ASTRO 346: SPRING 2007
Problem Set #4 - Due Wed. March 21
Problems from Zeilik, Gregory and Smith:
Ch. 13: 2, 4, 16, and 17b (don't do part a).
Ch. 16: 6, 9, 10, 11, and 12
X. The Salpeter IMF.
Suppose a star cluster forms with a total mass of 104 Msun, that all of its stars appear promptly on
the main sequence, and that the distribution of stars of stars of various masses follows the Salpeter
IMF (recall that this means that dN ∝ f(m) dm = m-α dm, with α = 2.35).
a) Suppose further that the low mass cutoff for this cluster is M = 0.5Msun and the high mass
cutoff is 25 Msun. Integrate over this range to normalize the IMF (i.e., get the constant of
proportionality). Then integrate to get number of stars in following mass ranges:
(0.5, 1.0) (1.0, 3.0) (10.0, 25).
b) How would these numbers change if the lower mass cutoff equals 0.3 solar masses? How
critical is this lower mass limit?