Astr 498V Fall 2001

Galaxies Sylvain Veilleux

September 11, 2001 DUE: September 18, 2001

PROBLEM SET # 1

Problem 1.

Estimate the average density of the Local Group of galaxies and compare it with the critical density g cm-3. What are the implications of your result? Mention the references you use for your calculations.

Problem 2.

The time taken for a galaxy or cluster to grow to density must be at least as great as the free-fall time (G = gravitational constant), since cosmic expansion must first be halted locally. What is tff for (a) the Milky Way () and (b) a cluster of galaxies (). Compare with the Hubble time H-10.

Problem 3.

We saw in class that the power spectrum

(a)
Prove the last equality in the previous equation. [Hint: one method is to write the volume integral for P(k) in spherical polar coordinates and then set .
(b)
Show that because describes departures from the mean density, the above equation implies , and hence as .

(c)
Show that the power spectrum corresponds to a correlation function . Hence implies , approximately as observed.

Problem 4.

Linder's ? Think About 1.3'' on p. 16

Problem 5.

Linder's ? Think About 1.4'' on p. 17