PhotoMaster - Astrophysics

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HSC Physics Option Topic

ASTROPHYSICSWhat is this topic about?To keep it as simple as possible, (K.I.S.S.) this topic involves the study of:1. OBSERVING THE UNIVERSE FROM EARTH

2. PARALLAX & SPECTROSCOPY3. PHOTOMETRIC METHODS

4. BINARY SYSTEMS & VARIABLE STARS5. LIFE & DEATH OF STARS

1. OBSERVING THE UNIVERSE FROM EARTH

Galileo�’s Use of the TelescopeGalileo Galilei (1564-1642) was the first person to use atelescope to view the universe and make scientificobservations and measurements with it. He studied the planetJupiter and monitored its orbiting moons. He looked atVenus and saw that it went through phases like the Moon. Itwas the Moon itself he was able to study most closely.

He saw and mapped the features of the moonscape andeven calculated the height of the lunar mountains bymeasuring the length of the shadows they cast.

These observations brought Galileo into conflict with theChurch which supported the view that all the �“heavenly�”bodies were perfect and could not have Earth-like featureslike mountains, nor satellites of their own (as Galileoobserved for Jupiter). Any opinion opposing the Churchwas heresy and punishable by torture and death!

Galileo was forced to publically deny his findings, but it wastoo late... modern, telescopic Astronomy had begun!

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How We Study the Universe from EarthOur ability to detect and study the Universe from thesurface of the Earth is totally dependent onelectromagnetic radiation (EMR) being received by our eyesand scientific instruments.

The different parts (�“wavebands�”) of the EMR spectrumdo not all penetrate equally to the Earth�’s surface. Some arepartially or completely absorbed by the atmosphere.

Waveband Wavelength (m) Comment(approx)

Gamma < 10-10 Absorbed in highX-Ray 10-10 - 10-8 atmos. by O2 & N2

Ultra-Violet 10-8 Most absorbed by ozone

Visible light 10-7 Penetrates

Infra-Red 10-7 - 10-3 Absorbed by water vapourin lower atmosphere (**)

Microwave 10-3 - 10-2 Penetrates

Radio waves >10-2 Most waves Penetrate(v. long waves reflected)

Only those wavebands which penetrate to the surface canbe used for ground-based astronomy. To study the starsusing other wavebands the observatory must be launchedinto space aboard satellites.

** Infra-red is absorbed mainly by water vapour in thelower atmosphere so ground-based observatories can beused if situated on very high mountains, or flown in aircraftand balloons.

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HSC Physics Option Topic �“Astrophysics�”Copyright © 2006-7 keep it simple science



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Resolution & Sensitivity of TelescopesThe word �“telescope�”usually brings to mind adevice that magnifies lightimages.

You need to clearlyunderstand 2 importantpoints:

�• Telescopes do not necessarily use light radiation.Any waveband of EMR can be used, but only thosewavebands which penetrate to the surface can be used byground-based observatories.

�• Magnification is not the most important characteristicof a telescope. High magnification is useless if the image isunclear, or if it fails to detect faint or dull objects.

The important features of any telescope for Astronomy are Resolution and Sensitivity.

Notice (at left) that resolution of a telescope is alsodependent on wavelength. The main wavebands used byground-based astronomers are visible light and radiowavelengths. Since radio waves have much longerwavelengths than light, a radio telescope suffers from muchlower resolution than a light telescope of the same aperturesize. This is why radio telescopes are usually built with verylarge dish antennas... bigger is better!



Resolution is the ability of a telescope

to distinguish between 2 very close objects.

It is measured by theangular separation between2 objects that can be seen

to be separate.

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Resolution is increased by

�• a larger aperture(lens, mirror or dish)on the telescope,

and

�• using shorterwavelength radiationfor observations.

Sensitivity of a telescope is a measureof the amount of radiation

the telescope gathers.

Sensitivity determineswhether very faint objects

can be detected.

The larger the lens, mirroror dish which collects theradiation, the greater the

sensitivity.

Prac Work: Sensitivity & ResolutionYou may have done a practical activity to investigate why itis desirable to have a larger aperture on a telescope.

There are manyways this could bedone, but one ofthe simplestexperiments is toview distant objectswith telescopes orbinoculars of thesame magnification,but differentaperture.

By looking at exactly the same view with each device, youcan judge the detail and brightness of each image. Ifcomparing binoculars with a telescope, use only one eyewith the binoculars to try to make the experiment as fair aspossible.

The sort of results you get are shown in these photos,although these have been enhanced to make the point.

Naked-eyeview

Now you can appreciate why astronomers want bigger andbigger telescopes. It�’s not to necessarily get moremagnification, but to achieve greater resolution andsensitivity.

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Radio telescopes study the universe bygathering radio waves emitted by

celestial objects

Photo by Richard Styles



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Problems with Ground-Based AstronomyThe first problem with studying the universe from Earthhas already been covered. The atmosphere absorbs manyof the wavebands of the EMR spectrum and limits whichones are available for ground-based Astronomy.

The other main problem is atmospheric distortion. You arefamiliar with distortion of images on a very hot day. Themoving convection currents of air refract the light passingthrough it differently from moment to moment, creating adistorted and �“wobbly�” image.

If you look at the stars on a clear night they seem to�“twinkle�”. This is a similar effect... you are looking throughmany kilometers of air which is constantly moving

Many of the world�’s large light-gathering telescopes havetheoretical resolutions of 0.01�’�’ (1/100 of an arcsecond,equivalent to 0.0000028 of a degree) or less. However, inpractice they do not achieve such detailed views of theuniverse because of this atmospheric distortion.

Methods of Improving the ViewThere are several ways that have been developed to partiallyovercome atmospheric distortion and other viewingproblems, and improve the resolution of ground-basedtelescopes.

Adaptive OpticsMany large optical telescopes are fitted with a system whichattempts to �“smooth out�” the twinkle effect caused byatmospheric distortions.

The light from a bright �“reference star�” is sampled up to1,000 times per second and computer-analysed fordistortion effects. The computer then controls rapidcorrections to be made to the shape of the mirror(s) tocompensate for and smooth out the distortions.

The �“shape-changing�” of the mirror is achieved bypiezoelectric materials which exert small forces whenelectrical voltages are applied. These work rapidly to alterthe shape of the mirror by tiny amounts... only 0.000004 ofa millimetre in some cases.

Active OpticsModern, large telescopes are massive and heavy, and as thetelescope is moved to view the sky at different angles,gravity causes distortions in the shape of the mirrors.Temperature changes cause further distortions. Thesechanges are microscopically small, but cause distortion andloss of resolution in the telescope images.

To compensate and smooth out these distortions, a systemof computer-controlled actuators push or pull on the backof the mirror to microscopically adjust its shape.

This sounds indentical to the �“Adaptive Optics�” system,but the big difference is the times scale of adjustments.Correcting atmospheric �“twinkle�” requires adjustments upto 1,000 time per second, while Active Optics needs to bemuch slower. It looks for distortions only every minute orso... deliberately ignoring atmospheric effects and seekinggravity and temperature effects that can be adjusted for.

InterferometryWhile Adaptive and Active Optics are used mainly on lighttelecopes to compensate for distortions, Interferometry is ageneral method for improving the resolution of anytelescope by linking together many (relatively small)telescopes to create a huge �“virtual aperture�”.

Perhaps the best known interferometry observatory is theVery Large Array (�“VLA�”) in New Mexico, USA, which wasfeatured in the movie �“Contact�”. This radio telescopeconsists of 27 dishes which can be moved into differentpositions in a pattern up to 36km in diameter.

When the signals from multiple dishes are combined, theinterference patterns (due to the different path length toeach dish) can be computer-analysed to give a radio�“image�” with resolution equivalent to that of a single dish36km across!



Part of the VLA, New MexicoPPhhoottoo bbyy PPaauull CC..

These are some of the largest and most modernoptical observatories in the world. Equipped withboth Adaptive and Active Optics, they also use

Interferometry to achieve the best view of the universe currently

available from the ground

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Worksheet 1Fill in the blanks. Check your answers at the back.

The first person to use a telescope for Astronomywas a).................................. He observed theb)....................... of Jupiter and thec).............................. of Venus. He mapped thefeatures of the Moon and was able to calculated)............................................... from their shadows.

From ground level, we can observe the universeusing only the e).................................. of EMRwhich can penetrate the f)......................................Basically this means only visible g)..........................and h)................................ waves (includingmicrowaves). Additionally, i).....................................can be used as long as the observatory is locatedon high mountains.

Magnification is not the main attribute of atelescope. More important are:�• Resolution, defined as j)...............................................................................................................................,and�• k)..................................., which is a measure ofthe amount of l)..........................................................

Both of these attributes are improved byincreasing the size of the telescope�’sm).............................................. Resolution is alsoimproved at n).....................................(longer/shorter) wavelengths.

1. (5 marks)List the �“wavebands�” used by astronomers tostudy the universe, and discuss why some aremore easily detected from space.

2. (5 marks)Define the terms �“resolution�” and �“sensitivity�”of telescopes, and discuss the factors which affecteach.

One of the main problems of ground-basedastronomy is distortion cause byo).................................................................. This canbe �“smoothed out�” by a system of�“p)..................... ...............................................�”.Light from a reference star is sampled up toq)......................... times per second to detect thedistortion. The shape of the mirror is thenaltered by applying tiny forces usingr)............................................... materials.

Another problem is distortion of the telescopeitself as it moves to different positions. Thiscorrected by �“s)......................................... Optics�”,which works in much the same way, but on aslower time scale.

Interferometry is a method of achieving bettert)................................................ by combining theimages from many u)...........................................The resulting v)...............................................patterns are analysed by computer to generate animage equivalent to that achieved by a single,much larger telescope.

3. (6 marks)Compare and contrast �“Adaptive Optics�” and�“Active Optics�”, including reference to thereasons for applying each technology to atelescope.

4. (3 marks)What is �“interferometry�”?

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COMPLETED WORKSHEETSBECOME SECTION SUMMARIES

Practice Questions 1These are not intended to be "HSC style" questions, but to challenge your basic knowledge and

understanding of the topic, and remind you of what you NEED to know at the K.I.S.S. principle level.

When you have confidently mastered this level,it is strongly recommended you work on questions from past exam papers.

Mark values shown are suggestions only, and indicate the depth of answer required.




Calculating Distances From ParallaxTraditionally, the measurement of the distance to a star hasbeen done by photographing the star on 2 nights 6 monthsapart, and analysing the photographs to determine theparallax angle.

Photo 1 Photo 2

In the above simulation, one of the stars in thephotographs seems to have moved in relation to the rest ofthe star field. Careful measurements of the photos, with aknowledge of the angular positions of the stars, allows theparallax angle to be measured. In this example, the star�’sparallax is 0.035 arcsec horizontally, and 0.01 arcsecvertically. Using Pythagorus�’s Theorem, this gives a total of0.0364 arcsec.

From the parallax angle the distance to the star is calculatedas follows:

Limitations of Measuring Distance by ParallaxThe more distant the star, the smaller the parallax angle.Beyond a certain distance it becomes impossible for evenour best telescopes to detect and measure any parallax.

It turns out that the parallax method is only useful formeasuring the distance to stars which are relatively close.

Advances in technology help to push this limit outwards,(this is discussed on the next page) but for seriousastronomical distances the parallax method is useless. Asyou will learn later, there are other ways.

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2. PARALLAX & SPECTROSCOPY




ParallaxParallax is the apparent displacement of an object against amore distant background, when viewed from a differentangle.

Parallax can be used to measure the distance to a star, bymeasuring the angle �“p�” indicated in the diagram.

Units of Distance in AstronomyBefore going any further, you need to know the units ofdistance used by astronomers.

Beyond our Solar System it rapidly becomes inconvenientto measure distances in kilometres because the distancesare so large.

The Light Year A light year is the distance that a photon of light travels, ina vacuum, in one year. With a velocity, c = 3.00x108 ms-1

you can calculate that1 light year = 9.46x1015m

(that�’s about 10 billion billion kilometres)

The Parsec (pc)�“Parsec�” is short for �“parallax-second�” and is the distanceat which a star has a parallax angle (angle p in the diagramabove) of 1 arcsecond (1�’�’).

One arcsecond is an extremely small angle (1/3600 of 1degree) so 1 parsec turns out to be a long distance...

1 parsec = 3.26 light years

A Simple Example of Parallax:

Hold up one finger and view it with one eye against adistant tree or post. Hold the finger still whileswitching to view it with your other eye.

Your finger appears to move relative to the distant"landmark".

This apparent displacement is called "PARALLAX"

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Earth

Earth, 6 months later

line of observationStar beingobserved More

distantstars

The position of the starappears to change against

the background stars.

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d = 1 p

d = distance to the star, in parsecs (pc).p = parallax angle, in arcseconds (arcsec).

Example CalculationIn the photos above, one star shows a parallax angle of0.0364 arcsec.Calculate the distance to the star in parsecs and in lightyears.

Solutiond = 1/p = 1/0.0364 = 27.5 pc

In light years; d = 27.5 x 3.26 = 89.7 light years

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www.keepitsimplescience.com.auHSC Physics Option Topic �“Astrophysics�”Copyright © 2006-7 keep it simple science


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What Distance Can Parallax Measure?From ground-based observatories, the smallest parallaxangle that can be measured is about 0.03 arcsec.

The distance to a star with 0.03�’�’ parallax is:

d = 1/p = 1/0.03 = 33 pc== 108 light years

This might seem a long way, but considering that our galaxyis about 130,000 light years in diameter, 100 light years isreally not far at all.

Much better results are possible from space, above thedistortion of the atmosphere. There are a number ofsatellites in orbit (including the famous Hubble SpaceTelescope) which are capable of gathering data for parallaxmeasurements.

The Hipparcos satellite for example, can measure parallaxangles as small as 0.001 arcsec. A star with this parallax isat a distance of:

d = 1/p = 1/0.001 = 1,000 pc> 3,000 light years

Hipparcos was launched in 1989 and has mapped 100,000stars to high precision, and another million starsapproximately.

Construction is underway of a space observatory �“Gaia�” tobe launched in 2011. Gaia is basically a technologicalupdate of the Hipparcos system, and will be capable ofmeasuring parallax angles down to 0.00002 arcsec. (This isabout a billionth of one degree... enough to resolve a singlehuman hair at a range of 10,000km!)

Gaia will be able to accurately locate stars at a distance ofd = 1/p = 1/0.00002 = 50,000 pc

> 150,000 light yearsGaia will allow our entire galaxy to be accurately mapped asnever before, although the plan is to map �“only�” 1 billionof the 100 billion stars in the galaxy.

SpectroscopySpectroscopy is a technique which allows determination of�• chemical composition�• surface temperature�• velocity, and more......of stars and other celestial objects. Because of this,spectroscopy has become one of the most importanttechniques in astronomy.

First, understand the basics...

Continuous Light SpectrumYou should be familiar with the idea of a �“spectrum�” oflight. For example, if �“white�” light is passed through aprism, the different frequencies are separated, and thefamiliar rainbow colours appear.

(use your imagination...we can�’t print colours)

A perfect hot radiator of light (known as a �“Black Body�”)will emit every frequency of light to produce a continuousspectrum... a full and complete rainbow.

Emission & Absorption SpectraIf the light emitted by atoms of a particular element is putthrough a prism, the spectrum shows very narrow brightlines on a dark background because only certainfrequencies are given out. The pattern of lines ischaracteristic for each element.

If the same element absorbs light (from a continuousspectrum source) it will be at exactly the same characteristicfrequencies. The spectrum will have dark lines on a brightrainbow background.

The following diagram shows 3 ficticious elements, just togive the general idea.

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Artist�’s impression ofobservatory �“Gaia�” in orbit

150,000 km from Earth

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What Causes the Spectral Lines?You are reminded of atomic structure, especially the ideaof the electrons in orbits around the nucleus.

The �“jump�” from one orbit to another involves a precisequantity of energy. You are reminded of Plank�’s QuantumTheory and how the quantum energy of a photon of lightis related to its frequency: E = hf

Since each orbit �“jump�” involves a precise �“quantum�” ofenergy, any light energy absorbed or emitted must have aprecise frequency and wavelength.

The lines of an emission or absorption spectrum arephotons of precise frequency/wavelength, either beingemitted or absorbed as electrons jump from orbit to orbit.

Studying Astronomical SpectraIn its simplest form, a spectroscope is simply a prism (todisperse the different frequencies) and an optical system toview or photograph the spectral lines. A simplespectroscope is shown schematically in the diagram at left.

In modern astronomy things have improved a little...

Prisms have been replace with Diffraction GratingsGlass prisms absorb some of the light and reduce thesensitivity of the system, so they are no longer used.Instead, diffraction gratings are use to disperse thefrequencies of light and form the spectrum.

A diffraction grating uses interference effects to spread outthe frequencies. They have both superior resolution andsuperior sensitivity compared to a prism.

General Types of SpectraEach different type of celestial object produces a differenttype of spectrum.

Stars produce Absorption SpectraThe hot surface of a star is basically a �“Black BodyRadiator�” so it emits a full rainbow of frequencies.However, every star is surrounded by an �“atmosphere�” ofcooler gas. As the star�’s light passes through this gas somefrequencies are absorbed at the characteristic frequencies ofthe elements in the atmosphere.

Galaxies produce Continuous SpectraThe light from a galaxy is the combination of light frombillions of stars and glowing gas clouds and so it isessentially a continuous spectrum, not only of visible lightbut radio, infra-red and the entire EMR range.

Emission Nebulae produce Emission SpectraAn �“emission nebula�” is an immense cloud of gassurrounding very hot stars. The high energy radiation fromthe stars (e.g. ultra-violet) is absorbed by the gas cloud,which then re-radiates the energy as an emission spectrum.The spectral lines are those of the gases in the cloud,mainly hydrogen.

Quasars produce Emission SpectraQuasars are very distant, mysterious objects which produceenormous amounts of energy for their size. It is thoughtthey are associated with massive �“black holes�”, and theenergy they radiate may be produced as matter is�“swallowed�” into the intense gravitational field of the blackhole. The emission lines of a quasar�’s spectrum are highly�“Red-Shifted�” (see later) indicating high velocity away fromus, and that they are very far away.



Practical Work: Observing Emission SpectraYou may have observed some emission spectra by using aspectrometer to view the light from discharge tubes filledwith various low-pressure gases.Neon is one of the easiest to observe.

You will have seen that the light from a discharge tube iscomposed of separate lines of light. A neon discharge tube,for example, glows with light which looks pink-red to theeye. The spectroscope reveals several lines of light... red,green and blue.

Each line is one single, pure frequency of light.

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Tube glowswith emittedlight

SpectroscopeSlit & lens

Prism Opticalviewing system

�“Telescope�” can berotated to view thedifferent �“lines�” of theemission spectrum

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jump higher, or emitenergy to drop lower.nucleus

SpectroscopeSlit & lens

Diffraction OpticalGrating System

Spectrum is focused onto photographicfilm or electronic detectors (CCDs)

Light froma star




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Analysis of Stellar SpectraThe spectrum of light from a star gives an astronomerinformation about the composition, temperature, surfacedensity and motion of the star.

Spectra Allow Star ClassificationRemember that the spectrum of a star is an emissionspectrum formed by absorption of certain frequencies asthe �“full rainbow�” of frequencies pass through the star�’satmosphere.

However, which elements of the atmosphere are especiallyprominent in absorbing their unique spectral lines dependson the surface temperature of the star. For example, thereis always some helium in a star�’s atmosphere, but theabsorption lines due to helium do not become reallyprominent until the surface temperature is very high.

Astronomers have devised a classification system, based onthe spectral lines:

Spectral Colour Surface Spectral FeaturesClass Temp (K)

O Blue >30,000 Strong ionized He.

B Blue-White 15,000 to Strong 30,000 neutral He lines.

A White 10,000 to Prominent15,000 hydrogen lines.

F White-yellow 7-10,000 Strong metal lines and weak H lines

G Yellow 5-7,000 Prominent Ca2+

lines

K Orange 3,500-5,000 Strong lines frommetals

M Red 2,500-3,500 Strong lines due to molecules

To help you remember the order of the spectral classes, trythis mnemonic: �“Oh, Be A Fine Girl (Guy), Kiss Me�”.

Intensity-Wavelength GraphsThe colours listed in the table at left are generally notobvious to the naked eye, but when the intensity of eachpart of the spectrum is measured it is found that somecolours are more intense than others.

This connects with the distribution of frequencies emittedby �“Black Bodies�” at different temperatures which has beencovered in previous topics.

Basically, a hotter �“black body�” object (star) emits moreenergy than a cooler one. Not only is there more energy,but the distribution of wavelengths is different.

So, if the spectrum of a star is analysed to find the �“peak�”wavelength, this can be used to calculate the surfacetemperature.(Details of this calculation are not required by the syllabus)

For example, in the graph above, the �“example star�” hasmaximum energy emission at a wavelength of about5.6x10-7m (reading from the wavelength scale). Thiscorresponds to a dominant colour yellow and surfacetemperature of 5,200oK.

This star would be classified as spectral class �“G�” and itsspectrum would be expected to show prominentabsorption lines corresponding to ionized calcium Ca2+.

44xx1100-77 55xx1100-77 66xx1100-77 77xx1100-77

Wavelength (m) of RadiationCCoolloouurrss:: VViioolleett BBlluuee GGrreeeenn YYeellllooww OOrraannggee RReedd

very hot starat 30,000oK

cool star at3,000oK

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�“peak�”wavelengthshorter

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Spectral Lines Give Chemical CompositionAs well as helping to classify a star and give informationabout its surface temperature, the absorption lines in aspectrum can give information about the chemicalcomposition of the star�’s atmosphere. Since theatmosphere is made of atoms boiled off from the surface,this identifies the composition of the star itself.

As well as the very prominent lines (which help classify thestar as suggested in the table above) there are usually manyother, weaker absorption lines which can be matched upwith the lines known for each element. (Interestingly, theelement Helium was discovered by its previously unknownspectral lines in the Sun�’s spectrum. �“Helios�” = �“Sun�”)

Study the diagram at right to get the idea.

Spectral Lines of Star

element B

element C

Known Spectrum ofelement A

In this simulation, comparison of the star�’s spectrum withknown elements shows that A & B are present, but not C.




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Spectral Lines Indicate the Motion of a StarYou are reminded of the Doppler Effect:The waves emitted by a stationary object spread out evenlyin all directions, with the same wavelength.

However, when the object is moving, the waves in front get�“bunched up�” and their wavelength is shortened. Thewaves behind get �“stretched�” and the wavelength islengthened.

If a star is moving towards us or away from us its spectrallines will be altered as suggested by the diagrams:

These 4 spectral lines are the �“signature�” of hydrogenatoms and are present in the spectrum of every star. Theyare the best known lines of all, and immediatelyrecognisable by any astronomer.

If a star is moving towards the Earth these lines will beshifted to slightly shorter wavelengths... towards the blueend of the spectrum. This is called a �“Blue Shift�”.

If a star is moving away from Earth the spectral lines areshifted to longer (redder) wavelengths.

You are reminded that the predominance of Red-Shifts inthe light from distant galaxies is one of the major piecesof evidence telling us that the universe is expanding. It wasthis important observation which needed explaining andled to the development of the �“Big Bang Theory�” for theorigin of the universe.

Closer to home, stars within our galaxy can show either redor blue shifts according to their motion relative to Earth.

Rotation Can be Detected TooIf a star is rotating, with its axis of rotation more or less�“upright�” as seen from Earth, then one edge of the star isalways approaching us and the other is always moving away.

The result is that light from the approaching edge is blue-shifted, while light from the receding edge is red-shifted.The light from each side (plus the un-shifted light from thecentre) cannot be resolved into separate lines, but insteadresults in a �“blurred�” widening of each line.

High Density �“Smears�” the Lines TooIf a star is very dense and compact, its surface gravity ishigh. This in turn pulls on the atmosphere which will alsobe of higher density.

Since the atoms (and especially the charged particles) of theatmosphere are packed more closely together, the way thatlight is absorbed to produce the absorption lines is alteredin such a way to �“smear�” or widen each line.

The result is that the spectral lines show a blurred wideningfor compact, dwarf stars. Large, �“Giant�” stars, althoughhaving a large mass, have lower density and low surfacegravity. Their spectral lines are narrow and �“sharp�”.

The �“smearing�” effect due to rotation can be differentiatedfrom the widening due to density. The difference istechnical and beyond the scope of this course.

But Wait, There�’s More...Parallax reveals distance and the spectrum tells ustemperature, composition, motion and even density. As youwill see, in some cases we can also calculate the star�’s massand even estimate its age...

Even at immense distances we can learn many facts about a star!

Waves spreading outevenly from astationary object

In Front,wavelengthshortened

LLiigghhtt BBlluueerr

Behind,wavelengthlengthened

LLiigghhtt rreeddddeerr

Light Waves Spreading Out From a Moving Star

Approximate Wavelengths (m) and ColoursVViioolleett BBlluuee GGrreeeenn OOrraannggee YYeellllooww RReedd

44xx1100-77 55xx1100-77 66xx1100-77 77xx1100-77

Blue Shifted Lines

Red Shifted Lines

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This edge isapproaching

This edge isreceding

Normal HydrogenSpectral Lines

�“Smeared�” H Lines from a rotating star

HSC Physics Option Topic �“Astrophysics�”Copyright © 2006-7 keep it simple science www.keepitsimplescience.com.au


Parallax is the apparent a)....................................... of a staragainst a more distant background, when viewed from ab)...................................................... To measure the parallaxof a star its position must be measured twice, at timesc).............................. apart, so that the diameter of theEarth�’s orbit around the Sun provides the baseline.

Distance units commonly used in astronomy are:�• light-year, defined as the distance d)..........................................................................................�• parsec, defined as the distance at which the parallax angleequals e).................................... 1 parsec is approximatelyf)................... light years.

The use of parallax to measure the distance to a star islimited by our ability to measure the g)...................................From ground-based observatories this limit is abouth).................... arcsec, which gives a distance of about 33parsecs. From space, using satellites such as i)........................,smaller parallax angles allow distances out to j)...................parsecs are possible. The next generation of satellites willallow our entire k)............................... to be accuratelymapped.

Spectroscopy is the study of the l)............................. of thelight from a star. The different wavelengths arem)........................... by a prism or n).......................................grating in a o)...................................................... (instrument).Each chemical element absorbs or emits specificp)......................................... of light as electrons �“jump�” fromone orbit to another.

1. (3 marks)Complete the values of this table.

Star Parallax Angle Distance(arcsec) (pc)

P 0.554

Q 0.00475

R 65.9

2. (3 marks)Compare and contrast the appearance of the emissionspectrum and the absorption spectrum for the samechemical element.

3. (3 marks)Briefly explain how and why the spectrum associated witha particular element contains discrete �“lines�”, eitherabsorption or emission lines.

An �“emission spectrum�” shows q)..............................................................................., while an �“absorption spectrum�”shows r)............................... on a bright rainbow background.

Typically, a star shows an s)................................. spectrum, agalaxy shows a t).......................................... spectrum, while�“quasars�” and emission nebulae have u)...............................spectra.

The spectrum of a star can give information about:�• surface temperature, which scientists use to place eachstar into one of seven main categories labelled v)........, ........,......, .........., ........, ........ and ....... (letter labels in order). Thisclassification is based on both the peakw)........................................... of the �“black body�” radiation,and on the predominant x)........................................... lines,which are characteristic of different temperatures.

�• y)............................... composition, which is revealed bymatching absorption lines in the stellar spectrum againstthe known lines due to each z)..................................................

�• translational velocity. Due to the aa)........................ Effect,the spectral lines may be shifted towards the ab)..................end of the spectrum if the star is moving towards us, andac).........................-Shifted if moving away.

�• ad)............................. In this case, the edges of the starshow both red and blue shifts, resulting in the spectral linesbeing ae).......................................................................................

�• density. High density dwarf stars also have spectral lineswhich are af)..............................................................

4. (6 marks)Three different astronomical spectra are described asfollows:

Spectrum A: Emission spectrum, lines highly red-shifted.Spectrum B: Absorption spectrum, lines show slight blue-

shift.Spectrum C: Essentially continuous spectrum with few

lines. Lines are red-shifted.

Identify the celestial object

which most likely produced

each spectrum, explaining your answer in each case.

State how each spectrum differs from �“H�” and what thatreveals about the motion of the stars X, Y and Z.

10


Practice Questions 2

5. (6 marks)Diagram �“H�” shows theabsorption spectrum ofhydrogen, while �“X�”, �“Y�”and �“Z�” are part of theabsorption spectra from 3different stars.

blue yellow red

Star X

Star Y

Star Z

H


If spectrometry is one of the most important and usefultechniques in astronomy, then its partner is photometry...the measurement of the amount of light (i.e brightness)received from a star, or other celestial object.

This section will deal with how �“brightness�” of light fromstars is measured and used by astronomers, but be awarethat the same principles apply for other wavebands ofEMR, such as radio frequencies received by a radiotelescope.

Brightness (Intensity) and MagnitudesOver 2,000 years ago the Greek philosopher Hipparchusobserved and mapped the star-field of the night sky. Aspart of his study, he invented a �“scale of brightness�” toclassify each star he mapped.

His scale was:Brightest star visible = �“magnitude 1�”

2345

Dullest star visible = �“magnitude 6�”

Note that this is a reverse scale... brighter stars have smallernumber values.

For historical reasons, we still use this scale of magnitudes,but it is now mathematically defined and extended beyondthe original 6 values. Telescopes have revealed faint starsnot visible to the eye, so magnitudes 7,8,9,10... etc areincluded, and some stars are brighter than �“magnitude 1�”,so values of 0, -1, -2, etc are included.

The magnitude scale is not linear. By modern definition;magnitude 1 is 100x brighter than magnitude 5, soeach magnitude is different by 5 100 = 2.512 times.

This leads to the following relationship between brightness(intensity) and the magnitude scale:

Magnitudes and DistanceThe magnitudes dealt with so far are the �“apparentmagnitudes�” of a star as seen from Earth. This valuedepends on how luminous the star really is and how faraway it is.

You are reminded of the Inverse Square Law for how thebrightness (intensity) of light energy drops off with thesquare of the distance.

This means, for example, that if 2 stars have the sameluminosity (i.e. both emit the same amount of light energy),but one is twice as far away, it will appear only 1/4 as bright.If it was 3 times as far away it would be only 1/9 as bright,and so on.

So, when we see a bright star (e.g. magnitude 1) in the skyit could be a small, low-luminosity star which is relativelyclose to Earth, or it could be a huge, highly luminous starwhich is much further away.

To deal with this, astronomers have invented the concept of�“Absolute Magnitude�”. Read on...

11


3. PHOTOMETRIC METHODS




Photometryis the measurement of the brightness

of light or other radiation

IA = 100IB

IA/IB= brightness (intensity) ratio of star A compared to star B.

mA = magnitude of star AmB = magnitude of star B

These values have no units of measurement.

((mmB-mmA))//55

Example Calculation 1Star A has magnitude of 4, star B has magnitude 12.How much brighter is A compared to B?

Solution: IA/IB = 100

= 100(12 - 4)/5

= 1008/5 = 1001.6

IA/IB = 1.6x103

! Star A is 1.6x103 (1600) times brighter than star B

Example Calculation 2The star Sirius has visual magnitude = -2.1, while the starAlgol has magnitude of +2.1. What is the ratio of theirintensities?

Solution: IA/IB = 100(Sirius is brighter so let it be �“star A�”)

= 100(2.1 -(-2.1))/5

= 1004.2/5 = 1000.84

IA/IB = 48! Sirius is 48 times brighter than Algol.

((mmB-mmA))//55

((mmB-mmA))//55

x

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distance �“d�”

distance �“2d�”

2xSquare

Area x2

Square withsides twice aslong.

Area = 4x2

Same amountof light fallson 4 timesthe area



12

Since the standard distance chosen for measuring absolutemagnitude is 10 parsecs, it follows that:

�• a star that is closer to Earth than 10 parsecs (there aren�’tvery many) will be seen as brighter than it would at 10parsecs. This means that its apparent magnitude is greater(therefore a smaller value) than its absolute magnitude.

�• a star that is further away than 10 parsecs (most stars) willlook fainter from Earth (i.e. larger apparent magnitudevalue) than it would at the standard distance of 10pc.

If a star�’s absolute magnitude can be determined, and if wemeasure its apparent magnitude as seen from Earth, thenthe Inverse Square Law allows the distance to be calculated.

The relationship is:

So, determining the absolute magnitude of a star givesastronomers another way to determine the distance to astar.

How to Find Absolute MagnitudeThis all very nice, but how can the absolute magnitude of astar be measured? It�’s not possible to just jump into apassing spaceship and travel to a point 10 parsecs from astar and measure the intensity of the light to get its absolutemagnitude.

Time to revise the H-R diagram...

The H-R diagram shows that there is a relationshipbetween the spectral class of a star (which can bedetermined by studying its spectrum) and its absolutemagnitude.

So, for stars too distant to measure any parallax angle:

�• Measure the amount of light received to determine the apparent magnitude, (m).

�• Analyse the spectrum to determine spectral class, colourand temperature.

�• Use the H-R diagram to determine the (approximate) absolute magnitude (M) of the star.

�• Use the �“distance modulus formula�” to calculate distance.



Absolute Magnitudeis the magnitude a star would have

if viewed from a standard distance of 10 parsecs

M = m - 5log( d )10

or, m - M = 5log(d/10)

M = the absolute magnitude of a starm = the apparent magnitude of the stard = the distance to the star in parsecs�“log�” means the logarithm to base 10.

The term (m - M) is known as the �“distance modulus�”,and the equation is called the �“distance modulus formula�”

Example CalculationA star has an apparent magnitude of 1.25 and anabsolute magnitude of -3.72.a) How far is it from Earth?b) What parallax angle would it show?

Solutiona) m - M = 5log(d/10)

1.25 - (-3.72) = 5 x log(d/10)log(d/10) = (1.25 + 3.72)/5 = 0.994

! d/10 = 100.994 = 9.86!! d = 98.6 pc

The star is 98.6 parsecs from Earth.

b) d = 1/p, so p = 1/d = 1/98.6!! p = 0.0101 arcsec

The star will show a parallax angle of 0.0101�’�’.

Example CalculationA faint main-sequence star �“X�” has an apparentmagnitude of 8.2.Its spectrum reveals it is spectral class �“B�”.How far is it from Earth?

SolutionOn the H-R diagram above, its spectral class shows itshould have an absolute magnitude of (approx) -6.0

m - M = 5log(d/10)8.2 - (-6.0) = 5 x log(d/10)

log(d/10) = (8.2 + 6.0)/5 = 2.84! d/10 = 102.84 = 692

!! d "" 6,900 pc The star is approx 6,900 parsecs from Earth.

This method is called �“Spectroscopic Parallax�”, eventhough actual parallax measurements are not involved.

Hertzsprung-RRussell DiagramNote that the vertical scale shows absolute magnitudes

SSppeeccttrraall O B A F G K MCCllaassssColours Blue White Yellow Red

Temp. 30,000+ 10,000 5,000 2,500

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13

More on Spectroscopic ParallaxThe method described on the previous page for finding thedistance to a star can only give an approximate value. Thisis because on the H-R diagram the �“Main Sequence�” bandhas considerable thickness. Even if a star�’s position alongthe horizontal axis can be determined quite precisely, itsabsolute magnitude could have a range of values,depending on how wide the main sequence band is at thatpoint.

Furthermore, you are reminded that not all stars are �“mainsequence�”. The H-R diagram below shows some of theother types.

As an example, imagine that a star�’s spectrum identifies itas belonging to spectral class A. The diagram above showsthat even if it is main sequence, its absolute magnitudecould be any value from 0 to about -4. However, if it is a�“White Dwarf �” star its absolute magnitude is about +12,while if it happens to be a �“Supergiant�” the magnitude isabout -10.

This is where more spectral analysis can help. For example,if the spectral lines show the �“smeared�” appearance due tohigh density, the star can be identified as a White Dwarfand the H-R diagram used appropriately.

Different Detectors = Different MagnitudesOriginally, apparent magnitude values were assigned bynaked eye comparison with well-known �“reference stars�”.

Over 100 years ago, astronomers began taking photographsby telescope and measuring magnitudes by the degree ofexposure on the film. More recently, electronic detectorshave been used to measure the intensity of light.

Each method gives a different magnitude value because;

�• the human eye is most sensitive to the yellow-green portion of the spectrum, while;

�• photo film is commonly more sensitive to blue-violet, and�• electronic detectors respond equally to all wavelengths.This difference can be put to good use...

Colour IndexDetermining the �“colour index�” of a star is a relatively easy,simple way of determining the spectral class andtemperature of a star without the need to use aspectroscope to obtain the full, detailed spectrum.

The technique involves measuring the light intensity of astar after the light has passed through special filters whichonly allow a narrow range of wavelengths through.

For example, if a blue filter (designated �“B�”) is used:

Then the filter is switched to one which allows mainlyyellow-green light through, so it mimics the sensitivity ofhuman vision. This is designated as a �“V�” filter, where V =�“visual�”.

The difference between �“B-magnitude�” and �“V-magnitude�” gives the �“colour index�”.

Colour Index, C.I. = B -V

Blue stars (spectral classes O, B) score C.I. values which arenegative, while yellow to red stars (spectral classes G, K, M)have C.I. values which are positive. The point is that the C.I.value of a star correlates very well with its position alongthe horizontal axis of the H-R diagram, so absolutemagnitude (and distance) can be approximated rapidly.

Since C.I. readings can be collected quickly by automaticequipment (e.g. aboard a satellite) and the data processed bya computer, this technique is ideal for automatic starsurveys of thousands or millions of stars.

For greater precision, modern systems use up to a dozendifferent filters, not just �“B�” and �“V�”, and can include datain the UV and infra-red wavebands.



Hertzsprung-RRussell DiagramShowing the main star types


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14

Advantages of Photoelectric Technologiesover Photography

Originally, all astronomy was done by eye, with or withouta telescope.

Over 100 years ago, the use of photography revolutionizedastronomy, because photographs allowed accuratemeasurement of apparent magnitudes, detection andmeasurement of parallax angles and (combined with aspectroscope) the analysis of spectral classes, star motions,chemical composition, and so on.

For the last 40 years, and especially within the past 20 years,another �“technology revolution�” has occurred with theintroduction of electronic devices for measuring the lightreceived from a star.

These �“photoelectric�” technologies include �“ChargedCouple Devices�” (CCD�’s) and offer many advantages overphotographic film.

�• CCD�’s are much more sensitive to faint light sources.�• CCD�’s are sensitive to a wider range of wavelengths,including UV and infra-red wavebands.�• CCD�’s respond equally to light of every wavelength,whereas film tends to be unevenly sensitive.�• electronic devices can collect data remotely andautomatically (e.g. on a satellite)�• electronic signals can be fed directly to a computer forrapid analysis of huge volumes of data.

Impact of Improved Measurement Technologies on

our Understanding of Celestial ObjectsUntil relatively recently in human history there was no wayto tell how far away any star is, nor how big it is, nor itscomposition, motion, etc.

Our modern understanding of virtually all celestial objectsis entirely due to advances in the technology of detectingand measuring light and other wavebands. Advances inrocketry and computers and development of new materialshave obviously been important too, but basically ourmodern understanding of celestial objects is all due todetecting and measuring of radiation.

Photoelectric CCD�’s detailed at left, allow collection ofdata on a massive scale and at a rate never before possible,so that we are gaining a much greater understanding of ourgalaxy from a more complete picture of the positions andtypes of its billions of stars.

Radio Telescopes were developed in the 1950�’s after theaccidental discovery that the cosmos is awash with radioand microwave energy. This technology led to thediscovery of celestial objects such as pulsars and quasars.

By making more and more measurements astronomershave gained an understanding of pulsars which hascontributed to our understanding of how stars evolve anddie.

The �“Cosmic Background Explorer�” (COBE) satellitemeasured the microwave background radiation whichcontributed valuable evidence to the �“Big Bang�” theory bywhich we try to understand the universe and its origin.

Earlier in the topic the technologies of Interferometry,Active Optics and Adaptive Optics were mentioned asways to improve the resolution of telecopes. Thesetechnologies improve the quality of measurements so thatwe gain a better understanding of stars, nebulae, galaxies,quasars and black holes.



Prac Work: Photometry with FiltersYou may have carried out experiments to mimic thecollection of colour index data using equipment similar tothat shown.

A simple procedure would be to measure the light intensitythrough a blue filter (�“B�”), then through a yellow filter(�“V�”). Using the light meter data, assign �“brightnessmagnitudes�” to each reading.

A �“colour index�” can be calculated by C.I. = B - VYour C.I. need not bear any resemblance to astronomicalvalues.

Then, repeat the exercise at various voltage settings for theray-box lamp.

At low voltage the light insensities (brightness) will be low,and at higher voltages the intensities will be much higher,but this is not the point.

You may find that your �“colour index�” value changes withvoltage as the light bulb not only gets brighter, but alsochanges in its distribution of wavelengths and colours.These in turn, are filtered differently by �“B�” and �“V�”.

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Photometry is the measurement of a)......................................................................... Originally this was done by eye, bycomparing a star�’s brightness to �“reference�” stars, andallocating each star a value called its b)...................................This is a reverse scale, so that magnitude 1 is c).....................(brighter/fainter) than magnitude 2.

The d).............................. magnitude is what we observefrom Earth. This depends on the e).............................. of thestar, and on how f)........................................... it is.The g).................................. magnitude is the star�’s brightnessif viewed from a standard distance of h).............. parsecs. Ifyou know both i).............................. and ................................magnitude, the j)................................... to the star can becalculated. Absolute magnitude can be estimated from theH-R diagram if the star�’s k)............................................. isknown. This process of getting an approximate distance toa star is called �“l).........................................................................�”

1. (6 marks)For each of the following pairs of stars, calculate the ratioof their brightness, given the apparent magnitude of each.For each pair, state which star is the brighter.

a) Canopus (m = -0.62) and Mira (m = 6.5)b) Barnard�’s Star (m = 9.5) and Algol (m = 2.1)c) Rigel (m = 0.18) and Achenar (m = 0.45)

2. (2 marks)Define the term �“absolute magnitude�” and outline how itmay be estimated from knowledge of a star�’s spectral class.

3. (6 marks) The bright star Rigel has an apparent magnitude of 0.981and an absolute magnitude (determined from its spectralclass) of -3.55.

a) Use this data to calculate its distance from Earth.b) Rigel�’s parallax has been measured to be 0.0112 arcsec.

Calculate its distance from Earth based on parallax.c) Account for any discrepancy between your answers toparts (a) and (b) and discuss briefly any reasons to acceptone answer as more accurate than the other.

The m).......................... Index of a star is obtained bymeasuring its magnitude through differentn).......................... which only allow certain wavelengths topass through. The o)...................................... between the 2values gives the index, which is correlates well with thedifferent p)............................................................. of stars.This allows a quick and simple way to find a star�’s positionon the H-R diagram, then its q).................................... andfrom that its r)....................................... from Earth.

Modern s).............................................. technologies offermany advantages over the older t)...................................methods of photometry. These advantages include:�• CCD�’s are much more u).............................................. tofaint light sources.�• can detect a wider range of v)........................................, andrespond w).......................................... across the spectrum.�• can collect data x)............................. and ...............................,for example, on board a y).....................................................

4. (4 marks)The following photometry data have been determined for acertain star.

Apparent magnitude = + 3.5Absolute magnitude = + 4.8�“B filter�” magnitude = +3.2�“V filter�” magnitude = +3.7

Without doing any calculations, interpret this data to statea) the star�’s (approx) distance from Earthb) roughly the star�’s spectral class/colour

explaining your reasoning in each case.

5. (3 marks)The bright star Canopus shows a parallax angle of 0.0104arcsec, and has an apparent magnitude of -0.620

Calculate its absolute magnitude.

6. (6 marks)The absolute magnitudes of 2 stars have been determined:

Star A, M = +4.33Star B, M = + 9.57

Both stars are known (from parallax calculations) to belocated 3.58 parsecs from Earth.

Calculate each star�’s apparent magnitude and hence find thebrightness ratio of star A to star B.

15








The Importance of Binary StarsA binary star system is when 2 stars are in orbit aroundeach other. This situation is much more common than youmight guess... it is estimated that more than half of all mainsequence stars belong to multiple star systems of 2 or morestars in orbit around each other.

Despite all the data that can be extracted frommeasurements by parallax, spectrometry and photometry,there is one vital piece of information that cannot bemeasured about a single star... its mass.

Since mass is one of the most fundamental measurementsof physics, naturally astronomers want to learn the mass ofa star. Binary stars are the key, because the details of theirorbit around each other allows the masses to be calculated.

Discovering the masses of stars by studying binary systemshas been critical in understanding the processes occurringwithin a star, and how each star changes during its life-time.

Categories of Binary StarsWhen you look at some stars in the sky there are many starsthat are close together.

Are these 2 stars abinary pair?

Are they orbitingaround each other,

or are theynowhere near each

other, and simplyhappen to be inthe same line of

sight from Earth?

If these are a binary pair they are in orbit around thecommon centre of mass of the system...

...but how can you recognise them?

Visual BinariesIf a double-star system is close enough, a telescope may beable to resolve the image well enough to see the individualstars, and see their positions change with time.This is called a visual binary.

The system must be observed over a period of time(possibly years) to be certain the stars are orbiting eachother, rather than just being stars that appear close togetherby being in the same �“line of sight�”, as in the photo at left.Eventually, the period of their orbit can be measured.

Eclipsing BinariesSome binary systems cannot be visually resolved, but revealthemselves because, when carefully measured, the lightintensity is found to fluctuate in a regular way.

This occurs because the plane in which they orbit eachother is more-or-less edge-on to us, so each star regularlyeclipses the other and blocks some of the light reaching us.

The graph shows how the light intensity varies for a binarypair in which one star is much larger than the other.

The period of the orbit is the time from one primaryeclipse to the next, or from secondary eclipse to the next.Typically, the period of a binary orbit like this is between afew days, up to a few months.

16


4. BINARY SYSTEMS & VARIABLE STARS




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17

Spectroscopic BinariesA binary system can also be detected by �“Doppler Shifts�”in the spectra of the stars as each member of the pairalternates between approaching us (blue shift) and recedingfrom us (red shift). For this to occur the plane of the orbitmust be more-or-less edge-on to the Earth.

The period of the orbit is determined by the time betweenthe repeated changes to the spectral lines.

Astrometric BinariesIn some binary systems, one of the stars is so faintcompared to its partner that it cannot be resolved visually,nor detected photometrically or spectrometrically.However, its presence may be inferred by the �“wobble�” itcauses to the bigger star.

A smaller �“satellite�” star does not just orbit around thelarger. Instead, both orbit around a point which is thecommon �“centre of gravity�” of the total system. For alarge-star/small-star system this common centre is veryclose to the larger star, but it still appears to �“wobble�” as itorbits this point.

The unseen partners to a wobbling star have been found torange from planets (this is not a binary system, but a �“solarsystem�” of sun and planet(s)) to massive neutron stars oreven �“black holes�”.

The period of the orbit can be determined by careful studyto find repetition of the �“wobble�” of the visible partner.

Determining MassRegardless of how the binary system is detected, theimportant outcome of studying the system is thedetemination of the period of the orbit, and the averagedistance between the partner stars (i.e. the orbital radius).

Once these are known, masses can be calculated:



Shows Normal Hydrogen SpectrumAA

BBBoth stars moving

across our line of sight

Shows Normal Hydrogen Spectrum

AA

BB

Later, both starsmoving across our line

of sight again

Hydrogen Spectrum shows double lines,

AA BB

Later, Star A receding, Star B approaching

One line is red-shifted, the other blue-shifted

Hydrogen Spectrum shows double lines,

AABB

Later, Star B receding, Star A approaching

One line is red-shifted, the other blue-shifted, but in the opposite way to the previous doubling.

m1 + m2 = 4 ##2 r3

GT2

m1 and m2 = masses of stars 1 & 2 in the binary pair.(in kg)

r = radius of orbit (average distance between the stars) in metres.

G = Universal Gravitational Constant = 6.67x10-11

T = Period of orbit, in seconds

This formula is derived from Newton�’s �“Law ofUniversal Gravitation�”, and also contains Kepler�’s3rd Law (that r3/T2 = constant)

S.I. units must be used

Example ProblemA binary star system has been identified in which the 2stars are estimated to be 7.80x109 metres apart, and theperiod of the orbit is 4.86 days.a) Find the combined mass of the stars.b) It is known that one of the stars is 3 times heavierthan the other. Find the masses of the individual stars.

SolutionFirst, ensure all data are in S.I. units:

T = 4.86 days = 4.86 x 24 x 60 x 60 = 4.20x105s.

a) m1 + m2 = 4##2r3 / GT2

= 4#2x(7.80x109)3/6.67x10-11x(4.20x105)2

= 5.07x1029kg

b) Since one star is 3 times heavier than the other:m1 + (3xm1) = 5.07x1029

! 4m1 = 5.07x1029

m1 = 1.27x1029 kg! m2 = 3.80x1029 kg

PRACTICE PROBLEMS at the end of section

Computer Simulation of Eclipsing Binaries

The syllabus requires that you model the light curves of eclipsing binaries.

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eecclliippssee..hhttmm



18

The Importance of Knowing the MassWhen a binary star system is studied to find the mass, it isusually possible to also measure the luminosity of the star(e.g. absolute magnitude) and its spectral type as well.

When the known masses are graphed against luminosity, aclear relationship is found:

It is thought that this relationship holds for all �“mainsequence�” stars, so it follows that once the luminosity ismeasured, the mass of any star can be read from the graph.

This means that the mass of any star on the �“mainsequence�” section of the H-R diagram is known, at leastapproximately.

A knowledge of the masses of stars in different parts ofthe H-R diagram has been important in reaching anunderstanding of the the processes that occur within a star.This in turn has led to the development of theories abouthow stars form, evolve and die.

These ideas are explored in the next section.

Variable StarsMany stars vary in brightness over time. These �“variablestars�” can be of many different types, and the variations intheir brightness can have many causes. The first step tounderstanding them is to classify them into �“types�”.

Variable stars can be Periodic or Non-Periodic,

...and...

they can be either Intrinsic or Extrinsic variables:

Extrinsic, Periodic Variable Stars include eclipsingbinaries. The variations have a very regular period and arecaused by the eclipsing of/by a partner star. This is anextrinsic process because it is external to to the star itself.

Intrinsic, Non-Periodic Variable Stars includesupernovae, �“flare stars�”, and other �“weirdos�” of thecosmos.

A �“Supernova�” is a huge, one-off star explosion which willbe studied in the next section. The explosion occursbecause of events occurring inside the star.

A �“flare star�” is a star which suffers irregular, explosiveoutbursts due to events occurring within its outer layers.

Intrinsic, Periodic Variable Stars include the�“Cepheids�”. This type of star undergoes changes inbrightness of about 1 magnitude, with an extremely regularperiod, and have a �“brightness graph�” with a characteristicshape. The changes in brightness are due to cycles ofchanges occurring within the star, resulting in a regularpulsation of the star.

Cepheids are considered in more detail (next page)because they have become another vital tool

to help astronomers measure the size and structure of the universe,

and unravel its history, and probable future...



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19

Cepheid VariablesCepheids are named after a star called �“$-Cephei�”discovered and named in the 18th century. Later it wasdiscovered that the brightness varied in a very regular way.As more stars of its type were discovered, they becameknown as the �“Cepheids�”.

Almost 100 years ago, an important relationship wasdiscovered. An astronomer studied a number of Cepheidvariables all located in the same star cluster, at the samedistance from Earth, and noticed that the brighter the starthe longer the period of the oscillation of brightness.

Later, it was discovered that there are actually 2 differentpopulations of Cepheids, called simply �“Type I Cepheids�”and �“Type II Cepheids�”, which both showed thisrelationship between luminosity and period of brightnessvariation:

Using Cepheids to Measure DistancesSince the period of brightness variation of a Cepheid isdirectly related to its luminosity, if the periodic variation ismeasured, then the absolute magnitude can be determined.

Then, if the average apparent magnitude is measured, thedistance to the star can be calculated using the distancemodulus formula,

m - M = 5 log(d/10)

Since Cepheids can be detected in other galaxies, thistechnique offers a method of measuring distances that areway beyond the limits of parallax measurements.



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Example ProblemA star identified as a Type I Cepheid has been observedin another galaxy. Its average apparent magnitude is +21,with its brightness varying in a regular cycle of 4.5 days.How far away is it from Earth?

SolutionThe Luminosity-Period Graph (left) shows that with aperiod of 4.5 days, the star�’s absolute magnitude shouldbe about -2.7.

Using m - M = 5 log(d/10)+21 -(-2.7) = 5 log(d/10)

log(d/10) = (21+ 2.7)/5 = 4.74! d/10 = 104.74 = 55,000

!! d = 550,000 pcThe star (and the galaxy it�’s in) is 5.50x105 parsecs away.This is about 1.8 million light years.

RR-Lyrae VariablesThe following information is NOT specified by the syllabus, and ispresented for interest only.

Another group of variable stars that have become very useful are known as�“RR-Lyrae Variables�”. These are more common than the Cepheids.

Their value lies in the fact that they all have approximately the same periodof light variation of about 12 hours (this makes them easily identified) andall have the same absolute magnitude of approximately +0.6.

Like Cepheids, once spotted, and apparent magnitude measured, theirdistance can be calculated by applying the distance modulus formula.


The study of Binary Stars can reveal thea)......................... of the stars. When a pair of starscan be b).................................. by a telescope andobserved, over time, to be c)......................................... each other, they are calledd)................................. binaries.

e).................................. Binaries cannot beresolved, but have a distinctive �“light curve�”graph with regular dips as each starf)................................ the other.

g)................................ Binaries showh)........................... shifts in their spectral lines, anda doubling of the lines, as one star approaches usand the other recedes.

i).................................. Binaries are detected by the�“wobble�” caused to a star by its unseen partner.

Once the orbital period is known, andj)............................ of orbit measured or estimated,the total mass of the pair can be calculated. It hasbeen found that there is a link between mass of astar and its k)....................................... and positionon the l).......................... Diagram.

1. (6 marks)a) What important piece of information about a star can bedetermined from the study of binary star systems?b) List 4 categories of binary systems, and outline how theyare recognised.c) What 2 measurements of a binary system need to bemade before the calculation named in (a) can be done?

2. (6 marks)For each set of data calculate the total mass of the binarysystem. (hint: check for S.I. units in each case)a) r = 8.75x109m, T = 1.80x105s.b) T= 26,500 hours, r = 3.85x108km.c) r = 5.20x106km, T = 1.55days.

3. (4 marks)The light from a group of stars is found to vary inbrightness in an irregular and unpredictable way. Furtherstudy shows that the cause is a shifting dust cloud betweenthe stars and Earth, which is blocking some of the light.How should these stars be classified as �“variables�”? Explainyour answer.

Variable stars vary in m).................................. overtime. This can be a �“n).........................................�”regular cycle of changes, or a one-off event orirregular, �“o)................ - .................................�”variations. The causes of the variations can becaused by events occurring within the star(�“p)..........................................�”) or can be causedby external events (�“q).......................................�”).

An example of an extrinsic, periodic variablewould be an r)............................. binary system. Asupernova is an example of ans)................................., ........................................variable. A good example of an intrinsic, periodicvariable star is the type known as�“t).................................... variables�”. These havebecome useful for calculatingu)..................................... because it was discoveredthat their luminosity is directly related to thev)...................................... of their brightnessvariations.

a) Explain the features of the graph labelled X, Y and Z.b) Calculate the mass of each star in the system.

5. (5 marks)a) Sketch the light curve for a typical Cepheid variable. Novalues are required.b) Explain how, if the values of the graph are known, thedistance to the star can be determined.

20





Mark values shown are suggestions only, and indicate the depth of answer required.




5 10 15 20TTiimmee ((ddaayyss))

XY

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4. (6 marks)The graph shows the�“light curve�” from abinary system inwhich one star isknown to have 100xthe mass of the other.The stars are known tobe 3.50x1011m apart.

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Birth of a StarAlthough �“outer space�” is often described as being avacuum, this is not quite true. Each cubic metre of�“empty�” space may contain thousands or millions of atomsand molecules, mainly hydrogen. Some regions are denserthan others, and in some places there may be huge �“clouds�”of gas measuring 50 light years across, or more.

Slight irregularities in parts of the cloud may begin tocontract by gravitational attraction. As a zone ofcontraction becomes denser, its gravitational field becomesmore intense, causing further, faster collapse. As itcollapses, the temperature rises and the mass begins tospin.

Eventually, after perhaps several million years, the core ofthe �“protostar�” becomes dense and hot enough for nuclearfusion to begin, and the mass of collapsed gas begins its lifeas a star.

Typically, from dozens up to thousands of stars may allform at about the same time from one huge gas cloud. Thefirst act of the new star �“cluster�” is to �“blow away�” thesurrounding remnant gas cloud with the �“solar wind�”.

Stages in the Life of a StarEvery star begins its life on the �“main sequence�”. If youplot its spectral class (or temperature) against luminosity, itlies very close to the lower border of the main sequenceband on a H-R diagram. Because all new stars plot alongthis curve it is called the �“Zero Age Main Sequence�”(ZAMS) curve.

Exactly where each new star joins the ZAMS curvedepends entirely on its mass.

Small stars �“burn�” their fuel slowly and will stay on themain sequence for billions of years. A star the size of theSun, for example, can be expected to remain on the mainsequence for about 10 billion years, which the Sun iscurrently about half-way through.

The larger the star, the faster it burns its fuel and theshorter its life-time on the main sequence.

Eventually, every star reaches a stage when it leaves themain sequence, first expanding into a giant, then beginningthe process of star death as dwarfs. The generalizedpathways of a star�’s life are shown below.

21


5. LIFE & DEATH OF STARS




InterstellarGas Cloud

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22

Nuclear Reactions in StarsThe size of any star is the balance between 2 opposingforces:�• Gravity, which attempts to collapse and compress the starinwards, and�• Heat and Radiation Pressure, which would cause the starto explode outwards if not for gravity.

The heat and radiation within a star is produced by nuclearfusion reactions occurring in the star�’s core. There areseveral different reactions you need to know about.

The Proton-Proton ReactionThis is the �“classic�” fusion of hydrogen into helium and isparticularly important in small to medium sized mainsequence stars.

Reaction 1:Two hydrogen nuclei (protons) fuse to form Helium-2,which immediately undergoes radioactive decay to�“deuterium�” (�“heavy hydrogen�” or hydrogen-2).

positron neutrinoThe positron (positive electron) will eventually meet anordinary electron. They will then annihilate each other in aburst of gamma radiation.Reaction 2:The hydrogen-2 fuses with another proton forminghelium-3, and gamma radiation.

Reaction 3:Two helium-3 nuclei fuse to form helium-4 and release 2protons, which can re-cycle back to reaction 1.

Overall: Hydrogen Helium + energy

The Carbon Cycle ReactionThis reaction occurs in medium to large main sequencestars, and predominates in the larger ones. In a star the sizeof our Sun, both Proton-Proton and Carbon Cyclereactions occur, although the P-P reaction dominates.

A cycle of reactions occurs as follows:

Overall, the result is the same;

Notice that carbon is involved in the first step, and is re-generated by the last step. It could be said that carbon actsas a catalyst.

As before, any positrons formed will eventually meet anelectron and be annihilated in a burst of gamma rays.

Both these main-sequence reactions involve fusion which(overall) converts hydrogen to helium. In each reaction asmall amount of mass �“disappears�” and is converted toenergy according to Einstein�’s E = mc2 equation.

So, all main sequence stars turn hydrogen into helium viaone or both of the fusion reactions.

Eventually, the core of the star becomes depleted inhydrogen and rich in helium. When a critical level isreached, the star enters a new phase of its life...



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Main Sequence Stars FuseHydrogen into Helium



23

After the Main Sequence PhaseLarge mass stars burn fast and hot; smaller stars burnslower and cooler, but eventually they all end up with a coredepleted in hydrogen and rich in helium.

Up until now, the coreof the star has not beenhot enough for any otherfusion reactions beyond thehydrogen to helium reactions.

Now, as it runs out of hydrogen, the core ceases producingenergy and gravity causes it to collapse inwards. We�’retalking zillions of tonnes of collapsing matter whichrapidly converts gravitational potential energy into heat.

The core temperature skyrockets and at a certain point anew fusion reaction begins... the core starts fusing helium.

Meanwhile, the extra heat generated in the core hasaffected the layers (mainly unreacted hydrogen)surrounding the core. Depending on the size and density ofthe star, a �“shell�” of hydrogen may begin fusing around theoutside of the core, adding even more heat, and possiblycausing eruptions which may �“blow away�” outer layersof the star.

The main effect, however, is that the outermantle of the star swells enormously with theextra heat coming from within. The star swellshugely to become a giant star.

Being so much bigger, it becomes muchmore luminous (moves upwards on theH-R diagram). At the same time, theouter surface actually becomes cooler,and its colour redder...

it has become a Red Giant or Supergiant star.

Synthesis of the ElementsFusion in a giant star doesn�’t stop at carbon. Depending onthe size and core temperature of the giant, a variety offusions can occur, gradually producing nearly all theelements of the Periodic Table. For example:

carbon + helium oxygenoxygen + helium neonoxygen + carbon siliconneon + helium magnesiummagnesium + silicon iron

...and many more.

As far as iron, the fusion reactions release energy. Beyondiron the reactions tend to absorb energy, but atoms as largeas lead can be formed.

The universe began as entirely hydrogen and helium (ratioabout 3:1) and is still predominantly made of just these two.In some places such as the Earth, however, there are manyheavier elements. We believe that these have all been madeby fusion in giant stars.

Eventually, the energy-producing fusions begin to run outof fuel. Remember that fusion to anything larger than ironabsorbs energy rather than releasing it. As iron accumulatesin the core, the star�’s ability to release energy reachesanother critical stage...

... the star is about

to die!



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24

Small Stars Die With a WhimperIf the original mass of the star is less than about 5 times themass of the Sun, the star goes through its �“Red Giant�”phase (previous page) starting by burning helium to carbon,and possibly developing an �“onion-skin�” structure ofdifferent fusion reactions in successive shells.

In a dying red giant there are sudden outbursts or �“flashes�”of energy as a shell runs out of fuel, collapses inwards andthen rebounds.

These outbursts have the effect of blowing away an outerlayer as a hollow sphere of gas and dust called a �“planetarynebula�”.

After several such events there may be little left of the starexcept its iron-rich core. Without any remaining �“fuel�” forfusion reactions, this core collapses under gravity to form adense lump of �“dengenerate matter�”.

�“Degenerate matter�” is where the atoms themselves arecompressed into a smaller volume by squashing theelectron orbits closer to the atomic nuclei. A mass the sizeof the Sun can end up compressed down to the size of theEarth, and have a density of 1 tonne per cm3.

Fusion has ceased, but this star remnant has a lot ofresidual heat, so its surface temperature may be around10,000oK. Being very small, the total luminosity is quitelow.

On the H-R diagram, it plots at a point low down, but wellleft of the main sequence. This is a �“White Dwarf�” star.

Over millions of years it radiates its residual heat, graduallycooling and disappearing from our view.

Star DeathExactly what happens at the end of a star�’s life depends very much on the mass of the star.

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Big Stars Go Out With a BangIf the star�’s original mass is greater than about 5 times themass of our Sun, its death is quite spectacular.

A star this large will certainly have developed an �“onion-skin�” layer structure with some heavy elements in the core.When this runs out of fusion fuel, the core suddenlycollapses under gravity and rapidly implodes upon itself.

The outer layers suddenly have nothing holding them outthere, so they fall inwards at an enormous speed. Theseouter layers still contain fusionable �“fuel�” which nowignites in a cataclysmic detonation which explodesoutwards... a �“Supernova�” explosion.

Three significant things result immediately:�• large amounts of heavy elements (up to and beyonduranium) are formed in a rapid burst of fusion events.�• the force of the explosion in a shell around the core,further accelerates the core implosion.�• the outer layers of the star are blown outwards in a fireballthat briefly outshines a million stars, and continuesexpanding outwards as a cloud of debris for thousands ofyears.

What becomes of the imploding core depends on its mass:

If the core is biggerthan about 3 solar

masses, nothing canstop the implosion.

The matter iscrushed into a

�“singularity�” with anintense gravitationalfield which not even

light can escapefrom. Hence it is

called a �“black hole�”.

Inside the black holewe think that time

stops and all the normal laws of physicsno longer apply.

In effect, the matter has left our universe.

If the core is more than 1.4, butless than 3 solar masses, it forms a

neutron star. The atoms arecrushed together so that electrons

are forced into the nucleus ofatoms forming a solid ball of

neutrons about 20 km across with adensity millions of tonnes per cm3.

The neutron star spins rapidly andgives out beams of high frequencyEMR, such as X-rays. If the beamsweeps past the Earth we detectpulses of radiation. When firstdiscovered, these were called

�“pulsars�”.

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25

Plotting and Analysing H-R DiagramsYou may have been given data about a variety of stars and tried plotting it graphically to form H-R diagrams.

Your analysis of the resulting diagrams is an important test of your understanding.

H-R Plot of Nearby or Brightest StarsA common exercise is to start with data for 20 or more nearand/or bright stars visible from Earth.Data used is often;�• surface temperature, and�• luminosity compared to that of the Sun.

When graphing these it is essential that the luminosity scalebe logarithmic or exponential and that the temperaturescale increases to the left, to correspond to a H-R diagram.

A typical result is as follows. Each dot represents one localand/or bright star.

30 25 20 15 10 5

Surface Temperature (ooK x1033)

Lum

inos

ity (S

un =

1)

10-5

10-4

10

-310

-210

-11

10

102

103

104

Analysis & Interpretation�• Most stars lie very close to a single curving line.

(Dotted curve) The Sun is shown shaded grey.Interpretation: These are �“Main Sequence�” stars, anddemonstrate the relationship between luminosity andsurface temperature. There are fewer of them at top leftbecause large stars have short lives.

�• A smaller group of stars are located at top right. Theirposition shows they are very luminous but relatively cool.Interpretation: These are �“Red Giants�”. There are fewer ofthem because the life span as a giant star is generally short.

�• One star (arrowed) has low luminosity and medium-hottemperature.Interpretation: This a �“White Dwarf �”... a dying star.

H-R Plot of an �“Open Cluster�”So-called �“open clusters�” give a result as shown, quitedifferent to our �“local neighbourhood�”.

20 15 10 5Surface Temperature x1033

Lum

inos

ity (S

un =

1)

10-5

10-4

10

-310

-210

-11

10

102

103 Notice that there are

no red giants nor whitedwarfs.

The full range of mainsequence stars arepresent, and their

positioning is tightlyalong the same curve.

Interpretation:This is a

very young group of stars.

They haven�’t had time for any to leave the main

sequence.

An �“Open Cluster�”

gives a H-RR diagram

which isessentially a ZAMS plot

H-R Plot of a �“Globular Cluster�”So-called �“globular clusters�” give a different result again.

20 15 10 5Surface Temperature x1033

Lum

inos

ity (S

un =

1)

10-5

10-4

10

-310

-210

-11

10

102

103

The top end of themain sequence seems

to be missing, andthere are quite a few

red giant stars.

InterpretationThis cluster is

much older,and the larger,

shorter-lived stars have left the

main sequence

A �“Star Cluster�”is thought to be a group of stars

that all condensedfrom the same

gas cloud, and are all about

the same age.

Stars visible fromEarth seem to be

a mixed populationof stars



26

Estimating the Age of a Star ClusterThe differences between the graphs of star clusters(previous page) offers a way to estimate the age of differentclusters and galaxies.

Of particular interest is the �“turn-off point�” where thegraphical plot of the stars in a cluster leaves the mainsequence and turn upwards to the right. The lower this�“turn-off �” is, the older the cluster or galaxy.

The following graph shows star plots for severalhypothetical star clusters to give you the idea.

The very young cluster with a star plot as shown would be�“only�” 100 million years old, or less. If any �“Spectral ClassO�” stars are present it must be only about 10 million yearsold, since these have extremely short lives.

The oldest cluster, with its �“turn-off point�” near the Sun-size stars is at least 10 billion years old, and probablyformed very early in the history of the universe, soon afterthe Big Bang settled down and began producing galaxies.

The 2 in-between clusters shown could be estimated asbeing about 2 billion, and 5 billion years old.

H-R Pathways of a Star�’s LifeThe diagram below shows the approximate life-pathwaysfor a Sun-sized star, and a star about 5 times more massive,and one 10 times more massive.

In cases where the pathway goes off the H-R diagram, thepathway and its final position is not to scale, and may befanciful.




Lum

inos

ity

(Rel

ativ

e to

the

Sun.

Su

n =

1)10

-310

-210

-11

1

0

102

103

104

ZAAMS CCuurvvee

Very youngcluster Older clusters.

Upper main sequencestars have evolved

into giants

The oldest clusters havelower �“turn-ooff points and contain dying white dwarfs


Lum

inos

ity+

15

+10

+5

0

-

5

-

10

RReedd GGiiaannttss

Whitee Dwaarfs

MMaainn SSeequueence


1M

5M

5M star leaves acore about 2M

10M

Supernova.Briefly veryluminous &

hot

Neutron Star&

Pulsar.

Hot, but verylow luminosity

10M star leaves a core about5M, which will collapse to

form a BLACK HOLE.

Zero Luminosity!

ffaaddeess aawwaayy

HSC Physics Option Topic �“Astrophysics�”Copyright © 2006-7 keep it simple science www.keepitsimplescience.com.au


Stars are created in huge interstellar a)......................................which collapse due to b)............................... As they do so,the density and temperature c)..........................., until atomsare forced together and begin d)......................................... inthe core of the new star.

All new stars plot onto a H-R diagram on a line along thebottom of the e)..................................................... known asthe �“f)....................... curve�”. Generally, the more massivethe star is, the higher is its g)............................................ and....................................... The more massive a star, the faster itburns its fuel and the h)................................... its life-span.

In smaller main sequence stars the main fusion reaction isthe i).......................................................... reaction. This fusesj)...................................... to k)................................... In largerstars the same overall result is achieved via a more complexpathway involving l)......................, ............................and.......................... nuclei. This is called the �“m).................................................. reaction�”. Eventually, the core of the starbecomes depleted in n).............................., fusion slows andthe core o)..................................... under gravity.

1. (6 marks)a) Sketch a H-R diagram (label axes, but no values required)and show the positions of:

i) the ZAMS curveii) main sequence

iii) red giantsiv) white dwarfs

b) On your diagram, add an �“X�” to mark the approxposition of the Sun, and show with a dotted line its futureexpected evolution.

2. (4 marks)Outline the process of star formation, with reference to theeffect of star mass on a star�’s �“joining position�” on theZAMS curve.

3. (4 marks)Compare and contrast the proton-proton reaction with thecarbon cycle fusion reaction. Specific nuclear equations arenot required, but more general word equations are.

4. (4 marks)a) Write a nuclear equation to describe the �“heliumburning�” fusion reaction.b) Discuss the role of giant stars in altering the chemicalcomposition of the universe.

This heats the core enough for fusion of p)...........................into ..................................... to begin. The outer layers of thestar expand outwards so the star becomes q).........................luminous, but its surface temperture r)...................................It is now a s).............................................. star. In and aroundthe core many other fusion reactions occur which producemany other t).....................................

Eventually, the star runs out of fuel and begins to die. If itis small, there may be minor �“flashes�” of energy whichblow away the outer layers as a �“u)............................................................................�”. Meanwhile the core collapses to form�“v)....................................... matter�”, radiating residual heatwith w)........................... luminosity, but x)..............................temperature. This remnant is known as a y)........................................................... star.

If the star is larger than about 5 times z).................................,when the fuel runs out the core collapses very suddenly.The infalling outer layers explode as aaa).............................................., which briefly shines as brightas a million suns. This blows away all the outer layers, andcompresses the collapsing core even further. Depending onthe size of the core, it may collapse to form either aab).......................................... or a ...............................................

5. (12 marks) Explain each of the following terms, and for each discussbriefly how it forms.

a) planetary nebulab) degenerate matterc) supernovad) neutron stare) pulsarf) black hole

6. (4 marks)The following diagram shows a generalized H-R star plotfor the members of 2 star clusters.

a) Discuss any differences in the categories of stars likely tobe present in each cluster.b) State any other difference between clusters J & Ksuggested by the star plot. Explain your answer.

27




ZZAAMMSS

Star Clusters J K




28 www.keepitsimplescience.com.au


CONCEPT DIAGRAM (�“Mind Map�”) OF TOPICIn all the Core Topics you were given examples of a �“Mind Map�”

as a way to summarize the content of the topic.If you have found this a useful way to summarize and learn, then you may want to do it again.

By now you should have developed the skills to do it yourself...

Binary Systems &

Variable Stars

ASTROPHYSICS

Observing the Universe from Earth

PhotometricMethods

Parallax &

Spectroscopy

Life & Death of

Stars

PhotoMaster - Astrophysics

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Transcript of PhotoMaster - Astrophysics