# 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 Chapter 20 (Other Galaxies), Chapter 21 (Galaxy Evolution), Chapter 22 (Dark Matter and Dark Energy), and Chapter 23 (The Big Bang).

### Format of the Exam

The Final Exam will have a similar format to the midterm exams, including true/false and multiple choice questions. The previous home-works 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).
Newton's gravitational constant G = 6.67 x 10-11 m3 /kg / s2
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 light year = 9.46 x 1015 meters

### 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
• Hubble's Law : v = Hod where v is the recession velocity of the galaxy in km/s, d is its distance in Mly, and Ho is Hubble's constant, which has a value around 22 km/s/Mly
• 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.

### Things to Know and Understand.

A. Know the different types of galaxy as seen in the Hubble "tuning fork" classification scheme : Spiral, Elliptical, S0, Irregular, Barred, Unbarred. What kind of environments does one tend to find spirals and ellipticals?

B. Know the five "rungs" on the distance ladder used to measure distances to galaxies: Radar within the solar system; parallax; cepheid variable stars; Tully-Fisher rotation of galaxies; and white dwarf supernovae.

C. How did Hubble show that the spiral nebulae were external to the milky way, and therefore that they were separate galaxies?

D. Understand how galaxy velocities are measured using the Doppler effect, and how this led Hubble to discover "Hubble's Law" which is that galaxies are moving away from us with a speed proportional to their distance: V = H0 x d. What is Hubble's Constant and how can you use it to measure the distance to a galaxy given its recession velocity?

E. Understand how the Hubble law tells us that the entire universe is expanding, and that everyone sees the same expansion. A better way to think of the expansion is that it is space itself that is expanding and the galaxies are embedded within the space, being "carried along" by it. In this case, one understands redshift as the stretching of light waves as they move an expanding space, so the stretch in wavelength is equal to the cosmic stretch during the light's journey.

F. The cosmological principle states that on very large scales (greater than about 1/2 billion light years) the universe is smooth -- and endless mist of galaxies stretching out in all directions without end.

G. How do we use the Hubble law (and Hubble's constant) to estimate the age of the universe? Why is this only an approximation. What happens to our age estimate if we allow for the universe's expansion to decelerate or accelerate?

H. How did the first galaxies form? How did the initially almost smooth universe get rougher and rougher? Know that the first galaxies were small and chaotic compared to today's galaxies.

I. When galaxies collide the star birth rate goes way up, making a "starburst" galaxy. Because the rate of galaxy collisions decreased over cosmic time, so the rate of star formation in the universe has decreased over time.

J. Understand some of the theories of why some galaxies turn out to be spirals while others turn out to be ellipticals (differences in the nature of the protogalactic cloud; and the fact that when two spirals merge, an elliptical forms).

K. Black holes are discovered in many galaxies by measuring fast rotating gas or stars close to the galaxy's center. Galaxies with bigger bulges have more massive black holes, for reasons that are not yet understood.

L. Most black holes are invisible. But some become very visible when gas finds its way into the galaxy nucleus and falls into the black hole via an accretion disk. These disks can release 10-40% of the mass falling into them as energy, and the nucleus becomes extremely bright. Such galaxies are called "Active" of which "Quasars" are the most powerful example. In some cases, jets of gas can be ejected at nearly light-speed perpendicular to the disk, and these jets can be seen emitting radio waves.

M. Activity was much more common in the past (ie. quasars are common at great distances), and this nicely explains how most normal galaxies today have big black holes at their centers -- they were once quasars.

N. Understand how extended flat or rising rotation curves for galaxies indicate the presence of an extended halo containing dark matter. Know the three methods for showing dark matter in galaxy clusters: galaxy velocities, hot (X-ray emitting) atmospheres, and gravitational lensing. Know that the X-ray emitting atmosphere contains about 5 times more mass than the galaxies, but is still 5 times less massive than the dark matter.

O. Know that dark matter cannot be any kind of atomic matter, but is likely a massive weakly interacting particle (WIMP) yet to be observed. Overall, dark matter makes up 23% of all cosmic constituents.

P. Know how dark matter helped craft the web-like large scale structure, and how the seeds for this structure are thought to be laid down during the big bang's inflationary launch.

Q. Know that dark energy -- the weight of space itself -- is revealed by studying whether cosmic expansion is slowing down or speeding up. Supernovae distances reveal the expansion is accelerating (after an initial phase of deceleration) at a rate that indicates dark energy makes up 73% of today's cosmic constituents. The accelerating expansion will lead to a very empty universe in the distant future.

R. Know that the universe's total mass-energy sums to zero -- all the positive mass-energy in the stars, dark matter, and dark energy, are balanced by an equal but negative gravitational energy holding it all together. This suggests the universe might have come from nothing -- given the right mechanism to cause it's expansion.

S. Understand the nature of the microwave background: our vision of the big bang's brilliant flash. Know why it has a thermal spectrum of just 3K; how it shows the early universe was very smooth; and how it reveals the initial seeds of roughness that will become galaxies.

T. Understand how we can be confident about the period of nuclear fusion around 1-3 minutes after the big bang. Know that matching computer models to the observed abundances of helium, deuterium and lithium show that the total cosmic content of atomic matter is only 4.4%.

U. Know a little about conditions within the first second -- why the temperature was so high and how we briefly recreate such temperatures using particle accelerators. Know that at very high temperatures the gas became filled with particles and their antiparticles. Know that within that first second, the four forces of nature became defined, by splitting away from a single force.

V. Recognize that there are three features of the universe that cannot be explained in the standard big bang theory -- the structure problem; the smoothness problem; the size problem. However, the solution of these problems points to the nature of the launching mechanism, called inflation. In this theory, a rapid burst of accelerating expansion (caused by the existence of a dense vacuum) essentially "launched" our big bang expansion. This mechanism can take nothing and split it into huge quantities of mass-energy and equal negative quantities of gravitational energy. It is currently on less secure footing than the rest of the big bang theory.

### Sample Questions

1. Which of the following is NOT a characteristic of spiral galaxies?

1. a nuclear bulge
2. a flat disk
3. a halo of old stars
4. lack of cold gas and dust

2. 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

3. T/F When galaxies collide, many stars suffer head on impact.

4. 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 25 times the mass of all the individual galaxies

5. 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 ?

6. What is the distance (in Mly) to a galaxy which has a redshift of 12000 km/s, assuming a Hubble constant of 22 km/s/Mly ?

7. A galaxy which is known to be 300 Mly distant has a measured recession velocity of 7500 km/s. What value for the Hubble constant do these observations imply?

8. A quasar shines with a power of 1037 watts. If it is accreting mass and converting it into energy at an efficiency of 10%, how many kg per second is passing through its accretion disk?

9. T/F The black holes in quasars are thought to have formed by the core collapse of a massive star, giving a black hole mass of about 10 solar masses.

10. 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.

11. For a Hubble constant of 20 km/s/Mly, estimate the age of the universe assuming no deceleration since the Big Bang (1 ly = 9.46 x 1012 km; 1yr = 3.15 x 107 seconds).

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

13. Which of the following does NOT correctly describe the universe at the time the microwave background formed :

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.

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

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

16. 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.

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

18. Which of the following does the Inflationary Big Bang Theory NOT explain :

1. the existence of black holes.
2. the isotropy of the microwave background.
3. the existence of structure (galaxies and clusters) in the universe.
4. the fact that the universe is expanding close to the escape speed.

Do the questions, write down your answers, then check yourself with these Answers