#### ASTR 620 Galaxies Problem Set 2Due in class Monday 22 October 2007

1. Simple Population Synthesis

Consider an old and a young population of stars with the colors given in the table. Compute the colors of different mixes of each, ranging from 100% young to 100% old. Plot the locus of the colors of the mixed population in a color-color diagram. For comparison, also plot the observed mean colors of galaxies from Huchra (1977, ApJS, 35, 171). Can you explain the observed variation of colors with this simple two component model? Comments on what this might mean.

Old PopYoung Pop
U-B+0.49-1.00
B-V+0.95-0.20
NOTE: the entries in this table were scrambled prior to noon on Saturday 10/20. They are correct now.

2. Remnants

For a simple single population like a globular cluster, compute and plot the fractional mass in the form of white dwarfs up to an age of 13 Gyr. Assume a Salpeter IMF with lower and upper mass limits of 0.1 and 100 solar masses. You may ignore the evolution of the total mass of the cluster due to gas ejection.

3. Binney & Merrifield 9.4
Note that the real disk is not perfectly flat, but is warped in the outer galaxy. Answer this question as posed assuming no warp, but think about how things might change as a result of the warp. Just think about it; this is not an extra part of the question.

4. Binney & Merrifield 10.6
Think about how peri and apo relate to the epicycle approximation. In the absence of perfect knowledge about the Galactic potential, you do need to accept the observational input that is offered in the book.

5. Missing Satellites

A. Use the data in Binney & Merrifield Table 4.3 to plot the luminosity function N(MV) of Milky Way satellites.
How do you decide which of the tabulated galaxies are Milky Way satellites?
B. Make (and justify) some assumption about the stellar mass-to-light ratio in order to plot the cumulative stellar mass function N(>M*) of the satellites.
Refer to Fig. 5 of Diemand et al. (2007, ApJ, 657, 262) for the simulation results for the cumulative number of dark sub-halos. Plot their power law together with the data.
C. Treating the dark-to-stellar mass ratio as a free parameter, what do you need to do to reconcile the data with the simulations?
Does this seem plausible to you?