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Non-Gaussian Statistics of Nanohertz Stochastic Gravitational Waves
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Recent detection of nHz stochastic gravitational wave background (SGWB) by multiple pulsar timing arrays (PTAs) has stimulated intensive discussions about its physical origin. In principle, either supermassive black hole binaries (SMBHBs) or processes in the early universe may be the sources. One key difference between the two lies in the statistics of the SGWB frequency power spectrum. In particular, the often assumed Gaussian random SGWB does not accurately describe the distribution of the collective SMBHB emission. In this work, we present a semi-analytical framework for calculating the non-Gaussian statistics of SGWB power expected from SMBHBs. We find that (a) wave interference between individual SMBHBs with indistinguishable observed frequencies and (b) the Poisson fluctuation of the source numbers, together shape the non-Gaussian statistics. Implementing the non-Gaussian statistics developed in this work, we investigate the sensitivity of current and future PTA datasets in distinguishing the origin of the SGWB through non-Gaussian information. Additionally, we find an interesting approximation of the non-Gaussian statistics, which has implications for accurately and practically treating non-Gaussianity in PTA Bayesian analyses.
Forward citations
Cited by 6 Pith papers
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A practical theorem on gravitational-wave background statistics
For large but finite source counts, the PDF of rescaled GWB characteristic strain squared follows the universal form N^{1/3} times the reflected map-Airy distribution evaluated at N^{1/3}(y-1), fully determined by the...
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Population statistics of nanohertz gravitational wave sources
A hierarchical Bayesian inference framework combining free-spectrum reconstruction with population-level likelihoods distinguishes finite SMBHB populations from Gaussian primordial GWB using mock PTA data.
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A Joint Optimal Search for Gravitational Waves from Resolved and Unresolved Supermassive Binary Black Holes with Pulsar Timing Arrays
A joint model of GWB and resolvable SMBHBs for PTA data proposes N_c as astrophysical detection statistic and applies it to NANOGrav 15-year simulations, finding tensions with 21 of 114 AGN candidates and low (2-5%) d...
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Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries
With a physically motivated z_min cutoff, higher-order moments of the SGWB from SMBH binaries depend on the mass function solely via <M^{10/3}>, giving a variance-to-mean ratio for <M^{10/3}>/<M^{5/3}> and a kurtosis-...
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The Heavy Tailed Non-Gaussianity of the Supermassive Black Hole Gravitational Wave Background
The gravitational wave background from supermassive black hole binaries has a universal heavy-tailed amplitude distribution with power-law index -4, causing divergent higher moments and dominance of the strongest sign...
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Stochastic problems in pulsar timing
Analytical solutions to Langevin equations for red noise and GWB in pulsars show that an Ornstein-Uhlenbeck spin frequency model is inconsistent with stationary signals, while an overdamped oscillator model and a two-...
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