Harmonic analysis for pulsar timing arrays

We investigate the use of harmonic analysis techniques to perform measurements of the angular power spectrum on mock pulsar timing data for an isotropic stochastic gravitational-wave background (SGWB) with a dimensionless strain amplitude A₆ₖ=210^-15 and spectral index ₆ₖ=13/3. We examine the sensitivity of our harmonic analysis to the number of pulsars (50, 100, and 150) and length of pulsar observation time (10, 20, and 30 years) for an isotropic distribution of pulsars. We account for intrinsic pulsar red noise and use an average value of white noise of 100 ns. We are able to detect the quadrupole for all our mock harmonic analyses, and for 150 pulsars observed for 30 years we are able to detect up to the =5 multipole. We provide linear scaling relationships for the SGWB amplitude, the quadrupole, and =3 as a function of pulsar observation time and number of pulsars. We estimate the sensitivity of our harmonic approach to deviations of general relativity that produce subluminal GW propagation speeds.