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9.2 Space
9.3 Motors & Generators
9.4 Ideas-Implementation
9.7 Astrophysics
9.8 Quanta to Quarks

9.7 Astrophysics Page 2
9.7 Astrophysics Page 3
9.7 Astrophysics Page 4

 

NOTE: This page is a continuation of the notes and worksheets for topic 9.7 Astrophysics.  Four separate pages were used for this topic because of the large volume of material in the topic.  This will keep download time within acceptable limits.

 

9.7 OPTION - ASTROPHYSICS CONTINUED PAGE 4

PREPARED NOTES

NOTE: Numbers appearing in parentheses at the end of sentences or paragraphs refer to the references provided in the Bibliography at the end of these notes.

 

THE RED GIANT STAGE IN THE LIFE OF A STAR

When the hydrogen has been exhausted in the core of a main sequence star, hydrogen burning ceases.  This leaves a core consisting almost entirely of helium, surrounded by a shell through which hydrogen burning works its way outward in the star.

When the hydrogen burning stops in the core, the temperature there decreases causing a corresponding decrease in pressure.  The core contracts under the weight of the outer layers of the star.  As the core contracts it becomes hotter and the heat flows outwards warming the gases around the core and increasing the rate of shell hydrogen burning.  Helium produced by these reactions falls back into the core, which continues to contract and heat up as it gains mass.  Over the course of hundreds of millions of years, the core of a one solar mass star compresses to about one-third of its original radius, while the core temperature increases from about 15 million K to about 100 million K.  (3)

While the core contracts, the hydrogen burning continues to move outwards causing an increase in the star’s luminosity and an increase in the star’s internal pressure.  This increase in pressure makes the entire star expand to many times its original radius.  This massive expansion of the star’s outer layers causes the star’s surface temperature to decrease.  Once the surface temperature has reached about 3500 K, the gases glow with a reddish hue, in accordance with Wien’s Law.  The star is then called a Red Giant star.  Red Giant stars are stars that have finished their time on the main sequence and have evolved into a new stage of existence.  (3)

Examine the evolutionary track for a one solar mass star shown on H-R diagram (a) below.  Make sure you can explain the shape of this track in terms of the physical processes described above.

In a moderately low mass red giant, which the Sun will be in another 5 billion years or so, the dense helium core is about twice the size of the Earth and the star’s bloated surface has a diameter of about 1AU.

When a star first becomes a red giant, the temperature of the contracted helium core is still too low for helium fusion to commence.  In time, as the hydrogen burning shell continues to add mass to the helium core, the core contracts even more, further increasing the core temperature.  When the core temperature reaches about 100 million K, the fusion of helium (helium burning) begins there.  This process, also called the triple alpha process, converts helium to carbon and oxygen.  In a high-mass red giant (mass > 2 to 3 solar masses), with a hotter core, helium burning begins gradually whereas in a low-mass red giant (mass < 2 to 3 solar masses), it begins very suddenly, in a process called the helium flash.

Note that for red giants with masses less than about 0.5 solar masses, the core will never reach the temperature required for helium fusion and the core and shell both contract and become hotter until the star has become a white dwarf (9).
The reactions involved in the triple alpha process are as follows:

           

Clearly, in step 1, two helium nuclei combine to form a very unstable isotope of beryllium.  In step 2, a third helium nucleus collides with the beryllium nucleus to form a stable isotope of carbon.  A gamma ray photon is emitted in this process.  Note that the name “triple alpha process” arises from the common name for the helium nucleus – the “alpha particle”.

Some of the carbon produced in the triple alpha process can fuse with another helium nucleus to produce a stable isotope of oxygen, as shown below:

                         

The triple alpha process produces only 10% of the energy per kilogram of fuel compared with hydrogen burning (12).  A mature red giant burns helium in its core for about 20% as long as the time spent on the main sequence (3).  So, for example, in the distant future our Sun will burn helium for about 2 billion years.

Once the helium burning process has begun in the core of a red giant, the star undergoes further changes.  The star’s superheated core expands like an ideal gas.  Around the expanding core, temperatures fall, so the hydrogen burning shell reduces its energy output and the star’s luminosity falls.  This allows the star’s outer layers to contract and heat up.  Thus, after the onset of helium burning, a red giant is less luminous, is hotter at the surface and is smaller than it was before helium burning started.

Study the evolutionary track for a one solar mass star shown on H-R diagram (b) below.  In accordance with the physics described above, the track moves toward lower luminosity and higher surface temperature, following a track called the horizontal branch.  Stars along the horizontal branch have helium-burning cores surrounded by hydrogen-burning shells.

 

The changes that occur in red giants after the onset of helium burning cause some red giants to become unstable.  For instance, the hydrogen burning shell may become sufficiently unstable to cause the star to pulsate as a periodic variable, driven by the changed radiation pressure within (12).

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AFTER THE CORE HELIUM-BURNING STAGE 

Eventually all the helium in a star’s core is exhausted and core helium-burning ceases.  What happens next depends critically upon the ZAMS mass of the star.  (1)

 

STARS LESS THAN 4 SOLAR MASSES 

Let us deal first with low mass stars of less than 4 solar masses.  The core consists of carbon and oxygen.  Around the core is a shell of helium.  Surrounding the helium shell is the now dormant hydrogen shell.  Without thermonuclear reactions to maintain the core’s internal pressure, the core contracts, releasing heat into the helium shell.  Fusion of helium begins in this shell.  (3) 

The energy released from the shell helium burning causes the outer layers of the star to expand again.  Luminosity increases, surface temperature decreases and the star enters a second red giant phase.  These stars are called asymptotic giant branch stars (AGB stars) and their evolutionary tracks follow the asymptotic giant branch on the H-R diagram.  See below.  Stars of less than 4 solar masses in the AGB phase are nearing the final stage in their lives.  We will complete their story soon. 

Just as an aside, it is interesting to consider why stars of less than 4 solar masses cannot simply start fusing the carbon and oxygen in their cores to produce more energy.  The reason is that electron degeneracy pressure stops the cores of such stars from contracting sufficiently to produce the required temperatures for the fusion of carbon and oxygen.  The Pauli Exclusion Principle tells us that no two electrons can occupy the same quantum state at the same time.  This effectively places a limit on the degree to which a substance can be compressed because eventually the electrons will be so close together that any further compression would violate the exclusion principle.  (3) 

           

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STARS OF 4 OR MORE SOLAR MASSES 

Let us now consider what happens to a star of 4 solar masses or more after core helium burning ceases.  For such a star, the core is sufficiently massive to continue contracting, increasing the core temperature.  When the core temperature reaches 600 million K, carbon burning commences.  This fusion process produces oxygen, neon, sodium and magnesium.  (3)

                                   

For stars with a ZAMS mass of 8 solar masses or greater, the cessation of carbon burning results in further contraction and heating of the core.  At a core temperature of around 1 billion K neon burning begins, which uses up the neon accumulated from the carbon burning and increases the amounts of oxygen and magnesium in the star’s core.

                                   

Once the neon burning has finished, the core will contract again and oxygen burning will commence at around 1.5 billion K.  This reaction produces sulfur.

                                   

When oxygen burning is complete, the core will contract again and silicon burning commences at around 2.7 billion K.  Silicon fusion produces several nuclei from sulfur to iron.  (3)

                                   

Each new stage of core burning generates a new shell of material around the core.  After several such stages, the internal structure of a very massive star (eg a 25 solar mass star) resembles that of an onion as shown in the diagram below.  Note that iron is the final element that is produced by the fusion reactions occurring inside the core of a massive star.  The fusion of iron or any element heavier than iron consumes energy rather than releasing it.  (3) 

Between each new stage of core burning comes a period of shell burning and a new red giant phase for the star.  This means that the evolutionary tracks of high mass stars go through a series of back-and-forth gyrations on the H-R diagram.  See the diagram below showing the evolutionary track for a star of about 10 solar masses.  (3)

           

 

The energy released by the processes described above causes the star’s outer layers to expand greatly.  The result is a Supergiant star.  The largest supergiants are a thousand times larger than our present-day Sun, with diameters as large as the orbit of Jupiter around the Sun.  (3)

Betelgeuse and Rigel in the constellation of Orion and Antares in the constellation of Scorpius are easily observable examples of supergiant stars.  Spring/summer is best for observing Orion in Australia and autumn/winter for Scorpius.

           

 

The diagram above has been adapted from Figure 22-13 on p.550 of Ref.3.  It shows a high-mass star that has become a supergiant.  Its diameter is almost as large as the orbit of Jupiter around the Sun.  The star’s energy comes from six concentric burning shells, all contained within a volume roughly the size of Earth.  No thermonuclear reactions occur in the iron core, since fusion reactions that involve iron absorb energy rather than releasing it

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NUCLEOSYNTHESIS 

Nucleosynthesis is the process of creating elements by nuclear reactions (5).  The Syllabus requires that you are able to “discuss the synthesis of elements in stars by fusion”.  In the “Cosmic Engine” topic in the Preliminary Course we saw that hydrogen, helium and lithium were created in the Big Bang.  We have seen in this topic that hydrogen is fused into helium in main sequence stars, that helium is fused into carbon and oxygen in red giant stars and that all elements up to and including iron can be produced by fusion reactions in the cores of supergiants.  Theoretically, you already have sufficient information to successfully answer this Syllabus point, since the remaining elements in the Periodic Table are not produced by fusion reactions.

However, for completeness we will mention the two main processes that are believed to be responsible for the production of the elements heavier than iron.  The first of these is the slow neutron capture reaction that occurs in the shells of AGB stars.  The s-process, as the reaction is called, involves the capture of neutrons by existing nuclei (eg Fe-56) to form heavier ones.  Unstable nuclei formed in this way then undergo the beta-decay process to produce new elements.  This process can form elements up to and including lead.  Once s-process elements are formed, the AGB star conveniently convects these to the surface, where they may be released either in a stellar wind or in a subsequent supernova explosion.  The second process is the rapid neutron capture reaction, also called the r-process.  This occurs during type II supernova events and builds on iron to produce all of the heavier elements found in the periodic table.  (1 & 15)

Much research continues into the question of how the elements from iron to uranium were made.  The rapid proton capture reaction which is believed to be the cause of Nova explosions and X-ray bursts is being investigated as a possible source of heavier elements (15).  The possibility that fusion reactions involving iron and progressively heavier elements may be fueled by the huge energy output of a supernova explosion is also being examined (3).

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DETERMINATION OF THE AGE OF A STAR CLUSTER

A group of stars formed together from the same giant molecular cloud and held together by gravity is called a cluster (5).  There are two main types of cluster – Open Clusters and Globular Clusters.  These are distinguished on the basis of appearance, age, size and position in the galaxy.  Stars in a cluster are of approximately the same age.  (9) 

Open clusters contain from a few dozen stars up to a few hundred together with dust and gas from which new stars may be forming.  The stars are far enough apart to be resolved by the naked eye or a telescope.  Open clusters occur in the galactic plane and are therefore sometimes referred to as Galactic Clusters.  Open clusters contain some hot, massive O and B class stars.  Since such stars have short lifetimes, open clusters are relatively young.  Good examples of easy to find open clusters in the southern hemisphere include the Jewel Box, the Scorpio Clusters M6 and M7 and the Pleiades.  (9) 

Globular clusters contain from several thousand stars up to several million arranged in spherical-shaped geometries.  They contain relatively little dust or gas and no high mass main sequence stars.  In fact the stars in them are as old as the galaxy itself.  The stars are also very close together, astronomically speaking, and so most stars in the central region of a globular cluster cannot be resolved by earth-based telescopes.  Globular clusters are located in the galactic halo region above and below the galactic plane.  They are “left-overs” from the formation of the galaxy.  There are about 150 known globular clusters in our galaxy and possibly up to about 200 total (14).  The brightest example is w-Centauri, clearly visible with binoculars from Sydney’s latitude all year round.  (9 & 10) 

The age of a cluster can be determined by plotting an H-R diagram of the cluster.  In an H-R diagram for a very young cluster, all the stars lie on or near the main sequence.  As time goes by the high-mass, high-luminosity stars are the first to evolve away from the main sequence, as they become red giants.  Over the years the main sequence gets shorter and shorter.  (1 & 3) 

The age of a cluster can be determined from the turnoff point, which is the top of the surviving portion of the main sequence on the cluster’s H-R diagram.  The stars at the turnoff point are just completing their hydrogen-burning phase, so their main sequence lifetime is equal to the age of the cluster.  Stellar modelling based on the nuclear processes occurring in stars has enabled main sequence lifetimes to be associated with each particular turnoff point.  Thus, the age of the cluster can be determined.  (1 & 3) 

Age determinations have been made for many clusters.  The oldest clusters are of course the globular clusters and seem to be almost as old as the universe itself – 12 to 15 billion years.  Open clusters are much younger.  The Pleiades cluster, for example, is estimated to be about 100 million years old.  (12) 

Clearly, the accuracy and reliability of the turnoff point determination is paramount.  The position of the turnoff point can best be determined by overlaying a theoretical ZAMS (zero-age main sequence) plot drawn to the same scale on top of the H-R diagram for the cluster under study.  With the appropriate x-axis scales aligned, the ZAMS plot can then be moved vertically to obtain the best match of the theoretical ZAMS with the observed main sequence on the H-R diagram of the cluster.  The turnoff point, where stars are starting to move away from the main sequence, is then usually easy to define. 

Be aware that once the turnoff point is identified, there are a few different methods available for determining the age of the cluster depending on what information you have available. 

Let us look at an example of the process.  Study the colour-magnitude diagram (equivalent to an H-R diagram) for the M55 globular cluster, shown below.

 

           

 

This diagram was adapted from: 

http://antwrp.gsfc.nasa.gov/apod/ap010223.html

Each dot in this diagram represents the apparent magnitude (measured through a V filter) and surface temperature (as measured by the colour index, B – V, adjusted for interstellar reddening) of a star in the cluster.  Since all of the stars in a cluster are essentially at the same distance from Earth (about 6000 pc in this case), the apparent magnitude (a measure of apparent brightness) is a direct measure of luminosity.  (3) 

As described above a theoretical ZAMS H-R diagram would be fitted to the main sequence on the H-R diagram of the cluster.  This highlights the position of the turnoff point, making it easier to identify.  Once this has been done, one could use the B-V value at the turnoff point and some mathematical manipulation to obtain an age for the cluster.  Alternatively, one could use the luminosity value at the turnoff point, to calculate the mass of the stars at that point and then use an equation connecting star mass with main sequence lifetime to calculate the age of the cluster. 

In the example of the M55 globular cluster, the age of the cluster works out to be between 13 and 15 billion years depending on the method used. 

Note that in our study of the age determination of clusters we have stated that the age of the cluster is equal to the main sequence lifetime of stars at the turnoff point.  Some could argue that the age of the cluster must be measured from the time of the initial collapse of the molecular cloud (1).  Strictly speaking this is true.  However, the time taken for the pre-main sequence evolution of the stars at the turnoff point is only a very small fraction of the time spent by those stars on the main sequence (3).  Therefore, it is reasonable to approximate by saying that the age of the cluster is equivalent to the main sequence lifetime of stars at the turnoff point. 

 

Extension – Non-Examinable: 

Just for the record, horizontal branch stars are post-helium-flash, low-mass stars with luminosities of about 50 times that of the Sun and in which there is both core helium burning and shell hydrogen burning.  These stars will eventually move back toward the red giant region as their fuel is exhausted. 

Also for those who are interested, for main sequence stars, the relationships between the luminosity, mass and time on the main sequence are as follows: 

Luminosity is directly related to mass:

           

 

Lifetime on the main sequence, t, depends critically on both mass and luminosity:

                                               

Joining these two equations together we have:

                                               

These equations can be used to calculate estimates of main sequence lifetimes.

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STELLAR DEATH 

“Out, out brief candle! Life’s but a walking shadow, a poor player that struts and frets his hour upon the stage and then is heard no more.”  Shakespeare – Macbeth Act 5 Scene 5. 

All material things come to an end.  As powerful and as majestic as all stars are, eventually they grow old and die.  Eventually all stars reach a stage where the material in their cores cannot undergo further fusion.  This could be because the core cannot contract any further to reach the temperature required for the next possible set of fusion reactions or it could be that the core consists of iron, which will not fuse to produce energy.  Around these dormant cores, fusion continues in the various shells that each star has developed during its lifetime.  In their death throes all stars shed their shells into space and undergo core collapse by gravity.

 

STARS OF 8 SOLAR MASSES OR LESS 

Current research indicates that all stars with ZAMS masses of 8 solar masses or less shed a large portion of their mass during the AGB phase of their evolution.  During this phase, alternating ignitions of hydrogen and helium burning shells produce the energy in the star.  As each new helium-shell-burning episode begins bursts of energy known as thermal pulses spread outwards through the star blowing mass into space.  A 1 solar mass star loses about 40% of its mass.  The more massive the star, the higher the proportion of its initial mass that is lost.  (1 & 3) 

During these thermal pulses, the outer layers of the star can separate completely, exposing the hot core.  Ultraviolet radiation from the exposed core ionizes and excites the expanding shell of ejected gases.  These gases therefore glow and emit visible light, producing a planetary nebula.  Over time, perhaps no more than 50 000 years, the planetary nebula disperses, cools and fades from view.  Note that the name “planetary nebula” is really a misnomer.  It comes from the fact that through a small telescope the expanding shell of glowing gas can look like a planet.  (1 & 3) 

No more nuclear reactions take place in the exposed core.  If it has not already done so, the core collapses under gravity and provided its mass is not greater than 1.4 solar masses, it becomes a degenerate (non-contracting), dense sphere about the same size as the Earth.  The star is now called a White Dwarf.  The interior of a white dwarf consists mainly of carbon and oxygen atoms floating in a sea of degenerate electrons.  The White Dwarf gives off thermal radiation, which causes it to glow.  As it cools, it remains the same size, since the degenerate electron pressure does not depend on temperature but becomes less luminous, eventually fading into obscurity as a black dwarf.  (1 & 3) 

Note that the 1.4 solar mass limit to the size of a white dwarf is called the Chandrasekhar limit, after the Indian-American Physicist Subrahmanyan Chandrasekhar, who did pioneering research on white dwarfs.  The Chandrasekhar limit is the maximum possible mass of a degenerate star, above which it will be unable to support itself against the inward pull of its own gravity (5). 

It is worth considering at this stage what the evolutionary tracks of stars look like as they become white dwarfs.  Starting from the top of the AGB, the track moves horizontally from right to left across the H-R diagram as the temperature increases.  In some cases loops appear on the diagram corresponding to thermal pulses.  As the planetary nebula and core cool, luminosity decreases and the track turns down towards the lower right hand corner of the H-R diagram.  See the excellent H-R diagram below for a 1 solar mass star, taken from the Sloan Digital Sky Survey website at: 

http://cas.sdss.org/dr4/en/astro/stars/stars.asp

Note that an updated version of this diagram now appears at this link.

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STARS OF MORE THAN 8 SOLAR MASSES 

Stars with ZAMS masses of greater than 8 solar masses experience a different death. Stars with more than about 8 solar masses explode as type II supernovae after a lifetime of only a few million years and become neutron stars or black holes.  (3)

Such massive stars still experience the large mass loss due to thermal pulses and the core collapse that less massive stars experience.  The difference, however, is that with these more massive stars the core is greater than 1.4 solar masses when core collapse begins.  So, as the core collapses under its own gravity the electron degeneracy pressure is unable to stop the collapse.  In a fraction of a second, the core becomes so dense that electrons and protons are forced to combine to form neutrons.  This process releases neutrinos that carry large amounts of energy out of the core, cooling it dramatically.  If the mass of the core is less than about 3 solar masses, the neutron degeneracy pressure in the core brings the collapse to a sudden stop.  At this stage the density of matter in the core is about 1017 kg/m3 – the density of nuclear matter.  (3 & 5) 

Due to the sudden stop of the collapse, the innermost portion of the core bounces back and expands.  This causes a powerful pressure wave to spread outwards from the core.  At the same time, the dramatic cooling of the core caused by the escaping neutrinos reduces the pressure in the regions surrounding the core and causes the matter in these regions to fall inwards at speeds up to 15% the speed of light.  When the inward-falling material hits the rigid iron core, it meets the outward-moving pressure wave.  The result is an outward–moving shock wave that totally disrupts the star.  The energy released by this shock wave is of the order of 1046 joules – a hundred times more energy than the Sun has emitted in its whole lifetime.  (3) 

The energy spreading throughout the star drives the reactions that produce all the elements heavier than iron.  The shock wave blows most of the matter that made up the star out into space as a cloud of expanding gas and dust.  This matter will one day seed the formation of new stars.  (3) 

During this explosion, the luminosity increases up to several billion times as the core is partly exposed and the star appears brighter than an entire galaxy.  This increased brightness lasts for several days and fades away over a period of months.  This explosive event is called a supernova (plural - supernovae) and the dense, collapsed stellar core left behind is referred to as the supernova remnant.  (1 & 3) 

As an aside, it is worth mentioning that the event described above is a type II supernova, resulting from the death of a massive star.  SN1987A is an example of a type II supernova that was observed in the Large Magellanic Cloud in 1987.  The star that exploded in this case is believed to have been a blue supergiant star with a ZAMS mass of about 20 solar masses.  Other types of supernova exist. Type Ia supernovae for example result from the catastrophic explosion of a white dwarf star in a close binary system.  It is caused by runaway carbon fusion in the white dwarf triggered by mass transfer from its companion red giant star.  (3) 

The nature of the supernova remnant depends critically on the mass of the core of the progenitor star – the star that exploded.  For stellar cores greater than 1.4 solar masses but less than about 3 solar masses a neutron star results.  As described above, the matter within such a core has been crushed to nuclear densities and exists as neutrons.  The neutron star is protected against further gravitational collapse by the degenerate pressure of neutrons.  A typical neutron star with a mass a little greater than the Sun’s would have a diameter of only 30 km and a density such that the mass of the entire human race would occupy the volume of a sugar cube!  Neutron stars also possess huge magnetic fields, of the order of 1 x 108 T.  Compare this to the magnetic field at the surface of the Sun – around 10-4 T.  (3 & 5) 

All neutron stars spin rapidly due to the conservation of angular momentum of the original star.  As a star shrinks down to become a neutron star, its rotation must speed up.  Charged particles that have been accelerated near the neutron star’s magnetic poles produce two oppositely directed beams of radiation that emanate from the magnetic poles.  As the star rotates, these beams sweep through space.  If the Earth happens to lie in the path of the beams, we detect radiation that appears to pulse on and off.  Such a neutron star is called a pulsar.  The radiation it emits can be of varying kinds – radio, optical, X-ray and gamma.  See diagram below.  The first pulsar was discovered by Jocelyn Bell at Cambridge University in 1967.   The Crab Nebula is the remnant of a supernova explosion in the constellation Taurus first observed in 1054. The stellar corpse at its centre is a pulsar.  (3 & 12)

           

 

If the core of the exploding star is greater than about 3 solar masses, nothing can stop its gravitational collapse to a black hole.  A collapsing star becomes a black hole when its radius has shrunk to a critical size, known as the Schwarzschild radius, at which gravity is so strong that not even light can escape from the surface of the star.  The surface having this critical radius is called the event horizon and marks the boundary inside which all information is trapped.  Hence, events within a black hole cannot be observed from outside the event horizon.  Theory indicates that both space and time become distorted inside the event horizon and that an object collapses to a single point, a singularity, at the centre of a black hole.  (3 & 5)

Do black holes really exist?  Today, there is compelling astrophysical evidence that they do.  Many examples of possible black holes have been found.  Cygnus X-1 is a strong source of X-rays in our own galaxy that is believed to be a black hole.  Supermassive black holes are believed to lie at the centres of many galaxies including our own.  (3)

The following flowchart is a useful summary of stellar evolution.

           

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REVISION TEST No.1 

(a)   The accurate measurement of distance is extremely important in astronomy.  Careful measurement of a celestial object’s position in the sky may be used to determine its distance.

(i)               A certain star, has a parallax angle of 0.258 arcsec.  What is the distance of the star from Earth? (1 Mark)

(ii)            Define the terms “sensitivity” and “resolution” and explain why it is desirable for telescopes to have a large diameter objective lens or mirror in terms of both sensitivity and resolution. (3 Marks)


(b)   The study of binary and variable stars reveals vital stellar information.

(i)              A visual binary star system consists of two stars, one of which orbits the other in a near circular orbit, once every five years at an average  distance of 1.5 x 1012 m.  What is the sum of the masses of the two stars in kilograms? (3 Marks)

(ii)             The light curve below was obtained from the Algol binary star system.



Describe what must be happening to produce this light curve and mention specifically what happens at A, B and C. (3 Marks)


(iii)          The period-luminosity relationship for a Classical Cepheid variable star is shown below.



An astronomer observes a Type I Cepheid variable in a distant galaxy.  The Cepheid has a period of 3 days and an average apparent magnitude of +12.  The astronomer claims that this data indicates that the galaxy is approximately 12 600 parsecs away.

Use your knowledge of how the period-luminosity relationship can be used to calculate distance to justify the astronomer’s claim. (3 Marks)

(c) Spectroscopy is an essential tool for astronomers and provides a wealth of information.

(i)              Surface temperature, rotational velocity and chemical composition are three factors that can be determined from the spectrum of a star.  For each factor identify the feature of the spectrum that allows the factor to be determined. (3 Marks)

(ii)              Describe briefly the technology used to measure astronomical spectra. (2 Marks)

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MARKING GUIDELINES - Revision Test No.1 

(a)      (i)             1 mark for correct calculation.  (d = 1/p = 3.88 pc)

(ii)            1 mark for correct definition of “sensitivity”.
1 mark for correct definition of “resolution”.
1 mark for correct explanation of reason for large objective.

Notes for (a) (ii):
For optical telescopes, sensitivity refers to the light-gathering power of the telescope & is directly proportional to the square of the diameter of the objective.  The resolution (angular or optical) of a telescope is the minimum angular separation between two equal point sources such that they can be just barely distinguished as separate sources.

q
min = 1.22l /D in radians or qmin = 2.5 x 105 l/D in arcseconds
.

The smaller the angle, the finer the details that can be seen and the sharper the image.  Clearly, the larger the diameter, D, of the objective, the more sensitive the telescope (ie the larger D2) & the better the resolution (ie the smaller qmin).

(b)    

(i)              1 mark for use of correct formula.
1 mark for correct period in seconds.
1 mark for correct answer of 8.02 x 1031 kg.

(ii)            1 mark for recognizing Algol as an eclipsing binary.
1 mark for recognizing that at A & C the brighter member is moving behind the duller member.
1 mark for recognizing that at B the brighter member is moving across the duller.

(iii)          1 mark for determining that the absolute magnitude, M = - 3.5.
1 mark for use of correct formula (M = m – 5log[d/10]).
1 mark for SHOWING the whole calculation process and arriving at the correct answer (12 589 pc = 12 600 pc approx).  Students MUST show sufficient working to convince the marker that they know how to use the formula correctly.

(c)     

(i)             1 mark for stating that surface temperature is calculated from the wavelength of maximum emission in the spectrum of the star.
1 mark for stating that rotational velocity is determined from the Doppler broadening of lines in the spectrum of the star.
1 mark for stating that chemical composition can be deduced by identifying the groups of spectral lines characteristic of individual elements.

(ii)            Answers scoring 2 marks should accurately describe some form of spectrograph.  eg a Grating Spectrograph - an optical device that uses a diffraction grating to break up the light from a source into a spectrum.  A collimator ensures that light rays striking the grating are parallel.  A corrector lens and mirror then focus the spectrum onto a CCD (charge-coupled device), which records the image and usually feeds the data straight to a computer for analysis.
Answers scoring 1 mark would partially describe some form of spectrograph.
Note that diagrams are not essential here but could be drawn.

 

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Go to the previous page of the Astrophysics Topic

 

 

BIBLIOGRAPHY

 

1.      Carroll, B.W., & Ostlie, D.A. (1996).  "An Introduction To Modern Astrophysics", New York, Addison-Wesley Publishing Company Inc.

2.      Gondhalekar P. (2001). "The Grip of Gravity", Cambridge, Cambridge University Press

3.      Kaufmann, W.J. III, & Freedman, R.A. (1999).  "Universe", (5th Edition), New York, W.H. Freeman & Company

4.      "Sidereus Nuncius or the Sidereal Messenger". Translated with introduction, conclusion, and notes by Albert Van Helden. Chicago: University of Chicago Press, 1989

5.      Ridpath, I. (Ed.) (1997).  "Oxford Dictionary of Astronomy", Oxford, Oxford University Press

6.      Hollow, R.  "Why Build Big Telescopes?", paper presented at Science Teachers Workshop 2002

7.      http://www.eso.org/projects/aot/introduction.html and http://www.ls.eso.org/lasilla/sciops/ntt/telescope/esontt.html

8.      Eisberg, R. & Resnick, R. (1974).  "Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles", Canada, Wiley

9.      Playoust, D.F., & Shanny, G.R. (1991).  "An Introduction to Stellar Astronomy", Queensland, The Jacaranda Press

10. Bhathal R., (1993).  "Astronomy for the Higher School Certificate", Kenthurst, Kangaroo Press Pty Ltd

11.  Dawes, G., Northfield, P. & Wallace, K. (2003).  "Astronomy 2004 Australia – A Practical Guide to the Night Sky", Australia, Quasar Publishing

12.  Andriessen, M., Pentland, P., Gaut, R. & McKay, B. (2001). "Physics 2 HSC Course", Australia, Wiley

13. Schilling, G. (2004). "Evolving Cosmos", Cambridge, Cambridge University Press

14.   http://www.seds.org/messier/glob.html - Globular Star Clusters

15. Astrophysics & Cosmology at Florida State University
http://www.physics.fsu.edu/research/Astrophysics/AstroPhysics.html

Note that this link no longer works.

 

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