Optimal Strategies for Gravitational Wave Memory Detection in Pulsar Timing Arrays

2024/10/25 by Jerry P. Sun, X. Siemens, Sun, Jerry P. +3
Physics and Astronomy · #Pulsars and Gravitational Waves Research #Advanced Frequency and Time Standards #Radio Astronomy Observations and Technology

paper · pdf · doi:10.48550/arxiv.2410.19977

Abstract

In this work we derive two computationally efficient frequentist detection statistics that can be used in searches for gravitational-wave bursts with memory in pulsar timing data. By maximizing the likelihood ratio in two different ways we construct a coherent statistic and an incoherent statistic, which are analogs of the \pazocalF_e and \pazocalF_p statistics commonly used for continuous-wave searches in pulsar timing data. We show that both statistics are χ²-distributed with varying degrees of freedom and non-centrality parameters given by the signal-to-noise (SNR) ratio of the signal present in our data. The statistics can also be used to compute the maximum likelihood estimators of amplitude parameters of a possible gravitational-wave memory signal in pulsar timing data. We find that in the low-signal regime (SNR \lesssim 5), the estimators are inaccurate. However, in intermediate- to high-signal regimes, we show that these estimators can accurately determine the correct signal parameters.

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