Can we hear beats with pulsar timing arrays?

TL;DR

This paper investigates how beat phenomena from two close-frequency gravitational waves from different directions can alter pulsar timing array correlations, potentially affecting GW detection and interpretation.

Contribution

It introduces an analytic model for beat-induced modulation of pulsar timing correlations caused by multiple gravitational wave sources.

Findings

Beat modulation introduces non-stationary correlation patterns.

Analytic solution enables inference of beat frequency from pulsar data.

Potential impact on distinguishing GW sources in pulsar timing arrays.

Abstract

An isolated supermassive black hole binary (SMBHB) produces an identical cross-correlation pattern of pulsar timings as an isotropic stochastic background gravitational waves (GWs) generated possibly by inflation. Can there remain the identical cross-correlation pattern in the presence of a secondary SMBHB? To address this issue, the present paper focuses on GWs with similar amplitudes but slightly different frequencies $f_1$ and $f_2$ coming from two different directions. Beats between the two GWs can modify angular correlation patterns. The beat-induced correlation patterns are not stationary but modulated with a beat frequency $f_{beat} \equiv |f_1 - f_2|$. We obtain an analytic solution that allows us to infer $f_{beat}$ from the modulated angular correlations.