Spectral Variance in a Stochastic Gravitational-wave Background from a Binary Population
William G. Lamb, Stephen R. Taylor
Abstract
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, 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.