Quality over Quantity: Optimizing pulsar timing array analysis for stochastic and continuous gravitational wave signals

TL;DR

This paper develops and tests methods to optimally select pulsars for PTA analysis, significantly improving gravitational wave detection efficiency while reducing computational costs.

Contribution

It introduces ranking techniques based on signal-to-noise ratio and correlation minimization, enhancing pulsar selection for gravitational wave searches in PTA data.

Findings

Optimal pulsar selection doubles the log-Bayes factor slope compared to random selection.

A subset of 25 out of 40 pulsars achieves 89% of the full array's likelihood ratio.

Selection methods improve detection sensitivity and computational efficiency in PTA analysis.

Abstract

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic EPTA dataset, a subset of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is $89\%$ of the total, implying that an optimally selected subset of pulsars can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations.