Timingresidual power spectrum of a polarized stochastic gravitationalwave background in pulsartimingarray observation
Abstract
We study the observation of a stochastic gravitationalwave background (SGWB) made by a pulsartiming array in the spherical harmonic space of the observable. The observable is a timing residual which is the timeaveraged redshift fluctuation of a pulsar over the duration of observation. Using the SachsWolfe lineofsight integral for the redshift fluctuation, we derive the power spectrum of the timing residual, from which we develop a fast algorithm to compute the overlap reduction functions for the SGWB intensity and polarization anisotropies. We find that the algorithm is less complicated and more efficient than our previous work which is based on the expansion of the polarization basis tensors in terms of spherical harmonics. Also, we use the power spectrum to construct the bipolar spherical harmonic coefficients that characterize the statistical isotropy of the SGWB. In particular, the coefficients for the linearpolarization anisotropy are worked out for the first time. Our harmonicspace method is useful for the data analysis in future pulsartimingarray observation on a large number of pulsars as well as for the measurement of the statistical isotropy of the SGWB.
 Publication:

Physical Review D
 Pub Date:
 September 2022
 DOI:
 10.1103/PhysRevD.106.064004
 arXiv:
 arXiv:2201.06767
 Bibcode:
 2022PhRvD.106f4004L
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 10 pages. arXiv admin note: text overlap with arXiv:2107.00536