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 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 orbiting around the Milky Way. 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 orbit 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 answe: 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, that mass must be "dark matter."

Weak answer: The galaxy rotates to 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 quickly, and is about 2x1010 Lsun. Here is a 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)!
• You measure a pulsating star with a parallax of 0.005 arcseconds and an apparent magnitude of 12. What is its absolute magnitude? If it has a radial velocity of 100 km/s and a proper motion of 0.2 arcsec/yr, what is its total space motion. What part of the galaxy is this star likely a member of the disk, the bulge, or the halo?
If p=0.005, then distance = 1/p = 200pc. Since m-M=5logd-5, M=m-5logd+5=12-5log(200)+5=5.5 (so it is intrinsically less luminous than the Sun). Using the equation for tangential motion, vtan=4.74(mu)(d) if proper motion (mu) is in arcsec/yr and distance is in parsecs. So it has a tangential velocity of 190 km/s, or a total space velocity of vtot=sqrt(190 ²+100²)=214 km/s. Disk stars don't move anywhere near that fast with respect to the Sun (since we are part of the disk and moving together). Since the star is only 200 pc away, its probably not a bulge star, since they are found near the galactic center. Therefore it is most likely a halo star.

Essay

• Describe the structure of the Milky Way Galaxy. Be sure to talk about the properties and relative sizes of the different components of the Galaxy. Where is the Sun's location in the Galaxy? A sketch will probably be useful here!
I'm not going to write an essay for you, but for this question you should talk about things like the disk, bulge, and halo (both stellar and dark). You should talk about their shape and size -- I dont expect you to memorize numbers to the umpteenth decimal point, but you should know things like the disk has a scale length of 3-4 kpc, that the bulge is small (a few kpc total in size), and that the dark halo extends out to many 10s of kpc (or more). You should talk about the fact that the disk is relatively thin (scale height of a few hundred pc at most) and that the disk is exponential in length and height. You should mention that the disk rotates but that the halo does not, that the halo has stars and globular clusters, and the disk has gas and dust. The Sun is located about 8-9 kpc away from the center. Talk briefly about which parts are metal-poor and which are metal-rich. Basically I am looking for a brief but competant summary of the Milky Way.