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

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 European PTA (EPTA) data set, 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.

Automated summary

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a complex and computationally expensive analysis that requires source-specific noise studies. Optimizing the number of included pulsars is crucial in order to reduce the computational burden. In this study, we present a suite of methods to rank pulsars for use in PTA analysis, including maximizing the signal-to-noise ratio and minimizing the coupling between spatial correlation signatures. Testing these methods against mock data, we found significant improvements in the log-Bayes factor and log-likelihood ratio, suggesting that an optimally selected subset of pulsars can yield comparable results to using the whole array.