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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abstract
The NANOGrav 15-year data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15-year observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values, or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach sub-parsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations.
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representative citing papers
Self-consistently heated and cooled thin circumbinary disks still drive massive black hole binaries into long-lived non-accreting phases, producing X-ray-weak, optically variable sources that LSST and Roman could find.
Lattice simulations find the bounce action for metastable cosmic string decay suppressed compared to thin-string estimates, implying faster decay.
Implements full-Stokes SGWB map-making for ground-based networks, applies to LVK O3 data, and constrains polarized angular spectra while showing intensity-only models can be biased.
Hardening binaries experience deterministic self-acceleration of their center of mass, induced precession, and plane rotation in uniform isotropic media, driving outward spiraling and eccentricity growth in all cases rather than circularization.
Pulsar timing arrays can probe supermassive black hole binaries that merged prior to observations via the pulsar term, with SKA potentially detecting a few such zombie binaries at SNR > 3.
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.
Stupendously large black holes cast shadows on the CMB that rule out masses above 10^17 solar masses within the last scattering surface and limit their density parameter to below 10^-5 for masses 10^15 to 10^18 solar masses.
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
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.
Monte Carlo and ML surrogate framework projects PTA sensitivity to compact DM substructures and shows SGWB weakens it, with only Shapiro searches retaining sensitivity in optimistic cases.
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.
AM-CW lunar laser ranging achieves μHz SGWB sensitivity of 5.29×10^{-9} D_cov (80 μm range uncertainty) or 2.07×10^{-9} D_cov (50 μm) over 5 years, with discovery possible if covariance degradation stays below ~3.6-13.7.
A phenomenological dipole anisotropy in primordial perturbations induces dipolar and quadrupolar anisotropies in SIGW energy density spectra, producing frequency-dependent PTA overlap reduction functions that depend on pulsar sky distribution, but NANOGrav 15-year data yields no significant evidence
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.
Combined five-PTA dataset yields posterior on SGWB power-law amplitude and index consistent with nonzero signal but below 5-sigma significance, with reconstructed angular correlations matching the Hellings-Downs prediction.
Customized chromatic noise models for 67 pulsars detect non-dispersive delays in 21 cases, alter achromatic noise inferences in 19, and enable solar wind density estimates over 1.5 cycles.
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Simulations of continuous-wave searches show that PTA data first constrain GW frequency and strain amplitude together, then sky location, with chirp mass and inclination following later for evolving sources, with precision depending on source frequency and sky position.
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A review summarizing current observational, experimental, and theoretical results on dark matter.
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Self-consistently heated and cooled thin circumbinary disks still drive massive black hole binaries into long-lived non-accreting phases, producing X-ray-weak, optically variable sources that LSST and Roman could find.
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The decay rate of metastable cosmic strings beyond the thin-string approximation
Lattice simulations find the bounce action for metastable cosmic string decay suppressed compared to thin-string estimates, implying faster decay.
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Polarized Anisotropic Stochastic Gravitational Wave Background Search with Ground-Based Detector Networks
Implements full-Stokes SGWB map-making for ground-based networks, applies to LVK O3 data, and constrains polarized angular spectra while showing intensity-only models can be biased.
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Self-acceleration of Hardening Binaries
Hardening binaries experience deterministic self-acceleration of their center of mass, induced precession, and plane rotation in uniform isotropic media, driving outward spiraling and eccentricity growth in all cases rather than circularization.
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Probing Supermassive Black Hole Mergers with Pulsar Timing Arrays
Pulsar timing arrays can probe supermassive black hole binaries that merged prior to observations via the pulsar term, with SKA potentially detecting a few such zombie binaries at SNR > 3.
-
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 mean strain and a new cubic shot-noise scale.
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Shadows of Giants: Constraints on Stupendously Large Black Holes from Negative Sources against the Cosmic Microwave Background
Stupendously large black holes cast shadows on the CMB that rule out masses above 10^17 solar masses within the last scattering surface and limit their density parameter to below 10^-5 for masses 10^15 to 10^18 solar masses.
-
Quantum production of gravitational waves after inflation
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
-
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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Projecting the ultimate pulsar timing sensitivity to dark matter substructure in a stochastic gravitational wave background
Monte Carlo and ML surrogate framework projects PTA sensitivity to compact DM substructures and shows SGWB weakens it, with only Shapiro searches retaining sensitivity in optimistic cases.
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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%) detection probabilities for isolated sources.
-
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.
-
High-Power AM-CW Lunar Laser Ranging as a $\mu$Hz SGWB Detector
AM-CW lunar laser ranging achieves μHz SGWB sensitivity of 5.29×10^{-9} D_cov (80 μm range uncertainty) or 2.07×10^{-9} D_cov (50 μm) over 5 years, with discovery possible if covariance degradation stays below ~3.6-13.7.
-
Exploring the statistical anisotropy of primordial curvature perturbations with pulsar timing arrays
A phenomenological dipole anisotropy in primordial perturbations induces dipolar and quadrupolar anisotropies in SIGW energy density spectra, producing frequency-dependent PTA overlap reduction functions that depend on pulsar sky distribution, but NANOGrav 15-year data yields no significant evidence
-
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 signals by few loud sources.
-
Stochastic gravitational-wave background search using data from five pulsar timing arrays
Combined five-PTA dataset yields posterior on SGWB power-law amplitude and index consistent with nonzero signal but below 5-sigma significance, with reconstructed angular correlations matching the Hellings-Downs prediction.
-
The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models
Customized chromatic noise models for 67 pulsars detect non-dispersive delays in 21 cases, alter achromatic noise inferences in 19, and enable solar wind density estimates over 1.5 cycles.
-
Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
Tensor perturbations from FOPT and domain-wall sources are claimed to induce second-order scalar perturbations large enough to form primordial black holes, potentially all of the dark matter.
-
Expectations for the first supermassive black-hole binary resolved by PTAs II: Milestones for binary characterization
Simulations of continuous-wave searches show that PTA data first constrain GW frequency and strain amplitude together, then sky location, with chirp mass and inclination following later for evolving sources, with precision depending on source frequency and sky position.
-
Expectations for the first supermassive black-hole binary resolved by PTAs I: Model efficacy
Simulations of PTA data show that a full gravitational-wave signal template achieves the highest Bayes factors and most robust parameter estimation for individual supermassive black hole binaries compared to an Earth-term template and a novel Spike Pixel cross-correlation model.
-
Thermodynamical uncertainties for primordial black holes from cosmological phase transitions
A state-of-the-art thermodynamic analysis of supercooled phase transitions yields a universal lower bound β/H_* ≃ 5 and shows that viable PBH dark-matter parameter space in classically conformal gauge-Higgs theories is severely limited by percolation and QCD constraints.
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Dark Matter
A review summarizing current observational, experimental, and theoretical results on dark matter.