An Introduction to Modern Astrophysics · Problem 15.16

The Degenerate Remnants of Stars — Carroll & Ostlie

Physics — Astrophysics · grb-fluence-distribution-two-populations

Problem

Suppose there are two populations of gamma-ray burst sources with energies

E_1

and

E_2

. Show that if the sources are distributed homogeneously throughout the universe with number densities

n_1

and

n_2

, respectively, then the total number of bursts observed to have a fluence

\geq S

is proportional to

S^{-3/2}