 
Summary: ASTR 3830: Problem Set 1
(due in class Friday January 30th)
1. In class, we showed that if the progenitors of gammaray bursts are distributed
uniformly throughout (Euclidean) space, then the number of bursts N with a time
integrated flux above some threshold value Smin scales as
N µ Smin
3 2
. Suppose that,
instead, the sources were uniformly distributed only within the disk of the Milky
Way galaxy (i.e., they had a constant number density per unit area in the disk, but
there were no sources in the halo). How would N scale with Smin in this scenario?
2. For stellar masses above a Solar mass, the Initial Mass Function of stars can be
approximated as a power law:
dN
dM
= kMa
with k and a constants. Recall that the number of stars N with mass M between M1
and M2 is given by integrating this expression between appropriate limits:
