Consistency of the Parkes Pulsar Timing Array Signal with a Nanohertz Gravitational-wave Background

Pulsar timing array experiments have recently reported strong evidence for a common-spectrum stochastic process with a strain spectral index consistent with that expected of a nanohertz-frequency gravitational-wave background, but with negligible yet non-zero evidence for spatial correlations required for a definitive detection. However, it was pointed out by the Parkes Pulsar Timing Array (PPTA) collaboration that the same models used in recent analyses resulted in strong evidence for a common-spectrum process in simulations where none is present. In this work, we introduce a methodology to distinguish pulsar power spectra with the same amplitude from noise power spectra of similar but distinct amplitudes. The former is the signature of a spatially uncorrelated pulsar term of a nanohertz gravitational-wave background, whereas the latter could represent ensemble pulsar noise properties. We test the methodology on simulated data sets. We find that the reported common process in PPTA pulsars is indeed consistent with the spectral feature of a pulsar term. We recommend this methodology as one of the validity tests that the real astrophysical and cosmological backgrounds should pass, as well as for inferences about the spatially uncorrelated component of the background.

[1]  P. Meyers,et al.  Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects , 2022, Galaxies.

[2]  J. Greene,et al.  A Quasar-based Supermassive Black Hole Binary Population Model: Implications for the Gravitational Wave Background , 2021, The Astrophysical Journal.

[3]  J. Gair,et al.  Noise analysis in the European Pulsar Timing Array data release 2 and its implications on the gravitational-wave background search , 2021, 2111.05186.

[4]  J. Gair,et al.  Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search , 2021, 2110.13184.

[5]  H. Middleton,et al.  On the Evidence for a Common-spectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array , 2021, 2107.12112.

[6]  H. Middleton,et al.  The Parkes pulsar timing array second data release: timing analysis , 2021, Monthly Notices of the Royal Astronomical Society.

[7]  A. Melatos,et al.  Rapid parameter estimation of a two-component neutron star model with spin wandering using a Kalman filter , 2021, Monthly Notices of the Royal Astronomical Society.

[8]  D. Stinebring,et al.  Astrophysics Milestones for Pulsar Timing Array Gravitational-wave Detection , 2020, The Astrophysical Journal Letters.

[9]  OUP accepted manuscript , 2021, Monthly Notices of the Royal Astronomical Society.

[10]  OUP accepted manuscript , 2021, Monthly Notices of the Royal Astronomical Society.

[11]  E. Thrane,et al.  Identifying and mitigating noise sources in precision pulsar timing data sets , 2020, 2010.06109.

[12]  Stephen R. Taylor,et al.  The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background , 2020, The Astrophysical Journal Letters.

[13]  J. Dempsey,et al.  The Parkes Pulsar Timing Array project: second data release , 2020, Publications of the Astronomical Society of Australia.

[14]  E. Thrane,et al.  Is there a spectral turnover in the spin noise of millisecond pulsars? , 2019, 1910.05961.

[15]  Rutger van Haasteren,et al.  PTMCMCSampler: Parallel tempering MCMC sampler package written in Python , 2019 .

[16]  Stephen Taylor,et al.  ENTERPRISE: Enhanced Numerical Toolbox Enabling a Robust PulsaR Inference SuitE , 2019 .

[17]  P. Lasky,et al.  Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy , 2018, The Astrophysical Journal Supplement Series.

[18]  Colm Talbot,et al.  An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models , 2018, Publications of the Astronomical Society of Australia.

[19]  Daniel Foreman-Mackey,et al.  Data Analysis Recipes: Using Markov Chain Monte Carlo , 2017, 1710.06068.

[20]  R. Karuppusamy,et al.  High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array , 2016, 1602.08511.

[21]  D. Stinebring,et al.  From spin noise to systematics: Stochastic processes in the first International Pulsar Timing Array data release , 2016, 1602.05570.

[22]  D. Stinebring,et al.  The International Pulsar Timing Array: First Data Release , 2016, 1602.03640.

[23]  J. Gair,et al.  The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches , 2015, 1510.09194.

[24]  A. Lasenby,et al.  polychord: next-generation nested sampling , 2015, 1506.00171.

[25]  A. Melatos,et al.  Pulsar timing noise from superfluid turbulence , 2013, 1310.3108.

[26]  F. Feroz,et al.  TempoNest: A Bayesian approach to pulsar timing analysis , 2013, 1310.2120.

[27]  Chongqing,et al.  The Parkes Pulsar Timing Array Project , 2006, Publications of the Astronomical Society of Australia.

[28]  D. Stinebring,et al.  Gravitational Wave Astronomy Using Pulsars: Massive Black Hole Mergers & the Early Universe , 2009, 0902.2968.

[29]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[30]  Y. Levin,et al.  On measuring the gravitational-wave background using Pulsar Timing Arrays , 2008, 0809.0791.

[31]  R. Manchester,et al.  tempo2, a new pulsar timing package ¿ II. The timing model and precision estimates , 2006, astro-ph/0607664.

[32]  R. Hellings,et al.  Upper limits on the isotropic gravitational radiation background from pulsar timing analysis , 1983 .

[33]  J. Dickey.  The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters , 1971 .