Final Exam Info

Contents of the Exam

The Final Exam will cover the entire semester, with the material since the last test appearing proportionately more (since it has not yet been on a midterm, there will be approximately double the number of questions there would otherwise be --- maybe 40% of the total). The material since the last exam includes : Our Galaxy (Ch 15); Other galaxies (Ch 16); and Cosmology (Ch 18). Note we are OMITTING : Chapter 17 on Quasars and Active galaxies. As usual, I would suggest you use the following in decreasing priority for your review of the material : (1) My web/powerpoint notes together your lecture notes, (2) these web questions; (3) the concept list and the topics listed on the web; (4) questions from the text; (5) the text itself (which also contains more details). You may also want to review the notes and questions from Dr Hawley's ASTR 124 class and also Dr Murphy's class.

Format of the Exam

The Final Exam will have a similar format to the midterm exams, including true/false, multiple choice and short answer questions. The length (and value) of the final exam is double that of one of the midterm exams. Below are a few sample questions from the last part of the class to give you an idea of what to expect. The review questions at the end of the chapters will also help you review the material.

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

• Hubble's Law : v = Hod where v is the recession velocity of the galaxy in km/s, d is its distance in Mpc, and Ho is Hubble's constant, which has a value around 75 km/s/Mpc
• The age of the universe : tage = 1/Ho. The relation is approximate, since it assumes a constant rate of expansion. Dont forget one needs to convert the units of Ho to /sec or /yr.

Sample Questions From the material covered since the last exam.

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

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

1. a few parsecs

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

4. 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

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

6. 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.

7. Spirals are classified Sa, Sb, and Sc. The sequence is in order of which of the following?

1. decreasing tightness of the spiral arms
2. thickness of the disk
3. increasing size of the nuclear bulge
4. increasing size of the whole galaxy

8. When galaxies collide, many stars suffer head on impact.

9. The masses of clusters of galaxies can be estimated from measurements of the velocities of individual galaxies. Typically, what is found for the cluster mass ?

1. It is puzzlingly less than the mass of all the individual galaxies.
2. It is equal to the mass of all the individual galaxies
3. It is about twice the mass of all the individual galaxies since it includes the cluster atmosphere
4. It is puzzlingly about 10 times the mass of all the individual galaxies

10. Deep images of some galaxy clusters reveal thin arcs which seem to form segments of circles roughly concentric on the cluster center. What makes these arcs and why are the useful to astronomers ?

11. What is the distance (in Mpc) to a galaxy which has a redshift of 12000 km/s, assuming a Hubble constant of 75 km/s/Mpc ?

12. A galaxy which is known to be 300 Mpc distant has a measured recession velocity of 15000 km/s. What value for the Hubble constant do these observations imply ?

13. Because of the expansion of space, we see all distant galaxies moving away from us, with more distant galaxies moving faster. An observer on one of these distant galaxies would see :

1. All galaxies moving away, with more distant galaxies moving faster.
2. All galaxies on one side approaching, and all galaxies on the other moving away, with more distant galaxies moving faster.
3. All galaxies moving away, with closer galaxies moving faster.
4. All galaxies approaching, with more distant galaxies moving faster.

14. For a Hubble constant of 60 km/s/Mpc, estimate the age of the universe assuming no deceleration since the Big Bang (1pc = 3.08 x 1013 km; 1yr = 3.1 x 107 seconds).

15. T/F Some of the oldest known galaxies are found at the greatest distances.

16. Which of the following does NOT correctly describe the universe at the era of recombination :

1. The universe became transparent.
2. The temperature of the universe dropped to 3 K.
3. The universe was about 400,000 yrs old.
4. Electrons and protons combined to form neutral hydrogen atoms.

17. If the Big Bang was so hot, why does the Microwave Background Radiation yield such a low temperature, around 3 K ?

18. In cosmology, the phrase "critical density" refers to :

1. The density above which the universe is opaque to radiation.
2. The density below which stars will never form.
3. The smallest density that will produce inflation.
4. The density needed to produce precisely flat space.

19. Which of the following is TRUE for a big bang model that has negatively curved geometry ?

1. the density in the universe is greater than the critical density
2. the age of the universe is greater than the Hubble time
3. the universe will expand forever
4. the universe is finite in spatial extent

20. T/F For a universe whose expansion is decelerating, the time since the Big Bang is greater than the inverse Hubble constant.

21. How was the universe's geometry recently measured, from which we learnt that it was flat ?

22. The production of helium in the early Universe was finished about how long after the Big Bang.

1. one millionth of a second;
2. one second;
3. three minutes;
4. 300,000 years.

23. Name the four fundamental forces. Have they always been distinct ?

24. T/F Since the Big Bang created equal amounts of matter and antimatter, there are approximately equal numbers of galaxies made from matter and antimatter.

Here is a list of the major themes we have discussed in class since the last exam, 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. Know, roughly, the history of our understanding of the shape of our galaxy, including work by Galileo, Herschel, Shapley. How did Shapley's observations of Globular Clusters help establish that we are not at the center of the Milky Way? Know the role of interstellar dust in blocking our view of the galaxy. How can one overcome this problem ?

B. Know the galaxy's structure and size : Disk, ISM (Interstellar Medium), Bulge, Nucleus, Halo; Diameter is about 30 kpc (100 kly) with the sun about 8 kpc (25 kly) from the center. Know its motion : disk rotation, rotation curve, halo orbits. Understand the use of the rotation curve to calculate the mass of the galaxy, and the inference that dark matter is present in the galaxy's outer parts.

C. Know the two basic populations of stars : Pop II : old, halo, metal poor, random orbits; Pop I : young, disk, metal rich, circular orbits. Know how these populations fit into our theory of how the galaxy was formed. Recall that more chaotic events, such as collisions with other galaxies, or at least the assimilation of dwarf galaxies probably also played a role in the galaxy's history.

D. Understand how neutral hydrogen produces 21cm radio emission, and how this can be used to map out spiral structure in our galaxy. Know how star formation regions can also be used to trace spiral arms

E. What creates spiral arms ? Know that simple arm windup wont work. Understand (a) self propatating star formation and (b) spiral density wave theory. Why are spiral arms visible ?

F. Know, roughly, some of the properties of the galactic nucleus, including the increase in stellar density. What evidence points to the presence of a 2.6 million solar mass black hole at the center of our galaxy?

G Know, roughly, the history of the discovery of other galaxies, including the Shapley Curtis debate, and its resolution by Hubble using Cepheid variables in the Andromeda (M31) galaxy.

H. How are galaxies distributed throughout the Universe? Roughly, how many galaxies have had their distances measured? Recognize the now famous Sloan Digital Sky Survey (SDSS) of galaxies. How many galaxies exist in the visible Universe, and how was this estimated ?

I. Know the different types of galaxy as seen in the Hubble "tuning fork" classification scheme : Spiral, Elliptical, S0, Irregular, Barred, Unbarred. Know, roughly, some of the theories for the origin of the differences between galaxies. Know the rough spread in properties of galaxies, and that there are far more small galaxies than large (massive) ones.

J. How are galaxy distances measured. Understand the use of Cepheid variable stars, and supernovae as "standard candles". What is the "Distance Ladder"

K. Know the Hubble Law, which relates the recession velocity of a galaxy (V in km/s) to the galaxy's distance (d in Mpc) : V = Ho x d where Ho is the Hubble constant (in km/s/Mpc). Know current estimates for its value (about 70 km/s/Mpc). Know how to estimate any one of the variables from the other two, possibly using the doppler formula to estimate V.

L. Know about the interaction between galaxies, galaxy flybys, tidal tails, galaxy mergers. Understand how these trigger star formation and may lead to a change in the type of galaxy (eg spiral + spiral = elliptical). Realise that stars are too far apart to collide during galaxy mergers.

M. Know how galaxies occur in groups and clusters. Know, roughly, the population of the local group. Know the structure of clusters of galaxies --- the presence of a central dominant elliptical, the phenomena of galaxy cannibalism, the orbits of galaxies, the hot intercluster atmosphere.

N. Know roughly the three ways to measure the mass of clusters : using the speeds of the galaxy orbits; using the pressure in the cluster atmosphere; and using the lensing of distant galaxies. Know that there is more mass in the cluster atmosphere than in the galaxies, and that dark matter dominates the cluster's total mass, being about 10 times more massive than all the "atomic" matter in the gas and galaxies.

O. How can we study the early history of galaxy construction? Understand the term "Hierarchical Assembly". Know that star formation was much more common in young galaxies, and it has been decreasing since the first Gyr.

P. What does it mean to say that three global properties of the Universe are isotropy; homogeneity; and the universality of physical law?

Q. Understand why the Hubble Law implies that all galaxies see the same cosmic expansion. Know how to estimate the age of the universe from the Hubble constant.

R. Understand the concept of "lookback time" and its use in the direct study of galaxy evolution.

S. Understand the three possible geometries for the Universe : (1) high density, positive curvature, finite volume; (2) low density, negative curvature, infinite volume; (3) between these two (critical universe). Know the main parameter to measure this is the average density, and the critical value is about 9.5 x 10-27 kg/m3.

T. Know the content of the Universe : 4% atomic matter (baryons, of which 1% is in visible stars); 23% dark matter (whose nature we do not know); and 73% dark energy (whose nature we also dont know, but may be linked to the energy of empty space).

U. What is the Cosmic Microwave Background (CMB)? What are its properties : spectral form and smoothness ? Understand its origin in the early universe (380,000 yr after the BB), and how a 3000K hot gas is now seen with a microwave (ie cold) spectrum. What causes its small dipole anisotropy, and its even smaller ripples ? How, roughly, does slight lumpiness in the CMB ultimately result in the formation of galaxies ? Know that the collapse to form galaxies happens so quickly that there must be additional mass besides the atomic mass --- the dark matter.

V. know roughly how the microwave ripples have been used to measure the geometry the universe -- the longest sound waves form a triangle with us at one apex. Their angular extent on the sky allows us to check whether the triangle is "flat" or not. It is, to within 2% accuracy!

W. Know that recent results suggest the Universe is in fact ACCELERATING in its expansion. This is measured by looking at the expansion rate far away, ie long ago, and seeing whether it is more or less than the expansion rate today. The distance measures used are supernovae. Understand that the acceleration can be explained by a non-zero "lambda" parameter, or non-zero vacuum (or "dark") energy. Recognize that this dark energy wasn't important until about 6 Gyr when it equalled the matter density

X. Know about the "era of nucleosynthesis" : 1-3 minutes after the Big Bang, temperatures about 1 billion K, density similar to water. Nuclear reactions convert 25% hydrogen into helium, which is now observed everywhere. Small amounts of Deuterium are also produced, and can be used to infer the matter density in the universe.

Y. Understand how matter can arise out of thermal energy, leading to a sequence of threshold temperatures, one for each particle. Hence, know roughly the sequence of eras : Quark; Hadron; Lepton; Radiation; Matter; Dark Energy. Understand that the matter/antimatter asymmetry must have arisen very early.

Z. Know the four forces of nature, and how they merge successively at earlier and earlier epochs.