Harmonic Space Analysis of Pulsar Timing Array Redshift Maps
Abstract
In this paper, we propose a new framework for treating the angular information in the pulsar timing array (PTA) response to a gravitational wave (GW) background based on standard cosmic microwave background techniques. We calculate the angular power spectrum of the allsky gravitational redshift pattern induced at the Earth for both a single bright source of gravitational radiation and a statistically isotropic, unpolarized Gaussian random GW background. The angular power spectrum is the harmonic transform of the Hellings & Downs curve. We use the power spectrum to examine the expected variance in the Hellings & Downs curve in both cases. Finally, we discuss the extent to which PTAs are sensitive to the angular power spectrum and find that the power spectrum sensitivity is dominated by the quadrupole anisotropy of the gravitational redshift map.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 2017
 DOI:
 10.3847/15384357/835/1/21
 arXiv:
 arXiv:1609.06758
 Bibcode:
 2017ApJ...835...21R
 Keywords:

 gravitational waves;
 largescale structure of universe;
 methods: analytical;
 pulsars: general;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 11 pages, 6 figures. This version's content matches the published version