Spectral Variance in a Stochastic Gravitational-Wave Background From a Binary Population

TL;DR

This paper derives analytic relationships for the statistical moments of a stochastic gravitational-wave background from binary populations, enhancing understanding of spectral fluctuations and aiding interpretation of pulsar timing array signals.

Contribution

It introduces new analytic scaling laws for variance, skewness, and kurtosis of the gravitational-wave background due to finite source effects, validated by numerical simulations.

Findings

Excellent agreement between analytic and numerical results.

Power-law relationships for higher moments of the stochastic background.

Provides physical insight into spectral fluctuations in gravitational-wave signals.

Abstract

A population of compact object binaries emitting gravitational waves that are not individually resolvable will form a stochastic gravitational wave signal. While the expected spectrum over population realizations is well known from Phinney (2001), its higher order moments have not been fully studied before or computed in the case of arbitrary binary evolution. We calculate analytic scaling relationships as a function of gravitational-wave frequency for the statistical variance, skewness, and kurtosis of a stochastic gravitational-wave signal over population realizations due to finite source effects. If the time derivative of the binary orbital frequency can be expressed as a power-law in frequency, we find that these moment quantities also take the form of power-law relationships. We also develop a numerical population synthesis framework against which we compare our analytic results, finding excellent agreement. These new scaling relationships provide physical context to understanding spectral fluctuations in a gravitational-wave background signal and may provide additional information that can aid in explaining the origin of the nanohertz-frequency signal observed by pulsar timing array campaigns.