Graph-Based Method Detects Gravitational Wave Background in Pulsar Timing Arrays

This paper introduces a novel graph-based method for detecting the stochastic gravitational wave background (SGWB) using pulsar timing arrays (PTAs). The method constructs a correlation graph with pulsars as nodes and analyzes graph-based summary statistics to identify the SGWB in both real and synthetic datasets. The authors evaluate the impact of the number of pulsars, observation time span, and SGWB strength on the graph-based feature vector. Results indicate that the average clustering coefficient and edge weight fluctuation are discriminative summary statistics for common signal detection. The SGWB detection, performed after observing a common signal and excluding non-Hellings & Downs templates, utilizes the second cumulant of edge weight for angular separation thresholds. The lowest detectable SGWB strain amplitude is estimated to be around 1.2 x 10^-15. Fisher forecasts suggest that the uncertainty levels of the SGWB strain amplitude and spectral index can reach 1.5% and 19.5%, respectively. Applying the method to the NANOGrav 15-year dataset yields weak evidence for an SGWB at approximately 2.3 sigma level. This graph-based approach provides a complementary tool for analyzing pulsar timing data and potentially enhancing the detection of the stochastic gravitational wave background. Further refinement and application to larger datasets could improve the sensitivity and reliability of SGWB detection.

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