A standardizing coordinate transform turns PTA Fourier coefficients into near-standard normals so HMC/NUTS on GPU recovers NANOGrav-scale posteriors in ~15 minutes.
Sato-Polito and M
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The recent detection of gravitational waves (GWs) by pulsar timing array (PTA) collaborations spurred a variety of questions regarding the origin of the signal and the properties of its sources. The amplitude of a GW background produced by inspiralling supermassive black holes (SMBHs) can be predicted in a relatively robust manner from the present-day merged remnants, observed as single SMBHs at the centers of galaxies, but falls short of the signal measured by PTAs by a significant amount, requiring equal mass mergers, extremely short delay times, and no accretion in order to achieve a modest consistency. In this work, we revisit NANOGrav's 15-yr data set and reassess the aforementioned discrepancy using the full spectral information captured by PTA data. As previously noted in the literature, the discrete number of point sources contributing to the background may lead to deviations in the observed spectrum relative to the average ($h^2_c \propto f^{-4/3}$) due to Poisson fluctuations, providing additional information about the source population beyond the background amplitude. We derive a simple expression for the characteristic strain distribution given a SMBH model, which is generally applicable regardless of the method used to model the black hole population. We then refit the NANOGrav free spectrum using a minimal model based on the local mass function, showing that the current GW measurement requires roughly $\sim 10$ times more black holes than suggested by local observations and disfavors mass functions dominated by few very heavy sources, with the typical mass that contributes to the background $\lesssim 10^{10}M_{\odot}$. Given the range of SMBH models found to be consistent with the isotropic background, we address what is the typical number sources that would be individually detectable, given the current sensitivity.
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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 mean strain and a new cubic shot-noise scale.
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.
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%) detection probabilities for isolated sources.
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-skewness consistency relation independent of redshift evolution.
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 signals by few loud sources.
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A standardizing coordinate transform turns PTA Fourier coefficients into near-standard normals so HMC/NUTS on GPU recovers NANOGrav-scale posteriors in ~15 minutes.
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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 mean strain and a new cubic shot-noise scale.
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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 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%) detection probabilities for isolated sources.
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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-skewness consistency relation independent of redshift evolution.
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