The cross-correlation search for periodic gravitational waves

TL;DR

This paper develops a unified cross-correlation framework for detecting long-lived periodic gravitational waves, balancing sensitivity and computational cost by tuning coherence times, and bridging existing search methods.

Contribution

It adapts the cross-correlation statistic for periodic GW detection, accounting for non-stationarity and phase coherence, and unifies various search strategies into a flexible framework.

Findings

The method interpolates between semi-coherent and fully-coherent searches.

Sensitivity can be optimized by tuning the coherence time.

Provides a trade-off framework for computational cost and robustness.

Abstract

In this paper we study the use of cross-correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the non-stationarity and the long term-phase coherence of the signal. We study the statistical properties and sensitivity of this search, its relation to existing periodic wave searches, and describe the precise way in which the cross-correlation statistic interpolates between semi-coherent and fully-coherent methods. Depending on the maximum duration over we wish to preserve phase coherence, the cross-correlation statistic can be tuned to go from a standard cross-correlation statistic using data from distinct detectors, to the semi-coherent time-frequency methods with increasing coherent time baselines, and all the way to a full coherent search. This leads to a unified framework for studying periodic wave searches and can be used to make informed trade-offs between computational cost, sensitivity, and robustness against signal uncertainties.