lines as we know today.

13.4 The Harvard System

It soon became clear that the classification system of Secchi was too rudimentary. Based on a large number of spectra and preliminary work by Henry Draper, Edward Pickering (1846-1919) refined Secchi’s sys-tem by capital letters from A – Q. The letter A corresponded to the Secchi class type I for stars with dominant hydrogen lines. Finally this classification solely survived up to the present time! As director of the Harvard Observatory, he employed many women, for its time a truly avant-garde attitude. Three women of his staff took care of the classi-fication problem until after many detours and “meanders” the system of Annie J. Cannon (1863 - 1941) became widely accepted around the end of the World War I.

Its basic structure has survived until today and is essentially based on the letters O, B, A, F, G, K, M. The well-known and certainly later cre-ated mnemonic: Oh Be A Fine Girl Kiss Me. With this system, even today still over 99% of the stars can be classified. This sequence of letters follows the decreasing atmospheric temperature of the classi-fied stars, starting from the very hot O-types with several 10,000 K up to the cool M-types with about 2,400 –3,500 K. This reflects the abso-lutely ground-breaking recognition that the spectra depend mainly on the photospheric temperature of the star and secondarily only on other parameters such as chemical composition, density, rotation speed etc. This may not be really surprising from today's perspective, since the shares of hydrogen and helium with 75% and 24%, even about 13.7 billion years after the “Big Bang” still comprise about 99% of the elements in the universe. This systematic also forms the hori-zontal axis of the almost simultaneously developed Hertzsprung Russell Diagram (sect. 14). It was later complemented by the classes:

– R for Cyan (CN) and Carbon Monoxide (CO) – N for Carbon – S for very rare stars, whose absorption bands are generated, instead of TiO, by zirconium oxide (ZrO), yttrium oxide (YO) or lanthanum oxide (LaO). Moreover, the entire class system was further subdivided with additional decimal numbers from 0–10. Examples: Sun G2, Pollux K0, Vega A0, Sirius A2, Procyon F5.


13.5 “Early” and “Late” Spectral Types

One of the faulty hypotheses on the long road to this classification system postulated that the spectral sequence from O to M represents the chronological stages of a star. Unaware at that time of nuclear fusion as a "sustainable" energy source, also the hypothesis was dis-cussed, that the stars could generate their energy only by contraction, ie starting very hot and finally ending cool. This error has subsequently influenced the terminology until today.

Thus the O, B, A classes are called "early", the F and G classes "medium" and K and M as "late" types. This systematic is also applied within a class. So M0 is called an “early” and M8 a “late” M-type. Logically is for example M1 "earlier" than M7.

13.6 The MK (Morgan Keenan) or Yerkes System

Later on, the progress in nuclear physics and the increasing knowledge of the stellar evolu-tion required a further adaptation and extension of the system. It was eg recognised, that within the same spectral class, stars can show totally different absolute luminosities, mainly caused by different stages of stellar development.1943, as another milestone, the classification system was extended with an additional Roman numeral by Morgan, Keenan and Kellmann from the Mt Wilson Observatory. This second dimension of the classification specifies the so called six luminosity classes.

Luminosity class Star type

I Luminous Super Giants

Ia-0, Ia, Iab, Ib Subdivision of the Super Giants according to decreasing lu-minosity

II Bright Giants

III Normal Giants

IV Sub Giants

V Dwarfs or Main Sequence Stars

VI Sub Dwarfs (rarely used, as specified by prefix)

VII White Dwarfs (rarely used, as specified by prefix)

This system classifies the Sun as a G2V star, an ordinary Dwarf on the main sequence of the Hertzsprung Russel Diagram. Sirius, classified as A1Vm, is also a Dwarf on the main se-quence. Betelgeuse, as a Super Giant and rated with M1–2 Ia–Iab, moves as a variable be-tween M1 and M2 and fluctuates between the luminosity class Ia and Iab. It has given up the Dwarf stage on the main sequence long ago and expanded into a Super Giant.

13.7 Further Adaptations up to the Present

Up to the presence, this classification system has been adapted to the constantly growing knowledge. Thus, new classifications for rare, stellar "exotics" have emerged, which today even amateurs successfully deal with. Furthermore with additional lower-case letters at-tached as a prefix or suffix, unusual phenomena, such as a higher than average metal con-tent or "metallicity" are referred. Some of these supplements are, however, over determin-ing, eg because White Dwarfs, Sub Dwarfs and Giants are already specified by the luminos-


ity class. Caveat: Dwarf or main sequence stars must not be confused with the White Dwarfs. The latter are extremely dense, burned-out "stellar corpses" (sect. 14.3).

Examples: Sirius A: A1Vm, metal rich main sequence star (Dwarf), spectral class A1 Sirius B: DA2, White Dwarf (or „Degenerate“) spectral class A2 Omikron Andromedae: B6IIIep, Omikron Ceti (Mira): M7IIIe Kapteyn‘s star: sdM1V

Nowadays the special classes P (Planetary Nebulae) and Q (Novae) are barely in use!

The suffixes are not always applied consistently. We often see other versions. In the case of shell stars e.g. pe, or shell is in use.

Suffix

S Sharp lines

c Extraordinary sharp lines

B Broad lines

A Normal lines

comp Composite spectrum

e H- emission lines by B- and O Stars

F He- and N- emission lines by O-stars

Em Metallic emission lines

K Interstellar absorption lines

M Strong metal lines

n / nn Diffuse lines/strongly dif-fuse lines

Wk weak lines

p, pec peculiar spectrum

Sh Shell

V variation in spectrum

Fe, Mg… Excess or deficiency (–) of the spec. element

Prefixes

d Dwarf

sd Sub Dwarf

g Giant

Special classes

Q Nova

P Planetary Nebulae

D Dwarf, +additional letter for O, B, A spectral class

W Wolf-Rayet Star + additional let-ter for C-, N- or O- lines

S Stars with zirconium oxide ab-sorption bands

C Carbon stars

L, T,

Brown dwarfs

Y Theoretical class for brown dwarfs <600 K


13.8 The Rough Determination of the Spectral Class

The rough, one-dimensional determination of the spectral classes O, B, A, F, G, K, M, is easy and even feasible for slightly advanced amateurs. The distinctive criteria are striking fea-tures such as line- or band spectra, as well as absorption- or emission lines, which appear prominently in certain spectral classes and vice versa are very weak or even completely ab-sent in others. But the determination of the decimal subclasses and even more, the addi-tional determination of the luminosity class (second dimension), require well-resolved spec-tra with a large number of identified lines, as well as deeper theoretical knowledge. Possi-ble distinctive criterions are eg the intensity ratio or the FWHM values of certain spectral lines. On this topic exists an extensive literature eg [4]. Here follows just a brief introduc-tion into the rough, one dimensional determination of the spectral class. A further support is the Spectroscopic Atlas for Amateur Astronomers [33]. The following figure shows super-imposed and lowly-resolved the entire sequence of the spectral classes O - M, as it can be found in [33].

TAFEL 01 Übersicht Spektralklassen

O9.5

B1

B7

A1

A7

F0

F5

G2

G8

K1.5

K5

Te

lluri

cO

2

He

I 6

67

8

Hα

65

62

He

I 5

87

6N

a I

58

90

/95

He

II

54

11

He

I 5

04

86

He

I 5

01

6H

e I

49

22

Hβ

48

61

C I

II 4

64

7/5

1

Hγ

43

40

He

I 4

47

1H

e I

43

88

Hδ

41

01

Hε

39

70

CH

43

00

Ca

ll

H

Mg

l 5

16

7-8

3„M

g T

rip

let“

Ca

I 4

22

7

TiO

TiO

TiO

TiO

TiO

M1.5

M5

K

Vindemiatrix4‘990°K

Spica22‘000°K

Adhafera7‘030°K

Procyon6330°K

Sonne5‘700°K

Sirius10‘000°K

Altair7‘550°K

Arcturus4‘290°K

Alterf3‘950°K

Alnitak25‘000°K

Regulus15‘000°K

Antares3‘600°K

Rasalgethi3‘300°K

TiO

©R

ich

ard

Wa

lke

r 2

01

0/0

5


What is already clearly noticeable here?

– In the upper third of the table (B2-A5), the strong lines of the H-Balmer series, i.e. Hα, Hβ, Hγ, etc. They appear most pronounced in the class A2 and are weakening from here towards earlier and later spectral classes.

– In the lower quarter of the table (K5-M5) the eye-catching shaded bands of molecular absorption spectra, mainly due to titanium oxide (TiO).

– Just underneath the half of the table some spectra (F5-K0), showing only few prominent features, but charged with a large number of fine metal lines. Striking features here are only the Na I double line (Fraunhofer D1, 2) and in the “blue” part the impressive Fraun-hofer lines of Ca II (K + H), gaining strength towards later spectral classes. Fraunhofer H at λ 3968 starts around the early F-class to overprint the weakening Hε hydrogen line at λ 3970. In addition, the H-Balmer series is further weakening towards later classes.

– Finally on the top of the table the extremely hot O-class with very few fine lines, mostly ionised helium (He II) and multiply ionised metals. The H-Balmer series appears here quite weak, as a result of the extremely high temperatures. The telluric H2O and O2 ab-sorption bands are reaching high intensities here, because the strongest radiation of the star takes place in the ultraviolet whereas the telluric absorption bands are located in the undisturbed domain near the infrared part of the spectrum. By contrast the maximum radiation of the late spectral classes takes place in the infrared part, enabling the stellar TiO absorption bands to overprint here the telluric lines.

– In the spectra of hot stars (~ classes from early A – O) the double line of neutral sodium Na I (Fraunhofer D1,2) must imperatively be of interstellar origin. Neutral sodium Na I has a very low ionisation energy of just 5.1 eV and can therefore exist only in the atmos-pheres of relatively cool stars. The wavelengths of the ionised Na II lie already in the ul-traviolet range and are therefore not detectable by amateur equipment.


Here follow two different flow diagrams, for the rough one-dimensional determination of the spectral class: Sources: Lectures from University of Freiburg i.B. [56] and University of Jena.

Version 1

Applied lines: – Fraunhofer K (Ca II K 3934Å) – Fraunhofer H (Ca II H 3968Å) – Fraunhofer G Band (CH molecular 4300–4310Å) – Balmer line Hγ, 4340Å – Mangan Mn 4031/4036Å – Titanoxide Bandhead: TiO 5168Å

The intensity I of the compared lines (eg Ca II K/Hγ) is calculated by the Peak in-tensities (sect. 7.1).

__________________________________________________________________________________

Version 2

Applied lines: – Fraunhofer K (Ca II K 3934Å) – Fraunhofer H (Ca II H 3968Å) – Balmer line Hγ, 4340Å – Fe I, 4325Å

Balmerlinesvisible?

H and Kvisible?

Spectraltype O

Spectraltype K, M

Spectraltype B

H and Kvisible?

Spectraltype A0-A5

Spectraltype A5

Spectral typelater A5

K/Hγ<1? K/Hγ=1?

Hγ/Fe I=1?(4325)

Hγ/Fe I<1?(4325)

Spectraltype A6-F

Spectraltype G0-G4

Spectral typelater G5

nono

no

no no

yes

yes

yes yes

yes

yes

yes

no

no

Ca II and K? O, B

A5–A9 Ca II K/HγA0–A5

Ca II K/H

F0–F3

G-Band

G Mn 4031, 4036 F3–F9

M KG–Band/TiO 5168

<1

>1

>1

>1<1

~1

yes

yes

no

~1

no

no


Here some additional classification criteria (see also [3], [4], [33] and [80]).

Course of the Continuum curve:

Already by comparing of non-normalised raw spectra, eg an early B- star against a late K-star, one can observe that the intensity maximum of the pseudo continuum is significantly blue-shifted (Wien's Displacement Law). Extremely hot O- and early B- stars radiate mainly in the ultraviolet (UV), cold M- stars chiefly in the infrared range (IR).

O- Class: singly ionised helium He II, also as emission line. Neutral He I, doubly ionised C III, N III, O III, triply ionised Si IV. H- Balmer series only very weak. Maximum intensity of the continuum is in the UV range.

Examples: Alnitak (Zeta Orionis): O9 Ib, Mintaka (Delta Orionis): O9.5 II,

B- Class: Neutral He I in absorption strongest at B2, Fraunhofer K- Line of Ca II becomes faintly visible, further singly ionised OII, Si II, Mg II. H- Balmer series becomes stronger.

Examples: Spica: B1 III-IV, Regulus B7V, Alpheratz (Alpha Andromedae): B8 IVp Mn Hg Al-gol (Beta Persei): B8V, as well as all bright stars of the Pleiades.

A- Klasse: H- Balmer lines are strongest at A2, Fraunhofer H+K lines Ca II become stronger, neutral metal lines become visible, helium lines (He I) disappear.

Examples: Wega: A0 V, Sirius: A1 V m Castor A2 V m, Deneb: A2 Ia Denebola: A3 V, Altair: A7V,

F- Class: H- Balmer lines become weaker, H+K lines Ca II, neutral and singly ionised metal lines become stronger (Fe I, Fe II, Cr II, Ti II). The striking “line double” of G-Band (CH mo-lecular) and Hγ line can only be seen here and forms the unmistakable "Brand" of the middle F-class [33]!

Examples: Caph (Beta Cassiopeiae): F2III-IV, Mirphak (Alpha Persei): F5 Ib, Polaris: F7 Ib-II, Sadr (Gamma Cygni): F8 Ib, Procyon: F5 IV-V

G- Class: Fraunhofer H+K lines Ca II very strong, H- Balmer lines get further weaker, Fraun-hofer G- Band becomes stronger as well as many neutral metal lines eg Fe I, Fraunhofer D-line (Na I).

Examples: Sun: G2V, the brighter component of Alpha Centauri G2V, Mufrid (Eta Bootis): G0 IV, Capella G5IIIe + G0III (binary star composite spectrum).

K- Class: Is dominated by metal lines, H- Balmer lines get very weak, Fraunhofer H+K Ca II are still strong, Ca I becomes strong now as well as the molecular lines CH,CN. By the late K- types first appearance of TiO bands.

Examples: Pollux: K0IIIb, Arcturus: K1.5 III Fe, Hamal (Alpha Arietis): K2 III Ca, Aldebaran: K5 III

M- Class: Molecular TiO- bands get increasingly dominant, many strong neutral metal lines, eg Ca I. Maximum intensity of the continuum is in the IR range.

Examples: Mirach (Beta Andromedae): M0 IIIa, Betelgeuse: M1-2 Ia-Iab, Antares: M1.5 Iab-b, Menkar (Alpha Ceti): M 1.5 IIIa, Scheat, (Beta Pegasi): M3 III Tejat Posterior (mü Gemini): M3 III Ras Algheti: (Alpha Herculis): M5III,


The following chart shows the relative change in the line intensity of characteristic spectral lines as a function of the spectral type or the temperature. It was developed 1925 in a dis-sertation by Cecilia Payne Gaposhkin (1900 – 1979).

This chart is not only of great value for determining the spectral class, but also prevents by the line identification from large interpretation errors. Thus becomes immediately clear that the photosphere of the Sun (spectral type G2V) is a few thousand degrees too cold to show helium He l in a normal (photospheric) solar spectrum. He I is visible only during solar eclipses as an emission line in the so called flash spectrum, which is produced mainly in the much hotter solar chromosphere.

13.9 Effect of the Luminosity Class on the Line Width

Here we see within the same spectral class how the line width increases with decreasing luminosity. This happens primarily due to the so-called "pressure broadening", ie the broad-ening of spectral lines due to increasing gas pressure. The main reason is the increasing density of the stellar atmosphere with decreasing luminosity, ie the star becomes smaller, less luminous and denser.

Most densely are the atmospheres of the white dwarfs, class VII, least densely among the Super Giants of class I. This effect is strongest by the H-Balmer series of class A (below left). Already by the F-class (same wavelength domain, below right), this effect is barely no-ticeable. This trend continues towards the later spectral classes (excerpts from [33]).

O5 B0 A0 F0 G0 K0 M0 M7Spectral Type

Temperature of the Photosphere (K)

50‘000 25‘000 10‘000 8‘000 6‘000 5‘000 4‘000 3‘000

Lin

e I

nte

nsi

tyE

W

He II He I

HCa II

TiO

Ca IFe IFe IIMg II

Si IISi III

Si IV

TAFEL 31

Hδ

4101.74

Hγ

4340.47

Porrima γ VirF0 V

©Richard Walker 2010/05

Mirphak α PerF2 lb

Ca II 3933.66

Ca I 4226.73

Ti ll4395.04

Fe l/ll/Ti ll4415-18

Mg ll4481

Fe ll4583.83

Fe ll4629.34Cr ll4634.1

Y ll/V ll/Fe ll4177-79

Fe ll/Ti ll4172-73

Fe l 4271-72

Fe l 4045

Si ll4128/30

Auswirkung der Leuchtkraftklasse (Luminosity Effect) auf Spektraltyp F

Fe l/ll4384-85

Ti ll4444

Ti ll4470

Fe ll4550/56

Fe ll/Cr ll4585/88

CH/Fe ll4299-13

Sc ll/Ti ll4314

Sr ll4077.71Fe l 4064

Ti ll4368

Fe ll/Sc ll4666/70

Caph β CasF2lll-lV

Caph

Porrima

Ca II 3968.74

Fe l 4002/05

Zr ll4024

Fe l/Yll3983Fe l 3997

Mn l 4031-36

Mn l 4055

Fe l 4084

Fe l/ll4118/22

Fe l 4143Zr ll4149

Ti ll4154

Fe l/V ll4202Sr ll4215.52

Fe ll4231-33Sc ll4247Zr ll4258

Cr l/Ti ll4290

Mirphak

Fe l 4326

Fe ll/Cr l 4352

Ti ll4400

Ca l 4435

Fe ll4490Ti ll4501

Fe ll4508

Ti ll4534

Ti ll4564Ti ll4572

Cr ll/Fe ll4618-20

Ti ll4708

Ca I 4454.78

TAFEL 22

Hε

3970.07

Hδ

4101.74

Hγ

4340.47

Vega α LyrA0 V


Deneb α CygA2 la

Ca II 3933.66

Ca I 4226.73

Ti ll4395.04

Fe ll4416.8

Mg ll4481

Ti ll4501.27

Fe ll4583.8

Fe ll4629.9Fe ll4634.6

Fe ll4178.9Fe l 4173.1

Fe l 4271-72

Fe l 4045.82

Si ll4128/30

Auswirkung der Leuchtkraftklassen (Luminosity effect) auf Spektraltyp A

Deneb

Vega

Fe ll4384-85

Ti ll4444

Ti ll4470

Fe ll4550

Cr ll4617/19

Cr ll4588

Fe ll4520/23

Fe ll4303.2Sc ll/Ti ll4314

Sr ll4077.71Fe l 4067.6

Fe ll4366.17

Fe ll/Cr l 4666

Ruchbah δ CasA5III-IV

Deneb

Ruchbah

Vega

Fe l 4002/05

Zr ll/Ti ll4024/28

Fe ll4352

Fe ll4233.17

Deneb α CygA2 Ia

Ruchbah δ CasA5 III – IV

Vega α LyrA0 V

Mirphak α PerF2 Ib

Caph β CasF2 III – IV

Porrima γ VirF0 V


14 The Hertzsprung - Russell Diagram (HRD)

14.1 Introduction to the Basic Version

The HRD was developed in 1913 by Henry Russell, based on the work by Ejnar Hertzsprung. It is probably the most fundamental and powerful illustrating tool in astro-physics. On the topic of stellar evolution and HRD an extensive literature exists, which must be studied anyway by the ambitious amateur. Here it is illustrated, how a wealth of informa-tion can be gained about a star just with the help of the spectral class and the HRD. The fol-lowing figure shows the basic version of the HRD with the luminosity (compared to the sun), plotted against the spectral type. The luminosity classes Ia – VII are marked by lines within the diagram. Further visible is the Main Sequence, identical to the line for luminosity class V, and the two branches, where the Red Giants and White Dwarfs are gathering.

The spectral class unambiguously determines the position of a star inside the diagram and vice versa. The position of the sun, with the classification G2V is already marked (yellow disk). With this diagram the luminosity of the spectral class, in comparison to the sun, can already be determined – in the case of the sun

In the following it will be demonstrated, how further parameters of the star can be deter-mined, just by modification of the HRD-scales.

Red Giant BranchMain

Sequence

SunVI

V

IV

III

II

Ib

Iab

IIab

Spectral Type

Lum

ino

sity

com

par

edto

th

eSu

n

106

105

104

103

102

101

100

10-1

10-2

O5 B0 B5 A0 A5 F0 F5 G0 G5 K0 K5 M0 M5

White DwarfsVII


14.2 The Absolute Magnitude and Photospheric Temperature of the Star

The following version of the HRD shows on the horizontal axis at the upper edge of the dia-gram, the corresponding temperature of the stellar atmosphere, ie the photosphere of the star, where the visible light is produced. The position of the Sun (G2V) is here also marked with a yellow disc. At the top of the chart the temperature of about 5,500 ° K can be read, on the left the absolute brightness (Absolute Magnitude) with ca. 4M5. This corresponds to the apparent brightness, which a star generates in a normalised distance of 10 parsecs, or some 32.6 light-years.

Redrawn and supplemented following a graphics from: www.bdaugherty.tripod.com

The chart is further populated with a variety of common stars. The sun, along with Sirius, Vega, Regulus, Spica, etc. is still a Dwarf star on the Main Sequence. Arcturus, Aldebaran, Capella, Pollux, etc. have already left the main sequence and shining now on the Giant Branch with the Luminosity Class III, Betelgeuse, Polaris, Rigel, Deneb, in the range of the giants, with their respective classes Ia-Ib. On the branch of the White Dwarfs we see the companion stars of Sirius and Procyon.

STELLAR TEMPERATURE

50,000K 25,000K 10,000K 7,500K 6,000K 4,900K 3,500K 2,400K

SPECTRAL CLASSO B A F G K M

3 5 0 5 0 5 0 5 0 5 0 5 0 5

AB

SOLU

TE

MA

GN

ITU

DE

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

Alnitak

RigelSaiph DenebBetelgeuse

68 Cygni

Spica

Achernar

Mirfak Antares

Gacrux

MiraAldebaranPollux

Arcturus

Regulus Algol

Vega

Sirius ACastor

AltairProcyon A

Sun

α Centauri B

61 Cygni A

61 Cygni B

Sirius B

Procyon B

Proxima Centauri

Super Giants - Ia

AdharaPolaris

Capella

Subgiants - IV

Giants - III

Bright Giants - II

Super Giants - Ib

http://www.bdaugherty.tripod.com/


14.3 The Evolution of the Sun in the HRD

The following simplified short description is based on [1]. It demonstrates how the spectral class allows the determination of the stellar state of development. In the diagram below, the evolutionary path of the sun is shown. By the contraction of a gas and dust cloud, at first a protostar is formed, which subsequently moves within some million years on the Main Sequence. Here, it stabilises at first the luminosity by about 70% of the today's value. Within the next 9-10 billion years the luminosity increases to over 180%, whereby the spectral class G2, eg the photospheric temperature, remains more of less constant [1]. Dur-ing this period as a Dwarf- or Main Sequence star, hydrogen is fused into helium.

Towards the end of this stage the hydrogen is burning in a growing shell around the helium core. The sun becomes now unstable and expands to a Red Giant of the M-class (luminosity class ca. II). It moves now on the Red Giant Branch (RGB) to the top right of the HRD, where after 12 billion years it comes to the ignition of the helium nucleus, the so called Helium Flash. The photosphere of the Red Giant expands now almost to the Earth's orbit. By this huge expansion the gravity acceleration within the stellar photosphere is reduced dramati-cally and the star loses therefore at this stage about 30% of its mass [1].

Subsequently the giant moves with merging helium core on the Horizontal Branch (HB) to the intermediate stage of a Yellow Giant of the K-class (lasting about 110M years) and then via the reverse loop of the Asymptotic Giant Branch (AGB) to the upper left edge of the HRD (details see [33]). The experts seem still be divided whether the sun is big enough to push off at this stage the remaining shell as a visible Planetary Nebula [1], [2]. Assured however is the final shrinkage process to an extremely dense White Dwarf of about Earth's size. Af-ter further cooling, down on the branch of the White Dwarfs, the sun will finally get invisi-ble as a Black Dwarf, and disappear from the HRD. During its live the Sun will pass through a large part of the spectral classes, but with very different luminosities.

White Dwarf

Giant Branch

Suntoday

III

II

Ib

Iab

Ia

Spectral Type

Lum

ino

sity

com

par

edto

th

eSu

n

106

105

104

103

102

101

100

10-1

10-2

O5 B0 B5 A0 A5 F0 F5 G0 G5 K0 K5 M0 M5

AGB

Planetary Nebula

Proto Star


14.4 The Evolution of Massive Stars

In the next subsection it will be shown how the length of stay on the main sequence is dramatically reduced with increasing stellar mass. Highly complex nuclear processes cause complex pendulum like movements in the upper part of the HRD, showing various stages of variables (more details see [33]). During this period also many of the heavy elements in the periodic table are generated. Massive Stars about >8–10 solar masses, will not end as White Dwarfs, but explode as Supernovae [2]. Depending on the mass of the star it finally remains a Neutron Star, if the rest of the stellar mass is not greater than about 1.5–3 solar masses (TOV limit: Tolman-Oppenheimer-Volkoff). Above this limit, eg stars with initial >15–20 solar masses, it ends in a Black Hole.

14.5 The Relation between Stellar Mass and Life Expectancy

The effect of the initial stellar mass is crucial for its further life. First, it decides which place it occupies on the Main Sequence. The larger the mass the more left in the HRD or "earlier" in respect of the spectral classification. Second, it has a dramatic impact on his entire life expectancy, and the somewhat shorter period of time that he will spend on the Main Se-quence. This ranges from roughly some million years for the early O- types up to >100 bil-lion years for Red Dwarf stars of the M class. This is due to the fact that with increasing mass the stars consume their "fuel" over proportionally faster. This relationship becomes evident in the following table for Dwarf Stars on the Main Sequence (luminosity class V), together with other parameters of interest. The values are taken from [53]. Mass, radius and luminosity are given in relation to the values of the Sun ( ).

Spectral class, Main Sequence

Mass

Stay on Main Sequence [Y]

Temperature stellar atmos-phere

Radius

Luminosity

O 20 – 60 10 – 1M >25 – 30‘000 K 9-15 90‘000 –800‘000

B 3 – 18 400 – 10M 10‘500–30‘000 K 3.0–8.4 95 – 52‘000

A 2 – 3 3bn – 440M 7‘500 – 10‘000 K 1.7–2.7 8 – 55

F 1.1 – 1.6 7bn – 3M 6‘000 – 7‘200 K 1.2–1.6 2.0 – 6.5

G 0.9–1.05 15bn – 8bn 5‘500 – 6‘000 K 0.85–1.1 0.66 – 1.5

K 0.6–0.8 >20bn 4‘000 – 5‘250 K 0.65–0.80 0.10 – 0.42

M 0.08–0.5 2‘600 – 3‘850 K 0.17–0.63 0.001 – 0.08

The length of stay of the K- and M-class Dwarf Stars differs, considerably depending on the source. It has anyway more theoretical importance, since these stars have a significantly longer life expectancy than the current age of the universe from estimated 13.7bn years!


14.6 Age Determination of Star Clusters

The relationship between the spectral class and the according time, spent on the Main Se-quence, allows the age estimation of star clusters – this under the assumption that such clusters are formed within approximately the same period from a gas and dust cloud. If the spectral classes of the cluster stars are transferred to the HRD, it gives the following inter-esting picture: The older the cluster, the more right in the diagram (ie, "later") the distribu-tion of stars turns off from the Main Sequence up to the realm of giants and Super Giants (so called Turn off Point). M67 belongs with more than 3 billion years to the oldest open clusters, ie the O-, B- and A-, as well as the early F-types have already left the Main Se-quence, as shown on the chart. However all the bright stars of the Pleiades (M45), still be-long to the middle to late part of the B-class. This cluster must therefore necessarily be younger than M67 (about 100M years). One can also say that the Main Sequence "burns off" with increasing age of the cluster like a candle from top to down.

Source: [50] Lecture astrophysics, MPI

The horizontal axis of the HRD is divided instead of spectral types with the equivalent val-ues of the Color-Magnitude Diagram (CMD). This photometrically determined B – V color index is the brightness difference of the object spectrum (magnitudes) between the blue range (at 4,400 Å) and the "visual" range at 5,500 Å (green). The difference = 0 corre-sponds to the spectral class A0 (standard star Vega). Earlier classes O, B have negative val-ues, later classes are positive. For the Sun (G2), this value is + 0.62, for Betelgeuse (M1) +1.85.

Alter eines Sternhaufens


15 The Measurement of the Radial Velocity

15.1 The Doppler Effect

The Doppler principle, named after the Austrian physicist Christian Doppler 1803 – 1853, enables the determination of the radial velocity. One of the classic explanation models is the changing pitch, emitted by the siren of a passing emergency vehicle. The same effect can be observed in the entire range of electromagnetic waves, including of course the visual light. Observed from this effect is caused by the radial velocity component of a radiation source (eg a star), moving with the velocity .

If is directed away from the observer, the observed wavelength appears stretched and the spectrum therefore redshifted. In the opposite case it appears compressed and the spectrum blue shifted.

Source: Wikipedia

In the spectrum of , we can measure the wavelength shift . The radial velocity can then simply be calculated with the Doppler formula:

= Measured shift in wavelength of a given spectral line Wavelength of the considered spectral line in a stationary system = Speed of light 300‘000 km/s – If the spectrum is blue shifted, the object is approaching us and becomes negative – If the spectrum is red shifted, the object is receding and becomes positive.

Vr

S

B

V

Vr

V

V

S

S

Vr = 0

http://upload.wikimedia.org/wikipedia/commons/e/e4/Redshift_blueshift.svg


15.2 The Measurement of the Doppler Shift

For radial velocity measurements ( ) in most cases, the Doppler shift is determined by the difference between a specific spectral line (eg Hα) and their well-known "nominal wave-length" in a stationary laboratory spectrum. For this purpose with the unchanged spec-trograph setup a calibration lamp spectrum is recorded, immediately before and/or after the object spectrum. The calculation of is finally enabled by formula {15}. A rudimentary and less accurate alternative to the calibration lamp is to record a spectrum of a star with intensive, well known lines and a very low radial velocity.

15.3 Radial Velocities of nearby Stars

The radial velocities of stars in the vicinity of the solar system reach for the most part only one-or two-digit values in [km/s]. Examples: Aldebaran +54 km/s, Sirius –8.6 km/s, Betel-geuse +21 km/ s, Capella +22 km/s [100].

The corresponding shifts are therefore very low, usually just a fraction of a 1Å. For and based on the Hα line (6563 Å), corresponds to ~46 km/s (formula {15}). Therefore highly-resolved and accurately calibrated spectra are necessary.

15.4 Relative Displacement within a Spectrum caused by the Doppler Effect

Textbook examples for this effect are the so-called P Cygni profiles (sect. 5.5). For the de-termination of the expansion velocity of the stellar envelope neither an absolutely wave-length calibrated spectrum nor a heliocentric correction [30] is required. The measurement of the relative displacement between the absorption and the emission part of the P Cygni profile is sufficient. For P Cygni this displacement within the Hα line amounts to some 4.4 Å, corresponding to an expansion velocity of ~200 km/s [33].

15.5 Radial Velocities of Galaxies

Even for the brightest galaxies in the Messier catalogue the re-cording of the spectra requires large telescope apertures and expo-sure times of dozens of minutes. In this area the famous cosmologi-cal Red Shift by Edwin Hubble (1889-1953, usually depicted with a pipe) has now to take into account by the interpretation of extraga-lactic spectra. The difficulty here is the distinction between the ki-nematic Doppler Shift, due to the relative proper motions of the gal-axies and the cosmological Red Shift, caused by the intrinsic expan-sion of the relativistic space-time lattice. The latter phenomenon has nothing to do with the Doppler Effect!

Within the range of the Messier Galaxies, i.e. a radius of about 70M ly, the proper motion of the Galaxies still dominates. Six of the 38 galaxies are moving against the "cosmological trend", ie with blue-shifted spectra, towards our Milky Way! These include M31 (Andro-meda) with about –300 km/s, and M33 (Triangulum) with some –179 km/s [101]. With increasing distance, however, the cosmological share of the measured Red Shift becomes more and more dominant. From a distance of some 100 mega-parsecs [1 Mpc = 3.26M ly], the influence of the Doppler Effect due to the proper motion gets virtually negligible. For such objects the distance is usually expressed as –value, which can be easily determined by the measured and heliocentrically corrected Red Shift [30].

In this extreme distance range replaces usually the absolute distance information, be-cause this value is easy to determine from the spectrum and independent of any cosmo-logical models. Due to the finite and constant speed of light, is also used as a measure of


the past. In contrast to the determination of , the "absolute" distance is dependent on further parameters. Formula {18} allows a rough distance estimate with the so-called Hub-ble Parameter . This requires first, to express the cosmological Red Shift in formula {19}, as an apparent, heliocentric "recession velocity" (using the Doppler Princi-

ple).

≈ ca. 73±8 km s-1 Mpc-1 = Distance in Megaparsec Mpc

Thus the apparent "recession velocity" ∙ and the Red Shift of the spectrum grow propor-tionally with the distance to the galaxy {20}. Today it is known that the Hubble Parameter

, seen over time, doesn’t remain constant. This term has therefore displaced the histori-

cally used "Hubble constant" . The current value for was determined in the so-called Key Project, using the Hubble Space Telescope. The linear formulas {18} {20} are only applicable up to about D ≈ 400 Mpc or z <0.1 [431]. Larger distances require the use of cosmological models. Instead of formula {19} a "relativistic" formula must then be applied

which takes into account the effects of SRT [7]. Otherwise for , the simplified formula

{19} would yield values greater than the speed of light !

For radial velocities >1000 km/s, instead of the conventional Doppler formula {15}, also the relativistic version should be used, which takes into account the effects of SRT [7].

The range of the observed - values reaches at present (2010) up to the galaxy Abell 1835

IR 1916 with , discovered in 2004 by a French/Swiss research team with the VLT at ESO Southern Observatory.

Example:

Calculation of the cosmological related share of the apparent "recession velocity" for the Whirlpool galaxy M51, based on the known distance from 27M ly:

according to formula {18} follows

The share of the -value for M51, which is caused by the cosmological redshift, is calcu-

lated with formula {19} to just , which is still very low, considering the cosmic scale.

15.6 Short Excursus on "Hubble time" tH

In this case, it is worthwhile to take a small excursus, since the Hubble parameter allows in a very simple way to estimate the approximate age of the universe! With the simplified as-sumption of a constant expansion rate of the universe after the "Big Bang", by changing formula {18}, it can be estimated, how long ago the entire matter was concentrated at “one point”. This time span is also called Hubble time and is equal to the reciprocal of the Hubble Parameter . This reciprocal value also corresponds to the Division of distance D by the expansion or "recession velocity" and thus the desired period of time !


To calculate the “Hubble time” we just need to put the units of the Hubble Parameter in to equation {23} and to convert [ ] to [ ] and to [ ].

15.7 Radial- and Cosmological Recession Velocities of the Messier Galaxies

The table on the following page shows, sorted by increasing distance D, the measured he-liocentric radial velocities for 38 Messier galaxies, according to NED NASA Extragalactic Database [101] and the cosmological related recession velocities , calculated according

to {18}. Positive values = Red shifted, negative values = Blue shifted.

These figures clearly indicate that in this “immediate neighbourhood”, the kinematic proper motion of the galaxies still dominates. Nevertheless, the trend is already evident here that the measured radial velocities tend, with increasing distance, more and more to the cosmological "recession velocity". Anyhow in more than 50M ly distance two galaxies can be found (M90 and M98) with relatively strong negative values (blue coloured rows). This behaviour show 6 of 38, or about 16% of the Messier Galaxies. Most distant galaxy is M109 with about 81M ly.


Messier Galaxy Distance [Mpc / M ly]

–value Radial velocity [km/s]

Cosmologic "Recess velocity". [km/s]

M31 Andromeda 0.79 / 2.6 –0.0010 –300 +58

M33 Triangulum 0.88 / 2.9 –0.0006 –179 +64

M81 3.7 / 12 –0.0001 –34 +270

M82 3.8 / 12 +0.0007 +203 +277

M94 5.1 / 17 +0.0010 +308 +372

M64 5.3 / 17 +0.0014 +408 +387

M101 6.9 / 22 +0.0008 +241 +503

M102 6.9 / 22 +0.0008 +241 +504

M83 7.0 / 23 +0.0017 +513 +511

M106 7.4 / 24 +0.0015 +448 +540

M51 Whirlpool 8.3 / 27 +0.0020 +600 +606

M63 8.3 / 27 +0.0016 +484 +606

M74 9.1 / 30 +0.0022 +657 +664

M66 10.0 / 32 +0.0024 +727 +730

M95 10.1 / 33 +0.0026 +778 +737

M104 Sombrero 10.4 / 34 +0.0034 +1024 +759

M105 10.4 / 34 +0.0030 +911 +759

M96 10.8 / 35 +0.0030 +897 +788

M90 12.3 / 40 –0.0008 –235 +898

M65 12.6 / 41 +0.0027 +807 +919

M77 13.5 / 44 +0.0038 +1137 +986

M108 14.3 / 47 +0.0023 +699 +1043

M99 15.4 / 50 +0.0080 +2407 +1124

M89 15.6 / 51 +0.0011 +340 +1138

M59 15.6 / 51 +0.0014 +410 +1138

M100 15.9 / 52 +0.0052 +1571 +1160

M98 16.0 / 52 –0.0005 –142 +1168

M49 16.0 / 52 +0.0033 +997 +1168

M86 16.2 / 53 –0.0008 –244 +1182

M91 16.2 / 53 +0.0016 +486 +1183

M60 16.3 / 53 +0.0037 +1117 +1189

M61 16.5 / 54 +0.0052 +1566 +1204

M84 16.8 / 55 +0.0035 +1060 +1226

M87 16.8 / 55 +0.0044 +1307 +1226

M85 17.0 / 55 +0.0024 +729 +1241

M88 18.9 / 62 +0.0076 +2281 +1380

M58 19.6 / 64 +0.0051 +1517 +1431

M109 24.9 / 81 +0.0035 +1048 +1917


15.8 Recess Velocity of the Quasar 3C273

The very low above listed z-values, clearly show that Messier’s world of galaxies still be-longs to our "backyard" of the universe. As a contrast we consider now the impressively red shifted H-emission lines of the apparently brightest quasar 3C273 in the constellation Virgo. They demonstrate that the above formulas are not just “gimmicks at an academic level”. Thanks to advances in technology also amateur astronomers have nowadays the pleasure to deal with cosmologically relevant distance ranges. We must therefore be aware of the effects of the SRT as well as of the cosmological models, which are still under de-bate. Until recently such faint objects were generally regarded as the domain of the (slitless used) transmission grid [480]. Nowadays it can much better be recorded with a low resolu-tion slit spectrograph – details see [35].

The –values have been measured at Gaussian fitted lines and calculated with formula {17}. The obtained values, for Hβ: 0.1586, Hγ: 0.1574 and Hδ 0.1574, are consistent here up to almost three decimal places with the accepted value according to [100], [101]. The splitting of the Hα line is caused here by the superposition with the intense Fraunhofer A band (O2).

With the known –value we can estimate now the apparent “recess velocity” of 3C273.

"Apparent" means that the object is not cinematically moving away from us, but the space in between or the so-called "space-time lattice" is expanding [431]. This enormous distance allows to equalise with the apparent "recession velocity" , because the kinematic

proper motion of this object is no more relevant. Applying formula {19} ), we ob-

tain 47‘490 km s-1, i.e. almost 20% of the speed of light! Therefore the modified Dop-

pler formula {22} must be applied. Thereby the "recess velocity" of 3C273 is significantly reduced now to: km s-1. This is well consistent with 43‘751 km s-1, the accord-

ing value in the CDS database [100]. If – despite – the distance is estimated with the conventional Hubble Law {20}

results about 650 Mpc or 2.12 bn ly. The accepted value is slightly higher ~2.4bn ly. Important: In addition to such considerations we should always be aware that the light which we analyse today from 3C273, was “on the road”, since 2.4 bn years when our earth was still in the Precambrian geological age! But compared with for Abell 1835, this is still relatively "close". This example also shows why the current and future space tele-scopes (eg Herschel, James Webb) are optimised for the infrared range.

Hβ 5632

Hα 7580

Hδ 4748

Δλ≈1017Å

Δλ≈771Å

Δλ≈683 Å

Δλ≈646 Å

Hγ 5023

Quasar 3C273, Redshift of the Hydrogen Balmer LinesDADOS: Grating 200L mm-1, 50μm slit, recorded may 26, 2012 with Atik 314L+ -10°C, 5x1200sThe indication of the wavelength, determined with Vspec at Gaussfits, is provided red shifted on the original scaleThe profile is normalised to the continuum Ic = 1, the intensity on the level of the wavelength axis is Ic = 0.6.

I

0.6

1.0

Red shifted, calibrated original scale©Richard Walker 2012/06


16 The Measurement of the Rotation Velocity

16.1 Terms and Definitions

The Doppler shift , caused by the different radial velocities of the eastern and western limb of a rotating spherical celestial body, allows the determination of the rotational surface speed. Here we limit ourselves to the spectroscopically direct measurable portion of the rotation speed, the so-called value, which is projected into the visual line to Earth.

This term, read as a formula, allows calculating this velocity share with given effective equatorial velocity and the inclination angle between the rotation axis and the visual line to Earth. The Wikipedia graph shows here differently as .

If the rotation axis is perpendicular to the sight line to Earth then and s Exclusively in this special case, we can exactly measure the equatorial velocity . If , we look directly on a pole of the celestial body and thus the projected rotational velocity becomes s

16.2 The Rotation Velocity of the Large Planets

If the slit of the spectrograph is aligned with the equator of a rotating planet, the absorption lines of the reflected light appear slightly leaning. This is caused by the Doppler shift due to the radial velocity difference between the eastern and western limb of the celestial body. The rough alignment of the slit can be done by Jupiter with help of its moons and by Saturn with its ring.

The radial velocity difference is calculated from the obliquity of the spectral lines. For this purpose from a good quality spectrum two narrow strips, each on the lower and upper edge are processed and calibrated in wavelength. The difference between the upper and lower edge gives the Doppler Shift and with formula {15} or {22} the velocity difference can be obtained (detailed procedure, see [30]).

Δλvsin i

-vsin i

vr

vr

-vr

-vr


16.3 The Rotation Velocity of the Sun

This method allows also the estimation of the Sun’s rotational surface speed, of course with an attached energy filter (!). This velocity however is so low (~2 km/s), that a high resolution spectrograph is required. In this case, the picture of the Sun on the slit plate would be too large, respectively the slit much too short to cover the entire solar equator. Required in such cases is the recording of two separate wavelength-calibrated spectra, each on the east- and west-limb of the Sun. This method was first practiced 1871 by Hermann Vogel.

16.4 The Rotation Velocity of Galaxies

This method can also be applied to determine the ro-tation velocity in the peripheral regions of galaxies. This works only with objects, which we see nearly “edge on” eg M31, M101 and M104 (Sombrero). For Face On galaxies like M51 (Whirlpool), we can just measure the radial velocity according to sect. 15.

16.5 Calculation of the Value with the Velocity Difference

Here two cases must be distinguished:

1. Light-Reflective Objects of the Solar System:

For light-reflecting objects of our solar system, eg plan-ets or moons, the Doppler Effect seen from earth, acts twice. A virtual observer at the western limb of the planet sees the light of the sun (yellow arrow) as al-ready red shifted by an amount, corresponding to the radial velocity of this point, relative to the Sun. This ob-server also notes that this light is reflected unchanged towards Earth with the same red shift (red arrow).

An observer on Earth measures the value of this reflected light, red-shifted by an addi-tional amount, which is equal to the radial velocity of the western limb of the planet, rela-tive to the Earth. This total amount is too high by the share, the virtual observer on the western limb of the planet has already found, in the incoming sunlight. When the outer planets are close to the opposition, both red-shifted amounts are virtually equal. A halving of the measured total amount therefore yields with formula {15} the velocity difference between the eastern and western limb of the planet. This velocity difference must now be halved again to obtain the desired, rotation velocity s . This corresponds finally to ¼ of the originally measured red shift (½ x ½=¼).

s = Projected rotation velocity of light reflecting objects s

= Velocity difference calculated with the measured shift

2. Self-Luminous Celestial Bodies

For self-luminous celestial objects, e.g. the Sun or galaxies, only a halving of the measured velocity difference is required:

s = Projected rotation velocity of self-luminous objects s

= Velocity difference calculated with the measured shift

Ost WestEast


16.6 The Rotation Velocity of the Stars

Due to the huge distances, with few exceptions, even with large telescopes, stars can’t be seen as discs, but just as small Airy disks due to diffraction effects in optics. In this case the above presented method therefore fails and remains reserved for 2-dimensional appearing objects. Today, numerous methods exist for determining the rotational speed of stars, eg with photometrically detected brightness variations or by means of interferometry. The idea to gain the projected rotational velocity s from the spectrum is almost as old as the spectroscopy itself.

William Abney has proposed already in 1877 to determine s analysing the rotationally induced broadening of spectral lines. This phenomenon is also caused by the Doppler Ef-fect, because the spectrum is composed of the light from the entire stellar surface, facing us. The broadening and flattening of the lines, is created by the rotationally caused different radial velocities of the individual surface points. This so-called "rotational broadening" is not the only effect that influences the of the spectral line (sect. 7.2 and 13.9). A successful approach was to isolate the Doppler Broadening-related share with various methods, eg by comparison with syn-thetically modelled spectra or slowly rotating standard stars. The graph on the right [52] shows this influence on the shape of a Mg II line at 4481.2 Å, for a star of the spectral class A.

The numerous measured rotational veloci-ties of main sequence stars show a remark-able behaviour in terms of spectral classes. The graph shows a decrease in speed from early to late spectral types (Slettebak).

From spectral type G and later, s amounts only to a few km/s (Sun ~2 km/s). The entire speed range extends from 0 to >400 km/s. It has also shown that stars, after leaving the Main Sequence on their way to the Giant Branch in the HR dia-gram (sect. 14), as expected greatly reduce the rotation speed.

Since the s values get very low, from the spectral class G on and later (so-called slow rotators), the demand on the resolution of the spectrograph is drastically increased. The focus of this method is therefore, particularly for amateurs, on the early spectral classes O - B, which are dominated by the so-called fast rotators. A typical example is Regulus, B7V, with s . The shape of this star is thereby strongly flattened. But there are also outliers. Sirius for example, as a representa-tive of the early A-Class (A1V), is with 16 km/s a clear slow rotator [126].

An interesting case is Vega (A0V) with s , which for a long time has also been considered as an outlier. But various studies, e.g. Y. Takeda et al. [120], have shown that Vega is likely a fast rotator, where we look almost exactly on a pole ( ≈7°). This is sup-ported by interferometrically detected, rotationally induced darkening effects (Peterson, Aufdenberg et al. 2006). The spread of the newly estimated effective values for Vega is broad and ranges in these studies of approximately 160 - 270 km/s. This example clearly


shows the difficulties, to determine the inclination and the associated effective rotation velocity , – this compared with the relatively simply determinable s value! Today the - Method is complemented e.g. by a Fourier analysis of the line profile. The first minimum point represents here the value for s with a resolution of some 2 km/s [125]. This method requires high-resolution spectra.

Various studies have shown, that the orientation of the stellar rotation axes is randomly dis-tributed – in contrast to most of the planets in our solar system axes. Since the effective equatorial velocity can be determined only in exceptional cases, the research is here limited almost exclusively on statistical methods, based on extensive s - samples. Most ama-teurs will probably limit themselves to reproduce well known literature values with high ro-tation velocities, typically for the earlier spectral classes.

Empirical Formulas for s depending on , s =

A considerable number of astrophysical publications in the SAO/NASA database (~1920 to the presence) deal with the calibration of the rotational speed, relative to FWHM. Some of the numerous "protagonists" are here A. Slettebak, O. Struve, G. Shajn, F. Royer and F. Fe-kel. Probably the most cited standard work in this respect is the so called „New Slettebak System“ from 1975. Anyway recent studies have shown that the provided s values are systematically too low. That's why I present here more recent approaches. The variable in most such formulas is , given in [Å] {3}. But in some formulas is also expressed as a Doppler velocity [km/s]. In one case, also the Equivalent Width EW [Å] is in-volved (sect. 7).

The Method according to F. Fekel

This well established method [122, 123] is based on two different calibration curves, each one for the red and blue region of the spectrum. The two polynomial equations of the sec-ond degree calibrate the "raw value" for s in [km/s], relating to the measured and ad-justed {3} in [Å]. Below are the two calibration polynomials {26a, 27a} according to Fekel, for the spectral ranges at 6430 Å and 4500 Å, followed by two further formulas {26b, 27b}, which I have transformed from equations {26a, 27a} according to the explicitly requested – Values:

The procedure for the determination of is described in detail and supported by an example in [30]. Here follows a short overview:

First, several FWHM values [Å] are measured and averaged by weakly to moderately in-tense and Gaussian fitted spectral lines (no H-Balmer lines). Further these values are cleaned from the "instrumental broadening" ( ). Then the X values are calculated by inserting the values in the above formulas {26b} or {27b}, according to the wavelength ranges at 4500 Å or 6430 Å. These X-values must then be cleaned from the line broadening due to the average macro turbulence velocity in the stellar atmosphere, using the following formula. This will finally yield the desired value [km/s]


The variable depends on the spectral class. For the B- and A- class Fekel assumed . For the early F- classes , Sun like Dwarfs , K- Dwarfs , early G- Giants , late G- und K- Giants and F – K Sub Giants

Below, the commonly used spectral lines for determining the FWHM values are listed. The lines, proposed by Fekel are in bold italics, such used by other authors only (eg Slettebak) are written in italics. The supplement “(B)” means that the profile shape is blended with a neighbouring line. “(S)” means a line deformation due to an electric field (Stark Effect):

– Late F–, G– and K– spectral classes: Analyse of lines preferably in the range at 6430Å: eg Fe II 6432, Ca I 6455, Fe II 6456, Fe I 6469, Ca I 6471. – Middle A–Classes and later: Analyse of moderately intense Fe I, Fe II and Ca I lines in the range at 6430Å. For A3 – G0–Class Fe I 4071.8 (B) und 4072.5 (B). – O–, B– and early A–classes: Analyse of lines in the range at 4500 Å: – Middle B– to early F–classes: several Fe II and Ti II lines, as well as He I 4471 and Mg II 4481.2. – O–, early B– and Be– classes: He I 4026 (S), Si IV 4089, He I 4388, He I 4470/71 (S,B), He II 4200 (S), He II 4542 (S), He II 4686, Al III, N II,

As an alternative to F. Fekel, A. Moskovitz [121] in connection with K-Giants, analysed ex-clusively the relatively isolated Fe I line at 5434.5 with formula {26a}, respectively {27a}.

16.7 The Rotation Velocity of the Circumstellar Disks around Be Stars

Be stars form a large subgroup of spectral type B. Gamma Cassiopeiae became the first Be star discov-ered in 1868 by Father Secchi (sect. 13.3), who wondered about the "bright lines" in this spectrum. The lower case letter e (Be) already states that here appear emission lines.

In contrast to the stars, which show P Cygni profiles due to their expanding matter (sect. 17), it is here in most cases a just temporarily formed, rotating cir-cumstellar disk of gas in the equatorial plane of the Be star. Their formation mechanisms are still not fully understood. This phenomenon is accompanied by hydrogen emission, and strong infrared- as well as X-ray radiation. Outside of such episodic phases, the star leads a seemingly normal life in the B-class. In research and monitoring programs of these objects, many amateurs are involved with photometric and spectroscopic monitoring of the emis-sion lines (particularly Hα). That's why I've gathered some information about this exciting class, since here also applications for the EW and FWHM values can be presented. Here follow some parameters of these objects, based on lectures given by Miroshnichenko [140], [141], as well as publications by K. Robinson [5] and J. Kaler [3]:

– 25% of the 240 brightest Be stars have been identified as binary systems.

– Most Be stars are still on the Main Sequence of the HRD, spectral classes O1–A1 [141]. Other sources mention the range O7–F5 (F5 for shell stars).

– Be stars consistently show high rotational velocities, up to >400 km/s, in some cases even close to the so-called "Break Up" limit. The main cause for the spread of these val-ues should be the different inclination angles of the stellar rotation axes.

University Western Ontario


– The cause for the formation of the circumstellar disk and the associated mass loss is still not fully understood. In addition to the strikingly high rotational speed [3], etc. it is also attributed to non-radial pulsations of the star or the passage of a close binary star com-ponent in the periastron of the orbit.

– Such discs can arise within a short time but also disappear. This phenomenon may pass through overall three stages: Common B star, Be–star and Be–shell star [33]. Classic example for that behaviour is Plejone (Plejades M45), which has passed all three phases within a few decades [147]. Due to its viscosity, the disk material moves out-wards during the rotation [141].

– With increasing distance from the star, the thickness of the disk is growing and the den-sity is fading.

– If the mass loss of the star exceeds that of the disc, the material is collected close to the star. In the opposite case it can form a ring.

– The X-ray and infrared radiation is strongly increased.

If a B star mutates within a relatively short time to a Be star (eg scorpii δ), the Hα absorp-tion from the stellar photosphere is changing to an emission line, now generated in the cir-cumstellar disk. At the same time it becomes the most intense spectral feature (extensive example see [30] sect. 22). It represents now the kinematic state of the ionised gas disk. It is, similar to the absorption lines of ordinary stars, broadened by Doppler Effects, but here due to the rotating disk of gas and additional, non-kinematic effects. Therefore the FWHM value of the emission line is now a measure for the typical rotation velocity of the disc ma-terial. For δ scorpii in [146] it is impressively demonstrated, that since about 2000 the FWHM and EW values of the Hα emission line are subject to strong long-period fluctua-tions. Between the first outbursts in 2000 to 2011, the Doppler velocity of the FWHM value fluctuated between about 100–350 km/s and the EW value from –5 to –25 Å, indicating highly dynamic processes in the disk formation process. Furthermore the chronological pro-file of FWHM and EW values is strikingly phase-shifted.

Formula for the Rotation Velocity of the Disk Material:

Several formulas have been published, which allow to estimate the rotation speed of the disc material from Be stars. In most cases is calculated with values at the Hα line.

Following a formula by Dachs et al which Soria used in [145]: It expresses explicitly the value, based on the [km/s] at the Hα emission line, combined with the (negative) equivalent width EW [Å].

s

Example: The Hα Linie of Soria‘s Be–star yields , corresponding to a

Doppler Velocity of 278 km/s and . This results to .

In [30] sect. 22.3 this formula is applied to a DADOS spectrum of δ scorpii. The accuracy of this method is limited to ±30 km/s. Therefore "estimate", is here probably the better ex-pression than "calculate".

Hanuschik [127] shows a simple linear formula, which expresses just with the [km/s] of the Hα emission line. It corresponds to the median fit of a strongly scattering sample with 115 Be stars, excluding those for which an underestimation of the value was assumed; [127], {1b}.


With Soria’s (see above) results a different

The following formula is applicable for the –values at the emission lines Hβ (4861.3) and FE II (5317, 5169, 6384, 4584 Å).

,

The Distribution of the Rotation Velocity on the Disk

Assuming that the disk rotation obeys the kinematic laws of Kepler, the highest rotational velocity occurs on its inner edge – In many cases, probably identical with the star equator. It decreases to-wards the outside (formula according to Robinson [5]).

The application of this formula is limited to high values ( or known inclina-tion angle .

The Analysis of Double Peak Profiles

The emission lines of Be stars often show a double peak. The gap between the two peaks is explained with the Doppler-, self-absorption- and perspective effects. Looking at the edge of the disk in the range of the symmetry axis the gas masses apparently move perpendicularly to our line of sight, ie the ra-dial velocity there is . Indicated are important dimensions, which are used in the literature.

Distance between the Peaks

The chart on the right shows according to K. Robinson [5] the modelled emission lines for different inclination angles (sect. 16.1). It seems obvious that the distance

increases with growing inclination . At the same time also the –values are increasing, if for all inclination an-gles a similar effective equatorial velocity and a fixed disc radius are assumed. is expressed as a velocity

value according to the Doppler principle: according to {15}: .

<

R

v

<

Wavelength λ

No

rma

lise

dIn

ten

sity

0

1 Continuum level Ic=1

V

R

Ic

λHα

∆V peak

i=82°

65°

30°

15°

0°WavelengthλHα


Also according to Hanuschik [143] a rough correlation exists between the [km / s] at

the Hα line and .

According to Miroshnichenko [141] and Hanuschik [143] a decreasing disk radius R is also associated with, an increasing . This statement is consistent with formula {33}

and {34}.

The outer disc radius

The formula by Huang [143] allows the estimation of the outer disk radius , expressed as [stellar radii r], based on and the

velocity at the inner edge of the disc, probably touching the star’s equator in most of the cases ( ).

The application of this formula is limited to high values ( or known inclination angle .

Peak Intensity Ratio (Violet/Red)

The V / R ratio is one of the main criteria for the description of the double peak emission of Be stars. S. Stefl et al. [144] have supervised this ratio for about 10 years, at a sample of Be stars. They have noted long-periodic variations of 5-10 years. One of the discussed hy-potheses are oscillations in the inner part of the disk.

At δ scorpii the V / R ratio of the He I line (6678.15 Å) shows a strong variation since the outbreak of 2000 [146]. See also example in [30] sect. 22.3.

According to Kaler [3] the V/R ratio also reflects the mass distribution within the disc and may show a rather irregular course.

In Be-Binary systems a pattern of variation seems to occur, which is linked to the orbital pe-riod of the system.

According to Hanuschik [143] asymmetries of the emission lines, eg , are related to radial movements and darkening effects.

If no double peak is present in the emission line, according to [128] the asymmetry in the steepness of the two edges can be analysed. V>R means the violet edge is steeper and vice versa by R>V the red one.

<

Rs

r


17 The Measurement of the Expansion Velocity

Different types of stars repel at certain stages of evolution more or less strongly matter. The speed range reaches from relatively slow 20–30 km/s, typical for planetary nebulae, up to several 1000 km/s for Novae and Supernovae (SNR). This process manifests itself in different spectral symptoms, dependent mainly on the density of repelled material.

17.1 P Cygni Profiles

The P Cygni profiles have been already introduced in sect. 5.5, as examples for mixed absorption- and emission line spectra. They are a common spectral phenomenon which occurs in all spectral classes, and are a reliable sign for expanding star material. The evaluation of this effect with the Doppler formula is demonstrated here at the expansion velocity of the stellar envelope of P Cygni.

The offset [Å] is measured between the emission and the blueshifted absorption part of P Cygni profiles. In the example for the Hα line of P Cygni itself, the measured difference yields:

(single measurement of 07.16.2009, 2200 UTC, DADOS and 900L/mm grating)

with , , yields:

The accepted values lie in the range of –185 bis – 205 km/s ±10km/s.The heliocentric correction is not necessary here, since the Doppler shift is measured not absolutely but relatively, as the difference, visible in the spectrum. P Cygni forms not a separate class of stars. Such profiles are a common spectral phenomenon, which can be found in all spectral classes and are a reliable indication for expanding stellar matter.

17.2 Inverse P Cygni Profiles

In contrast to the normal P Cygni profiles, the inverse ones are always a reliable sign for a contraction process. The absorption kink of this feature is here shifted to the red side of the emis-sion line. Textbook example is the Protostar T Tauri which is formed by accretion from a circumstellar gas and dust disk. The forbidden [O I] and [S II] lines show here clearly inverse P Cygni profiles, indicating large-scale contraction movements within the accretion disk, headed towards the protostar. The Doppler analysis showed here contraction velocities of some 600 km/s. The excerpt of the T Tauri spectrum is from [33], Table 18.


17.3 Broadening of the Emission Lines

P Cygni profiles are not only characteristic for stars with strong expansion movements, but also for Novae and Supernovae. Anyway such extreme events show more often just a strong broadening of the emission lines. This applies also to Wolf Rayet stars, even though with significantly lower FWHM values (see [33]). According to [160] the expansion velocity can be estimated, by putting in to the con-ventional Doppler formula, instead of :

The scheme [160] shows for the Nova V475 Scuti (2003) four developmental phases within 38 days. Here, nearly the tenfold expansion velocity of the P Cygni occurred, already an order of magnitude at which the relativistic Doppler formula should be applied {22}.

17.4 Splitting of the Emission Lines

In sect. 16.7 the determination of the rotation velocity by evaluating the double peak pro-files in Be stars, was already presented. Split emission lines can also be observed in spectra of relatively old, strongly expanded and thus optically transparent stellar envelops. Text-book example is here SNR M1.

The chart at right explains the split up of the emission lines due to the Doppler Effect. The parts of the shell which move towards earth cause a blue shift of the lines and the retreating ones are red shifted. Thereby, they are deformed to a so-called velocity el-lipse. This effect is seen here at the noisy [O III] lines of the M1 spectrum [33].

The chart at right shows the splitting of the Hα line in the central area of the Crab Nebula M1 ([33] Table 85). Due to the transpar-ency of the SNR, with the total expansion velocity is calculated, related to the diameter of the SNR, (here about 1800 km/s). The radial velocity is finally obtained by halving this value. It yields therefore just below 1000km/s

SNR M1 NGC 1952 TAF

EL 8

5

He

I 58

75

.6

He

II 46

85

.7

Olll

49

58

.91

Olll

50

06

.84

Hα

65

62

.82

N ll

65

83

.6

A

BB1

B2

A

Anregungsklasse E > 5

S ll

67

18

.3

S ll

67

32

.7

O I 6

30

0.2

3

N

W

Δλ ≈ 31Å

Δλ ≈ 41Å

Δλ ≈ 28Å

Δλ ≈ 30Å


50μ Spalt

Hβ

48

61

.33

Hα

Directionearth

O III


18 The Measurement of the Stellar Photosphere Temperature

18.1 Introduction

Depending on the spectral class, stellar spectra and their measurable features reflect to a different extent also the physical state of the photosphere. For the spectroscopic determi-nation of the effective temperature (sect. 3.2), numerous methods exist with different

degrees of accuracy but also corresponding complexity.

18.2 Temperature Estimation of the Spectral Class

The spectral class reflects directly the sequence of the corresponding photospheric tem-peratures (sect. 14.2). It is therefore the most direct, simple, but relatively imprecise way to estimate the effective temperature . For main sequence stars of intermediate and late

spectral classes, the accuracy, realistically achievable by amateurs, should lie within some 100 K. In literature numerous tables can be found, assigning the effective temperatures to the individual spectral classes. In addition, for the luminosity class III and V, separate and significantly different values are presented. In the region of early spectral classes, even be-tween renowned sources, differences may arise up to >1000 K. Thus, especially for the early types of the spectral type O, for the same star often significantly different classifica-tions are published. This shows that this method, at least for amateurs, is limited to the main-sequence stars, since the determination of the luminosity class is quite difficult. As an example, follows here a table with data, taken from a lecture at the University of Northern Iowa: http://www.uni.edu/. At the early spectral classes, some of these values significantly differ from those, shown in the table in sect. 14.5, or in [33].

Spectral

Type

Main Sequence

(V) (K) Giants (III)

(K)

Super Giants (I)

(K)

O5 54,000

O6 45,000

O7 43,300

O8 40,600

O9 37,800

B0 29,200 21,000

B1 23,000 16,000

B2 21,000 14,000

B3 17,600 12,800

B5 15,200 11,500

B6 14,300 11,000

B7 13,500 10,500

B8 12,300 10,000

B9 11,400 9,700

A0 9,600 9,400

A1 9,330 9,100

A2 9,040 8,900

A3 8,750

A4 8,480

A5 8,310 8,300

A7 7,920

F0 7,350 7,500

F2 7,050 7,200

http://www.uni.edu/


F3 6,850

F5 6,700 6,800

F6 6,550

F7 6,400

F8 6,300 6,150

G0 6,050 5,800

G1 5,930

G2 5,800 5,500

G5 5,660 5,010 5,100

G8 5,440 4,870 5,050

K0 5,240 4,720 4,900

K1 5,110 4,580 4,700

K2 4,960 4,460 4,500

K3 4,800 4,210 4,300

K4 4,600 4,010 4,100

K5 4,400 3,780 3,750

K7 4,000

M0 3,750 3,660 3,660

M1 3,700 3,600 3,600

M2 3,600 3,500 3,500

M3 3,500 3,300 3,300

M4 3,400 3,100 3,100

M5 3,200 2,950 2,950

M6 3,100 2,800

M7 2,900

M8 2,700

18.3 Temperature Estimation Applying Wien’s Displacement Law

A further approach is the estimation of with the principle of Wien's displacement law

(sect. 3.2). It is based on the assumption that the radiation characteristic of the star corre-sponds approximately to that of a black body. Theoretically could be calculated, apply-

ing formula {2}, based on the wavelength , which has been measured at the maximum in-tensity of the profile. This requires, however, a radiometrically corrected profile as de-scribed in sect. 8.7. In sect. 3.3 it has already been demonstrated that the position of the intensity maximum in the pseudo-continuum gives only a very rough indication for the tem-perature of the radiator.

Further, the maximum intensity must lie within the recorded range – for a typical amateur spectrograph about 3800 – 8000 Å. In the graphic below this criterion is met only by the yellow graph for 6000 K. According to formula {2}, within this section, only profiles with of about 7600 – 3600 K can be analysed by their maximum intensity. This corre-

sponds roughly to the spectral types M1 – F0.


Therefore, the coverage of all spectral classes requires an adaptation of this method. One possibility is enabled by the relationship between the continuum slope and .

This method is provided by the Vspec software, applying the function Radiometry/Planck. Thereby the radiometrically corrected profile is iteratively fitted by displayed continuum curves, corresponding to entered values. This principle is demonstrated by the follow-

ing graph with a synthetically generated solar spectrum from the Vspec Library. Displayed in red is the continuum curve, fitting to the Sun’s profile with 5800 K. The maximum inten-sity of this curve lies at about 4900 Å, which, for this temperature, is also in accordance with Wien’s displacement law (formula {1}). Further displayed for comparison is the black curve for 10,000 K and the green one, belonging to 4,000 K.

Inten-sity

Wavelength [Å]

0 5000 10‘000 15‘000 20‘000

I

λ


Of course, in practice, the temperature estimation of the investigated star is requested, rather than the reproduction of an already known temperature of a synthetic profile. This requests a radiometric correction of the obtained pseudo-continuum with a recorded stan-dard star, according to sect. 8.7. Therefore, the accuracy of this measurement is also di-rectly dependent on the quality of this relatively demanding correction procedure.

The following chart shows, in the context of the synthetic solar spectrum, the continua of various effective temperatures according to Vspec Radiometry/Planck. In the range be-tween 3,000 and 20,000 K, the increasingly closer following curves are displayed in 1,000 K steps. Above 20,000 K the intermediate spaces become so close, that here only the con-tinua for 30,000 and 40,000 K are shown. It also shows that this estimation method is lim-ited to the middle and late spectral types. In addition, with increasing temperature, the dif-ferentiating influence of the spectral class to the radiometric correction is significantly de-creasing (sect. 8.7).

I

λ

SyntheticSolar Spectrum

I

λ

SyntheticSolar spectrum

7000 K


18.4 Temperature Determination Based on Individual Lines

Generally these methods are based on the temperature dependency of the line intensity . However, according to sect. 6.2, the intensity and shape of the spectral lines are determined by many other variables, such as element abundance, pressure, turbulence, metallicity Fe/H and the rotation speed of the star. Similar to the determination of the rota-tion velocity (sect. 16), all such methods must therefore be able to significantly hide such interfering side influences or analyse lines, which are specifically sensitive to temperature [11]. If the temperature should not only be "estimated" but rather accurately "determined", therefore relatively sophisticated methods remain, based on high-resolution spectroscopy and detailed analysis of selected, especially temperature-sensitive metal lines.

18.5 The “Balmer-Thermometer“

The temperature determination, based on the intensity of the H-Balmer lines, is often called "Balmer-Thermometer". This method is rather rudimentary, but it provides an in-teresting experimental field. The H-lines are well suited, because the stellar photo-spheres of most spectral classes consist to >90% of hydrogen atoms. Only this element can exclusively be detected and evaluated over almost the entire temperature se-quence (class O – M). In contrast, ionised calcium Ca II appears only within the spec-tral classes A – M. The often proposed so-dium double line D1,2 is analysable just at type ~F – M because Na I becomes ionised at higher temperatures and Na II absorp-tions appear exclusively in the UV range of the spectrum. In the earlier spectral classes, Na I is therefore always of interstellar origin and hence useless for this purpose.

The graphic on the right shows the intensity profile of the Hβ line – a cutout of the over-view to the spectral sequence in sect. 13.8 and [33]. From all Balmer lines, this absorp-tion can be observed within the largest wavelength range. At this low resolution, it remains analysable, even in the long wave-length region, down to about K5. The maxi-mum intensity is reached at the spectral class A1. The quantum-mechanical reasons for this effect are discussed in sect. 9.2.

In the diagram below, the Hβ-equivalent widths (EW) of 24 Atlas stars [33] are plot-ted against the effective temperatures . Due to the bell-shaped curve

an ambiguity arises, which requires a clarification by additional spectral information. A prominent feature, indicating the profile segment on the long wavelength side of 10,000 K, is the Fraunhofer K-line (Ca II) at 3934 Å – further details see [33]. The average tempera-ture range is here almost exclusively represented by main-sequence stars, the peripheral

O9

B1

B7

A1

A7

F0

F5

G2

G8

K2

K5

4‘990 K

22‘000 K

7‘030 K

6‘330 K

5‘700 K

10‘000 K

7‘550 K

4‘290 K

3‘950 K

25‘000 K

15‘000 KH

β4

86

1

Hβ

48

61


sections also by giants of the luminosity class I – III.Despite of relatively few data points and a low resolution (DADOS 200L/mm), the curve shape can clearly be recognised and is manually inserted here as an approximate "least square fit". It is just intended to demon-strate the principle. For more accurate results the analysis of high-resolution spectra would be required and further the separation between the luminosity classes.

18.6 Precision Temperature Measurements by Analysis of Individual Lines

Such methods are applied in the professional field, mainly at non ionised metal lines of the late spectral classes K – M. A representative impression provides [190], [191], [191b]. Here, ratios are calculated with the relative line depths of differently temperature-sensitive metal absorptions [11]. These are subsequently calibrated in respect of known values (LDR Line Depth Ratio). According to the authors an accuracy of a few K can be

achieved. With a longer lasting, permanent temperature monitoring, eg the detection and even measurement of giant dark sun spots is possible, typically observed at the late spec-tral type K [191b].

Effective temperature Teff [K]

EWHβ[Å]

α Gem

α CMa78 Vir

α Aql

γ Virζ Leo

α Cmiα Leo

γ Crv

α Vir

68 CygSun

η Booδ Ori

ζ Oriε Oriε Virα Ori

61 Cygα Sco


19 Spectroscopic Binary Stars

19.1 Terms and Definitions

> 50% of the stars in our galaxy are gravitationally connected components of double or multiple systems. They concentrate primarily within the spectral classes A, F and G [170]. For the astrophysics these objects are also of special interest because they allow a deter-mination of stellar masses independently of the spectral class. Soon after the invention of the telescope, visual double stars were also observed by amateur astronomers. Today the spectroscopy has opened for us also the field of spectroscopic binary stars.

An in-depth study of binary star orbits is demanding and requires eg celestial mechanics skills. Here should only be indicated, what can be achieved by spectroscopic means. Scien-tifically relevant results are usually only possible associated with long term astrometric and photometric measurements. Spectroscopic binary stars are orbiting in such close distances around a common gravity center, that they can’t be resolved even with the largest tele-scopes in the world. They betray their binary nature just by the periodic change in spectral characteristics. For such close orbits Kepler's laws require short orbital periods and high-track velocities, significantly facilitating the spectroscopic observation of these objects.

In contrast to the complex behaviour of multiple systems, the motion of binary stars follows the three simple Kepler’s laws. Its components rotate at variable velocities in elliptical orbits around a common Barycenter B (center of gravity). The following sketch shows a fic-tional binary star system with stars of the unequal sizes and . For simplicity their ellip-tical orbits are running here exactly in the plane of the drawing as well as the sight line to Earth which in addition runs parallel to the minor semi-axes. For this perspective special case the orbital velocity at the Apastron (farthest orbital point) and Periastron (closest orbital point) corresponds also to the observed radial velocity . The recorded maximum values (amplitudes) are referred in the literature with . The following layout corresponds to an orbit- inclination of (sect. 19.3).

ApastronB

M1

ApastronPeriastron Periastron

M1M2

VrM1 P= K1

VrM2 A

VrM2 P= K2

VrM1 A

M2

Sight line toEarth

VrM1 A = Radial velocity M1 at ApastronVrM1 P = Radial velocity M1 at PeriastronVrM2 A = Radial velocity M2 at ApastronVrM2 P = Radial velocity M2 at Periastron

Major semi axis a

Min

or

sem

ia

xis

b


– Both orbital ellipse: – must be in the same plane – have different sizes depending on the mass

– must be similar to each other, i.e. have the same eccentricity

– The more massive star always runs on the smaller elliptical orbit and with the lower velocity around the barycenter.

– The barycenter lies always in one of two focal points

– und always run synchronously:

– During the entire orbit the connecting line between and runs permanently through the barycenter

– and always reach the Apastron as well as the Periastron at the same time.

19.2 Effects of the Binary Orbit on the Spectrum

Due to the radial velocities the Doppler shift causes striking effects in the spectrum. The above assumed perspective special case for the orbit orientation would maximize these phenomena for a terrestrial observer (see below phase D). Generally, two different cases can be distinguished [180].

1. Double stars with two components in the spectrum – SB2–systems

If the apparent brightness difference between the two components lies approximately at , we can record the composite spectrum of both stars. The following phase diagrams are based on the above assumptions and show these effects within one complete orbit:

Here the orbital velocities are di-rected perpendicular to the line of sight and thus the radial velocity with respect to the Earth becomes The spec-trum remains unchanged, i.e.

In the Apastron the orbital velocities are minimal. But they run now parallel to the line of sight, and correspond here to the radial velocities, so . The spectral line appears splitted:

Here the orbital velocities are di-rected perpendicular to the line of sight and thus the radial velocity with respect to the Earth becomes The spec-trum remains unchanged, i.e.

In the Periastron the orbital velocities are maximal. They run now parallel to the line of sight, and correspond here to the radial velocities, so . The spectral line appears here more splitted compared to phase B.

∆λ

∆λA

∆λP

∆λ

A

B

C

D


The above introduced formulas for the Doppler shift allow, after a simple change, to cal-culate the sum of the radial velocities with the line splitting . For the general

case:

The Calculation of the Individual Radial Velocities and

If the mass difference is large enough, the splitting of the spectral line occurs asymmetrically with respect to the neu-tral wavelength . With these uneven distances and and by analogy to {39} the individual radial velocities can be calculated separately [172].

As a result of the heliocentric radial movement of the entire star system [100], the wavelength of the "neutral",

unsplitted spectral line is shifted by the Doppler Effect from the stationary laboratory wave-length to [170].

This is now the adjusted reference point for the measurement of the two distances , .

But first the , values must be heliocentrically corrected to , according to [30], sect.

18, step 7. Then it follows:

, ,

If no asymmetry occurs of the splitted line with respect to , and are approximately equal and the sum of the two radial velocities just needs to be halved.

2. Double stars with only one component in the spectrum – SB1–systems

In most cases the apparent brightness difference between the two components is signifi-cantly . Here with amateur equipment, only the spectrum of the brighter star can be recorded. Extreme cases are entirely invisible black holes as double star components, or extrasolar planets, which shift the spectrum of the orbited star by just a few dozen me-ters/sec! In such cases, a splitting of the line isn’t recognisable, but only the shift of to the right or left in respect of the neutral position .

The following example, recorded with DADOS 900L/mm shows this effect, using the spectroscopic A components within the quintuple system β Scorpii. Impressively visible is here the Hα-shift of the brighter component, within three days. With this Vspec plot just this ef-fect shall be demonstrated. A serious investigation of the orbital parameters would require the recording of multiple orbits at least at daily intervals! The lineshifts are plotted here with respect to . The X-axis is scaled here in Dop-pler velocity, according to [30], sect. 19, and allows a rough reading of the radial velocity. The values , have been determined by Gaussian fit on the heliocentrically

corrected profiles. Detailed procedure see [30] sect. 24.2.

λr0

∆λ1 ∆λ2

λ1 λ2

08.15.2009 22‘00 UTC ∆λ = +1.71Å = +78 km/s08.18.2009 22‘00 UTC

∆λ = –1.37Å = –63 km/s

λr0 Adjusted reference point


Here are some orbital parameters of β Scorpii according to an earlier study by Peterson et al. [177]. These values are based on the measured, maximum radial velocities und , obtained from the spectra of both components. The terms in the data list, and for the masses, demonstrate that the inclination is unknown and therefore the values are uncertain by this factor (for details see sect. 18.3 and 18.4).

- Spectral class of the brighter component: B0.5V, of the weaker component: unknown - Orbital period: - Stellar masses:

,

ss

- Mass Ratio: - Max. recorded radial velocities: , - Major semi axes of the orbital ellipse: s s

These figures show that the mass and brightness difference is substantial. With the large telescopes, involved in this study [177], the spectrum of the weaker component could still be recognised, but analysed just with substantial difficulties.

19.3 The Perspectivic Influence from the Spatial Orbit-Orientation

The orientation of the binary star orbital planes, with respect to our line of sight, shows a random distribution. The angle between the axis, perpendicularly standing on the orbital plane (normal vector), and our line of sight is called inclination [175]. Thus the definition for the inclination of stellar and binary system rotation axes (sect. 16) is the same. Analogi-cal, s is here the spectroscopically direct measurable share of the radial velocity , which is projected into the sight line to Earth. For we see the orbital ellipse exactly "edge on" i.e. s .

– This elliptical orbit, with a given and fixed inclination , may be rotated freely around the axis of the sight line, without any consequences for their apparent form.

– Thus for circular binary orbits the inclination fixes the only degree of freedom, which affects the apparent shape of the orbit.

– For elliptical binary star orbits, the situation is more complex. In contrast to the circle, the orientation of the ellipse axes in a given orbital plane forms an additional degree of freedom, determining the apparent ellipse form.

If remains unknown, the results can statistically only be evaluated, similar to the s values of the stellar rotation (sect. 16.6).

Caveat:

There are also reputable sources that define as the angle between the line of sight and the orbital plane, similar to the inclination angle convention between planetary orbits and the ecliptic. Consequence: There must always be clarified which definition is used. The two conventions can easily convert to each other as complementary angle .

i

vr

vr sin iSight Line to Earth

vr sin i

vr


19.4 The Estimation of some Orbital Parameters

Based on purely spectroscopic observation some of the orbital parameters of the binary system can be estimated. First, the measured radial velocities and are plotted as a

function of the time . The graph shows an orbital period of Mizar (ζ Ursae Majoris, A2V), one of the showpieces for spectroscopic binaries with double lines (SB2 systems). Another similar example is β Aurigae with an orbital period of about 4 days. The more these curves show a sinusoidal shape, the lower is the eccentricity of the orbit ellipse [179].

Source: Uni Jena [170]

The Orbital Period

The orbital period T can directly be determined from the course of the velocity curves. As the only variable it remains largely unaffected by perspective effects and is thus relatively accurately determinable.

Simplifying to circular orbits

Since we are mostly confronted with randomly oriented, el-liptical orbits, a reasonably accurate determination of orbital parameters is very complex. For this purpose, in addition to the spectroscopic, complementary astrometric measure-ment data would be needed. Only for eclipsing binaries, such as Algol, already a priori, a probable inclination of can be assumed. For the rough estimation of other parameters various sources suggest the simplification of the elliptical to circular orbits. Thus, the radii and thus the orbital velocities become constant. The mostly unknown inclination is expressed in the formulas with the term .

The Orbital Velocity

To determine the orbital velocity we need from the velocity diagram, the maximum

values for both components. They correspond by definition, to the maximum amplitudes and . For the circular orbit velocity follows:

s

s

Determination of the orbital radii

With the orbital period and the velocity s for a circular orbit the corresponding radius can be calculated. From geometric reasons follows generally:

s

K1

K2

BM1 M2

rM1 rM2VM2

VM1


s

If both lines can be analysed, then with the obtained und the corresponding radii and can be calculated separately.

Calculation of the Stellar Masses in SB2 Systems

If both lines can be analysed, then with the following formula the total mass of the system , can be determined. This is obtained if {44}, changed as a sum of radii , is used in the formula of the third Kepler's law, instead of the semi-major axis .

.

The partial masses can then be calculated by their total mass with the partial radii and

For binary star systems is often expressed in solar masses

and the distance in AU. To convert:

Calculation of the Stellar Masses in SB1 Systems

The analysis of only one line has logically consequences on the information content and ac-curacy of the system parameters to be determined. For SB1–systems in the spectrum, only the radial velocity curve of the brighter component can be analysed, and therefore just the amplitude can be determined. So with formula {44}, only the corresponding orbital radius can be calculated. Unfortunately, neither their total mass nor their partial masses , are directly determinable. Just the so called mass function , can be deter-mined [51 sect. VI], [179]. This expression is not really demonstrative and means the cube of the invisible partial mass

in relation to the square of the total mass . For a calculated example, see [171].

,

s

It can be roughly determined eg by estimation of the visible mass by the spectral type. For a rough guide refer to the table in sect. 14.5. Such results still remain loaded with the "uncertainty" of s .


20 Balmer–Decrement

20.1 Introduction

In spectra where the H-Balmer series occurs in emission, the line intensity fades with de-creasing wavelength . This phenomenon is called the Balmer Decrement D. The intensity loss is reproducible by the laws of physics and is therefore a highly important indicator for astrophysics. The hydrogen emission lines are formed by the electron transitions, which end, as well known, in "downward direction" on the second-lowest energy level . The probability, from which of the higher levels an electron comes, is determined for the indi-vidual lines by quantum mechanical laws. From this it follows that the intensity is highest at the line and gets continuously weaker at the shorter wavelength lines, , , , , etc. The extent of this decrease (decrement) is additionally, but only moderately, de-pendent on the density and temperature of the electrons and .

20.2 Qualitative Analysis

For most amateurs probably qualitative applications of this effect are in the focus. On a low-resolution spectrum of P Cygni (DADOS 200L), the intensity-decrease of the dominant hy-drogen emission lines, normalised on a unified continuum intensity, is demonstrated.

Contrary to this trend Mira (o Ceti) shows only Hδ, and significantly, Hγ in emission. These impressive lines indicate what enormous intensities the Hα and Hβ-Balmer emissions should really show, according to the Balmer decrement. But these lines are covered in the long-wave region by titanium oxide absorption bands, which are apparently generated in higher layers of the star's atmosphere, as the H emission lines, details see [33].

Balmer – Decrement P Cygni Hα

Hβ

HγHδ

Balmer – Decrement Mira, o Ceti

HγHδ

TiO

TiOTiO

TiO

TiO

TiOTiO

TiO


20.3 Quantitative Analysis

Quantitatively, the Balmer Decrement is mainly used for the spectroscopic determination of the interstellar extinction, the so-called "interstellar reddening". The "reddening" of the light occurs, because the blue part is absorbed or scattered stronger than the red. The steeper the decrement runs, compared to theoretically calculated values , the stronger is the extinction of light by dust particles. The decrement intensities are defined by convention relatively to Hβ . Particularly high is the effect of the reddening in the plane of the Milky Way, ie on the Galactic latitude of ~0° [209]. This relationship has already been detected by A. Shajn 1934.

For the determination of the "Interstellar reddening" with the Balmer decrement, appropri-ate objects are required, radiating the emission-lines of the H-Balmer series completely and not selectively attenuated - for example most of the emission nebulae and LBV stars. Rep-resentatives of the Mira Variables are unsuitable for the aforementioned reasons.

The following table shows by Brocklehurst [200] the theoretical decrement values , quantum mechanically calculated for gases with a very low and high electron density and electron temperatures of 10000K and 20000K.

Line Case A for thin gas (Ne = 102 cm-3)

Case B für dense gas (Ne = 106 cm-3)

Te =10 000 K Te =20 000 K Te =10 000 K Te =20 000 K

Hα 2.85 2.8 2.74 2.72

Hβ 1 1 1 1

Hγ 0.47 0.47 0.48 0.48

Hδ 0.26 0.26 0.26 0.27

Hε 0.16 0.16 0.16 0.16

H8 0.11 0.11 0.11 0.11

In the specialist jargon the two density cases are called "Case A" and "Case B".

Case A: A very thin gas, which is permeable for Lyman photons so they are enabled to es-cape the nebula.

Case B: A dense gas, which retains the short-wavelength photons, which are therefore available for self-absorption processes.

The gas densities in emission nebulae are in the range between Case A and -B, by expand-ing stellar envelopes (Be- and LBV stars, Planetary Nebulae) Case B [33]. The electron tem-perature has in this range apparently only little influence on the decrement. The influ-ence of the electron density is here noticeable only at the Hα line. Depending on the source, these values may differ in some cases.

Possible amateur applications are here rough decrement comparisons between different objects, eg various planetary nebulae, as well as Be- or LBV stars, located on different ga-lactic latitudes.

20.4 Quantitative Definition of the Balmer-Decrement

For most astrophysical analysis the measured intensity ratio of the Hα and Hβ lines is required. This corresponds to the quantitative definition of the Balmer decrement:

{50}


20.5 Experiments with the Balmer Decrement

The following graph shows the Balmer-decrement of P Cygni, recorded with the DADOS spectrograph. Once the decrements are referred to a radiometrically corrected profile (red), which corresponds to the intensity profile of a B2 II star from the Vspec library, and once based on a continuum with a normalised energy flow (blue). The labelled decrements are intensity values , directly measured in the strongly reddened P Cygni profile and subse-quently divided by the corresponding Hβ intensities .

Within the intensity-normalised, blue profile, the roughly determined decrements match pretty well to the spread of the accepted values –> for I(Hα)/I(Hβ) between 4.3 – 5. The red profile, represents approximately the intensity course of the original- and unattenuated spectrum. It shows however drastically different and physically even impossible decrement values. The defined Balmer-decrement is here only 1.8, ie substantially lower than !

Since a literature research on this phenomenon has ended unsuccessfully, here follows my own interpretation: The theoretical Balmer-decrement is based on the probabilities for certain electron transitions, determined by the laws of quantum physics. This statistical regularity is overprinted in the radiometrically corrected profile by the unevenly distributed and wavelength-dependent radiation intensity of the star . The intensity of the in-dividual emission lines depends in stellar atmospheres, inter alia on the number of the oc-curring direct- or resonance absorptions and thus also on the photon density at the corre-sponding wavelength . In this respect, the blue, intensity-normalised profile behaves here neutrally, due to

If a continuum is present, even in the professional sector, the Balmer-decrement is deter-mined with the EW value and therefore also based on an intensity-normalised profile. At the example of extra-galactic spectra this is demonstrated in The Balmer Decrement of SDSS Galaxies, by Brent Groves et al. [210].

Hα

1

λ

Hβ

HγHε

1

5

0.3

1.8

0.5

Irel

Flux normalised continuum


21 Spectroscopic Determination of Interstellar Extinction

21.1 Spectroscopic Definition of the Interstellar Extinction

With the Balmer decrement , the interstellar extinction can spectroscopically be deter-mined. The extinction parameter characterises the entire extinction along the line of sight between the object and the outer edge of Earth's atmosphere. It is defined as the logarith-mic ratio between the theoretical (Th) and measured (obs) intensity of the line [8]:

, also called “logarithmic Balmer-Decrement” [201], is determined by the ratio be-tween the measured and theoretical Balmer decrement and . The value –0.35 cor-responds to the extinction factor at , according to the standard extinction curve from Osterbrock (chart below) [201].

In the context of such calculations in the literature the value (Case B) has been established for the theoretical Balmer decrement. inserted in yields:

21.2 Extinction Correction with the Measured Balmer Decrement

The extinction is not constant but depends on the wavelength. With the correction function [10], the emission lines are adapted relatively to (“Dereddening”).

is defined as follows, where is the extinction at and .

Thus, the measured intensities are reduced for and raised for (note the sign of )! The value of is determined with an extinction curve, which exists in different versions with slightly different values. For amateur applications intermediate val-ues may be roughly interpolated. Bottom left is the galactic standard extinction curve from Osterbrock (1989) with values [238]. The table values to the right are from Seaton (1960).

–0.35

0.0

+0.14

λ f(λ)

3500 +0.42

4000 +0.24

4500 +0.10

4861 0.00

5000 -0.04

6000 -0.26

7000 -0.45

8000 -0.60

Galactic Extinction Law from Osterbrock1989 From Seatons 1960


21.3 Balmer Decrement and Color Excess

The measured Balmer Decrement also determines the color excess in [mag] for the Balmer lines [10].

If follows: , in this special case, as expected, exists no

reddening.

The link to the "classical" photometry in the system provides the formula of C.S.

Reynolds [208]:

The associated parameters for:

Logarithmically transformed and inserted :

21.4 Balmer-Decrement and Extinction Correction in the Amateur Sector

For amateurs, neither the accurate determination of the extinction nor of the reddened Balmer-decrement is really important. This requires the removal of the "Instrumental- and Telluric Response" according to formula in sect. 8.7, so the result-ing profile remains just loaded with the demanded .

The most important application however is the special case of the emission nebulae, which mostly produce an extremely weak and diffuse continuum and thus do not allow any reli-able continuum-related measurements such as the peak intensity or the value. Fortunately these objects produce H-emission lines, generated chiefly far away from the star and mainly by recombination of ionised H-atoms. In the original spectrum, those inten-sities correspond nearly to the undisturbed Balmer decrement and – in relation to the measured decrement values – they can be applied as a kind of "correction template".

This procedure is indeed intended for the partial correction of the interstellar ing . For amateur purpose formula {53} enables, within the relevant range of Hα – Hβ, also for the other attenuating influences, and in a reasonable approximation, a very rough total intensity correction of the emission lines. and show a similar characteristic with an increasing attenuation towards shorter wavelengths. Anyway some-what different behaves as most of the today’s amateur cameras show a damping characteristic, starting just from the green sector of the spectrum. Supplementary notes see sect. 22.11.

In the professional sector, extinction corrections are performed with software support and are indispensable by the analysis of extragalactic emission line objects. Even for objects within our neighbour galaxy M31, usually does [201].


22 Plasma Diagnostics for Emission Nebulae

22.1 Preliminary Remarks

In the “Spectroscopic Atlas for Amateur Astronomers” [33], a classification system is pre-sented for the excitation classes of the ionised plasma in emission nebulae. Further this process is practically demonstrated, based on several objects. Here, as a supplement, fur-ther diagnostic possibilities are introduced, combined with the necessary physical back-ground.

22.2 Overview of the Phenomenon “Emission Nebulae”

Reflection nebulae are interstellar gas and dust clouds which passively reflect the light of the embedded stars. Emission nebulae however are shining actively. This process requires that the atoms are first ionised by hot radiation sources with at least 25,000K. This re-quires UV photons, above the so-called Lyman limit of 912 Å and corresponding to an ioni-sation energy of >13.6 eV. This level is only achievable by very hot stars of the O- and early B-Class generating this way a partially ionised plasma in the wider surroundings. By recom-bination the ions recapture free electrons which subsequently cascade down to lower lev-

els, emitting photons of discrete frequencies , according to the energy difference

. Thus, this nebulae produce by the fluorescence effect, similar to gas discharge lamps, mainly "quasi monochromatic" light, i.e. a limited number of discrete emission lines, which, with exception of the Supernova Remnants (SNR), are superimposed to a very weak emission-continuum. The energetic requirements are mainly met by H II regions (e.g. M42), Planetary Nebulae PN (e.g. M57) and SNR (e.g. M1). Further mentionable are the Nuclei of Active Galaxies (AGN) and T-Tauri stars (sect. 17.2). The matter of the Nebulae consists mainly of hydrogen, helium, nitrogen, oxygen, carbon, sulphur, neon and dust (silicate, graphite etc.). Besides the chemical composition, the energy of the UV radiation, and the temperature as well as density of the free electrons characterise the local state of the plasma. This manifests itself directly in the intensity of emission lines, which simply allows a first rough estimation of important plasma -parameters.

22.3 Common Spectral Characteristics of Emission Nebulae

In all types of emission nebulae, ionisation proc-esses are active even if with very different exci-tation energies. This explains the very similar appearance of such spectra. The diagram shows an excerpt from the spectrum of M42 with the two most striking features:

1. The intensity ratio of the brightest [O III] lines is practically constant with .

2. The Balmer decrement D. From the ratio be-tween the measured and theoretical course the interstellar extinction can be determined (sect.21).

22.4 Ionisation Processes in H II Emission Nebulae

These processes are first demonstrated schematically with a hydrogen atom. The high-energy UV photons from the central star ionise the nebula atoms and are thus completely absorbed, at latest at the end of the so-called Strömgren Sphere. Therefore here ends the partially ionised plasma of the emission nebula. Since the observed intensity of spectral lines barely varies, a permanent equilibrium between newly ionised and recombined ions must exist. Rough indicators for the strength of the radiation field are the atomic species,

Hα

65

62

.82

Olll

50

06

.84

Olll

49

58

.91

Hβ

48

61

.33


the ionisation stage (sect. 11) and the abundance of the generated ions. The first two pa-rameters can be directly read from the spectrum and compared with the required ionisation energy (see table below and [33]).

The kinetic energy of the electrons, released by the ionisation process, heats the nebula particles. corresponds to the surplus energy of the UV Photons, which remains after photo ionisation and is fully transformed to kinetic energy of the free electrons. The elec-tron temperature and -density affect the following recombination- and collision exci-tation processes. is directly proportional to the average kinetic energy of the free elec-trons (Boltzmann constant ).

Formula {55} yields in Joule with the electron mass and . The short formula {55a} gives directly in electron volts [eV].

22.5 Recombination Process

If an electron hits the ion centrally, it is captured and ends up first mostly on one of the upper excited levels (terms). The energy, gen-

erated this way is emitted as a photon . It corresponds to the

sum of the original kinetic energy of the electron and the dis-crete energy difference due to the distance to the Ionisation Limit. Since the share of the kinetic energy varies widely, from the recombination process a broadband radiation is contributed to the anyway weak continuum emission.

22.6 Line Emission by Electron Transition

After recombination the electron “falls” either directly or via sev-eral intermediate levels (cascade), to the lowest energy ground state . Such transitions generate discrete line emission, ac-cording to the energy difference . Most of these photons leave the nebula freely – including those which end in the pixel field of our cameras! This process cools the nebula, because the photons remove energy, providing thereby a thermal balance to the heating process by the free electrons. This regulates the elec-tron temperature in the nebula in a range of ca. 5,000K < < 20,000K [237].

Ionisation by UV-Photons λ<912Å

High-energyRadiator Teff>25‘000K

Y

Electron gas

Star

Photon Elektron

Te Ne

Recombination

Photon

Electron

+ΔEn

Electron Transition

n=1

Photon

ΔEn


22.7 Line Emission by Collision Excitation

If an electron hits an ion, then in most cases not a recombination but much more frequently a collision excitation occurs. If the impact energy is ≥ the electron is briefly raised to a higher level. By allowed transitions it will immediately fall back to ground state and radiate a photon of the discrete frequency , according to the energy difference.

Remark: Similarly, this process takes place in fluorescent lamps with low gas pressure. Due to the connected high tension, the elec-trons reach energies of several electron volts [eV], which subse-quently excite mercury atoms to UV radiation. By contrast in dense gases, the excitation occurs mainly by collisions between the ther-mally excited atoms or molecules.

22.8 Line Emission by Permitted Transitions (Direct absorption)

In H II regions with O5 type central stars (eg M42) emission nebu-lae have Strömgren spheres with diameters of several light years, what extremely dilutes the radiation field. Thus, particularly in the extreme outskirts of the nebula, the probability gets extremely small, that the energy of a photon exactly fits to the excitation level of a hydrogen atom. Therefore the direct absorption of a pho-ton doesn’t significantly contribute to the line emission. Further the main part of the photons is radiated in the UV range. Conse-quently many atoms are immediately ionised, once the energy of the incident photons is above the ionisation limit. Therefore a sub-stantial line emission of permitted transitions is only possible by the recombination process. The high spectral intensity of Hydrogen and Helium, the main actors of the permitted transitions, is caused by the abundance which is by several orders of magnitude higher than the remaining elements in the nebula. The frequency of a specific electron transition also determines the relative intensity of the corresponding spectral line.

22.9 Line Emission by Forbidden Transitions

Emission nebulae contain various kinds of metal ions, most of them with several valence electrons on the outer shell. These cause electric and magnetic interactions, which multi-plies the possible energy states. Such term schemes (or Grotrian diagrams) are therefore extremely complex and contain also so-called "Forbidden Transitions" (sect. 12). But the extremely thin nebulae provide ideal conditions, because the highly impact-sensitive and long-lasting metastable states become here very rarely untimely destroyed by impacts.

But first of all, these metal atoms must be ionised to the corresponding stage, which re-quires high-energy UV-photons. The required energies are listed in the following table, compared to hydrogen and helium [eV, λ]. The higher the required ionisation energy, the closer to the star the ions are generated (so called “stratification”) [10] [201].

Ion [S II] [N II] [O III] [Ne III] [O II] H II He II He III

E [eV] 10.4 14.5 35.1 41.0 13.6 13.6 24.6 54.4

λ [Å] 1193 855 353 302 911 911 504 227

On the other hand The forbidden transitions of the metal ions need to populate the meta-stable initial terms from the ground state just a few electron volts [eV]. This small amount of energy is plentifully supplied by the frequent collision excitations of free electrons!

Collision Excitation

n=1

Photon

Electron

ΔEn

Direct Absorption

PhotonPhoton


In comparison, for the permitted Hα line, at least 12.1 eV would be required from the ground state (n1 – n3). For this, the electrons in the nebula are by far too slow, i.e. by about one order of magnitude (see diagram below). This explains the strong intensity of the for-bidden-as compared to the allowed transitions. These metal ions are also called "cooler" [237] in the context of model computations. Influenced by the highly effective line emission they contribute significantly to the cooling of the nebula and therefore to the thermal equi-librium. The following chart shows just the relevant small excerpts of the highly complex term diagrams [10], [222]. For the most important metal ions, the required excitation ener-gies and the wavelengths of the “forbidden” emissions are shown.

The following chart shows by Gieseking [222], the Maxwellian frequency distribution of electron velocities for relatively "cool" and "hot" nebulae, calculated for Te 10,000K and 20,000K. Mapped are the two minimum rates for the excitation of the [O III] lines. The up-per edge of the diagram I have supplemented with the values of the kinetic electron energy. The maximum values of the two curves correspond to the average kinetic energy according to formula {54} (0.86eV and 1.72eV).

0

1

2

3

4

5

6

7

[eV]

[S II] [N II] [O III] [Ne III] [O II]

67

31

67

17

40

76

40

68

10

32

0

10

27

81

03

73

10

33

8

65

83

65

48

57

55

30

71

30

63

50

07

49

59

49

32

43

63

40

14

39

67

38

69

33

44

18

15

17

94

37

29

37

26

73

31

73

19

.6

73

18

.6

73

30

0 200 400 600 800 1000 1200 1400 1600 1800

Electron Velocity [km/s]

Re

lati

ve F

req

ue

ncy

Kinetic Energy [eV]

0 1 2 3 4 5 6 7 8 9 10 110.50.25

O III 5007/4959/ 4932

O III 4363

0.86 eV

1.72 eV

2.5

eV

5.3

eV


22.10 Scheme of the Photon Conversion Process in Emission Nebulae

This scheme summarises the previously described processes in H II regions and PN and il-lustrates important relationships. Not shown here are the bremsstrahlung processes, which become typically relevant just in SNR due to the relativistic electron velocities. Processes with photons are shown here in blue, those with electrons in red. So-called bound-bound transitions between the electron shells are marked with black arrows. The broad, gray ar-rows show the two fundamentally important equilibriums in the nebula:

The Thermal Equilibrium in the nebulae between the heating process by the kinetic en-ergy of free electrons and the permanent removal of energy by the escaping photons, regulates and determines the electron temperature Te.

The Ionisation Equilibrium between ionisation and recombination, regulates and de-termines the electron density Ne. If this balance is disturbed, the ionisation zone of the nebula either expands or shrinks [239].

Star

Electron

Te Ne

CollisionExcitation

Electron

Recombination DirectAbsorption

Ionisation

ExactlyFittingPhoton

Electron

UV Photon

Escaping Photons cooling the Nebula

Fee Electrons heatingthe Nebula

ThermalEquilibrium

Ionisation-, Recombination- and Excitation Processes in Emission Nebulae


IonisationEquilibrium

Teff > 25‘000K

Photons

Photons

Photons


22.11 Practical Aspects of Plasma Diagnostics

The main focus for amateurs is here the determination of the excitation class of emission nebulae. Their diagnostic lines are relatively intense and quite close together. Moreover, some of them are located in an area, where the difference between the original and pseudo-continuum is relatively low – see early spectral classes in the last graph of sect. 8.6. This allows for galactic objects, even at the raw profile, ie without any extinction- or other corrections, a reasonable classification with accuracy of about 1 class. Due to the slightly greater distance of the He II diagnosis line (λ 4686), at middle and high excitation classes the classification may result up to one step to low. For more precise analyses, the intensity of the individual lines should be corrected according to formula {53}, see com-ments sect. 21.4.

Own tests have shown that the alternatively applied division of the pseudo continuum by instrumental response profiles (sect. 8.6, 8.7), usually provides poor results, probably due to the diffuse and noisy residual continuum.

Typical galactic decrement values are in the range of D ≈ 3.0–3.5 [10]. However, there are stark outliers like NGC 7027 with D ≈ 7.4 [10]! Since the classification lines lie close to-gether, for a rough determination of the excitation class even this effect can usually be ne-glected. In such extreme cases, a substantial part of the extinction can also be caused by massive dust clouds around the star itself. E.g. at the extremely young T-Tauri objects the measured deviation from the Balmer-decrement is even used as a classification criterion, see [33] sect. 13.2!

Special cases are here the faint, not two dimensional but rather star-like appearing Plane-tary Nebulae. In contrast to M27 and M57 they generally require relatively short exposure times. Further they cannot be recorded on a specific area within the nebula but only in the total light, integrated within the slit of the spectrograph. Since within these tiny discs, lar-ger intensity differences at individual emissions occur. So even the measured Balmer dec-rement may be distorted, aggravated by possible shifts in the slit position during recording due to bad seeing and/or poor autoguiding. However, even this influence on the determina-tion of the excitation class has been found as low.

The determination of additional plasma parameters such as the electron temperature Te and the electron density Ne specifically requires low-noise spectra with high resolution, re-garding these faint objects, a real challenge with amateur equipments. In addition, some of the used diagnostic lines are extremely weak and the error rate is correspondingly high. Even between values in professional publications, often major deviations are noted!

22.12 Determination of the Excitation Class

Since the beginning of the 20th Century numerous methods have been proposed to deter-mine the excitation classes of emission nebulae. The 12-level “revised” Gurzadyan system [10], which has been developed also by, Aller, Webster, Acker and others, is one of the cur-rently best accepted and appropriate also for amateurs. It relies on the simple principle that with increasing excitation class, the intensity of the forbidden [O III] lines becomes stronger, compared with the H-Balmer series. Therefore as a classification criterion the in-tensity sum of the two brightest [O III] lines, relative to the Hβ emission, is used. Within the range of the low excitation classes E: 1–4, this value increases strikingly. The [O III] lines at λλ4959 and 5007 are denoted in the formulas as and .

For low excitation classes E1 – E4:

Within the transition class E4 the He II line at λ 4686 appears for the first time [225]. It re-quires 24.6 eV for the ionisation. That's almost twice the energy as needed for H II with


13.6 eV. From here on, the intensity of He II increases continuously and replaces the now stagnant Hβ emission as a comparison value in the formula. The ratio is expressed here logarithmically (base 10) in order to limit the range of values for the classification system:

For middle and high Excitation Classes E4 – E12:

The 12 -Classes are subdivided in to the groups Low ( , Middle and

High . In extreme cases 12+ is assigned.

Low Middle High

–Class – Class – Class

E1 0 – 5 E4 2.6 E9 1.7

E2 5 – 10 E5 2.5 E10 1.5

E3 10 – 15 E6 2.3 E11 1.2

E4 >15 E7 2.1 E12 0.9

E8 1.9 E12+ 0.6

22.13 The Excitation Class as an Indicator for Plasma Diagnostics

Gurzadyan (among others) has shown that the excitation classes are more or less closely linked to the evolution of the PN [10], [226]. The study with a sample of 142 PN showed that the E-Class is a rough indicator for the following parameters; however in reality the values may scatter considerably [8].

1. The age of the PN Typically PN start on the lowest E- level and subsequently step up the entire scale with increasing age. The four lowest classes are usually passed very quickly. Later on this pace decreases dramatically. The entire process takes finally about 10,000 to >20,000 years, an extremely short period, compared with the total lifetime of a star!

2 The Temperature of the central star

The temperature of the central star also rises with the increasing E-Class. By pushing of the envelope, increasingly deeper and thus hotter layers of the star become "exposed". At about E7 in most cases an extremely hot White Dwarf remains, generating a WR-like spectrum. For [K] the following, very rough estimates can be derived [33]:

E-Class E1-2 E3 E4 E5 E7 E8-12

35,000 50,000 70,000 80,000 90,000 100,000 – 200,000

3. The Expansion of the Nebula The visibility limit of expanding PN lies at a maximum radius of about 1.6 ly (0.5parsec). With increasing E-class, also the radius of the expanding nebula is growing. Gurzadyan [226] provides mean values for [ly] which however may scatter considerably for the individual nebulae.

E-Class E1 E3 E5 E7 E9 E11 E12+

0.5 0.65 0.72 1.0 1.2 1.4 1.6


22.14 Estimation of Te and Ne with the O III and N II Method

Due to the very weak diagnostic lines, these methods can be applied only to spectra with high resolution and quality. Further J. Schmoll outlines in his dissertation [201], what influ-ence the slit width and the method of background subtraction exert on the analysis of weak lines! The procedure is based on the fundamental equations by Gurzadyan 1997 [10], which uses for the O III method the lines at λλ 5007, 4959 and 4363, and for the N II method at λλ 6548, 6584 and 5755.

For the calculation of the electron temperature, these equations can’t be explicitly con-verted and solved by and contain additionally the variable . But for , empirical formu-las exist, which are valid for thin gases (typical for H II regions and SNR). “ “ is the natural logarithm to base e.

For the explicit calculation of , with known , I have converted the formulas {57} {58} accordingly:

If the recording of a spectral profile can be limited on a defined region within the nebula, in both equations {61} and {62} the variables become identical. can then be eliminated by equalisation of {61} and {62}. The implicitly remaining variable anway requires finally an iteratively solving of the equation. However this requires that the values of all diagnostic lines, for both methods, are available in good quality.

22.15 Estimation of the Electron Density from the S II and O II Ratio

The electron density can be estimated by Osterbrock from the ratio of the two sulfur lines [S II] λλ 6716, 6731 or the oxygen lines [O II] λλ 3729, 3726 [201]. The big advan-tage of this method: These lines are so close together, that the extinction and instrumental responses can’t exert any significant effect on the ratio. The disadvantage is, that the two lines, except by SNR, are generally very weak and therefore difficult to measure.


22.16 Distinguishing Characteristics in the Spectra of Emission Nebulae

Due to the synchrotron and bremsstrahlung SNR show, especially in the X-ray part of the spectrum, a clear continuum see [33], Table 85. This appears especially pronounced in the X-ray domain, so X-ray telescopes are highly valuable to distinguish SNR from the other nebula species, particularly at very faint extragalactic objects. For all other types of Emis-sion Nebulae the detection of a continuum radiation is difficult.

In the optical part of SNR spectra, the [S II] and [O I] lines are, relative to Hα, more intense than at PN and H II regions. This effect is caused here by shock wave induced collision ioni-sation, see [33], Table 85. The [S II] and [OI] emissions are very weak at PN and almost to-tally absent in H II regions [201].

The electron density is very low in SNR, ie somewhat lower than in H II regions. It amounts in the highly expanded, old Cirrus Nebula to about 300 cm-3:

By the still young and compact Crab Nebula it is about 1000 cm-3 [201]. By PN, gets highest and is usually in the order of 104 cm-3 [201]. In the H II region of M42, is within the range of 1000–2000 cm-3 [224].

In H II regions, the excitation by the O- and early B-class stars is relatively low and there-fore the excitation class in the order of E = 1-2 only modest [33].

Planetary nebulae usually pass through all 12 excitation classes, following the evolution of the central star.

In this regard the SNR are also a highly complex special case. By very young SNR, eg the Crab Nebula (M1), dominate higher excitation classes whose levels are not homogeneously distributed within the nebula, according to the complex filament structure [231]. The diag-nostic line He II at λ 4686 is therefore a striking feature in some spectra of M1, see [33], Table 85.

Inte

nsi

tyR

ati

o

Electron Density [cm-3]

[S II] 6716 / 6731

[O II] 3729 / 3726

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

101 102 103 104 105


23 Analysis of the Chemical Composition

23.1 Astrophysical Definition of Element Abundance

In astrophysics, the abundance of an element is expressed as decadic logarithm of the amount of particles per unit volume , to that of the hydrogen , whose abundance is defined according to convention to [57], [11]. The mass ratios do not matter here.

By transforming logarithmically we directly obtain the relationship

:

23.2 Astrophysical Definition of Metal Abundance Z (Metallicity)

Of great importance is the ratio of iron to hydrogen . This is also computed with the relative number of atoms per unit volume and not with their individual masses. The metal-licity in a stellar atmosphere, also called , is expressed as the decadic logarithm in relation to the sun:

values, smaller than found in the atmosphere of the Sun, are considered to be metal poor and carry a negative sign (–).The existing range reaches from approximately +0.5 to –5.4 (SuW 7/2010). Fe is used here as a representative of the metals because it appears quite frequently in the spectral profile and is relatively easy to analyse.

23.3 Quantitative Determination of the Chemical Composition

The identified spectral lines (sect. 24) of the examined object inform directly:

– which elements and molecules are present – which isotopes of an element are present (restricted to some cases and to high resolution profiles) – which stages of ionisation are generated

In this context the quantitative determination of the abundance can be outlined only roughly. It is very complex and can’t be obtained directly from the spectrum. It requires ad-ditional information, which can partly be obtained only with simulations of the stellar pho-tosphere [11]. The intensity of a spectral line is an indicator, which provides information on the frequency of a particular element. However this value is influenced, inter alia, by the effective temperature , the pressure, the gravitational acceleration, as well as the

macro-turbulence and the rotational speed of the stellar photosphere. Furthermore

also affects the degree of ionisation of the elements, which must be calculated with the so-called Saha Equation [11].

These complications are impressively demonstrated in the solar spectrum. Over 90% of the solar photosphere consists of hydrogen atoms with the defined abundance of . Nevertheless, as a result of the too low temperature of 5800 K, the intensity of the H Balmer series remains quite modest. The dominating main features of the solar spectrum, however, are the two Fraunhofer H and K lines of ionised calcium Ca II, although its abun-dance is just [Anders & Grevesse 1989]. According to {65}, this corresponds to a ratio of . From Quantum-mechanical reasons, at the solar photospheric


temperature of 5800 K, Ca II is an extremely effective absorber. The optimum conditions for the hydrogen lines, however, are reached not until nearly 10,000 K (see sect. 9.2). In the professional area the element abundance is also determined by the iterative compari-son of the spectrum with simulated synthetic profiles of different chemical composition [11].

23.4 Relative Abundance-Comparison at Stars of Similar Spectral Class

A simplified special case is formed by stars with similar spectral- and luminosity class and comparable rotational velocities. Thus the physical parameters of the photospheres are very similar. Here the equivalent widths EW of certain lines can simply be compared and thus the relative abundance differences at least qualitatively be seen. In the Spectroscopic Atlas [33] this is demonstrated at the classic example of the two main-sequence stars Sir-ius A1Vm and Vega A0V. The basic principle is the so called Curve of Growth. It shows that within its unsaturated and somewhat linearly running part, the equivalent width EW of a certain spectral line of an element, behaves roughly proportional to its number of atoms within a plasma mixture.

Eq

uiv

ale

nt

wid

thE

W [

Å]

Number of atoms

Linear regionLinie profile deepening

Saturated line

Curve of Growth


24 Spectroscopic Parallax

24.1 Spectroscopic Possibilities of Distance Measurement

Distances can spectroscopically be determined either with the spectroscopic parallax or in the extragalactic range, with help of the Doppler-related Redshift, combined with the Hub-ble’s Law (sect. 15.5). These methods are supplemented by radar and laser reflectance measurements (solar system), the trigonometric parallax (closer solar neighborhood) and the photometric parallax (Milky Way and extragalactic area). The latter is based on the brightness, compared with precisely known, so-called "standard candles" as Cepheids and supernovae of type Ia.

24.2 Term and Principle of Spectroscopic Parallax

The spectroscopic parallax allows the rough distance-estimation to a star, based solely on the spectroscopically determined spectral class and photometrically measured, apparent brightness. Therefore the term "parallax" is here a misnomer. However, it is correct for the trigonometric parallax. This corresponds to the apparent shift of the observed celestial body relative to the sky background, caused by the Earth's orbit around the sun. The principle of spectroscopic parallax works similar to the photometric parallax. The absolute magnitude of an object is generally defined for the distance of 10 parsecs [pc] or 32.6 light years [ly]. This value is first compared with the actually measured, apparent brightness, enabling the calculation of the distance. Applying the spectroscopic parallax, the absolute brightness of a star is determined by its spectral class.

24.3 Spectral Class and Absolute Magnitude

The following table shows the values of the absolute magnitudes for the main sequence stars (V) from a lecture at the University of Northern Iowa http://www.uni.edu/. Their devia-tion, in comparison with known literature values, remains, for our purpose, within accept-able limits. For instance, the table value for the spectral class G2V does 5.0M, compared to the literature value for the sun of 4.83M. For the giants (III) and supergiants (I), I have col-lected some literature values of known stars from different sources in order to give an im-pression of the magnitude and the enormous spread. At these luminosity classes no usable conjunction with the spectral classes can be recognised. Further supergiants of early spec-tral classes are often spectroscopic binaries. These facts also drastically demonstrate the limitations of this method. Therefore the determination of the distance, applying the spec-troscopic parallax is, at least for amateurs, restricted to main-sequence stars. To find In the annex to Gray/Corballi [4] is a calibration table of the absolute magnitudes for all spectral- and luminosity classes of the MK System.

Spectral

Class

Main Sequence (V)

Giants (III)

Supergiants (I)

O5 –4.5

O6 –4.0

O7 –3.9

O8 –3.8 Meissa, λ Ori –4.3

O9 –3.6 Iota Ori –5.3 ζ Ori, Alnitak –5.3

B0 –3.3 Alnilam, ε Ori –6.7

B1 –2.3 Alfirk, β Cep –3.5

B2 –1.9 Bellatrix, γ Ori –2.8

http://www.uni.edu/


B3 –1.1

B5 –0.4 δ Per –3.0 Aludra, η Cma –7.5

B6 0

B7 0.3 Alcione, η Tau –2.5

B8 0.7 Atlas, 27 Tau –2.0 Rigel, β Ori –6.7

B9 1.1

A0 1.5

A1 1.7

A2 1.8 Deneb, α Cyg –8.7

A3 2.0

A4 2.1

A5 2.2 α Oph, 1.2

A7 2.4 γ Boo, 1.0

F0 3.0 Adhafera, ζ Leo –1.0

F2 3.3 Caph, β Cas 1.2

F3 3.5

F5 3.7 Mirfak, α Per –4.5

F6 4.0

F7 4.3

F8 4.4 Wezen, δ CMa –6.9

G0 4.7 Sadalsuud, β Aqr –3.3

G1 4.9

G2 5.0 Sadalmelik, α Aqr –3.9

G5 5.2

G7 Kornephoros, β Her –0.5

G8 5.6 Vindemiatrix, ε Vir 0.4

K0 6.0 Dubhe, α Uma –1.1

K1 6.2

K2 6.4 Cebalrai, β Oph 0.8

K3 6.7

K4 7.1

K5 7.4 Aldebaran, α Tau –0.7

K7 8.1 Alsciaukat, α Lyn –1.1

M0 8.7

M1 9.4 Scheat, β Peg –1.5 Antares, α Sco –5.3

M2 10.1 Betelgeuse, α Ori –5.3

M3 10.7

M4 11.2

M5 12.3 Ras Algethi, α Her –2.3

M6 13.4

M7 13.9

M8 14.4


24.4 Distance Modulus

The distance modulus is defined by the difference between the apparent- [m] and absolute magnitude [M], expressed in the generally used, logarithmic system of the photometric brightness levels [mag].

In contrast to the Apparent Distance Modulus , the so called True Distance Modulus applies to the simplified calculation, assuming no Interstellar Extinction, [12].

24.5 Calculation of the Distance with the Distance Modulus

Assuming no Interstellar Extinction, the relationship between the distance and the True Distance Modulus can be expressed as:

If the interstellar extinction is considered, must still be added:

( average interstellar extinction .

By logarithmic transforming can be expressed explicitly:

According to [12] in worst case, ie within the galactic plane, results . If dark clouds are located on the line of sight, may rise up to 1 to 2 . Further it becomes recognisable, that the extinction starts normally to be noticable not until about 100 pc.

Anyway [58] proposes the rule of thumb to take for the solar neighbor-

hood. The problem here is that depends also on the desired distance {69}.

24.6 Examples for Main Sequence Stars (with Literature Values)

Sirius, α Cma A1Vm m=–1.46 M=1.43 r = 2.64 pc = 8.6 Lj

Denebola, β Leo A3V m= 2.14 M=1.93 r = 11.0 pc = 36 Lj

61 Cyg A, K5 m= 5.21 M= 7.5 r = 3.5 pc = 11 Lj


25 Identification of Spectral Lines

25.1 Task and Requirements

With the line identification, to an absorption- or emission line with the wavelength , the responsible element or ion is assigned. Considered purely theoretical this would have to be relatively simple, as shown by the adjoining excerpt of the "lineident" table, provided by the Vspec software. In practice, however, inter alia the following should be noted:

– The spectrum must show a high S/N ratio, further be calibrated very precisely and adjusted by possible Doppler shifts. Only that way we can exactly deter-mine the wavelength of each line.

– The higher the resolution of the spectrum, the more accurate can be determined and the fewer lines are merging into so-called “Blends”.

25.2 Practical Problems and Solving Strategies

However the table shows, that in certain sections of the spectrum, the distances between the individual positions are obviously very close. This happens from quantum mechanical reasons for several of the metal lines, generating corresponding ambiguities, especially in stellar spectra of the medium and later spectral classes.

Commonly concerned are also noble gases, as well as the so-called rare earth compounds – eg praseodymium, lanthanum, yttrium etc. Such we find in the spectra of gas-discharge lamps, acting here as dopants, alloy components and fluorescent agents.

Here, in most of the cases, helps the process of elimination. Most important is the knowl-edge of the involved process temperature. For stellar spectra it is supplied by the according spectral class. With this parameter the graphic at the end of sect. 13.8, provides on one hand possible proposals, but excludes a priori also certain elements or corresponding ioni-sation stages. As there already discussed, eg for normal photospheric solar spectra, Helium He I can be excluded.

At certain stages of stellar evolution, detailed knowledge of the involved processes are necessary. Since e.g. stars, in the final Wolf Rayet stage, first of all repel their entire outer hydrogen shell, this element can therefore subsequently hardly be detected in such spec-tra. Critical is here the mostly very significant He II emission at 6560.1 Å, which is often misinterpreted by amateurs as Hα line at 6562.82 Å, see [33] tables 5 and 6.

Relatively easy is the line identification for calibration lamps with known gas filling. Thus Vspec allows the superimposing of the corresponding emission lines, with their relative in-tensities, directly into the calibrated lamp spectrum (see below). For such "laboratory spec-tra" in Vspec [411] the "element" database has proven (Tools/Elements/element). For stel-lar profiles, however, the "lineident" database is to prefer (Tools/Elements/lineident).

In cases of unknown gas filling, on a trial basis, the emission lines of the individual noble gases He, Ne, Ar, Kr and Xe can be superimposed to the calibrated Lamp spectrum. In most cases already the pattern of these inserted lines instantly shows, if the corresponding ele-ment is present or not. This was also the most successful tactic for the line identification in [32] [33] [34] [35]. However some of the noble gas emissions can be located very close to each other such as Ar 6114.92 Å and Xe 6115.08 Å, see [33] Table 102.


25.3 Tools for the Identification of Spectral Lines

For stellar spectra, a spectral atlas is probably the safest way to identify spectral lines (see bibliography). For rare stellar types, object related publications are often very helpful.

The software solutions based on model spectra are primarily used in the professional as-tronomy and are hardly suitable for most amateurs. For a detailed analysis of individual elements and their ions also online databases are available, such as from the U.S. American NIST (National Institute of Standards and Technology) [103]. The following screenshot shows the calibrated Vspec DADOS spectrum [401] of the Wolf Rayet star WR 136, with the superimposed He II emission lines from the "lineident" database. For a commented spectrum refer to [33], Table 6.

This Vspec screenshot shows a high-resolution Echelle SQUES spectrum [400] around the Hα line from δ Scorpii. It is superimposed with the atmospheric water vapor absorptions (H2O), displayed in red by the "lineident" database function. For a commented spectrum re-fer to [33], Table 95A.


26 Literature and Internet

Literature:

[1] Klaus Peter Schröder, – Feuriger Weltuntergang, Juli 2008, Sterne und Weltraum.

– Vom Roten Riesen zum Weissen Zwerg, Januar 2009

Interstellarum Sonderheft: Planetarische Nebel

[2] Klaus Werner, Thomas Rauch, Die Wiedergeburt der Roten Riesen, Februar 2007,

Sterne und Weltraum.

[3] James Kaler, Stars and their Spectra

[4] Richard O. Gray, Christopher Corbally, Stellar Spectral Classification, Princeton Series in Astrophysics

[5] Keith Robinson, Spectroscopy, The Key to the stars

[6] Stephen Tonkin, Practical Amateur Spectroscopy

[7] Fritz Kurt Kneubühl, Repetitorium der Physik, Teubner Studienbücher Physik, Kap. Relativistischer Doppler-Effekt der elektromagnetischen Wellen

[8] J.-P. Rozelot, C. Neiner et al. EDP Sciences: EAS Publication Series, Astronomical Spectrography for Amateurs, Volume 47, 2011.

[10] G.A. Gurzadyan, 1997,The Physics and Dynamics of Planetary Nebulae,

[11] David F. Gray, 2005, The Observation and Analysis of Stellar Photospheres,

[12] A. Unsöld, B. Baschek, Der neue Kosmos

Articles by the Author and Reviews to the Spectroscopic Atlas:

[20] Richard Walker, Die Fingerabdrücke der Sterne – Ein Spektralatlas für Amateurastronomen, Ju-ne/July 2012, Interstellarum No. 82

[21] Urs Flückiger, Kostenfreier Spektralatlas, April 2011, Sterne und Weltraum

[22] Thomas Eversberg, Spektralatlas für Astroamateure von Richard Walker, VDS Journal für Astro-nomie, III/2011

Internet Links:

Author:

The following publications on the topic can be downloaded at this link: http://www.ursusmajor.ch/astrospektroskopie/richard-walkers-page/index.html

[30] Das Aufbereiten und Auswerten von Spektralprofilen mit den wichtigsten IRIS und Vspec Funktionen (German language only).

[31] Kalibrierung von Spektren mit der Xenon Stroboskoplampe (German language only)

[32] Atomic Emission Spectroscopy with Spark- or Arc Excitation, Experiments with the DADOS

Spectrograph and Simple Makeshift Tools

[33] Spectroscopic Atlas for Amateur Astronomers (Download in German and English)

[34] Kalibrierung von Spektren mit dem Glimmstarter ST 111 von OSRAM (German language only)

[35] Quasar 3C273, Optical Spectrum and Determination of the Redshift

[36] Glow Starter RELCO SC480 – Atlas of Emission Lines – Recorded by the Spectrographs

SQUES Echelle and DADOS

http://www.ursusmajor.ch/astrospektroskopie/richard-walkers-page/index.html


Lectures/Practica:

[50] Vorlesung Astrophysik, Max Planck Institut München:

www.mpa-garching.mpg.de/lectures/TASTRO

[51] Vorlesung Astrophysik, Astrophysikalisches Institut Potsdam http://www.aip.de/People/MSteinmetz/classes/WiSe05/PPT/

[52] F. Royer: Rotation des étoiles de type A, Lecture Ecole d’Astronomie de CNRS

http://adsabs.harvard.edu/abs/1996udh..conf..159R

[53] Gene Smith, University of California, San Diego, Astronomy Tutorial, Stellar Spectra http://cass.ucsd.edu/public/tutorial/Stars.html

[54] Kiepenheuerinstitut für Sonnenphysik, Uni Freiburg: Grobe Klassifikation von Sternspektren http://www.kis.uni-freiburg.de/fileadmin/user_upload/kis/lehre/praktika/sternspektren.pdf

[55] Michael Richmond: Luminosity Class and HR Diagram http://spiff.rit.edu/classes/phys440/lectures/lumclass/lumclass.html

[56] Alexander Fromm, Martin Hörner, Astrophysikalisches Praktikum, Uni Freiburg i.B. http://www.physik.uni-freiburg.de/~fromm/uni/Protokollschauinsland.pdf

[57] University Heidelberg, Vorlesung Kapitel 3: Kosmische und Solare Elementhäufigkeit http://www.ita.uni-heidelberg.de/~gail/plvorl/Vorlesung-4.pdf

[57a ] University Heidelberg, Anhang A: Elementhäufigkeiten http://www.ita.uni-heidelberg.de/~gail/astrochem/appA.pdf

[58] Uni Karlsruhe: Spektroskopische Entfernungsbestimmung von Sternen oder Sternhaufen http://www.lehrer.uni-karlsruhe.de/~za3832/Astronomie/Spektroskopische%20Entfernungsbestimmung.pdf

Spektroscopic atlases and commented spectra:

[80] An atlas of stellar spectra, with an outline of spectral classification, Morgan, Keenan, Kellman (1943): http://nedwww.ipac.caltech.edu/level5/ASS_Atlas/frames.html

[81]Digital Spectral Classification Atlas, R.O. Gray: http://nedwww.ipac.caltech.edu/level5/Gray/frames.html

[82] Moderate-resolution spectral standards from lambda 5600 to lambda 9000, Allen, L. E. & Strom, K. M: http://adsabs.harvard.edu/full/1995AJ....109.1379A

[83] An atlas of low-resolution near-infrared spectra of normal stars Torres Dodgen, Ana V., Bruce Weaver: http://adsabs.harvard.edu/abs/1993PASP..105..693T

[84] Christian Buil: Vega Spectrum Atlas, a fully commented spectrum http://astrosurf.com/buil/us/vatlas/vatlas.htm

[85] Paolo Valisa, Osservatorio Astronomico Schiaparelli, Varese. http://www.astrogeo.va.it/astronom/spettri/spettrien.htm

[86] High resolution solar spectrum Bass2000 http://bass2000.obspm.fr/download/solar_spect.pdf

[87] Lunettes Jean Roesch (Pic du Midi), High resolution solar spectrum, Jungfraujoch (Université de Genève): http://ljr.bagn.obs-mip.fr/observing/spectrum/index.html

[88] Caltech: Spectral atlases (also) for extragalaktic Objects http://nedwww.ipac.caltech.edu/level5/catalogs.html

[89] UCM: Librerias de espectros estelares http://www.ucm.es/info/Astrof/invest/actividad/spectra.html

[90] various spectra of lamps: http://ioannis.virtualcomposer2000.com/spectroscope/index.html

http://www.mpa-garching.mpg.de/lectures/TASTRO

http://www.aip.de/People/MSteinmetz/classes/WiSe05/PPT/

http://adsabs.harvard.edu/abs/1996udh..conf..159R

http://cass.ucsd.edu/public/tutorial/Stars.html

http://www.kis.uni-freiburg.de/fileadmin/user_upload/kis/lehre/praktika/sternspektren.pdf

http://spiff.rit.edu/classes/phys440/lectures/lumclass/lumclass.html

http://www.physik.uni-freiburg.de/~fromm/uni/Protokollschauinsland.pdf

http://www.ita.uni-heidelberg.de/~gail/plvorl/Vorlesung-4.pdf

http://www.ita.uni-heidelberg.de/~gail/astrochem/appA.pdf

http://www.lehrer.uni-karlsruhe.de/~za3832/Astronomie/Spektroskopische%20Entfernungsbestimmung.pdf

http://nedwww.ipac.caltech.edu/level5/ASS_Atlas/frames.html

http://nedwww.ipac.caltech.edu/level5/Gray/frames.html

http://adsabs.harvard.edu/full/1995AJ....109.1379A

http://adsabs.harvard.edu/abs/1993PASP..105..693T

http://astrosurf.com/buil/us/vatlas/vatlas.htm

http://www.astrogeo.va.it/astronom/spettri/spettrien.htm

http://bass2000.obspm.fr/download/solar_spect.pdf

http://ljr.bagn.obs-mip.fr/observing/spectrum/index.html

http://nedwww.ipac.caltech.edu/level5/catalogs.html

http://www.ucm.es/info/Astrof/invest/actividad/spectra.html

http://ioannis.virtualcomposer2000.com/spectroscope/index.html


Databases

[100] CDS Strassbourg: SIMBAD Astonomical Database http://simbad.u-strasbg.fr/simbad/

[101] NASA Extragalactic Database (NED) http://nedwww.ipac.caltech.edu/

[102] The SAO/NASA Astrophysics Data System, http://adsabs.harvard.edu/index.html

[103] NIST Atomic Spectra Database: http://physics.nist.gov/PhysRefData/ASD/lines_form.html

[104] MILES Spectral Library, containing ~1000 spectra of reference stars http://miles.iac.es/pages/stellar-libraries/miles-library.php

Publications to the Stellar Rotation Velocity:

[120] Y. Takeda et al.: Rotational feature of Vega and its impact on abundance determinations, 2007 Observat. of Japan http://www.ta3.sk/caosp/Eedition/FullTexts/vol38no2/pp157-162.pdf

[121] Nicholas A. Moskovitz et al.: Characterizing the rotational evolution of low mass stars: Implica-tions for the Li-rich K-giants, University of Hawaii at Manoa, http://eo.nso.edu/ires/IRES08/Nick_tech.pdf

[122] F. Fekel: Rotational Velocities of B, A, and Early‐F Narrow‐lined Stars (2003) NASA Astrophysics Data System or http://www.jstor.org/stable/10.1086/376393

[123] F. Fekel: Rotational Velocities of Late Type Stars (1997) NASA Astrophysics Data System or http://articles.adsabs.harvard.edu/full/1997PASP..109..514F

[124] F. Royer: Determination of v sin i with Fourier transform techniques (2005) http://sait.oat.ts.astro.it/MSAIS/8/PDF/124.pdf

[125] J.L. Tassoul: Stellar Rotation, 2000, Cambridge Astrophysics Series 36, book preview: http://books.google.ch/books?q=tassoul

[126] R.L. Kurucz et al.: The Rotational Velocity and Barium Abundance of Sirius, The Astronomical Journal, Nov. 1977 http://adsabs.harvard.edu/full/1977ApJ...217..771K

[127] Reinhard W. Hanuschik: Stellar V sin i and Optical Emission Line Widths in Be Stars, 1989 As-tronomisches Institut Universität Bochum. http://articles.adsabs.harvard.edu/full/1989Ap%26SS.161...61H

[128] Christian Buil: Characterization of the Line Profile http://www.astrosurf.com/~buil/us/spe2/hresol7.htm

Publications and Presentations to Be Stars

[140] A. Miroshnichenko: Spectra of the Brightest Be stars and Objects Description, University of North Carolina, www.astrospectroscopy.de/Heidelbergtagung/Miroshnichenko2.ppt

[141] A. Miroshnichenko: Summary of Experiences from Observations of the Be-binary δ Sco, Uni-versity of North Carolina, www.astrospectroscopy.de/Heidelbergtagung/Miroshnichenko1.ppt

[142] A. Miroshnichenko et al.: Properties of the δ Scorpii Circumstellar Disk from Continuum Model-ing, University of North Carolina, http://libres.uncg.edu/ir/uncg/f/A_Miroshnichenko_Properties_2006.pdf

[143] Reinhard W. Hanuschik: High resolution emissionline spectroscopy of Be Stars, I. Evidence for a two-component structure of the Hα emitting enveloppe, Astronomisches Institut Universität Bo-chum. http://articles.adsabs.harvard.edu/full/1986A%26A...166..185H

[144] S. Stefl et al. :V/R Variations of Binary Be Stars , ESO 2007 http://www.arc.hokkai-s-u.ac.jp/~okazaki/Meetings/sapporo/361-0274.pdf

[145] R. Soria: The Optical Counterpart of the X-ray Transient RX J0117.6-7330, Siding Spring Ob-servatory Coonabarabran, Australia http://articles.adsabs.harvard.edu/full/1999PASA...16..147S

[146] E. Pollmann: Spektroskopische Beobachtungen der Hα- und der HeI 6678-Emission am Dop-pelsternsystem δ Scorpii, http://www.bav-astro.de/rb/rb2009-3/151.pdf

http://simbad.u-strasbg.fr/simbad/

http://nedwww.ipac.caltech.edu/

http://adsabs.harvard.edu/index.html

http://physics.nist.gov/PhysRefData/ASD/lines_form.html

http://miles.iac.es/pages/stellar-libraries/miles-library.php

http://www.ta3.sk/caosp/Eedition/FullTexts/vol38no2/pp157-162.pdf

http://eo.nso.edu/ires/IRES08/Nick_tech.pdf

http://www.jstor.org/stable/10.1086/376393

http://articles.adsabs.harvard.edu/full/1997PASP..109..514F

http://sait.oat.ts.astro.it/MSAIS/8/PDF/124.pdf

http://books.google.ch/books?q=tassoul

http://adsabs.harvard.edu/full/1977ApJ...217..771K

http://articles.adsabs.harvard.edu/full/1989Ap%26SS.161...61H

http://www.astrosurf.com/~buil/us/spe2/hresol7.htm

http://www.astrospectroscopy.de/Heidelbergtagung/Miroshnichenko2.ppt

http://www.astrospectroscopy.de/Heidelbergtagung/Miroshnichenko1.ppt

http://libres.uncg.edu/ir/uncg/f/A_Miroshnichenko_Properties_2006.pdf

http://articles.adsabs.harvard.edu/full/1986A%26A...166..185H

http://www.arc.hokkai-s-u.ac.jp/~okazaki/Meetings/sapporo/361-0274.pdf

http://articles.adsabs.harvard.edu/full/1999PASA...16..147S

http://www.bav-astro.de/rb/rb2009-3/151.pdf


[147] D. K. Ojha & S. C. Joshi: On the Shell Star Pleione (BU Tauri), 1991, Uttar Pradesh State Obser-vatory, Manora Peak, http://www.ias.ac.in/jarch/jaa/12/213-223.pdf

Publications to Novae

[160] Donn Starkey, Photometry, Spectroscopy, and Classification of Nova V475 Scuti, JAAVSO Vol-ume 34, 2005 http://articles.adsabs.harvard.edu/full/2005JAVSO..34...36S

Publications/Practica to Spectroscopic Binaries

[170] Juergen Weiprecht, Beobachtungsmethoden und Klassifikation von Doppelsternen, 2002, Praktikum Uni Jena http://www.astro.uni-jena.de/Teaching/Praktikum/pra2002/node155.html und http://www.astro.uni-jena.de/Teaching/Praktikum/pra2002/node156.html

[171] Praktikum Uni Nürnberg-Erlangen, Die Masse eines Neutronensterns, http://pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/haus7_solution.pdf

[172] Leifi, Uni München, Spektroskopische Doppelsterne, visuelle Doppelsterne: http://leifi.physik.uni-muenchen.de/web_ph12/materialseiten/m12_astronomie.htm

[173] Southwest Research Institute Boulder, Eclipsing Binary Star Parameters, http://binaries.boulder.swri.edu/atlas/

[174] Diablo Valley College, Analyzing Binary Star Data, http://voyager.dvc.edu/faculty/kcastle/Analyzing%20Binary%20Star%20Dat4.htm#Introduction

[175] Kiepenheuer Institut für Sonnenphysik: Einführung in die Astronomie und Astrophysik Kap. 2.4 Zustandsdiagramme, http://www3.kis.uni-freiburg.de/~ovdluhe/Vorlesungen/E2_2/einf_2_Pt2.html

[176] Dept. Physics & Astronomy University of Tennessee, Spectroscopic Binaries http://csep10.phys.utk.edu/astr162/lect/binaries/spectroscopic.html

[177] D.M. Peterson et al. The Spectroscopic Orbit of β scorpii A, 1979, Astronomical Society of the Pacific, http://adsabs.harvard.edu/abs/1979PASP...91...87P

[178] Uni Freiburg: Einführung in die Astronomie und Astrophysik, 2.5 Zustandsdiagramme http://www3.kis.uni-freiburg.de/~ovdluhe/Lehre/Einfuehrung/Einf_2_3-5.pdf

[179] Uni Heidelberg: Vorlesung Lektion 8: Doppelsterne und Binäre Pulsare, http://www.lsw.uni-heidelberg.de/users/mcamenzi/API_Lect8.pdf

[180] Vorlesung TLS Tautenburg: Einiges über junge Sterne, http://www.tls-tautenburg.de/research/eike/vorles/entstehung_sterneEG04.pdf

[181] Vorlesung University of Pennsylvania: Introduction to Least Squares Fit (with Excel) http://dept.physics.upenn.edu/~uglabs/Least-squares-fitting-with-Excel.pdf

[182] Wikiversity: Least squares/Calculation using Excel: http://en.wikiversity.org/wiki/Least_squares/Calculation_using_Excel

Publications to Temperature of Stellar Photospheres

[190] Measuring Starspot Temperature from Line Depth Ratios, Part I, S. Catalano et al. http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/abs/2002/42/aa2543/aa2543.html

[190b] Measuring Starspot Temperature from Line Depth Ratios, Part II, http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/ref/2005/11/aa1373/aa1373.html

[191] Effective Temperature vs Line-Depth Ratio for ELODIE Spectra, Gravity and Rotational Velocity Effects, K. Biazzo et al. http://web.ct.astro.it/preprints/preprint/biazzo2.pdf

Publications to the Balmer Decrement and IS Extinction

http://www.ias.ac.in/jarch/jaa/12/213-223.pdf

http://articles.adsabs.harvard.edu/full/2005JAVSO..34...36S

http://www.astro.uni-jena.de/Teaching/Praktikum/pra2002/node155.html

http://www.astro.uni-jena.de/Teaching/Praktikum/pra2002/node156.html

http://pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/haus7_solution.pdf

http://leifi.physik.uni-muenchen.de/web_ph12/materialseiten/m12_astronomie.htm

http://binaries.boulder.swri.edu/atlas/

http://voyager.dvc.edu/faculty/kcastle/Analyzing%20Binary%20Star%20Dat4.htm#Introduction

http://www3.kis.uni-freiburg.de/~ovdluhe/Vorlesungen/E2_2/einf_2_Pt2.html

http://csep10.phys.utk.edu/astr162/lect/binaries/spectroscopic.html

http://adsabs.harvard.edu/abs/1979PASP...91...87P

http://www3.kis.uni-freiburg.de/~ovdluhe/Lehre/Einfuehrung/Einf_2_3-5.pdf

http://www.lsw.uni-heidelberg.de/users/mcamenzi/API_Lect8.pdf

http://www.tls-tautenburg.de/research/eike/vorles/entstehung_sterneEG04.pdf

http://dept.physics.upenn.edu/~uglabs/Least-squares-fitting-with-Excel.pdf

http://en.wikiversity.org/wiki/Least_squares/Calculation_using_Excel

http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/abs/2002/42/aa2543/aa2543.html

http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/abs/2002/42/aa2543/aa2543.html

http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/ref/2005/11/aa1373/aa1373.html

http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/ref/2005/11/aa1373/aa1373.html

http://web.ct.astro.it/preprints/preprint/biazzo2.pdf


[200] Calculations of level populations for the low levels of hydrogenic ions in gaseous nebulae, 1971, M. Brocklehurst, http://adsabs.harvard.edu/full/1971MNRAS.153..471B

[201] 3D Spektrophotometrie Extragalaktischer Emissionslinien Objekte, AIP 2001, Dissertation Jürgen Schmoll http://www.aip.de/groups/publications/schmoll.pdf

[202] The Balmer Decrement in some Be Stars, 1953, G. and M. Burbidge http://articles.adsabs.harvard.edu/full/1953ApJ...118..252B

[203] Paschen and Balmer Series in Spectra of Chi Ophiuchi and P Cygni, 1955 G. and M. Burbidge http://articles.adsabs.harvard.edu/full/1955ApJ...122...89B

[204] Effects of Self-Absorption and Internal Dust on Hydrogene Line Intensities in Gaseous Nebu-lae, 1969, P. Cox, W. Mathews http://adsabs.harvard.edu/full/1969ApJ...155..859C

[205] Comparison of Two Methods for Determining the Interstellar Extinction of Planetary Nebulae, 1992, G. Stasinska et al. http://articles.adsabs.harvard.edu/full/1992A%26A...266..486S

[206] The Effect of Space Reddening on The Balmer Decrement in Planetary Naebulae, 1936, Louis Berman, http://adsabs.harvard.edu/full/1936MNRAS..96..890B

[207] The Extinction Law in The Orion Nebula, R. Costero, M. Peimbert

[208] A multiwavelength study of the Seyfert 1 galaxy MCG-6-30, C. S. Reynolds et al. http://adsabs.harvard.edu/abs/1997MNRAS.291..403R

[209] A three-dimensional Galactic extinction model, F. Arenou, M. Grenon, A. Gomez http://articles.adsabs.harvard.edu/full/1992A%26A...258..104A

[210] The Balmer decrement of SDSS galaxies, Brent Groves, Jarle Brinchmann, Carl Jakob Walcher http://arxiv.org/abs/1109.2597

Publications/Practica to Emission Nebula

[220] Emission Lines Identified in Planetary Nebulae, Y.P. Varshni, et al., 2006 Univ. Ottawa http://laserstars.org/ http://laserstars.org/data/nebula/identification.html

[221] Gallery of Planetary Nebula Spectra, Williams College http://www.williams.edu/astronomy/research/PN/nebulae/ http://www.williams.edu/astronomy/research/PN/nebulae/legend.php

[222] Planetarische Nebel, Frank Gieseking, 6-teilige Artikelserie, SUW 1983.

[223] Balmer Line Ratios in Planetary Nebulae, Osterbrock et al., Univ. Wisconsin 1963 http://adsabs.harvard.edu/full/1963ApJ...138...62O

[224] Complex ionized structure in the theta-2 Orionis region, J. R. Walsh, Univ. Manchester, 1981 http://articles.adsabs.harvard.edu/full/1982MNRAS.201..561W

[225] An Evaluation of the Excitation Parameter for the Central Stars of Planetary Nebulae, W. A. Reid et al, Univ. Sydney 2010 http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.3689v2.pdf

[226] Excitation Class of Nebulae – an Evolution Criterion? G. A. Gurzadyan, A.G. Egikyan, Byurakan Astrophysical Observatory 1990 http://articles.adsabs.harvard.edu/full/1991Ap%26SS.181...73G

[227] The Planetary Nebulae, J. Kaler, http://stars.astro.illinois.edu/sow/pn.html

[228] A High-Resolution Catalogue of Cometary Emission Lines, M.E. Brown et al. http://www.gps.caltech.edu/~mbrown/comet/echelle.html

[229] Optical Spectra of Supernova Remnants, Danziger, Dennefeld, Santiago de Chile 1975, http://articles.adsabs.harvard.edu/full/1976PASP...88...44D

[230] Optical and Radio Studies of SNR in the Local Group Galaxy M33, Danziger et al. 1980, ESO http://www.eso.org/sci/publications/messenger/archive/no.21-sep80/messenger-no21-7-11.pdf

http://adsabs.harvard.edu/full/1971MNRAS.153..471B

http://www.aip.de/groups/publications/schmoll.pdf

http://articles.adsabs.harvard.edu/full/1953ApJ...118..252B

http://articles.adsabs.harvard.edu/full/1955ApJ...122...89B

http://adsabs.harvard.edu/full/1969ApJ...155..859C

http://articles.adsabs.harvard.edu/full/1992A%26A...266..486S

http://adsabs.harvard.edu/full/1936MNRAS..96..890B

http://adsabs.harvard.edu/abs/1997MNRAS.291..403R

http://articles.adsabs.harvard.edu/full/1992A%26A...258..104A

http://arxiv.org/abs/1109.2597

http://laserstars.org/

http://laserstars.org/data/nebula/identification.html

http://www.williams.edu/astronomy/research/PN/nebulae/

http://www.williams.edu/astronomy/research/PN/nebulae/legend.php

http://adsabs.harvard.edu/full/1963ApJ...138...62O

http://articles.adsabs.harvard.edu/full/1982MNRAS.201..561W

http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.3689v2.pdf

http://articles.adsabs.harvard.edu/full/1991Ap%26SS.181...73G

http://stars.astro.illinois.edu/sow/pn.html

http://www.gps.caltech.edu/~mbrown/comet/echelle.html

http://articles.adsabs.harvard.edu/full/1976PASP...88...44D

http://www.eso.org/sci/publications/messenger/archive/no.21-sep80/messenger-no21-7-11.pdf


[231] Emission-line spectra of condensations in the Crab Nebula, Davidson 1979 http://adsabs.harvard.edu/abs/1979ApJ...228..179D

[237] Übungen zur Vorlesung Stellare Astronomie und Astrophysik, Konstruktion eines einfachen Modellprogramms für einen Gasnebel, H.P. Gail, W.M. Tscharnuter, Univ. Heidelberg, http://www.ita.uni-heidelberg.de/~gail/aastern/uebSS06-hii.pdf

[238] Astronomisches Praktikum, Versuchsanleitungen, Spektroskopische Diagnostik einer Emissi-onsliniengalaxie, Univ, Hamburg http://www.hs.uni-hamburg.de/usr/local/hssoft/prakt/doku/Anleitungen/Praktikum.pdf

[239] Astrophysics graduate course 25530-01 Lecture 6 and 7, Uni Basel http://phys-merger.physik.unibas.ch/~cherchneff/Site_2/Teaching_at_UniBasel.html

Publications to Calibration and Normalisation of Spectral Profiles

[300] A Method of Correcting Near-Infrared Spectra for Telluric Absorption, William D. Vacca et al http://arxiv.org/abs/astro-ph/0211255

[301] Common Methods of Stellar Spectral Analysis and their Support in VO, Petr Skoda http://arxiv.org/abs/1112.2787

[302] SISD Training Lectures in Spectroscopy - Anatomy of a Spectrum, Jeff Valenti, STSCI www.stsci.edu http://www.stsci.edu/hst/training/events/Spectroscopy/Spec02Nov09.pdf

[303] SN Factory Spectrophotometry Requirements Document, Greg Aldering http://snfactory.lbl.gov/snf/ps/flux_calib.ps

[304] ESO RA Ordered List of Spectrophotometric Standards http://www.eso.org/sci/observing/tools/standards/spectra/stanlis.html

[305] Precision Determination of Atmospheric Extinction at Optical and Near Infrared Wavelengths, David L. Burke et al. http://iopscience.iop.org/0004-637X/720/1/811

[306] Flux Calibration Issues, A J. Pickles, Caltech, 2007 http://adsabs.harvard.edu/abs/2007IAUS..241...82P

[310] A Stellar Spectral Flux Library, 1150-25000 Å. A. J. Pickles http://adsabs.harvard.edu/abs/1998PASP..110..863P http://www.stsci.edu/hst/HST_overview/documents/synphot/AppA_Catalogs5.html

[311] A Library of Stellar Spectra, G.H. Jacobi et al http://cdsarc.u-strasbg.fr/viz-bin/Cat?III/92

[312] Absolute Flux Calibrated Spectrum of Vega, L. Colina, R. Bohlin, F. Castelli www.stsci.edu

[313] Measurement of Echelle Spectrometer Spectral Response in UV, J. Rakovský et al. www.mff.cuni.cz

[314] Towards More Precise Survey Photometry for PanSTARRS and LSST: Measuring Directly the Optical Transmission Spectrum of the Atmosphere, W. Stubbs et al. http://arxiv.org/pdf/0708.1364.pdf

[315] Addressing the Photometric Calibration Challenge: Explicit Determination of the Instrumental Response and Atmospheric Response Functions, and Tying it All Together, W. Stubbs, J. L. Tonry http://arxiv.org/abs/1206.6695

[316] Toward 1% Photometry: End-to-end Calibration of Astronomical Telescopes and Detectors, W. Stubbs, J. L. Tonry http://arxiv.org/pdf/astro-ph/0604285v1.pdf

Spectrographs and Cameras:

[400] SQUES Echelle Spektrograf, Eagleowloptics Switzerland

http://adsabs.harvard.edu/abs/1979ApJ...228..179D

http://www.ita.uni-heidelberg.de/~gail/aastern/uebSS06-hii.pdf

http://www.hs.uni-hamburg.de/usr/local/hssoft/prakt/doku/Anleitungen/Praktikum.pdf

http://phys-merger.physik.unibas.ch/~cherchneff/Site_2/Teaching_at_UniBasel.html

http://arxiv.org/abs/astro-ph/0211255


http://www.stsci.edu/

http://www.stsci.edu/hst/training/events/Spectroscopy/Spec02Nov09.pdf

http://snfactory.lbl.gov/snf/ps/flux_calib.ps

http://www.eso.org/sci/observing/tools/standards/spectra/stanlis.html

http://iopscience.iop.org/0004-637X/720/1/811

http://adsabs.harvard.edu/abs/2007IAUS..241...82P

http://adsabs.harvard.edu/abs/1998PASP..110..863P

http://www.stsci.edu/hst/HST_overview/documents/synphot/AppA_Catalogs5.html

http://cdsarc.u-strasbg.fr/viz-bin/Cat?III/92

http://www.stsci.edu/

http://www.mff.cuni.cz/

http://arxiv.org/pdf/0708.1364.pdf


http://arxiv.org/pdf/astro-ph/0604285v1.pdf


[401] DADOS Spektrograph, Baader Planetarium: http://www.baader-planetarium.de/dados/download/dados_manual_english.pdf

[402] Shelyak Instruments: http://www.shelyak.com/

[403] SBIG Spectrograph DSS-7. http://ftp.sbig.com/dss7/dss7.htm

Spectroscopic Software:

[410] IRIS and ISIS, Webpage of Christian Buil http://www.astrosurf.com/buil/

[411] Vspec: Webpage of Valerie Désnoux http://astrosurf.com/vdesnoux/

[412] RSpec: Webpage of Tom Field http://www.rspec-astro.com/

[413] SpectroTools: Freeware program by Peter Schlatter for the extraction of the H2O Lines http://www.peterschlatter.ch/SpectroTools/

[414] MIDAS, ESO http://www.eso.org/sci/software/esomidas//

[415] IRAF, NOAO, http://iraf.noao.edu

General Astro-Info, Forums and Homepages:

[430] Verein Astroinfo, Service für astronomische Informationen www.astronomie.info

[431] Lexikon Astronomie Wissen, Andreas Müller, TU München http://www.wissenschaft-online.de/astrowissen/

[440] SAG: http://www.astronomie.info/forum/spektroskopie.php

[441] VdS: http://spektroskopie.fg-vds.de/

[480] Regulus Astronomy Education, John Blackwell http://regulusastro.com/blog/?page_id=2

[481] Robin Leadbeater's observatory http://www.threehillsobservatory.co.uk/

http://www.baader-planetarium.de/dados/download/dados_manual_english.pdf

http://www.shelyak.com/

http://ftp.sbig.com/dss7/dss7.htm

http://www.astrosurf.com/buil/

http://astrosurf.com/vdesnoux/

http://www.rspec-astro.com/

http://www.peterschlatter.ch/SpectroTools/

http://www.eso.org/sci/software/esomidas/

http://iraf.noao.edu/

http://www.astronomie.info/

http://www.wissenschaft-online.de/astrowissen/

http://www.astronomie.info/forum/spektroskopie.php

http://spektroskopie.fg-vds.de/

http://regulusastro.com/blog/?page_id=2

http://www.threehillsobservatory.co.uk/

analysis of astronomical spectroscopy

Documents

absorption spectrum

emission spectrum

absorption band spectrum

continuous spectrum

composite spectrum

photons messengers

continuum level

pseudo continuum