Simulation and analysis of gravitational wave memory effects in Pulsar Timing Arrays

Gravitational wave memory effects are distinctive spacetime perturbations arising from extreme astrophysical events such as supermassive binary black hole mergers, whose detection holds significant implications for verifying nonlinear effects in general relativity and understanding black hole evolution. Pulsar timing arrays (PTAs), through monitoring millisecond pulsar timing residuals, provide a crucial observational approach for studying memory effects in the nanohertz gravitational wave band. This study employs Bayesian inference and Markov Chain Monte Carlo (MCMC) methods to construct four simulated datasets (pure white noise, injected signals with 5/10/20 pulsars), systematically evaluating PTA sensitivity and parameter estimation capabilities for gravitational wave memory signals. Results demonstrate: with injected gravitational wave memory signals of amplitude 5 × 10^-14and event epoch MJD 54500, 5-pulsar PTAs constrain event epochs to MJD 54500 15 d at 95% confidence level but exhibit approximately 3-fold amplitude overestimation; 10-pulsar PTAs constrain event epochs to MJD 54510 ± 10 d at 95% confidence level and recover amplitudes at the 10^-13level; 20-pulsar PTAs further reduce amplitude errors to below 5% and epoch uncertainties to 5 d. The research demonstrates that increasing pulsar count through improved sky coverage and data redundancy significantly enhances parameter estimation precision. These findings provide theoretical support for optimizing PTA observational strategies (e.g., expanding pulsar networks, refining noise modeling) and establish a foundation for future gravitational wave memory detection.