# Exam Two Info

### Contents of the Exam

The Second Exam will cover material since the last exam. The current exam includes material from: Chapters 15, (omit Ch 16), 17, 18 (omit 18.4) and 19.

### Format of the Exam

The Exam will have a similar format to the first exam, including true/false and multiple choice questions. The previous homeworks and review questions at the end of the chapters will help you review the material. Below are a few sample questions to give you an idea of what to expect.

### Physical Constants you do not need to remember

Speed of light, c = 3.0 x 105 km/s = 3.0 x 108 m/s.
Planck's constant, h = 6.62 x 10-34 J s (Joules x seconds).
Wein's constant, 2.9 x 106 nm K (nanometers x Kelvins).
Stefan-Boltzmann constant, sigma = 5.67 x 10-8 J/m2.K4.s
1 parsec = 3.08 x 1016m.

### Formulae you will be given

• Wave equation : c = fw     (c=speed of wave, f=frequency, w=wavelength)
• Photon energy : E = hf = hc/w     (h=Planck's constant)
• Temperature conversion : T(K) = T(C) + 273     (K=Kelvin, C=centigrade)
• Wein's law : wpeak(nm) = 2.9 x 106 / T(K)     (w is wavelength of peak of thermal spectrum, measured in nanometers).
• Stefan-Boltzman law : L = A s T4     (L= total power emitted by a black body of surface area A at temperature T(K), where s is the Stefan-Boltmann constant).
• the Stefan-Boltzmann law applied to stars : L = 4 pi R2 s T4     (where the stars surface area is 4 pi R2 and R is the radius of the star).
• Doppler shift : (w - w0) / w0 = vr/c     (where w is the observed wavelength, w0 is the original, ie rest, wavelength, vr is the componant of velocity towards (-ve) or away (+ve) from the observer, c=speed of the wave).
• Parallax relation : dpc = 1/parcsec     (d=distance in parsecs, p=parallax angle in arcsec).
• Energy - mass relation : E = m c2     (keep units consistent : E(J) m(Kg) c(m/s) )
• Luminosity brightness relation : L = 4 pi d2 b     (L is the luminosity, d is the distance to the object, b is its apparent brightness).
• Schwarzchild radius for a black hole : Rs = 2GM/c2 = 3M km (where M is in solar masses).
• Mass within a circular orbit of speed V and radius R is: M = RV2/G

### Things to Know and Understand.

A. What is the difference between a star's apparent brightness and its luminosity, and how are these two quantities related? What is the inverse square law of brightness?

B. How do we measure distances to stars; how is a "parsec" defined; know the relation between parallax angle (in arcsec) and distance to a star (in parsecs). Know how to combine a star's measured apparent brightness and distance to calculate its luminosity

C. How do we know the surface temperature of stars? Understand how the color and (separately) the spectrum of a star reveals its temperature.

D. Understand the spectral (temperature) sequence: O,B,A,F,G,K,M; and know what kinds of absorption lines are associated with hot, medium, or cool stars. Why are hydrogen Balmer lines strongest at spectra type A, while being fainter for hotter and cooler stars?

E. How do we know the sizes of stars? Understand how to use the formula that gives the stars luminosity in terms of its size and surface temperature: L = 4 pi R2 s T4 (where s is the Stefan-Boltzmann constant).

F. Know the Herzsprung Russell diagram, and what types of stars appear where on the diagram - main sequence, giants, white dwarfs.

G. Know how stars are divided into "Luminosity Classes", which for our purposes are: class V (main sequence); III (giants); and I (supergiants). Hence be able to unpack a full spectral classification such as: G2V, or K3III.

H. Know that for main sequence stars, the mass of the star determines where it is on the main sequence - (mass increases from lower right to top left), Know the mass luminosity relation (L increases rapidly with increasing mass); and understand why this means luminous stars have shorter lives.

I. Know which stars are common and which are rare: Main sequence stars are the most common, with M stars more common than O stars. Understand that although giant stars are rare the night sky has many of them because they are bright and can be seen far away.

J. Understand how a cluster of stars appears on the HR diagram -- they form an 'isochrone' since they all have the same age. Know how the age of the cluster can be measured from the "main sequence turn off point".

K. What defines the limits to the masses of stars that can form. Know what brown dwarf "stars" are, and why they are considered to be "failed stars". Why can't stars more massive than about 60 Msun form? In a young cluster of stars, which is more common, low mass stars or high mass stars? Which stars form fastest, high mass or low mass stars?

L. What slight changes occur during the main sequence life of a star? Why does the luminosity increase slightly?

M. What happens when low mass stars (like the sun) move off the main sequence? Understand how shell burning begins, and why the star turns into a red giant. Know what the helium flash is, and the structure of the star while it is on the horizontal branch. Know about double shell burning, and why the star ascends the "asymptotic giant branch". Understand the different kinds of nuclear reactions (p-p chain; triple-alpha), and why the C/O core doesn't ignite. How do low mass stars die? What is a planetary nebula? What does the cooling core become?

N. How do high mass stars evolve, and how does their evolution differ from low mass stars? Why does hydrogen burning occur via the CNO-cycle rather than the p-p chain? Understand the nature of the nuclear binding energy graph, and how it leads to the sequence of nuclear burning fuels, culminating in iron. What are the alpha-elements, and why are they more abundant relative to other elements? What is meant by "onion shell structure" for the core of a supergiant star.

O. Understand (roughly) how core collapse happens, and how the star explodes in a Supernova (Type II) explosion. How is the energy released shared amongst neutrinos, kinetic energy and light? Know that Gravity is the ultimate origin of the energy. How did SN 1987A help confirm the basic understanding of this type of supernova? What does the supernova light curve look like, and what determines the gradual (exponential) fading of the supernova remnant?

P. Understand the constant cycle of matter from the interstellar medium into stars and then back again. Understand also that stellar evolution (in particular supernova explosions) gradually add new chemical elements to the interstellar medium. Realize that almost all the elements in the earth (and in you) were created in earlier generations of stars that died several billion of years ago. Know, roughly, how the trans-iron elements are made by neutron addition.

Q. Know the basic properties of white dwarf stars, and that they are supported by electron degeneracy pressure. Know (roughly) what degeneracy pressure is, and that is it independent of temperature. Know that the size of white dwarf stars decreases with increasing mass. Know that white dwarfs have no nuclear reactions -- they were created hot and are simply cooling down. What is the Chandrasekar mass limit, and why does it occur?

R. Know what can happen when a white dwarf is in a binary system where the other star is dumping mass onto it? A Nova occurs when the transferred hydrogen degenerate atmosphere explodes. If the mass is pushed above the chandrasekhar limit the white dwarf explodes by carbon detonation as a supernova (type I). Know that the ultimate source of energy in this type of supernova is nuclear.

S. What stellar corpses remain at the end of the life of a High Mass star? Know the basic properties of Neutron stars --- size, mass range, density, surface gravity. What kind of pressure supports these types of stars. Are higher mass neutron stars larger or smaller than lower mass neutron stars. Know that there is an upper mass limit of about 3 solar masses for neutron stars. What happens above this limit?

T. Know, roughly, the history of discovering pulsars. What are pulsars? Why do neutron stars spin fast when they are created? Why do they have such high magnetic fields? Know, roughly, the reason we see regular pulses of radio emission. Know that young pulsars spin faster than older ones, but that pulsars in binary systems can spin fastest of all when they are "spun-up" by mass accretion. Know that accretion onto a neutron star from a binary companion occurs via an accretion disk, and that such systems give off intermittent X-ray bursts when helium undergoes thermonuclear detonation.

U. Understand the basic term "Black Hole" -- why is it black and why is it a hole? How is the Schwarzchild radius of a black hole defined? Know that it is proportional to the mass of the black hole, with a value of 3km for each solar mass. Understand that above 3 solar masses, no kind of pressure can support the mass because pressure adds to gravity and helps the collapse.

V. Appreciate that black holes require Einstein's theory of gravity (General Relativity), and this uncovers some rather unusual properties. Know some of these: that time slows near the black hole, and that light is redshifted as it tries to move away from the hole. Understand how two astronauts might witness one of them falling into a black hole rather differently. Appreciate the existence of strong tidal stretching near a black hole.

W. How are black holes detected? Understand that black holes in binary systems can emit powerful X-rays if mass is transferred via an accretion disk. If the binary orbit suggests the companion mass is is above the 3 Msun limit, then it is a black hole rather than a neutron star.

X. Know the galaxy's structure and size: Disk, Interstellar Medium, Bulge, Nucleus, Halo; Diameter is about 100,000 ly with the sun about 25,000 ly from the center. Know that the halo contains older stars than the disk.

Y. Know the kinds of motions in these components: Disk rotation and random orbits for halo and bulge stars. Know how orbital motion can be used to measure the mass of the galaxy.

Z. Know the continuous star-gas-star cycle that occurs within the galaxy's disk, and how this leads to a gradual increase in the heavy element fraction.

AA. Know about the various gas phases of the interstellar medium -- their different densities and temperatures. Know how one sees these components: 21 cm radio from neutral hydrogen atoms; CO radio emission from molecular gas; X-rays from the hot component; dust emits far infrared light.

BB. Know how we identify newborn stars: near dense molecular clouds; blue massive stars; glowing nebulae ionized by the hot young stars. Where do stars form in our galaxy? Mainly in spiral arms within the disk. Why is that? How do the nested orbits of stars generate a spiral pattern which in turn helps compress gas to form stars.

CC. Know that the halo stars contain very few heavy elements compared to the disk stars, and therefore probably formed first. How does this help construct a theory for the formation of our galaxy? Recognize the basic steps in that formation process.

DD. What's the evidence for a massive black hole at the center of our galaxy, and roughly what is it's mass?

### Sample Questions

1. T/F Pushing a star to 5 times its current distance, it will appear 5 times fainter.

2. T/F A star with a parallax of 0.2 arcsec is 2 parsecs away.

3. The spectral sequence sorts stars according to:

1. mass
2. luminosity
3. surface temperature
4. core temperature

4. On a Hertzsprung-Russell diagram, where would we find stars that are cool and low luminosity?

1. upper right
2. lower right
3. upper left
4. lower left

5. Star A is 144 times more luminous the sun, and has twice the surface temperature. How big is it compared to the sun?

1. 3 times the radius of the sun
2. 10 times the radius of the sun
3. 16 times the radius of the sun
4. half the radius of the sun

6. A 3 solar mass star is 80 times more luminous than the sun. If the sun's main sequence lifetime is 10 billion years, what's the main sequence lifetime of this star?

1. 30 billion years
2. 375 million years
3. 800 million years
4. 30 million years

7. Which of the following characteristics of stars has the greatest range in values?

1. mass
3. core temperatures
4. surface temperature
5. luminosity

8. Which of the following luminosity classes refers to stars on the main sequence?

1. I
2. II
3. III
4. IV
5. V

9. T/F As a star gradually uses up the hydrogen in its core, it begins to cool off and the star moves down the main sequence.

10. When the supply of hydrogen is exhausted in the core, a star's

1. radius increases and surface temperature increases
2. radius decreases and surface temperature decreases
3. radius decreases and surface temperature increases
4. radius increases and surface temperature decreases

11. Consider the evolution of the Sun, from birth to death. For each stage, describe how energy is generated, and where on the HR diagram the sun located.

12. T/F It is likely that the sun will become a white dwarf without any mass loss.

13. White dwarf stars

1. are composed entirely of neutrons
2. are supported against gravitational collapse by electron degeneracy pressure
3. can have a mass from a fraction of a solar mass up to ten solar masses

14. Cluster 1 has a main-sequence turnoff at spectral type A2; Cluster 2 has a turnoff at spectral type F2. Which of the following must be true?

1. Cluster 1 is younger than cluster 2
2. Cluster 1 is more massive than cluster 2
3. Cluster 1 is closer than cluster 2

15. There are several important differences between the interiors of high mass stars (eg 10 solar masses) and low mass stars (eg 1 solar mass). Which of the following is NOT true for high mass stars compared to low mass stars:

1. they have higher core temperatures
2. they can 'burn' heavier elements than helium
3. their nuclear reactions proceed more quickly
4. they have a more uniform composition

16. T/F Neither fission nor fusion of iron nuclei yields any energy

17. T/F Supernova core collapse takes about an hour

18. T/F In a type II supernova (core collapse) most of the energy emerges as kinetic energy of the expanding ejecta.

19. T/F A neutron star of mass 2.2 solar masses is larger than neutron star of mass 1.8 solar masses

20. T/F The Crab pulsar spins 30 times per second and weighs 10 solar masses.

21. Which of the following is NOT a property of ALL pulsars?

1. a pulsar is a neutron star
2. a pulsar is rapidly rotating
3. a pulsar has a strong magnetic field
4. a pulsar is in a binary system

22. Pulsars slow their pulse rate because

1. they convert energy of rotation into radiation
2. they drag companion stars around
3. of the conservation of angular momentum
4. they accrete material from binary companions

23. Novae are caused by nuclear explosions:

1. on the surface of a neutron star.
2. on the surface of a white dwarf star.
3. near the event horizon of a black hole.
4. in the cores of massive stars.

24. T/F A Million solar mass black hole has a Schwarzschild radius 1 million times larger than that of a one solar mass black hole.

25. Gas about to cross through the event horizon of black hole emits radiation in the form of an emission line. This radiation is observed to be:

1. blue-shifted.
2. red-shifted.
3. split into many emission lines.
4. It is unobservable.

26. Which of the following would be sensible strategies for finding a black hole :

1. Look for Hawking radiation produced by the evaporating black hole
2. Look to see a star wink out as it falls into the black hole
3. Look for a dark circle in the sky where no other stars were visible
4. Look for a very bright, rapidly varying, X-ray source

27. T/F Globular star clusters are only found in the disk of our galaxy.

28. How far is the Sun from the center of the galaxy?

1. a few light years

29. T/F The Hubble Telescope has provided some of the best images so far of the stars at the galactic center.

30. The motion of the Sun around the center of the galaxy gives a value of about 1011 solar masses. This mass represents

1. the total mass of the galaxy
2. the total mass of the disk of the galaxy
3. the mass of that part of the galaxy closer to the center than the Sun
4. only the mass of the stars in the galaxy

31. T/F As hydrogen fuses to produce helium, it produces photons of wavelength 21 cm which pass unimpeded through the galaxy.

32. T/F Like a Catherine Wheel, the spiral arms in galaxies result from jets which emerge from a spinning nucleus and then wind back as the galaxy rotates.

Do the questions, write down your answers, then check yourself with these Answers Think about the ones you missed. If you feel you need help, don't forget my office hours are T R 2:00pm - 3:00pm, but please email ahead to let me know you're coming.