Astr 222 Practice Midterm #1 Answers

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Short Answer

• Describe what is meant by Population I objects and Population II objects. Give examples.

Good answer: Population I and II refers to different stellar populations in our Galaxy, and was coined by Walter Baade in the 1940s. Population II objects are older, metal-poor stars and globular clusters like those found in the Galaxy's halo. Population I refers to  more metal-rich objects like disk stars, the Sun, or young open star clusters.

Weak answer: Populations II stars are old stars, while the Sun is a Population I star.


• Describe the Magellenic Clouds.



Good answer: The Magellenic Clouds are two dwarf irregular galaxies in the Milky Way's halo. They are gas-rich and actively forming stars. They are small (kpc or smaller) and low mass (a few percent or less of the Galaxy's mass) and lie ~ 50-60 kpc away. They are interacting with one another and also orbiting our Galaxy with a period of a few billion years.

Weak answer: The Magellenic Clouds are dwarf galaxies that orbit the Milky Way.


• Why do we believe there is a lot of dark matter in the galaxy?
  
  
Good answer: If we look at the rotation curve of the Galaxy -- the orbital speed as a function of radius -- we find that the rotation curve stays flat well beyond the point where there are no more stars. Since V² ~ GM/R, M ~ RV²/G so that if the rotation curve is flat there must be more and more mass in the Galaxy as we go to large radius. But since we have run out of stars and gas at those distances, that mass can't be due to normal stars and gas -- it must be "dark matter."

Weak answer: The galaxy rotates too fast to be held together by the stars' gravity alone.


• Describe what is meant by the "luminosity function" of galaxies. In this context, what is L*? Sketch what this function looks like.



Good answer:  luminosity function describes the relative numbers of galaxies of different luminosities -- i.e., how many bright galaxies, how many faint galaxies. There are a lot more faint galaxies than bright ones. L* is the galaxy luminosity above which the number of galaxies drops exponentially, and is about 2x10¹⁰ Lsun. For galaxies fainter than L*, the luminosity function rises like a power law as you go fainter and fainter, meaning that there are many many more galaxies at fainter luminosity. Here is a sketch:

Weak answer: The luminosity function tells you how many bright galaxies there are are. (no sketch, or unlabelled sketch)

• Why does the X-ray variability of the galactic center place a limit on the size of the object at the center?



Good answer: In order for the light output of an object to vary appreciably, it must coordinate itself so that the entire object varies its light output coherently. In other words, one side needs to know what the other is doing, so they can both "get bright" or fade. But the fastest that information (ie "time to get bright!") can be conveyed from one side to the other is at the speed of light, and that takes a time t=R/c. So if an object varies over a time t, it must have a size which is no larger than ct.

Weak answer: Big things cannot change their brightness quickly.

Numerical Problem

• You are studying a distant star cluster, and find that the stars appear too red for their spectral type -- their colors are too red by 0.25 in B-V color. You also find that there is a Cepheid variable star in this cluster, with a period of 10 days and a mean apparent V magnitude of 7.0. How far away is the cluster?
  
  
If the stars are "too red" by 0.25, that means E(B-V)=0.25. But since A_V=3.2E(B-V), stars which are too red by 0.25 are extincted by 3.2x0.25=0.8 magnitudes. So if we correct for dust, the mean apparent V magnitude is actually 6.2 (ie 7.0-0.8). If the Cepheid has a period of 10 days, then it has an mean absolute magnitude of M=-2.8xlog(10)-1.43=-4.23. Then we can get distance from m-M=5logd-5, so 6.2-(-4.23)=5logd-5, or d=1200 pc.


• If your telescope can reliably measure the brightnesses of stars down to 20th magnitude, what is the fathest away you could detect a Cepheid variable? Remember that the most luminous Cepheids have period of about 100 days.
  
  
If a luminous Cepheid has a period of 100 days, it has an absolute magnitude of -7.0. If you detect them down to 20th magnitude, that means m-M=20-(-7)=27, or a distance of d=2.5 million parsecs (Mpc). And yes, we have measured Cepheids out that far (and farther)!

Essay