Harmonic space analysis of pulsar timing array redshift maps

Understand

In this paper, we propose a new framework for treating the angular information in the pulsar timing array response to a gravitational wave background based on standard cosmic microwave background techniques.

• We calculate the angular power spectrum of the all-sky gravitational redshift pattern induced at the earth for both a single bright source of gravitational radiation and a statistically isotropic, unpolarized Gaussian random gravitational wave 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.