State-space analysis of a continuous gravitational wave source with a pulsar timing array: Inclusion of the pulsar terms

Abstract

Pulsar timing arrays (PTA) can detect continuous nanohertz gravitational waves (GW) emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a GW from a single source. The modulation is the sum of terms proportional to the GW strain at the Earth and at every pulsar in the array. Here, we generalize previous state-space formul..