Pulsar Timing Response to Gravitational Waves with Spherical Wave Fronts from a Massive Compact Source in the Quadrupole Approximation

Abstract Pulsar timing arrays (PTAs) are searching for nanohertz-frequency gravitational waves (GWs) through cross-correlation of pulse arrival times from a set radio pulsars. PTAs have relied on frequency-shift formula the pulse, where planar GWs usually assumed. Phase corrections due to wave front curvature been recently discussed. In this paper, and timing-residual formulae derived with fully spherical fronts compact source such as binary supermassive black holes, differences in GW amplitude direction between Earth pulsar examined quadrupole approximation. By using new formulae, effects beyond plane-wave approximation discussed, galactic center PTA nearby candidates also mentioned.