Shot noise in the astrophysical gravitational-wave background

Abstract

We calculate the shot noise induced in the anisotropies of the astrophysical gravitational-wave background by finite sampling of both the galaxy distribution and the compact binary coalescence event rate. This leads to a white noise term in the angular power spectrum ${C}_{\ensuremath{\ell}}$, for which we derive a simple analytical expression. Failing to account for this term (as previous analyses have done) biases any measurement of the ${C}_{\ensuremath{\ell}}$'s. We find that the shot noise dominates over the true astrophysical power spectrum in any reasonable observing scenario, and that only with very long observing times and removal of a large number of foreground sources can the true power spectrum be recovered.