The spectral density of astrophysical stochastic backgrounds

TL;DR

This paper derives the spectral density of astrophysical stochastic backgrounds from coalescing binaries, analyzing the effects of shot noise on polarization and anisotropy, with explicit calculations for binary populations.

Contribution

It provides a detailed derivation of the spectral density and explores how shot noise influences polarization and anisotropy in the background.

Findings

Shot noise induces polarization in isotropic backgrounds.

Explicit calculations for binary black hole and neutron star populations.

Averaging over extrinsic parameters simplifies the spectral density expression.

Abstract

We provide a detailed derivation of the spectral density of the stochastic background generated by the superposition of coalescing compact binaries. We show how the expression often used in the literature emerges from an average over the extrinsic parameters of the binaries (times of arrival, polarization angles, arrival directions and orbit inclinations) and how the Stokes parameters related to circular and linear polarization are set to zero by such averaging procedure. We then consider the effect of shot noise, i.e. the fact that for the superposition of a finite number of sources these averages are only approximate, and we show how it generates circular and linear polarizations (even for isotropic backgrounds) as well as spatial anisotropies, and we compute them explicitly for a realistic population of binary black holes and binary neutron stars.