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.

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

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• 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