Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars

TL;DR

This paper evaluates the detectability of a nanohertz gravitational wave background using pulsar timing arrays, emphasizing the impact of red and white noise and establishing detection criteria for different noise regimes.

Contribution

It introduces a comprehensive framework for assessing gravitational wave detection prospects with pulsar timing, accounting for red noise effects and specifying requirements for pulsar sample sizes and timing precision.

Findings

Detection is feasible with 20 stable pulsars with residuals below 20 ns.

Red noise significantly hampers detection unless mitigated.

Large-scale pulsar timing campaigns are necessary for weak signals.

Abstract

We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.