All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar-timing arrays

TL;DR

This paper introduces two novel methods to assess the significance of detecting a stochastic gravitational-wave background in pulsar-timing arrays by eliminating spatial correlations in real data, enhancing detection reliability.

Contribution

The paper presents two innovative, correlation-elimination techniques for evaluating gravitational-wave background significance directly on real datasets, avoiding noise simulations.

Findings

Methods effectively distinguish true signals from noise.

Techniques are applicable to current pulsar-timing array data.

Approach improves detection confidence in gravitational-wave searches.

Abstract

We present two methods for determining the significance of a stochastic gravitational-wave (GW) background affecting a pulsar-timing array, where detection is based on evidence for quadrupolar spatial correlations between pulsars. Rather than constructing noise simulations, we eliminate the GWB spatial correlations in the true datasets to assess detection significance with all real data features intact. In our first method, we perform random phase shifts in the signal-model basis functions. This phase shifting eliminates signal phase coherence between pulsars, while keeping the statistical properties of the pulsar timing residuals intact. We then explore a method to null correlations between pulsars by using a "scrambled" overlap-reduction function in the signal model for the array. This scrambled function is orthogonal to what we expect of a real GW background signal. We demonstrate the efficacy of these methods using Bayesian model selection on a set of simulated datasets that contain a stochastic GW signal, timing noise, undiagnosed glitches, and uncertainties in the Solar system ephemeris. Finally, we introduce an overarching formalism under which these two techniques are naturally linked. These methods are immediately applicable to all current pulsar-timing array datasets, and should become standard tools for future analyses.