Future microhertz detections combined with nanohertz pulsar terms can serve as gravity echoes to measure supermassive black hole binary inspiral rates from hundreds to thousands of years in the past.
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A Practical Theorem on Gravitational Wave Backgrounds
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abstract
There is an extremely simple relationship between the spectrum of the gravitational wave background produced by a cosmological distribution of discrete gravitational wave sources, the total time-integrated energy spectrum of an individual source, and the present-day comoving number density of remnants. Stated in this way, the background is entirely independent of the cosmology, and only weakly dependent on the evolutionary history of the sources. This relationship allows one easily to compute the amplitude and spectrum of cosmic gravitational wave backgrounds from a broad range of astrophysical sources, and to evaluate the uncertainties therein.
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representative citing papers
Solar wind plasma noise correlated between LISA and Taiji can bias stochastic gravitational wave background parameter estimates by up to 19% of Fisher uncertainty under large-scale correlation assumptions.
A full-covariance formalism for PTA-astrometry ORF estimators forecasts graviton-mass upper limits of 4.41e-24 eV/c2 for current-like setups and 0.48e-24 eV/c2 for SKA/Theia-like future setups, with astrometry adding significant power in the latter case.
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.
First spectral covariance analysis of SGWB data yields upper bounds on non-stationary correlations that translate into mass-dependent limits on high-redshift PBH merger rates.
Targeted PTA searches for CWs from 114 AGN in NANOGrav 15 yr data yield no detections, factor-of-two tighter limits than all-sky searches, and updated constraints ruling out part of the parameter space for a binary in 3C 66B.
Proposes APTA with 6 satellites and 10^{-18} relative clock uncertainty at 1s averaging to achieve sensitivity for observing 10^3-10^4 solar-mass black hole mergers in the decihertz band.
Discovery of a binary quasar at z~0.2 with 430 pc separation indicating a bound SMBH pair each >4e8 Msun, with 2.5 Gyr upper limit on merger timescale and implications for the PTA gravitational wave background.
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.
Bayesian multiband analysis shows LISA and Taiji reconstruct PTA-compatible domain wall parameters in the strong-signal regime, with joint PTA priors reducing 10D degeneracies.
Presents a new Fourier-expansion Bayesian hierarchical model with Lorentzian hyperprior for waveform-agnostic searches of nanohertz gravitational wave sources in pulsar timing array data.
Binary neutron star mergers with evolving merger rates or yields are strongly preferred over constant scenarios to explain Milky Way r-process enrichment, with Bayes factors exceeding 10^20, yet remain in tension with short gamma-ray burst observations.
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.
New simulations show that cross-correlating gravitational wave background anisotropies with galaxy distributions can enable discovery at angular scales of 4-6 degrees with next-generation observatories.
PTA statistical tests cannot distinguish Gaussian and non-Gaussian GWB amplitude distributions in a model-agnostic way after decorrelation.
A neural posterior estimator trained on simulated LISA foreground spectra recovers galactic binary population parameters, including total number, with good accuracy in validation tests.
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.
Finite source number and finite observation time make PTA gravitational-wave-background Fourier coefficients non-Gaussian, with an analytically computed excess kurtosis and a Cauchy-distributed argument probe.
Third-generation gravitational-wave detectors can constrain frequency-dependent beyond-GR waveform modifications in the stochastic background, but modified propagation effects remain degenerate with astrophysical population parameters.
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-component neutron star model resolve nonstationarity through damped and diffusive e
Simulations of ET and CE networks show delays degrade localization metrics far more than SNR, with LIGO India greatly reducing the impact for multi-messenger and stochastic searches.
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.
Customized chromatic noise models applied to NANOGrav 15 yr data raise the Bayes factor for Hellings-Downs GWB correlations by a factor of ~8, lower the amplitude to 2.1e-15, and increase the spectral index to 3.5.
Joint SKA PTA and astrometry analysis improves gravitational wave background detection sensitivity by 10-50%.
citing papers explorer
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Gravity Echoes from Supermassive Black Hole Binaries
Future microhertz detections combined with nanohertz pulsar terms can serve as gravity echoes to measure supermassive black hole binary inspiral rates from hundreds to thousands of years in the past.
-
Effects of Solar Wind Plasma Noise on Stochastic Gravitational Wave Background Searches with the LISA-Taiji Network
Solar wind plasma noise correlated between LISA and Taiji can bias stochastic gravitational wave background parameter estimates by up to 19% of Fisher uncertainty under large-scale correlation assumptions.
-
Forecasting graviton-mass constraints from the full covariance of PTA-astrometry ORF estimators
A full-covariance formalism for PTA-astrometry ORF estimators forecasts graviton-mass upper limits of 4.41e-24 eV/c2 for current-like setups and 0.48e-24 eV/c2 for SKA/Theia-like future setups, with astrometry adding significant power in the latter case.
-
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.
-
The First Upper Bound on the Non-Stationary Gravitational Wave Background and its Implication on the High Redshift Binary Black Hole Merger Rate
First spectral covariance analysis of SGWB data yields upper bounds on non-stationary correlations that translate into mass-dependent limits on high-redshift PBH merger rates.
-
The NANOGrav 15 yr Data Set: Targeted Searches for Supermassive Black Hole Binaries
Targeted PTA searches for CWs from 114 AGN in NANOGrav 15 yr data yield no detections, factor-of-two tighter limits than all-sky searches, and updated constraints ruling out part of the parameter space for a binary in 3C 66B.
-
Artificial Precision Timing Array: bridging the decihertz gravitational-wave sensitivity gap with clock satellites
Proposes APTA with 6 satellites and 10^{-18} relative clock uncertainty at 1s averaging to achieve sensitivity for observing 10^3-10^4 solar-mass black hole mergers in the decihertz band.
-
Discovery of a close-separation binary quasar at the heart of a z~0.2 merging galaxy and its implications for low-frequency gravitational waves
Discovery of a binary quasar at z~0.2 with 430 pc separation indicating a bound SMBH pair each >4e8 Msun, with 2.5 Gyr upper limit on merger timescale and implications for the PTA gravitational wave background.
-
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.
-
PTA-Compatible Domain Walls at LISA and Taiji: Bayesian Reconstruction and Multiband Inference
Bayesian multiband analysis shows LISA and Taiji reconstruct PTA-compatible domain wall parameters in the strong-signal regime, with joint PTA priors reducing 10D degeneracies.
-
Searching for a waveform-agnostic gravitational wave signal in pulsar timing arrays
Presents a new Fourier-expansion Bayesian hierarchical model with Lorentzian hyperprior for waveform-agnostic searches of nanohertz gravitational wave sources in pulsar timing array data.
-
Binary Neutron Star Merger Evolution and r-Process Enrichment in the Milky Way Disk
Binary neutron star mergers with evolving merger rates or yields are strongly preferred over constant scenarios to explain Milky Way r-process enrichment, with Bayes factors exceeding 10^20, yet remain in tension with short gamma-ray burst observations.
-
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.
-
Prospects for multi-messenger discovery of the gravitational-wave background anisotropies via cross-correlation with galaxies
New simulations show that cross-correlating gravitational wave background anisotropies with galaxy distributions can enable discovery at angular scales of 4-6 degrees with next-generation observatories.
-
Are PTA measurements sensitive to gravitational wave non-Gaussianities?
PTA statistical tests cannot distinguish Gaussian and non-Gaussian GWB amplitude distributions in a model-agnostic way after decorrelation.
-
Inferring the population properties of galactic binaries from LISA's stochastic foreground
A neural posterior estimator trained on simulated LISA foreground spectra recovers galactic binary population parameters, including total number, with good accuracy in validation tests.
-
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.
-
Finite Populations & Finite Time: The Non-Gaussianity of a Gravitational Wave Background
Finite source number and finite observation time make PTA gravitational-wave-background Fourier coefficients non-Gaussian, with an analytically computed excess kurtosis and a Cauchy-distributed argument probe.
-
Modeling Uncertainties in Modified Gravity Predictions for the Stochastic Gravitational-Wave Background
Third-generation gravitational-wave detectors can constrain frequency-dependent beyond-GR waveform modifications in the stochastic background, but modified propagation effects remain degenerate with astrophysical population parameters.
-
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-component neutron star model resolve nonstationarity through damped and diffusive e
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Impact of facility timing and coordination for next-generation gravitational-wave detectors
Simulations of ET and CE networks show delays degrade localization metrics far more than SNR, with LIGO India greatly reducing the impact for multi-messenger and stochastic searches.
-
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.
-
The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses
Customized chromatic noise models applied to NANOGrav 15 yr data raise the Bayes factor for Hellings-Downs GWB correlations by a factor of ~8, lower the amplitude to 2.1e-15, and increase the spectral index to 3.5.
-
Synergies Between Pulsar Timing Array and Astrometry
Joint SKA PTA and astrometry analysis improves gravitational wave background detection sensitivity by 10-50%.
-
Sensitivity of Weak Lensing Surveys to Gravitational Waves from Inspiraling Supermassive Black Hole Binaries
Weak lensing surveys cannot detect nanohertz-microhertz gravitational waves from supermassive black hole binaries under realistic conditions; only unattainable idealized surveys could probe this band.
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Model Parameter Reconstruction of Electroweak Phase Transition with TianQin and LISA: Insights from the Dimension-Six Model
Simulations show TianQin and LISA can reconstruct the dimension-six model parameter Λ to sub-percent statistical precision for strong signals using Fisher, Bayesian sampling, and machine learning on data with noise and foregrounds.