hsc physics astrophysics notes

8/10/2019 HSC Physics Astrophysics Notes

1/26

1

HSC Physics Summary

Ben 2010-present UNIT #4: Astrophysics

NOTE: Elements, graphics and diagrams used in this summary have been gathered from websites such as Google to

produce a better quality summary for purely personal educational purposes. All copyright rights and responsibilities of

phrases/graphics/diagrams belong to their respective owners.

Definitions

Annual Parallax

A change in apparent position of a nearby star (angle) with

respect to distant stars as the observers position changes.

The diameter of Earths elliptical orbit is used as the base

line for determining the annual parallax of a star. The

annual parallax of a nearby star (


2/26

2

Parallax Angle (p)

HALF the corresponding angle

subtending at a star when the star is

viewed on two different paths from

earth (6 months apart.) The angle is

measured from the perpendicular to

the sight path:

*logically, the smaller the parallax

angle, the further away the star (pc)

Nearby Star A star less than 300 light years away.

Parsec (pc)

The distance that a star would have to be placed away from

earth in order subtend a parallax angle of 1when lines are

drawn from either side of a 1AU base line (e.g. avg. radius

of earths orbit around the sun)

1pc = 3.26 ly

Light-Year (ly)

The DISTANCEtravelled by light in one year

1 ly = 9.5x1015 m

Astronomical Unit

(AU)

Average distance between the sun & earth (orbital radius)

1 AU = 1.496x108

km

1AU = 1.496x1011

m

63 000 AU = 1 ly

Limitations of

TrigonometricParallax

Distant stars have an angle too small to be measured

(smallest measurable angle is approx. p=0.01)

The Atmosphere blurs images, making angle harder tomeasure (only stars


3/26

3

1.Telescopes

Electromagnetic

Spectrum

All forms of EMR make up the Electromagnetic Spectrum

All EMR travels at the same speed, c (speed of light), while

different forms of EMR possess different amounts of energy

due to their different frequencies.Visible Light

EMR with a wavelength between 350-700nm (x10-9

m)

Blue Light (400nm) high freq. / Red Light (700nm) is low

Resolution

The ability of a telescope to distinguish between two

objects that are close together (e.g. sharpness.) Resolution

is described in terms of the smallest angle between two

points at which the telescope still represents the stars as

two distinct figures. For most large astronomical telescopes

have a limit of resolution of 1 arc minute, meaning that iftwo stars subtended an angle of 1 with the telescope, the

telescope will represent the stars are two distinct, separate

stars. (Any angle smaller than the limit of resolution and

the two stars will appear as one blurred mass.)

Resolution depends upon the diameter of the lens/mirror

and the wavelength of the incident light.

Telescopes with poor resolution blur the apparent

boundaries between two close stars making them appear

as one. High-resolution telescopes produce sharp images in

which the two close stars appear distinct and separate.

Diffraction and resolution problems are worse with radio

waves, as they have longer wavelengths than light waves

they are also worse for small apertures (e.g. cameras)

Smaller apertures have less resolving power (blurrier)

Two factors limit a telescopes resolution: aberrations(imperfections in the mirror/lenses) and diffraction (the

bending of light around objects and through gaps.

Sensitivity

The photon-gathering power of a telescope. The sensitivity

is dependent upon the area of the telescopes aperture.

Sensitivity is enhanced by increasing the apertures area

(thereby maximising the number of photons entering the

lens from a source) or exposing the film for a long time

(allows a sustained stream of photons to enter.) To avoid

star trails, the telescope needs to track the star being

observed over a period. Astronomers do not observe any


4/26

4

more, they take pictures, which they then observe.)

Doubling the diameter of a telescopes aperture results in

an increase of sensitivity by a factor of 4.

Diffraction

The ability of a wave to bend its path around corners and narrow

openings. Light passing through telescope apertures diffract,

resulting in an interference pattern where the stars are surroundedby rings. These interference patterns are the cause of blurriness

and the cause of resolution limits.

TwinkleTwinkling of stars is caused by changing refractive indexes of the

lights path as gusts gasses, water vapour and dust come between

the observer and the star.

Galileo and the Moon

The first telescopes were thin refracting telescopes which used lenses. Using a telescope,

Galileo made the following astronomical discoveries:

1) The moons surface is not smoothit was punctuated with craters and mountains.

Galileo sketched numerous drawings of the moons surface as seen through a

telescopehe also estimated the height of the moon mountains by looking at the

length of the shadows they cast.

2) Sun Spotsthe sun wasnt perfect but had dark blemishes or spots

3) The phases of VenusVenus had phases, just like the moon4) Jupiter has 4 moons

5) The planets, sun and moon were not perfect spheresthis revelation and that of

sun spots debunked Ptolemys theory that heavenly bodies were flawless

EMR Reaching Earth

While there are many different types of EMR approaching Earth, Earths atmosphere

particularly the ionosphere and stratospheresblock much of this harmful radiation. Thereare only 3 types of EMR that reach earths surface without being blocked.

Visible Light

Radio Waves

Milimetre Radiation (Between Radio & Infrared)

Atmospheric molecules (e.g. O3 ) are selective in the EMR frequencies that they absorb

this is due to the fact that electrons can only absorb photons of a particular frequency that

energise them sufficiently to jump to a different energy level. Most high-energy /

potentially harmful forms of EMR are blocked by atmospheric molecules. These rays


5/26

5

ionise molecules (transfer their energy to electrons) before they hit the ground. Even in

the visible light spectrum, however, CO2and water vapour cause absorption lines.

There are, however, many different types of telescopes that are designed to observe the

different types of EMR:

Radio telescopes (e.g. Australian Parkes) Microwave Telescopes (e.g. COBECosmic Background Explorer)

Infra-red Telescope (e.g. ISOInfrared Space Observer)

Visible Telescope

UV Telescope

X-ray Telescope (e.g. Chandra X-ray)

Gamma-ray Telescope (e.g. EGRET)

Note: Only Radio and Visual Telescopes are ground based, all other types are satellites,

above the atmosphere where the EMR is not blocked

Optical Telescopes

There are 2 different types of telescopes:

1) Refracting TelescopesUtilise an objective lens to bend incident parallel

light rays towards a focal point to magnify the image. After passing through a

single lens, however, the image is upside-down.

A Galilean Refracting Telescope has an additional eyepiece lensthat inverts the image

(right-way up) and enlarges it.The advantage of using refracting telescopes is that there is nothing inside the barrel to

obstruct the light. The disadvantagesof using refracting lenses are that badly ground

lenses can cause aberrations and reduce precision,

while refraction bends the different colours of light

at different anglesresulting in a discoloured image.

2)Reflecting telescopesHave a parabolic mirror at the bottom of the barrel

that focuses the light onto a plane mirror, into which the observer looks from

a side-mounted eyepiece lens.

*Note: Larger, fatter lenses will have a

smaller focal length and will produce the

greatest magnification.


6/26

6

Problems with Ground-based Astronomy

1)Atmospheric Absorption Certain types of EMR are absorbed by molecules

(ionisation) as they pass through earths atmosphere. (e.g. UV rays) Only

radio and optical telescopes are used, as Visual Light and Radio waves are the

only EMR that reach Earths surface. Optical telescopes are placed on

highestmountains to minimise the amount of light absorbed on its journey

through the atmosphere.

2)Atmospheric Distortion Twinkling of stars is caused by atmospheric

turbulence as the light passes through migrating atmospheric cells(layers of

gases and water vapour) with different refractive indexes. Light from the star

is refracted and scattered while passing through these different mediums. To

overcome atmospheric distortion, optical telescopes are built on mountain

tops, where there is less weather fluctuation. Adaptive Optics are also

utilised to minimise atmospheric distortion.

Unlike optical telescopes, radio telescopes are largely unaffected by

atmospheric cells they can see through clouds. However, optical

telescopes are better at resolving images than Radio telescopes because

light has a shorter wavelength(similar to use of x-rays to determine lattice.)3)Gravity While building bigger telescopes with wider apertures allow us to

achieve higher resolution images, big heavy telescopes bend and flex under

gravity, reducing the precision and accuracy of astronomical measurements.

Adaptive Optics

A highly sensitive computerised system that is used to

minimise atmospheric distortion caused by atmospheric

cells. High speed cameras continuously sample light from a

nearby reference star, recognising any distortions. It then

compensatesfor these detected distortions by making tiny

(x10-8

m) adjustments to hexagonal mirror plates. This

measuring/adjusting occurs rapidly up to 1000times/sec.

Active Optics

Active optics are utilised to counter the issue of a large,

thick mirror flexing or distorting under gravity. Instead a

series of tesselating hexagonal mirror plates, each

possessing mechanical manoeuvrability, are utilised. Thisallows the concavity of the mirror to be alteredit is more

lightweight and greater aperture areas can be reached.


7/26

7

Interferometry

Technique that involves linking two distinct telescopes

together so that they act as a single aperture. Does not

increase sensitivity, but improves resolution dramatically,

as there are two or multiple vantage points from which the

star is viewed fromall calibrated and synchronised using

computers to attain a greater depth with the images.Hawaiis Kek 1 and 2 telescopes are linked to achieve a

higher resolution. Mexicos Very Large Array (VLR)is a field

of satellites.

2.Parallax

See definitions for Parallax, Parsec, Light-Year

3.Spectroscopy

Emission

Spectrum

May be either continuous or line/band spectra. Line Emission

Spectra is obtained when an element is excited by heating it to

incandescence. The electrons in the atoms jump to higher energy

levels, and re-radiate the energy they posses as they fall to the

ground state at particular discrete frequencies, according to how far

they fall through the shells. Viewing this emission through aspectroscope reveals the a pattern of coloured lines on a black

background, revealing the particular frequencies emitted by the

atoms, which are indicative of that atoms nature (i.e. whether it has

the fingerprint of hydrogen or helium)

Absorbtion

Spectrum

A series of dark bands on a coloured background. These bands

correspond to the frequencies that the atoms absorbed as the

energy passed through them, and are indicative of the jump made

by the electrons up through the energy shells. Each element absorbs

its own unique set of frequencies, which are the same frequenciesthat it will produce in an emission spectrum.

Absorption occurs in a hydrogen atom when the electron absorbs an

incoming photon of discrete energy that allows it to jump to a

higher energy shell. Though the electron falls to its ground state

almost instantly, the atoms spherical shape means that the energy

is re-radiated in all directions, meaning that the light of that

particular frequency has a significantly less intensity than the other

frequencies, and hence appears as a darker gap, relative to the

incident light.

SpectroscopyThe analysis of an objects spectra particularly that of a starto

determine its chemical composition. The absorption spectrum of a


8/26

8

star can be compared to the absorption spectrum of known

elements using correlation methods to ascertain the composition of

the star. From analysing a stars spectrum we can determine its:

1) Surface Temperature

2) Speed of Approach / Retreat (Doppler Effect)

3) Density4) Chemical Composition

Spectroscopy has made numerous contributions to

astronomy including:1) Identification of elements in the atmosphere of stars and

galaxies

2) Detection of invisible astrometric binary partners due to

recognition of the Doppler shift

3) Detection of the expansion of the universe

4)Discovery of the helium in the sun before it was discovered onEarth.

Spectroscope

(Spectrometer)

A device used to illustrate the visual spectrum of a star for

the observer, using either a prism or diffraction grating.

Bohrs Model

Used to explain spectra emission. When an atomic of hydrogen is

excited by an incoming photon of energy, the electron is energised

and jumps to a higher energy level. The electron then (almost

immediately) falls back to its ground state, releasing the energy it

absorbed as a discrete photon of energy of a particular frequency,corresponding to a particular wavelength or colour. The falling

electron only emits frequencies that correspond to how far it falls

through the energy shells. Because this happens many times per

second with many billions of atoms, it is assumed that the electrons

fall down in every possible arrangement through the energy levels,

so that a number of different discrete frequencies are released.

Spectrograph Instrument used to photograph a spectrum.

Spectrogram A visual photographic image of a spectrum.Collimated Made into a parallel beam (within spectroscopy)

Quasara.k.a. Quasi-stellar radio source/ Galactic Nucleus -- Distant starlike

source that exhibit strong red-shifts. They emit enormous amounts

of energyespecially radio waves.

Emission Spectra

As an object is heated, it changes colour from red, orange, yellow, blue and eventually

white. When viewed through a spectroscope, a continuous spectrum is seen, illustrating all

of the colours in a smooth gradient. As Plancks black body curves show, each object

radiates all of the frequencies in different proportions, according to its heat and

irrespective of its composition.


9/26

9

Absorbtion Spectra (See Definition)

Spectrometers are devices used to visually observe spectra.

There are two types of spectroscopes: Prismand Diffraction Telescopes--

1) Prism Spectroscopes - light from a source passes through a slight and collimated. The

light is the dispersed by a prism, each frequency being refracted by a different amount

(e.g. red bends more than blue)Another lens focuses the coloured pattern onto a

detector or screen (e.g. photographic plate) appearing as a gradient of colours

transitioning from red to blue dark absorption bands become visible where light of

particular frequencies have been absorbed by atoms during the lights journey:

One ERROR associated with prism spectroscopes is that they absorb some of the

radiation. The glassof the prism, for example, absorbs ultraviolet and infrared

frequencies.

2)Diffraction SpectroscopeLight from a source passes through a collimatorbefore

striking a reflection gratingthat dispersesand focuses one particular frequencyof light

into a photomultiplier. The grating can be rotated to allow the observation of each

individual frequency discretely.

Alternatively, a transmission grating is used to slightly diffract the collimated light

passing through it, so that only a very narrow frequency band strikes the photomultiplier

at any one time. The grating can again be rotated to allow the observer to examine the

intensities of different frequencies. Numerous miniature slits in the diffraction grating

cause interference between the light causes the different wavelengths to spread out into

a spectrum.

Diffraction gratings have better resolving power than Prisms


10/26

10

Stellar Spectra

Astronomical Spectra can be produced from 4 main sources:

1) Stars A stars spectra is directly related to its surface temperature, according to

Plancks black body radiation curves. The spectrum of a star is an absorption

spectrum, which reveals what elements are surrounding the immediate atmosphere

of the star that the EMR has to pass through.

2) Emission NebulaeThe heat and light energy emitted by a protostar core strikes the

atoms that are within a nebula cloud (mostly hydrogen, nitrogen and oxygen) causing

them to become excited and emit energy of a particular frequency resulting in the

acquirement of an emission spectrum of the gasses surrounding a protostar.

3) Galaxy SpectraSpectrometers gather a blend of different spectrafrom galaxies, as

they are composed of stars, planets, nebula and quasars. Most galaxies exhibit red-shift, indicating their movement away from our planet. Galaxy spectra have

absorbtion bands that indicate the presence of molecular hydrogen, nitrogen,

carbonand silicon, as well as other forms of EMR from the entire spectrum radio

wavesand infraredin particular.

4) Quasars Stellar objects that emit massive amounts of all types of spectra (radio

waves, x-rays, light) This allegedly occurs when gas is being swallowed by a black

hole, the gravitational energy being converted to kinetic.

Key Features of Stellar Spectra

A stellar spectrum is the spectrum of EMR emitted by a star. The stars surface temperature

determines the spectral pattern formedhydrogen absorption lines are the dominant type

observed, while calcium and sodium may also be observed. The type of EMR and hence

spectrum produced by a star, however, is independent of its composition. It depends

entirely upon the surface temperature of the star.

To produce a line in the visible spectrum, an electron must be in the 2ndenergy level when

it absorbs a photon. Too little energy (low surface temperature) equates to weaker

absorption lines (less electrons are excited sufficiently to absorb the photons.) Too much

energy will ionise the atoms, stripping their electrons and no absorption lines will be visible.

To produce HYDROGEN absorption lines, the stars temperature must be 4 000K-12 000K

To produce HYDROGEN absorption lines, the stars temperature must be 15000K30000K

The strongest intensity emission from a star will peak in the frequency that corresponds to

the blackbody curve associated with its surface temperature.


11/26

11

From observing the strength (boldness) of the Hydrogen absorption lines, we can ascertain

a stars surface temperature and assign it a spectral classa letter from O, B, A, F, G, K, M.

Each class has 10 divisions (e.g. F4, G5, K9). This can be determined by comparing the stars

emission intensity in each frequency band with other stars of known spectral classor by

comparing the emission intensity to a black body curve and observing in what frequency

the stars emission spectra peaks.

Spectral Class ColourSurface

Temperature (K)Spectral Features

O Blue 30 000

Strong lines of ionised helium.

Doubly Ionised Oxygen, Nitrogen &

Carbon lines

Ionised He, Weak H

B Blue-white 15 000

Neutral Helium lines more

prominent. Hydrogen linesstronger than on O class.

Neutral He, Weak H

A White 10 000H-lines most prominent. Ionised

Mg, Si, Fe, Ca appear

Strong H

F White-yellow 7000H-lines are weaker than A class

neutral metals are stronger

Weak H, metals (Ca, Fe)

G Yellow 5000

Lines of ionised calcium are

strongest feature. H-lines are weak.

Lines of many neutral metallic ions

present.

Strong Metals (Ca)

K Orange 4000

Neutral metal lines most

prominent. H-lines virtually non-

existent.

Strong metals (CH and CN)

M Red 3000

Molecular bands are most

prominent. Titanium oxide bands

are very prominent.

Strong molecules (TiO)


12/26

12

What Spectra Reveals about a Star

1) Structure Emission lines indicate that the stars emission is proceeding unimpeded;

Absorption lines indicate that the star is surrounded by gas that absorbs the EMR.

2) Chemical CompositionComparing stellar spectra with spectra of elements on Earth

with known spectral lines correlating the 2 spectral patterns to determine what

elements are present.

3) Rotational / Translational VelocityThe observance of red-shift / blue-shift of a stars

spectral pattern indicates the motion of the star away from / towards Earth. The

displacement of the line from its regular position is an indication of the speed at which

the star is moving away from / toward earth (i.e. greater red-shift means moving away

faster.) The rotational velocity of a star can be determined by pointing a spectrometer

at the approaching or receding end of a star as it spins, and observing the degree to

which red/blue shift occurs. The stars period and hence speed can then be calculated.4) DensityUnder the influence of gravity, atoms possess more energy due to the extra

density and gravitational pull of a nearby star. Undisturbed, the atom absorbs emission

as per usual. Dwarf stars, with high density, produce broad absorption lines;

supergiants with less dense atmospheres produce narrow absorption lines.

5) Surface Temperature According to Plancks black body curves, there is a direct link

between the colour of a star and its surface temperature. The dominant wavelength

emitted by a star indicates the stars temperature.

Typical Astronomical Spectra

Starsproduce continuous spectra with superimposed absorption lines (appear as divets)

Doppler shift may be identifiablestars are capable of receding from / approaching Earth.

Emission NebulaeReleases light as a dominant frequency almost always characteristic

pink of hydrogen and orange-yellow glow of helium. Gas cloud EMISSIONenergy of specific

frequency according to the elements present (most hydrogen & helium.) Little Doppler

effect is observableNebulae rarely move.

Galaxies Continuous spectrum of superimposed ABSORBTION lines of NUMEROUS

elements from different types of stars. Doppler effect is evident galaxies show great red

shift because they are receding from earth a great rate (universe is expanding.) There are a

few spikes corresponding to the most abundant elements in the galaxy (hydrogen, helium.)

QuasarsEnormous amounts of EMR EMISSIONin all spectrums. Very large Doppler shifts

very far away and moving away at a fast rate. Large emission spikes occur usuallyhydrogen excited by enormous energy release from the quasar.


13/26

13

Practical: Using a hand-held Spectroscope

AIM: To observe the spectra of sunlight and that of a sodium vapour lamp using

a hand-held spectroscope.

SAFETY: Do not look directly at the sun- to measure sunlight just look outside

METHOD:

1.Point the hand-held spectroscope outside and look into the lens. A bright

continuous spectra should be observed, showing colours from red to blue.

2.Next, point the spectroscope at a sodium lamp source and observe two

bright orange lines form on the spectra.

RESULTS: A continuous spectrum was visible from sunlight and two distinctly

brighter orange lines were also present in the sodium lamps spectra.

ERRORS: The room was not darkened when viewing the spectra of the sodium

lamp, meaning that other spectra were visible (sunlight was still present.)

4.Photometric Measurements (Absolute Magnitude)

Apparent

Magnitude (m)

(Apparent

Brightness)

The brightness of a star as it appears from earth.

On a magnitude scale, seeminglyBRIGHT stars are ranked

with negative values, while fainter stars are given high

positive values (e.g. ranking system 1st

100th

brightest)

Each increase of m by 1.0 corresponds to a decrease in

apparent brightness by a factor of 2.512

(e.g. m=1 is 100 times brighter than m=6)

Absolute

Magnitude (M)

(Absolute

Brightness)

A comparative measure of the amount of light a star emits

(a measure of the stars true luminosity.) The absolute

magnitude would be the apparent magnitude of the star if

all stars were placed at a distance of 10 parsecsfrom earth

so that the only factor affecting their brightness is their

size. The most negative values equate to the brightest stars.

Luminosity The amount of light energy radiated by a luminous object.The intrinsic brightness of a star. (i.e. Absolute magnitude)

Brightness RatioHow many times brighter one star is in comparison to

another star.


14/26

14

Distance modulusThe value of mM of a star (difference between apparent

and absolute brightness)

Colour Index

(BV)

Measuring the apparent magnitude in two different colours

(Blue / Yellow) allows one to find the Colour Index which is

associated with a particular spectral class (proportional to

temperature) C.I. ranges from0.6 to +2.0 (bluered)Hence C.I. may be considered a measure of a stars redness

(white stars have a C.I. = 0)

Photographic

Magnitude (B)

The magnitude of a star measured by a photographic plate

or blue filter, which is more sensitive to short-wavelength

light (400nm / more BLUE light) Blue stars hence appear

brighter (lower magnitude) upon a photographic plate.

Yellow-sensitive film is used to obtain photographic

magnitude.

Visual Magnitude

(V)

The magnitude of a star measured by the human eye or a

yellow-green filter, which is more sensitive to long-

wavelength light (550nm / yellow-green)

The brightnessratioof 2 stars is equal to 2.512 to the power of the magnitude difference:

= 2.512

m2m1

Where I1/2= brightness of star 1/2

m1/2= magnitude of star 1/2

*The ratio is an expression of how many times brighter the top star is than the bottom

star (i.e. a ratio of 1.5 means that I1is 1.5x brighter than I2) star 1 compared to star 2

The same formula can also be applied to determine the absolute magnitude ratio by

replacing m2and m1with M2and M1:

= 2.512

M2M1

Where I1/2= absolute brightness of star

M1/2= absolute magnitude of star 1/2

If a star is exactly 10 parsecs away: absolute brightness = apparent brightness

If a star is closer than 10 parsecs away, it is apparently brighter than its absolute

brightness. Since low integers equate to high brightness (numerical ranking)

apparent brightness < absolute brightness

(the star needs to be pushed away to 10pc, numerically increasing its brightness rank to its

absolute rank [e.g. from -16] )


15/26

15

If a star is further than 10 parsecs away, its apparent brightness > absolute brightness

(the star needs to be pulled closer to 10pc, decreasing its brightness value to its absolute

[e.g. brightness 6-1] )

Rearranging the formulas that are used to determine apparent and absolute brightness, we

can formulate an equation that expresses the difference in apparent and absolute

magnitude of a single star in terms of distance of the star from earth:

mM = 5 5

where m = apparent brightness of star

M = absolute brightness of star

D = distance of star from Earth in parsecs (pc)

PRACTICAL: Filters and Photometric Measurements

1. Each student provided with TWO PHOTOGRAPHS of the star cluster M67; one taken with

a YELLOW FILTER (VISUAL) and the other with a BLUE FILTER.

2. Particular stars in the cluster were labelled A-P, and a plastic overlay with a reference

scale was used to assign an apparent magnitude value to each star in each photograph

3. This data was tabulated in a table similar to that below:

STAR BLUE MAGNITUDE (B) VISUAL MAGNITUDE (V) COLOUR INDEX (B-V)

A

4. The results were then graphed with Visual Magnitude (V) on the vertical axis and Colour

Index (B-V) on the horizontal Axis.

Photoelectric Photometry vs. Photographic Photometry

Photometry is a method by which the brightness of a star is ascertained. An

apparent luminosity value or rank can be assigned to each star using two

methods (though the latter is more accurate):

Photographic

Photometry

A measurement of the apparent luminosity of a star based

upon visual comparisons of star images on photographic

plates.

This method is less accuratebecause there is an element of

error when determining visually from an image. The stars

brightness also cannot be calibrated, because of the

complex size/density-brightness relationship.


16/26

16

Photoelectric

Photometry(Photoelectric effectto calculate the

apparent magnitude)

Light from a star is captured by a photomultiplier, that

converts the weak light signal into a strong electric current.

Photons of light enter through a thin glass window into an

excavated tube, striking a photocathode. Photoelectrons

are emitted as per the photoelectric affect and an applied

voltage accelerates the photoelectrons downphotomultiplier, bouncing off dynodes as it goes. The

output pulse is a measurable current proportional to the

light input.

The fast response and proportional nature of the current

makes it an effective detector of starlight.

(e.g. Accuracy + Sensitivity)

5.Binary Stars

Binary StarA stellar system in which two stars orbit around each other.

(e.g. Alpha Centauri)

There are 4 types of Binary Stars:

Visual Binary Two stars that can be resolved with the naked eye orthrough the use of a telescope.

Astrometric

Binary

A star that appears to regularly wobble the star has an

invisible partner that is exerting a gravitational pull upon

the star, causing it to wobble about its centre of mass.

Used as evidence for black holes.

Spectroscopic

Binary

These stars cannot be resolved visually. Using a

spectroscope, such binary stars demonstrate red shift

(moving away) or blue shift (moving closer) as per the

Doppler effect. (This is because the star in orbit is moving awayfrom us or towards us, and its spectral lines hence appear shifted to

either the red or blue end of the spectrum. This can only be

observed when the star is moving away or towards the observer,

not when the star is moving across the observers vision.) The star

needs to be observed over a sustained periodso that the

shifting can be confirmed as occurring at regular intervals.

(The size of the gap between a spectral lines normal and

red shifted position indicates the speed at which the star is

moving away.)


17/26

17

Eclipsing Binary

When the orbital plane of the binary system is edge-on, the

observer will observe changes in light intensity as one of

the stars eclipses the other. This is only considered in the

context of visual binaries. When the light intensity of the

star is plotted as a function of time, the intensity is at its

maximum as both stars are visible, then decreases greatlyas the brightest star eclipses the other. Then full brightness

is restored before brightness decreases slightly when the

brighter star partially eclipses the other.

(Square dips in the graph indicate that the system is

completely edge-on and total eclipses are occurring.

Curved dips indicate partial eclipses when the orbiting

system both stars are at least partially visible at all times.)

Importance of Binary Stars for Determining Stellar Masses

Astronomers need to determine the mass of a star to better understand its spectral class

and chemical composition. Because binary systems are held together by gravity, which acts

a centripetal force towards a common centre of mass, the mass of a binary system can be

calculated if the orbital period and distance of separation is known. This is because the

stars within a binary system have to obey Keplers 3rd

Law:

=


18/26

18

Rearranging this formula, and splitting the total mass of the system (M) into m1+ m2

M = m1+ m2=

Where r is STAR SEPARATION (metres between stars 1 and 2)

m1/2is the mass of star (kg)

M is the total mass of the system (kg)

T is the orbital period of the binary second (seconds)

Employing these calculations, however, lend themselves to numerous errors:

Simplified formula to assume perfectly circular orbit (orbit is actually elliptical) Measurements do not have a great degree of accuracy (only calculates powers of 10)

Variable Star

A star thats brightness alters periodically over time due to

the influence of an internal factor (intrinsic) or external

factor (extrinsic)

Intrinsic Variable

A star that displays regular or irregular changes in

brightness due to some change within itself.

(e.g. Nova, chemical composition, pulsating star)

Extrinsic Variable

A star with varying brightness caused by some external

factor (e.g. astrometric binary wobble due to invisible

partner)

Periodic

Variable star whose brightness alters in a regular, repeated

pattern over time. Cepheids are examples of periodic

intrinsic variables that have varying luminosity as they

expand and contract in a regular pattern due to their own

gravitational and chemical forces. Most extrinsic variables

occur periodically.

Non-periodic

The brightness of non-periodic variables alters irregularly

with time. Nova and supernova are examples they are

eruptive variables that exhibit no regular pattern in their

varying brightness as they collapse.


19/26

19

Cepeid Variables are intrinsic, periodic variables that have varying luminosity

as they expand and contract in a regular pattern due to their own gravitational

and chemical forces. This regular change in brightness is due to the changing

surface temperature of the star, which becomes hotter as it contracts (denser =

more kinetic energy) and cooler as it expands (bigger = more gravity.)

The period of a Cepheid variable is related to its average luminosity (period-

luminosity relationship) Cepheids with a longer period (60 days max) are more

luminous (i.e. lower luminosity value) than those with shorter periods (2 days

min) Many Cepheids are present in the Small and Large Magellanic Clouds.

This means that the luminosity of a star can be ascertained if the stars period of

variation (the time taken in seconds for the brightness pattern to perform a

complete cycle) is known. Once the luminosity of the star is determined through

the use of a luminosity-period graph (above), the luminosity can be compared

to the apparent brightness in order to calculate the distance to the Cepheid:

mM = 5 5

Understanding the period-luminosity relationship allows astronomers tocalculate the distances to distant galaxies containing Cepheids by examining

their period, calculating their luminosity, calculating the distance modulus using


20/26

20

the apparent brightness and hence calculating the distance using the above

equation. This method has been instrumental in astronomers exploration of the

universe.

2nd

Hand Data: Impact of technology on Astronomy

The development of electronic data collection, storage and computation

technology has greatly improved the efficiency and accuracy with which

astronomers perform their observations.

Cosmic Background Explorer (COBE); Chandra X-ray Telescope; Hubble Space

Telescope; etc;

Practical: Computer Simulation of Eclipsing Binaries

An online applet was used to simulate the motion and corresponding apparent

brightness of eclipsing binary systems when observed from different angles. Many of the

intrinsic and extrinsic factors influencing the system could be altered, and the effects

upon the apparent brightness observed.

+ves:

+ Allows us to observe a simplified model of a binary system from different angles+ Allows us to manipulate intrinsic and extrinsic factors that influence the stars apparent

brightness (orbital radius, surface temperature, size, density, star radius etc;)

+ Provides a luminosity-period graph that illustrates how the brightness varies periodically

over time (curved for partial overlap + square graphs for complete overlap)

-ves

- Simplification of the model: represents circular orbit, not elliptical

- Does not allow students to simulate non-periodic variables

- Does not account for how the luminosity is calculated from the period (circumvents

calculations)


21/26

21

6.Life Cycle of Stars

Planetary Nebula

Massive cloud of dust and Hydrogen ions, atoms and molecules.

Planetary nebula may be dark or bright if illuminated by a protostar

from within. Massive planetary nebula, containing more material,

form larger stars (blue giants.) Planetary nebula are the remnants of

previous stars gone nova.

ProtostarA dust cloud with a hot, dense core that illuminates the surrounding

dust particles, making the entire system appear luminous and

colourful.

Main SequenceA star with varying brightness caused by some external factor (e.g.

astrometric binary wobble due to invisible partner)

p-p reaction

A 3-step reaction occurring in main sequencestars cooler than Sol:

C.N.O reaction

Faster reaction undergone by large main sequence stars another

reaction that fuses Hydrogen to produce Helium that uses higher

activation energy. Carbon is present as a catalyst that speeds the

reactionpartial contributor to the short lifespan of main sequencestars

Protostar

A protostar forms when the gas and dust in a planetary nebula

congeal on a centre of mass. This core grows due to accretion,

becoming denser and converting the GPE of the system into KE. The

system becomes a protostar when the GPE balances the KE of the

core. The protostars bright core usually illuminates the nebula as it

continues to contract and grow hotter. A protostar behaves like a

non-periodic intrinsic variable, plotted in the top-right of the H-R

diagram due to its size. When the cores temperature reaches

8millionoK, fusion reactions begin and the ZAMs stabilises.

SolThe name given to our own G2, yellow-coloured, medium-sized sun.

It has a luminosity of 1, to which all of the other stars are assigned

comparative luminosity values.

Helium Flash

Large stars transition slowly from main sequence red giants.

Smaller main sequence stars, however, experience a sudden onset

of helium fusion as they transition rapidly to red giants, resulting in

a HeliumFlash.

Blue Main

Sequence Stars

Possess 30x as much fuel as our sun and are 10,000x as luminous.

They only survive a few million years due to their quick decay. There

are no old blue stars. Large stars have an abundance of Hydrogen.


22/26

22

Yellow Main

Sequence Star

A star like our sun lasts 10 billion years. Appear brighter from earth

as the human eye is more sensitive to yellow light than blue light.

Red main

Sequence Stars

(red dwarfs)

Possess much less fuel than our sun and use it very slowly. They

have lifetimes 100s of billions of years.(90% of main sequence stars

are old red dwarfs that have not yet expired due to coolness)

Positron Decay

A type of radiation decay in which an atom loses a positivelycharged electron, a neutrino and energy. The product is an atom of

the same atomic weight with one less atomic number (proton.)

ZAMs Zero Age Main Sequencewhen a protostar reaches 8millionoK

Electron

Degeneracy

Phenomenon causing the collapse of massive stars.

Stellar Wind A stream of radiated energy and fast particles emitted from a star.

Stellar Formation

Dust particles within a planetary nebula, heated by solar winds, begin to congeal due to

attractive forces between the minute particles

The surrounding dust particles converge upon an exponentially growing core. The

energy possessed at this stage is in the form of gravitational potential energy(GPE)

Gravity causes the cold (no kinetic energy) dust cloud to collapse upon the core,

generating heat (GPE Kinetic Energy) The surrounding dust cloud absorbs energy

from the mass (thermal, EMR) and radiates it into space, aiding the contraction.

(Massive protostars form more rapidly than small stars heat increases reaction rate)

The star continues to collapse until a balance is attained between the radiation pressure

and gravity it is now named a protostar. The time taken to progress to this stage is

about 1 million years. The surrounding nebula cloud is dispersed by stellar winds

produced by the protostar, preventing additional matter adding to the star.

At this stage, due to its low heat and density, the mass appears red-giant-like: bright,cool and not dense. The protostar is not undergoing nuclear reactions, but is behaving as

a bright, non-periodic intrinsic variable star.

Because the kinetic/heat energy within the star is insufficient to counter the inward

contraction of gravity, the star continues to contract, becoming less luminous but also

hotter and denser. The surrounding planetarynebula(dust cloud) also spins faster with

the steadily-heating star. Dust particles converge quickly into masses which become

stars, which fragment to form orbiting planetssolar systems are formed.

When the core temperature reaches 8 million oK, it begins fusing Hydrogen to Helium

becoming a ZAMSZero Age Main Sequence Star


23/26

23

The ZAMS quickly stabilises when a balance is attained between gravity (which

condenses and heats the star) and internal fusion reactions (which push outward and

prevent further contraction.) To progress to this stage for a star of 1 solar mass usually

takes about 50 million years.

Key Stages of a Stars Life

1.Material in a planetary nebula congeals and collapses into a core due to

gravitational attraction, forming a hot core of matter. This luminous core

lights up the surrounding dust cloud. The luminous cloud with its hot core is

known as a protostar. The increasing density and heat of the core generates

stellar winds that prevent the addition of matter. The core itself appears red

giant-like, being large, red and cool. The star continues to contract slowly,becoming hotter and more dense.

2. Once the core temperature reaches 8 million, the star begins fusing Hydrogen to Helium

becoming a ZAMSZero Age Main Sequence Star. Where the ZAMS enters the main

sequence is dependent upon its mass. The ZAMS quickly stabilises when a balance is

attained between gravity (which condenses and heats the star) and internal fusion

reactions (which push outward and prevent further contraction.) The surrounding

nebula cloud is dispersed by stellar winds produced by the main sequence, preventing

additional matter adding to the star.

3.The main sequence may be a large, hot blue star if it was formed from a large nebula, or

a cool, small yellow-red main sequence star like our own sun. 90% of a stars lifespan is

spent as a main sequence, undergoing hydrogen fusion. The star only consumes 15% of

its Hydrogen reserves before nova, bequeathing hydrogen for the daughter stars to fuse.

The mass of the star determines the position in which it enters the main sequence. All

main sequence stars migrate slightly along the main sequence throughout the duration

of their existence, becoming slightly brighter and hotter towards the end of their life as a

main sequence star. Large, hot blue stars have a shorter lifespan than small, yellow-red

stars.


24/26

24

4.Once the stars helium content reaches 12%, fusion of Hydrogen ceases. Without the

outward push of the hydrogen fusion reaction, the star collapses, becoming much hotter

and denser. This induces Helium fusion, the energy of which pushes the surface of the

star outwards causing the star to expand to a large, cool star known as a red giant.

Large main sequence stars may become a supergiant. There are no old blue stars, as

blue is an indicator of extremely high temperatures which equate to a rapid rate ofdecay.

5. A stars life ends when it exhausts is fuel and is unable to fuse any lighter elements to

form heavier ones. The fusion reactions cease and the star collapses under its own

gravity, an event known as Nova. The nova of small stars forms white dwarfs, small, hot

dense stars that are the remnants of the stars core. They are luminous due to the

kinetic energy they still possess after nova. Larger stars go supernova, becoming a

super-dense pulsarstar or a blackhole.

Blue Main Sequence Stars

Star Fuel Reactions

There are 2 main reactions that occur within a main sequence star, depending on its size:

Proton-proton chain reaction: P-p reactions are the dominant type of reaction within

smaller, cooler main sequence stars like our own sun. P-p reactions require lower activation

energy to proceed. P-p reactions fuse 4 hydrogen nuclei (protons) into helium in 3 steps:

1) Two H-atoms (protons) combine to produce Heavy Hydrogen (deuterium) nucleusa

positron (positively charged electron), a neutrino (v) and energy are also released.

2) Heavy hydrogen fuses with another hydrogen atom to produce a neutron-deficient

Helium atomgamma radiation and energy are also released

3) Two of the neutron-deficient Helium atoms fuse together to form a stable Helium

atom, 2 Hydrogen nucleuses (protons) and energy.

Carbon-Nitrogen-Oxygen Reaction (CNO): CNO reactions dominate within large, hot, blue

main sequence stars, plotted on the left of the HR-Diagram. This reaction has a much higher

activation energy, but still accomplishes the production of Helium from the fusion of

Hydrogen. Carbon atoms are present as catalysts for the 6-step reaction:


25/26

25

The CNO reaction is much faster than the p-p reaction, causing the hotter, larger blue stars

to expire faster. This is also why the CNO reaction releases heat faster.

The core Helium content reaches 15%, the star transitions to a red giant or supergiant and

begins undergoing Triple-alpha reactions to fuse Helium into heavier elements (such as

carbon and iron.) Three helium atoms combine to form Carbon, and Carbon and Helium

atoms combine to form oxygen:

34He2

12C6+ gamma + energy

Star Clusters

Depending on their age, star clusters may be either open star clusters or globular clusters:

Open Star Clusters are NEWCLUSTERSthey have no red giants or white dwarfs in

them. The stars of open clusters are just babiesall main sequence stars. (e.g. Pleiades) Globular Clusters are OLD CLUSTERS - typically globe shaped with millions of distant

suns. Many older starsred giants and white dwarfsare present, because hotter,

bluer stars age faster than the cooler main sequence stars. (e.g. Omega Centauri)

Visually, a globular cluster appears as a blot of light at the centre, that disperses as it

moves out.

Hotter, larger stars age quicker they use up their fuel faster and progress through their life

stages quicker.

Determining the Age of a Star using H-R Diagrams

The age of a star can be determined by examining the cluster of which it is part:

All the stars in a cluster are about the same age and distance

Open Clusters are young, sparse clusters consisting of a few hundred loosely bound

stars. Open cluster stars have spectra that reveal and abundance of metals.

Globular clusters contain hundreds of thousands of stars bound together in a roughsphere. Globular clusters have a fewer metallic spectral lines.

The metal abundance of a cluster is an indicator of its age.


26/26

26

Open Cluster Globular Cluster

MB type stars occupy the main sequence

(most of the stars are main sequence)

Only the lower portion of the main sequence

is present (cooler stars age slower)

No Red Giants / White Dwarfs Many red giants / White dwarfs / highly

luminous, large stars

Stellar masses > 0.1M All stellar masses

hsc physics astrophysics notes

Documents