# Exam Two Info

### Contents of the Exam

The Second Exam will cover material since the last test. The current test includes all material presented in the lectures starting with the discussion of measuring star sizes. Corresponding text is : Chapter 9.3 - end, Ch. 10, 11, 12 (omit 12.4, variable stars), 13 (omit first two subsections of 13.2), 14 (omit 14.3).

### Format of the Exam

The Exam will have a similar format to the first exam, including true/false, multiple choice and short answer questions. The 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.

Dont forget Dr Hawley's web resources, including a concise narrative of the material, as well as additional test questions. Although the material in those notes is essentially identical to ours, he was using a different text so the order of the topics is slightly different (use your judgement to sort out what is relevant to our current exam). His main web page is here.

### 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 DO need to know

• 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; s = sigma, the Stefan-Boltzmann constant).
• Kepler's third law : (M1 + M2) = a3/P2 where M1 + M2 is the combined mass of the two stars in a binary, in solar masses; a is the semi-major axis of their orbit, in AU; and P is their orbital period in years.
• Mass Ratio : M1/M2 = V2/V1 where V refers to the orbital velocity of each star about the center of gravity.
• Mass-Luminosity Relation for Main Sequence Stars : L = M3.5 where L is in solar luminosities and M is in solar masses.
• Mass-Lifetime relation for Main Sequence stars : t = M-2.5 where t is the lifetime in units of 1010 years (ie the sun's lifetime) and M is in solar masses.
• Schwarzchild radius for a black hole : Rs = 2GM/c2 = 3M km (where M is in solar masses).

### Sample Questions

1. A binary star has an orbit major axis of 100 AU and a period of 100 years. What is the total (combined) mass of the two stars ?

2. In the previous question, if the stars have maximum Doppler velocities of 15 km/s and 30 km/s what are the individual masses of the two stars.

3. What is the approximate main sequence luminosity of a 2 solar mass star, in units of the suns luminosity ?

1. 11
2. 4
3. 2
4. 0.5

4. Which type of binary system provides the most information about its component stars' masses and sizes?

1. eclipsing binaries
2. spectroscopic binaries
3. visual binaries
4. astrometric binaries

5. What is Hydrostatic Equilibrium and what property of the sun does this give rise to.

6. Energy is transported in the Sun by

1. convection in the deep interior and radiative diffusion in the outer layers
2. convection in the outer layers and radiative diffusion in the deep interior
3. radiative diffusion in the deep interior and neutrinos in the outer layers
4. convection in the deep interior and magnetic fields in the outer layers

7. Describe, briefly, the four major gas phases of the interstellar medium. How do we detect each of these ?

8. Which of the following is NOT a property of interstellar dust?

1. dust increases the apparent magnitude number of a star
2. dust makes stars look bluer
3. dust causes scattering to produce reflection nebulae
4. dust blocks our view of the center of the galaxy

9. Which of the following is FALSE

1. The Protostar stage is short compared to main sequence lifetimes
2. Protostars have much higher temperatures than main sequence stars
3. Protostars are surrounded by dust and gas
4. Protostars radiate mainly in the infrared

10. T/F HII region emission nebulae are generally found in association with hot O and B stars.

11. 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.

12. As 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

13. 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.

14. It is likely that the sun will become a white dwarf without any mass loss.

15. 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

16.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

17. 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

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

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

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

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

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

23. 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

24. 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

25. 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.

26. 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.

27. 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.

28. 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

Here is a list of the major themes we have discussed in class, presented partly in question form. This should give you some idea of the range and scope of the topics. It is compelmentary to the concept list you got at the beginning of the class, and should help you review the material.

A. How do we know the sizes of stars ? Know the formula that gives the stars luminosity in terms of its size and surface temperature.

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

B. Know the different classes of binary star. Is binarity rare or common ? know how to use Kepler's third law to find the sum of the masses of binary stars from the orbit size and period. Know that the stars orbit the center of gravity, with speeds whose ratio gives the ratio of their masses. What extra information do eclipsing binary stars give us ?

C. 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 proportional to M3.5); and understand why this means luminous stars have shorter lives (main sequence lifetime proportional to M-2.5). Given a stars mass, be able to evaluate its luminosity and lifetime relative to the sun's.

D. 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.

E. Know the galaxy has a tenuous "atmosphere" : the Interstellar Medium (ISM), held in place by the galaxy's gravity. Know that it contains about 5% of the mass of the stars, is very inhomogeneous, and has average density about 1 atom/cm3. Know its contents : gas and dust. Know the three kinds of visible nebulae : dark; emission; and reflection. Know about interstellar dust and how it affects the passage of light through the galaxy. Which is absorbed and scattered by dust more : blue or red light ? Know that stars behind dust appear dimmer and redder.

F. How is the ISM visible in other wavelengths ? Know that IR light is generated from cool (20K) dust. Why can we see IR emission even from regions heavily obscured in the optical? Know there is a hot phase visible in X-rays which is associated with supernova explosions. Know about the important 21cm emission line from hydrogen atoms. Why is it generated ? Know about radio emission from vibrating and rotating molecules, for example CO. Why cant molecular hydrogen, H2 produce this kind of radio emission?

G. Know the basic phases of the interstellar medium : cold molecular clouds; warm neutral hydrogen clouds; hot partially ionized regions; very hot low density gas. Know that the sequence of decreasing density and increasing density leads to approximate pressure balance between the four phases. Recognise the role played by the ISM in the life cycle of stars : born in molecular clouds; O/B stars ionize the HII regions; winds and supernovae disperse the gas; star death returns material back to the ISM, where the process repeats.

H. Know the basic stages of star formation --- starting from the interstellar medium, and ending on the main sequence. Know when gravity powers the star and when nuclear reactions do. What triggers star formation ? How is star formation best observed ? Why are disks and jets associated with star formation? How do planets figure into the star formation process ? What are HII regions, and why is the gas ionized. Do stars form in isolation or in groups. Know that groups of stars tend to disperse as time goes by.

I. 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 ?

J. Understand the basic physics that determines the structure of stars. What is Hydrostatic Equilibrium, and what does it tell us about how temperature, density and pressure vary as we go down towards the center of a star. How does energy get from the center of the sun to the surface. Understand the difference between conduction, radiation, and convection. Know that for the sun, radiation transport occurs for the inner 4/5 while convective transport occurs for the outer 1/5. Know roughly how this can be different for stars of different masses. Understand how these physical principals can be calculated on a computer to yield star "models", which can also be evolved with time to see how the star's grow older.

K. Know how low mass stars like the sun evolve with time --- what changes occur inside the star, how do these correspond to the location of the star on the HR diagram, and how long (approximately) do these stages last ? Know about core and shell burning; hydrogen and helium burning. Know the terms main sequence, red giant, horizontal branch, asymptotic giant branch, and where they are on the HR diagram.

L. 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". Know the two types of clusters : open clusters, young, in the disk, metal rich; and globular clusters, old, in the halo, metal poor.

M. 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 ? Know, roughly, the sequence of nuclear fuels, with its endpoint at Iron. What is meant by "Onion Shell Structure". 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.

O. 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.

P. 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 simpy cooling down. What is the Chandrasekar mass limit ?

Q. 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.

R. 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 ?

S. 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 what Synchrotron emission is. What is the simple evidence that pulsars gradually slow down.

T. 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.

U. Understand, roughly, the difference between Newton's and Einstein's description of Space, Time, and Gravity. Understand, roughly, what curved space-time is, and how motion across it can seem like a force is acting.

V. Know the properties of black holes : how time slows down near them, how light is redshifted, and how strong tides will shred objects near them. What three properties can black holes have?

W. How are black holes detected by astronomers ? Know about the two basic masses of naturally occurring black holes : stellar remnants (few solar masses) and galactic nuclei (million to billion solar masses).

Do the 28 questions, write down your answers, then check yourself with these Answers Think about the ones you missed. If you feel you need help, dont forget the TA office hours in room 267 Mon 5pm - 8pm, Tues 9am - 12pm, Wed 4pm - 7pm, Fri 2:30pm - 5:30pm. And my own office hours 2pm to 3pm (Wed, Thurs).