Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation

Abstract

We study the observation of stochastic gravitational-wave background (SGWB) made by pulsar-timing arrays in the spherical harmonic space. Instead of using the Shapiro time delay, we keep the Sachs-Wolfe line-of-sight integral for the timing residual of an observed pulsar. We derive the power spectrum of the timing residual, from which the overlap reduction functions and the bipolar spherical harmonics coefficients are constructed for the SGWB intensity and polarization anisotropies. We have reproduced the previous results, noting that we have developed a fast algorithm for computing accurate overlap reduction functions and the bipolar spherical harmonics coefficients for the linear-polarization anisotropy are worked out for the first time. Our harmonic-space method is useful for future pulsar-timing-array observation on a few thousand pulsars and provides optimal estimators for testing the statistical isotropy of the SGWB.

arXiv comment10 pages. arXiv admin note: text overlap with arXiv:2107.00536

References in corpus (42)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Characterization of the LIGO detectors during their sixth science run
• The Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) Project
• The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background
• The international pulsar timing array project: using pulsars as a gravitational wave detector
• European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background
• Gravitational waves from binary supermassive black holes missing in pulsar observations
• Upper Limits on the Isotropic Gravitational-Wave Background from Advanced LIGO's and Advanced Virgo's Third Observing Run
• Fundamental Physics with the Square Kilometre Array
• A guide to LIGO-Virgo detector noise and extraction of transient gravitational-wave signals
• 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
• Leptogenesis from Gravity Waves in Models of Inflation
• The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background
• The Astrophysics of Nanohertz Gravitational Waves
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Parity violation in the Cosmic Microwave Background from a pseudoscalar inflaton
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• Circular Polarization of Primordial Gravitational Waves in String-inspired Inflationary Cosmology
• 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
• Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays
• Searching For Anisotropic Gravitational-wave Backgrounds Using Pulsar Timing Arrays
• GEO 600 and the GEO-HF upgrade program: successes and challenges
• Search for anisotropic gravitational-wave backgrounds using data from Advanced LIGO and Advanced Virgo's first three observing runs
• Characterizing the Cosmological Gravitational Wave Background Anisotropies and non-Gaussianity
• Measurement of Parity Violation in the Early Universe using Gravitational-wave Detectors
• From Bright Binaries To Bumpy Backgrounds: Mapping Realistic Gravitational Wave Skies With Pulsar-Timing Arrays
• Pulsar-timing arrays, astrometry, and gravitational waves
• Probing circular polarization in stochastic gravitational wave background with pulsar timing arrays
• A unified view of anisotropies in the astrophysical gravitational wave background
• Large anisotropies of the stochastic gravitational wave background from cosmic domain walls
• Polarization of a stochastic gravitational wave background through diffusion by massive structures
• Fisher formalism for anisotropic gravitational-wave background searches with pulsar timing arrays
• Chirality of the gravitational-wave background and pulsar-timing arrays
• The effect of small inter-pulsar distance variations in stochastic gravitational wave background searches with Pulsar Timing Arrays
• The search for anisotropy in the gravitational-wave background with pulsar-timing arrays
• Insights into searches for anisotropies in the nanohertz gravitational-wave background
• Redshift-space fluctuations in stochastic gravitational wave background
• Statistics of Bipolar Representation of CMB maps
• Spherical harmonic analysis of anisotropies in polarized stochastic gravitational wave background with interferometry experiments

Cited by in corpus (8)

• Pulsar and cosmic variances of pulsar timing-array correlation measurements of the stochastic gravitational wave background
• Stochastic gravitational wave background phenomenology in a pulsar timing array
• Hunting the stochastic gravitational wave background in pulsar timing array cross correlations through theoretical uncertainty
• Beyond the Hellings-Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations
• Pulsar Timing Array Harmonic Analysis and Source Angular Correlations
• Correlations for an anisotropic polarized stochastic gravitational wave background in pulsar timing arrays
• Charting the Nanohertz Gravitational Wave Sky with Pulsar Timing Arrays
• Accurate pulsar timing array residual variances and correlation of the stochastic gravitational wave background