The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays

Abstract

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Their analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks. After fitting our fiducial model to real data, we generate a population of simulated data-set replications. We use the replications to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients are extreme. We recover Hellings--Downs correlations in simulated data sets at significance levels consistent with the correlations measured in the NANOGrav 15 yr data set. A similar test on spectral coefficients shows that their values in real data are not extreme compared to their distributions across replications. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2 $\sigma$ and 3 $\sigma$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background.

20 pages, 14 Figures, accepted to PRD

References in corpus (46)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• Binary Black Hole Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background
• The NANOGrav 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background
• The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
• The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• Systematic investigation of the expected gravitational wave signal from supermassive black hole binaries in the pulsar timing band
• The NANOGrav Nine-year Data Set: Observations, Arrival Time Measurements, and Analysis of 37 Millisecond Pulsars
• The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries
• Understanding and analysing time-correlated stochastic signals in pulsar timing
• The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• A study of spatial correlations in pulsar timing array data
• From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release
• Minding the gap: GW190521 as a straddling binary
• The NANOGrav Nine-Year Data Set: Measurement and Interpretation of Variations in Dispersion Measures
• Identifying and mitigating noise sources in precision pulsar timing data sets
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• The Most Massive Binary Black Hole Detections and the Identification of Population Outliers
• Modeling the uncertainties of solar-system ephemerides for robust gravitational-wave searches with pulsar timing arrays
• All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar-timing arrays
• Constraining the Solution to the Last Parsec Problem with Pulsar Timing
• The second data release from the European Pulsar Timing Array: VI. Challenging the ultralight dark matter paradigm
• The second data release from the European Pulsar Timing Array V. Search for continuous gravitational wave signals
• Towards Robust Gravitational Wave Detection with Pulsar Timing Arrays
• Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays
• Hellings and Downs correlation of an arbitrary set of pulsars
• Constraints On The Dynamical Environments Of Supermassive Black-hole Binaries Using Pulsar-timing Arrays
• The NANOGrav 15-year Gravitational-Wave Background Methods
• Probing Extremal Gravitational-Wave Events with Coarse-Grained Likelihoods
• Model exploration in gravitational-wave astronomy with the maximum population likelihood
• Gravitational waves carry information beyond effective spin parameters but it is hard to extract
• How to Detect an Astrophysical Nanohertz Gravitational-Wave Background
• Generalized optimal statistic for characterizing multiple correlated signals in pulsar timing arrays
• Toward robust detections of nanohertz gravitational waves
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: I. The optimal statistic
• Testing strengths, limitations and biases of current Pulsar Timing Arrays detection analyses on realistic data
• Systematic errors in searches for nanohertz gravitational waves
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: II. Posterior predictive distributions and pseudo Bayes factors

Cited by in corpus (3)

• Accurate pulsar timing array residual variances and correlation of the stochastic gravitational wave background
• The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models
• On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays