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Observational Astronomy Photometry...........................................................................................................................2

Magnitude system............................................................................................................2 Observing procedure........................................................................................................3

Relation magnitude-flux ..............................................................................................4 Atmospheric extinction correction ..............................................................................6 Transforming to standard system.................................................................................6

Photometric System.........................................................................................................7 UBV system.................................................................................................................7

Morgan-Keenan spectral classification system .............................................................10 Second parameter of MK system: luminosity classes ...............................................11 Relationship between color indices and absolute magnitude ....................................13

Effect of reddening ........................................................................................................14 Absolute calibration.......................................................................................................16 Other systems.................................................................................................................17

Strömgren system.......................................................................................................17 Narrow band filters ....................................................................................................19

Practical case .................................................................................................................20 Calculation of instrumental magnitudes and colors...................................................20 Extinction correction .................................................................................................20 First order extinction..................................................................................................21 Second order extinction.............................................................................................21 Zero point values .......................................................................................................22 Transformation coefficients .......................................................................................22

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Photometry

Magnitude system Based on human eye ⇒ non linear response to light – eye suppress difference in brightness Pogson scale (Pogson N. R. 1856): redefine magnitude scale so that a difference of 5 magnitudes ⇒ 100 in variation of flux Light flux ratios: 1 magnitude difference: 1 5100 or 2 510 or 2.512

2 magnitudes difference: ( )22 510

3 magnitudes difference: ( )32 510

( ) 2 12 51 2 10

m mf f

−= or 1 2 1 22.5logm m f f− = −

To make system consistent with old: Adebaran and Altair have magnitude 1.0 First photometer (19th century - Zöllner): light from artificial star adjusted to same brightness as object measured – error 0.1 magnitude Photography (1850’s – Bond et al. at Harvard): photographic magnitudes sensible to blue part of spectrum – visual magnitudes sensible to yellow-green part Photovisual = panchromatic photographic plates – obtained using yellow filters Ex. North Polar Sequence (NPS) or International System Mount Wilson Observatory: 139 secondary standards – as faint as 19 magnitudes – but not accurate because of non linearity of photographic plates Advantage of photographic plates = multiplexing = 1000 of images recorded at the same time 1800’s – photoelectric method:

• based on photoconductive cells: change resistance upon exposure to light • low sensitivity + narrow spectral response • not commercially made

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Photoelectric cell (1911)

• work at high voltage (300V) • linear • not available commercially until 1930 • limited of sensitivity 7 magnitudes

Photoelectric photometer 1920- 1930 Photon multiplier (1930): photocell + cascade secondary electrons ⇒noiseless amplification RCA 931 photomultiplier (before WWII) + RCA 1P21 (after WWII) Kron 11th magnitude stars measured on Lick 36 inch Photoelectric magnitudes ⇒ new magnitude system

• Based on choice of filters • Various standard stars

Late 1990’s : Charge Coupled Device (CCD) revolutionize astrometry

• Linear and digital • High sensitivity over large wavelength range • Commercially available ⇒ increasing quality and lowering price

Observing procedure Depends on goal of project:

• Differential photometry o Most accurate technique for measuring small variations in brightness –

error 0.005 magnitude o Used for variable stars – eclipsing binary systems o Principles: target observed in sequence with second stars (same brightness

+ color within 1o of target ⇒ extinction correction not necessary) o Changes in magnitude observed as difference between target and

comparison star o Usually use second comparison star for check

• Absolute photometry o general + demanding on time and quality of sky o numerous target in different region of sky ⇒ extinction correction

important o set of stars for extinction

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o set of stars for transformation coefficients

Relation magnitude-flux

1 2 1 22.5log 2.5logm m f f= − + Choosing stars 2 with zero magnitudes:

2.5logm q fλ λ λ= − Where fλ refer to observed flux convolved with:

• extinction + scattering due to atmosphere • departure of detecting instrument from ideal one

Two sources of extinction:

1. Interstellar = dust 2. Atmosphere ⇒UV mostly absorbed + scattering of light in blue

Response of telescope:

• Variation in coating + dust + quality • Lens in optical path or filters (no two filters alike)

No two observations measure the same flux ⇒ calibration process necessary to homogenize observations If *Fλ is the actual flux out of atmosphere, the measure flux Fλ :

( ) ( ) ( ) ( )0

A T F DF F dλ λλ λ λ λ λ∞ ∗= Φ Φ Φ Φ∫

AΦ : Fractional transmission of atmosphere

TΦ : Fractional transmission of telescope

FΦ : Fractional transmission of filters

DΦ : Fractional transmission of detector Expression can be very complicated and many factors are usually poorly known ⇒absolute calibration very difficult

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Magnitude scheme requires only that certain stars be defined to have magnitudes so that magnitudes of other stars can be determined from observed fluxes corrected for atmospheric absorption Remaining problems = Telescope + filters + detector

• set of standard stars ⇒ allows to determine transformation coefficients to transform instrumental magnitude into common standard system

Recorded quantity dλ is proportional to observed flux: F kdλ λ= [ ] 1 1counts s electrons s =ADU*GAINdλ

− −= = , where ADU is Analog to Digital Unit

and GAIN is the ratio electrons ADU (depends on CCD)

2.5log 2.5log 2.5logm q k f q fλ λ λ λ λ′= − − = − Where qλ′ is the instrumental zero point constant and mλ the instrumental magnitude Color index:

1 2 1 2 1 22.5log 2.5logm m q q d dλ λ λ λ λ λ′ ′− = − − + or 1 2 12 1 22.5logm m q d dλ λ λ λ λ− = −

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Atmospheric extinction correction Amount of light lost depends on height of stars above the horizon + wavelength of observation + atmospheric conditions Correction: 0m m k k c Xλ λ λ λ ′ ′′= − + Where kλ′ : principal extension coefficient kλ′′ : second order extinction coefficient c : observed color index X : airmass

secX z= where z is the zenith distance ( )90 altitude−o

Corrected color index: 0 c cc c k X k Xc′ ′′= − − Where kλ′ , kλ′′ , ck ′ and ck ′′ are determined observationally

Transforming to standard system Defined by set of standard stars (particular filter + detectors) Standard stars ⇒allows determining transformation from instrumental to standard system

0m m Cλ λ λ λβ γ= + + C : Standard color index

λβ : Color coefficient

λγ : zero point constant of instrument

0 cC cδ γ= +

0c : Observed color index δ : Color coefficient

cγ : Zero point constant

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Photometric System Defined by specifying Detector + filters + standard stars Wide band system: filters width ~ 900Å - Ex. UBV Intermediate filters: filters width ~ 200Å – Ex. Strömgren Narrow-band filters: filters width ~ 30Å – Ex. Hα or Hβ

• yields very specific information • needs large aperture telescope

UBV system Established by H. L. Johnson & W. W.Morgan

1. Photoelectric system yielding comparable results as yellow + blue magnitudes of International System

2. Third color for better discrimination of stellar attributes 3. Consistent to Morgan-Keenan (MK) spectral classification

Developed around RCA 1P21 photomultiplier tube + 3 broad filters = VBU

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V filter

• Peak at 5500Å • Magnitude almost identical to IS • Cutoff produced by RCA 1P21

B filter

• Peak at 4300Å – most of sensitivity range of 1P21 • Corresponds well with earlier blue photographic magnitudes • B + blocking UV filter ⇒not affected by Balmer discontinuity

U filter

• Peak at 3500Å • Red-leak ⇒ transmit light in NIR

o must be block or measured + subtracted • Cutoff set by earth’s atmosphere

o Depends on altitude of observatory + atmosphere condition (UV transmittance)

UBV standards

• Measured by Johnson’s original photometer without any transformation • Instrumental system of this photometer • Zero points of (B-V) and (U-B) defined by 6 A0V stars: α Lyr, γ UMA, 109 Vir,

α Crb, γ Oph, HR 3314 ⇒ average (B-V) = (U-B) = 0 • 10 primary standards + secondary standards + 3 open clusters

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UBV transformation equations Magnitudes: 2.5log vv d= −

2.5log bb d= − 2.5log uu d= −

Colors: ( ) 2.5log b vb v d d− = −

( ) 2.5log u bu b d d− =− Correction for atmosphere:

0 vv v k X′= −

( ) ( )( )01 bv bvb v b v k X k X′′ ′− = − − −

( ) ( )0 ubu b u b k X′− = − −

Where 0ubk ′′ = and vk ′ very small Transformations

( )0 vV v B Vε ζ= + − +

( ) ( )0 bvB V b vµ ζ− = − +

( ) ( )0 ubU B u bψ ζ− = − +

Where

, , ε µ ψ = transformation coefficients , , v bv ubζ ζ ζ = zero point constants

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Morgan-Keenan spectral classification system 1920s Harvard College Observatory § Henry Draper Catalog ~ 400 000 stellar spectra § Classification based on decreasing strength of hydrogen lines ( )A P→ § Groups dropped because of poor quality of spectra or because no logical sequence § Remaining groups: OBAFGKM from Early → Late § Higher quality ⇒10 subclasses 0-9, Ex. Sun G2, Vega A0 § Spectral sequence corresponds to surface temperature

Because of Balmer discontinuity, bvk ′′ and uvk ′′ do not vary smoothly with spectral type ⇒ to avoid correction defined to be zero ⇒error of 0.03 in U-B

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Second parameter of MK system: luminosity classes Some stars show narrower absorption line for their spectra class 1914-1935 Mount Wilson Observatory ⇒order spectra by strength of absorption line § Narrower line ⇒ lower density of atmosphere § Larger atmosphere § Brighter lines

Luminosity indicator = Luminosity classes I - Supergiants II – Bright giants III – Giants IV – Subgiants V – Main sequence (dwarfs) VI – Subdwarfs Subdivision: a (brightest), ab, b (dimmest) Low density in larger stars alters percentage of ionized atom such that spectra looks earlier

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Relationship between color indices and absolute magnitude 2 steps process:

1. Measure color indices of nearby stars with accurately known parallaxes 2. since few AFG stars – fill gaps using stars in clusters (NGC 2362, Pleiades,

Praesepe) after correcting for extinction ⇒Main sequence fitting In Color-Color diagram (unredened) MS stars deviate from BB because of absorption line

• From O to A0 hydrogen increases + Balmer discontinuity ⇒U decreases and U-B increases

• After A0, Balmer lines + discontinuity weaken ⇒U-B decreases • After F5 metal lines + Molecular bands become strong ⇒ U-B increases again • Near bump F5 abnormal abundance cause stars to plot higher than normal

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Effect of reddening

Color excess: ( )E B V− and ( )E U B−

Slope of reddening line: ( )( ) ( )0.72 0.05

E U BB V

E B V− = − −−

For early stars ( )B V− nearly zero( )( ) 0.72

E U BE B V

−⇒ =−

Stars later than A0 – not possible to use CC diagram to determine intrinsic color ⇒color excess obtained by comparing colors to that of spectra

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For B0 to A0 stars: ( ) ( )0.72Q U B B V= − − −

Where ( )U B− and ( )B V− are the observed colors and Q is independent of reddening

Total absorption in the visual:

V

B V

AR

A A=

−

Where VA and BA are the absorption in magnitude in V and B , reciprocally Since 0 BB B A= + and 0 VV V A= +

( ) ( ) ( )( ) ( ) ( )

0

0

B V

B V

E B V B V B V

B A V A B V

A A

⇒ − = − − −

= + − − − − =

= −

( ) ( )VV

AR A RE B V

E B V⇒ = ⇒ = −

−

Where 3.0R ≈ for most direction in the galaxy

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Absolute calibration Convert magnitude into flux:

2.5logm q Fλ λ λ= − ( )0.410 m qF λ λλ

− −⇒ =

Ex. flux reaching earth from star with 0 3.0V =

38.52vq⇒ = −

( )0.43.0 38.52 16.61 172

W10 10 2.47 10

cm ÅVF − + − −⇒ = = ≈ ×

Total flux ⇒ multiplied by band width of filter ( 1000∼ Å):

17 142 2

W W2.47 10 1000Å 2.47 10

cm Å cmVF − −⇒ × × ≈ ×;

Total power: 2

V V telP F Rπ= ⋅

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Other systems

Strömgren system Defined based on intermediate width filters Totally filter defined (no cutoff due to detector)

y :

• matches visual or V • no strong spectral features in early- type stars

b :

• 300Å to the red of B • Reduces effect of line blanketing • Since for types later than A0, metal absorptions become strong ⇒ Temperature

indicator; strong in later types For early type stars, b and y are free of blanketing. In later type both are affected by the same amount. v :

• Centered in region of strong line blanketing • but longwards of Balmer’s crowding

u :

• measure line blanketing + Balmer discontinuity • not affected by atmospheric condition

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Since the system is filter defined ⇒ no second order color term in extinction correction ( )b y− : Good indicator of color and temperature ( )v b− : affected by blanketing Metal index: ( ) ( )1m v b b y= − − −

• Measures the strength of line blanketing • In absence of line blanketing 1 0m ≈

( ) ( ) ( )1 2c u v v b u v b= − − − = − +

• Measures continuum slope affected by Balmer discontinuity • Subtracting 2v cancels effect of line blanketing • Measure Balmer discontinuity

Drawback of the system: faint stars difficult to measure ⇒ large aperture telescope

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Narrow band filters Narrow width filters centered on spectral features Ex. Hα , H β or [ ] 5007OIII λ , [ ] 6717,6739SII λλ Measures the strength of these features ⇒ related to star formation rate, age of stellar population or level ionization and density At least wo filters needed:

• Centered on the line • Centered on nearby continuum

Drawback: need large aperture telescope

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Practical case

Calculation of instrumental magnitudes and colors

2.5logv vv c d= −

2.5log bbv

v

db v c

d− = −

2.5log uub

b

du b c

d− = −

Where the constants are arbitrarily

IMPORTANT: [ ] ( )count GAIN

e ed ADU

s s ADU

− − = = ⋅

Extinction correction More than 30o above the horizon ( )60z < o ⇒ plane parallel model 0.2%±

Airmass: secX z= Where [ ] 1

sec sin sin cos cos cosz Hϑ δ ϑ δ−

= + Where: ϑ : Latitude of observatory δ : Declination of target H : Hour angle in degrees For zenith distance 60z > o :

[ ] [ ] [ ]2 3sec 0.0018167 sec 1 0.002875 sec 1 0.0008083 sec 1X z z z z= − − − − − −

Ex. for an object 10o above the horizon, airmass 6.8∼

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First order extinction

0 vv v k X′= −

( ) ( )0 bvb v b v k X′− = − −

( ) ( )0 ubu b u b k X′− = − −

Where [ ] magnitudek

airmass′ =

The value of the extinction coefficient is found by observing 1 or more standard stars through changing airmass and plotting the color index or magnitude vs X The slope = extinction coefficient Intercept = color index

0vv k X v′= +

( ) ( )0bvb v k X b v′− = + −

( ) ( )0ubu b k X u b′− = + −

Second order extinction

( )v v vk k k b v′ ′ ′′→ + − and ( )bv bv bvk k k b v′ ′ ′′→ + −

( )0 v vv v k k b v X′ ′′= − + − and ( ) ( ) ( )0 bv bvb v b v k k b v X′ ′′− = − − + −

Solve the equations observing close pairs with different colors (but airmass is the same)

( ) ( )01 02 1 21 2v v v vv v v k k b v X v k k b v X′ ′′ ′ ′′ − = − + − − − + −

( )

( )0

0

v

v

v v k b v X

v k b v X v

′′⇒ ∆ = ∆ − ∆ −

′′⇒ ∆ = ∆ − + ∆

And ( ) ( ) ( )0bvb v k b v X b v′′∆ − = ∆ − + ∆ − In practice vk ′′ very small and bvk ′′ is stable (only need to determine it once)

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Zero point values

( ) 0 vV B V vε ζ= − + + ( )0v V v B Vζ ε⇒ = − − −

( ) ( )0 bvB V b vµ ζ− = − + ( ) ( )0bv B V b vζ µ⇒ = − − −

( ) ( )0 ubU B u bψ ζ− = − + ( ) ( )0ub U B u bζ ψ⇒ = − − − Zero points = standard values – transformed values (corrected for extinction) One as to solve equation for each standard and take the mean Zero points must be determined nightly

Transformation coefficients Determined by measuring several stars whose magnitudes and colors are known Since ( )0 vV v B Vε ζ− = − + a plot of ( )0V v− vs ( )B V− yields the slope ε For the color terms:

( ) ( ) ( )0

11 bvB V b v B V

ζµ µ

− − − = − − +

Plot of left side vs ( )B V− yields a slope related to µ

( ) ( ) ( )0

11 ubU B u b U B

ζψ ψ

− − − = − − +

Plot of left side vs ( )U B− yields a slope related to ψ