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.
Understanding and analysing time-correlated stochastic signals in pulsar timing
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abstract
Although it is widely understood that pulsar timing observations generally contain time-correlated stochastic signals (TCSSs; red timing noise is of this type), most data analysis techniques that have been developed make an assumption that the stochastic uncertainties in the data are uncorrelated, i.e. "white". Recent work has pointed out that this can introduce severe bias in determination of timing-model parameters, and that better analysis methods should be used. This paper presents a detailed investigation of timing-model fitting in the presence of TCSSs, and gives closed expressions for the post-fit signals in the data. This results in a Bayesian technique to obtain timing-model parameter estimates in the presence of TCSSs, as well as computationally more efficient expressions of their marginalised posterior distribution. A new method to analyse hundreds of mock dataset realisations simultaneously without significant computational overhead is presented, as well as a statistically rigorous method to check the internal consistency of the results. As a by-product of the analysis, closed expressions of the rms introduced by a stochastic background of gravitational-waves in timing-residuals are obtained. Using $T$ as the length of the dataset, and $h_c(1\rm{yr}^{-1})$ as the characteristic strain, this is: $\sigma_{\rm GWB}^2 = h_{c}(1\rm{yr}^{-1})^2 (9\sqrt[3]{2\pi^4}\Gamma(-10/3) / 8008) \rm{yr}^{-4/3} T^{10/3}$.
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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.
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
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.
citing papers explorer
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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.
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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.
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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-component neutron star model resolve nonstationarity through damped and diffusive e
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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.