Document Type
Article
Publication Date
11-23-2023
Abstract
We show via both analytical calculation and numerical simulation that the optimal cross-correlation statistic (OS) for stochastic gravitational-wave-background (GWB) searches using data from pulsar timing arrays follows a generalized chi-squared (GX2) distribution—i.e., a linear combination of chi-squared distributions with coefficients given by the eigenvalues of the quadratic form defining the statistic. This observation is particularly important for calculating the frequentist statistical significance of a possible GWB detection, which depends on the exact form of the distribution of the OS signal-to-noise ratio ρˆ ≡ Aˆ 2 gw=σ0 in the absence of GW-induced cross correlations (i.e., the null distribution). Previous discussions of the OS have incorrectly assumed that the analytic null distribution of ρˆ is well approximated by a zero-mean unit-variance Gaussian distribution. Empirical calculations show that the null distribution of ρˆ has “tails” which differ significantly from those for a Gaussian distribution but which follow (exactly) a GX2 distribution. Thus, a correct analytical assessment of the statistical significance of a potential detection requires the use of a GX2 distribution.
Recommended Citation
Hazboun, Jeffrey S., Patrick M. Meyers, Joseph D. Romano, Xavier Siemens, and Anne M. Archibald. 2023. “Analytic Distribution of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave-Background Searches Using Pulsar Timing Arrays.” Physical Review D 108 (10): 104050. https://doi.org/10.1103/PhysRevD.108.104050
Publication Title
Physical Review D
DOI
10.1103/PhysRevD.108.104050
Comments
© 2023 American Physical Society. Original published version available at https://doi.org/10.1103/PhysRevD.108.104050