Astr 498V Fall 2001

Galaxies Sylvain Veilleux

October 30, 2001 DUE: November 8 + 5 = 13, 2001

**Problem 1.**

(a) What is your personal mass-to-light ratio in solar
units, ? Assume that you are emitting like a black
body with T_{bb} = 310 K.

(b) Using your answer in (a), find out how many ASTR 498V students per cubic parsec are needed to close the universe.

**Problem 2.**

The requirement that the highest velocity stars in the solar neighborhood are bound to our Galaxy provides a limit on the mass of our Galaxy. Show that the escape velocity for a star in a galaxy with a flat rotation curve like our own is

where *V*_{c} is the circular velocity at the galactocentric radius of
the Sun, *R _{0}*, and is the total mass of the Galaxy (=

**Problem 3.**

Linder's ``? Think About 4.1'' on p. 64.

**Problem 4.**

(a) Show that the particle horizon at *z* = 10^{3} (epoch of last
scattering when the cosmic background radiation can finally flow
freely) is *r*_{H} = 200 *h ^{-1}* Mpc as measured today (= 0.2

(b) Show that the angle subtended today by the particle horizon at *z*
= 10^{3} is in an
Einstein-de-Sitter universe with = 1. (hint: see p. 70 in
Linder's). The cosmic background radiation is observed to be uniform
in about one part in 10^{5} on a much larger scale than this. This is an
indirect argument in favor of an inflationary period in the early
universe.