Toward robust detections of nanohertz gravitational waves

Abstract

The recent observation of a common red-noise process in pulsar timing arrays (PTAs) suggests that the detection of nanohertz gravitational waves might be around the corner. However, in order to confidently attribute this red process to gravitational waves, one must observe the Hellings-Downs curve -- the telltale angular correlation function associated with a gravitational-wave background. This effort is complicated by the complex modelling of pulsar noise. Without proper care, mis-specified noise models can lead to false-positive detections. Background estimation using bootstrap methods such as sky scrambles and phase shifts, which use the data to characterize the noise, are therefore important tools for assessing significance. We investigate the ability of current PTA experiments to estimate their background with "quasi-independent" scrambles -- characterized by a statistical "match" below the fiducial value: $|M|<0.1$. We show that sky scrambling is affected by "saturation" after $O(10)$ quasi-independent realizations; subsequent scrambles are no longer quasi-independent. We show phase scrambling saturates after $O(100)$ quasi-independent realizations. With so few independent scrambles, it is difficult to make reliable statements about the $\gtrsim 5\sigma$ tail of the null distribution of the detection statistic. We discuss various methods by which one may increase the number of independent scrambles. We also consider an alternative approach wherein one re-frames the background estimation problem so that the significance is calculated using statistically dependent scrambles. The resulting $p$-value is in principle well-defined but may be susceptible to failure if assumptions about the data are incorrect.

arXiv commentPaper accepted for publication on ApJ on the 7th of August 2023

References in corpus (52)

• 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
• Gravitational Wave Experiments and Early Universe Cosmology
• The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background
• Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities
• The international pulsar timing array project: using pulsars as a gravitational wave detector
• The PyCBC search for gravitational waves from compact binary coalescence
• Sensitivity curves for searches for gravitational-wave backgrounds
• The Parkes Pulsar Timing Array Project
• The North American Nanohertz Observatory for Gravitational Waves
• Gravitational wave bursts from cosmic strings
• Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries
• Gravitational wave bursts from cusps and kinks on cosmic strings
• Low-Frequency Gravitational Waves from Massive Black Hole Binaries: Predictions for LISA and Pulsar Timing Arrays
• The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background
• On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the Parkes Pulsar Timing Array
• The International Pulsar Timing Array: Second data release
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Ultra-Low Frequency Gravitational Radiation from Massive Black Hole Binaries
• Detecting the stochastic gravitational wave background using pulsar timing
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• The stochastic background: scaling laws and time to detection for pulsar timing arrays
• Detection of 107 glitches in 36 southern pulsars
• The MeerKAT Telescope as a Pulsar Facility: System verification and early science results from MeerTime
• Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays
• Detection of gravitational waves from the QCD phase transition with pulsar timing arrays
• Blip glitches in Advanced LIGO data
• The Parkes Pulsar Timing Array Project: Second data release
• From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release
• Identifying and mitigating noise sources in precision pulsar timing data sets
• The MeerKAT Pulsar Timing Array: First Data Release
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• The LSC Glitch Group : Monitoring Noise Transients during the fifth LIGO Science Run
• Are we there yet? Time to detection of nanohertz gravitational waves based on pulsar-timing array limits
• Realistic sensitivity curves for pulsar timing arrays
• All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar-timing arrays
• 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
• Parameter Estimation and Model Selection of Gravitational Wave Signals Contaminated by Transient Detector Noise Glitches
• The disturbance of a millisecond pulsar magnetosphere
• On the background estimation by time slides in a network of gravitational wave detectors
• Gravitational wave background from rotating neutron stars
• Projected constraints on the cosmic (super)string tension with future gravitational wave detection experiments
• Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction Function
• Evidence for profile changes in PSR J1713+0747 using the uGMRT
• Systematic errors in estimation of gravitational-wave candidate significance
• Systematic errors in estimation of gravitational-wave candidate significance
• Gravitational wave detection without boot straps: a Bayesian approach
• Bayesian search for gravitational wave bursts in pulsar timing array data

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• The NANOGrav 15-year Gravitational-Wave Background Methods
• Pulsar Timing Arrays require hierarchical models
• Systematic errors in searches for nanohertz gravitational waves
• Reading signatures of supermassive binary black holes in pulsar timing array observations
• The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays
• On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays
• Measuring the crust-superfluid coupling time-scale for 105 UTMOST pulsars with a Kalman filter
• Model-agnostic search of gravitational wave echoes in LVK data