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A pulsar timing array is a Galactic-scale detector of nanohertz gravitationalwaves (GWs). Its target signals contain two components: the `Earth term' andthe `pulsar term' corresponding to GWs incident on the Earth and pulsarrespectively. In this work we present a Frequentist method for the detectionand localization of continuous waves that takes into account the pulsar termand is significantly faster than existing methods. We investigate the role ofpulsar terms by comparing a full-signal search with an Earth-term-only searchfor non-evolving black hole binaries. By applying the method to synthetic datasets, we find that (i) a full-signal search can slightly improve the detectionprobability (by about five percent); (ii) sky localization is biased if onlyEarth terms are searched for and the inclusion of pulsar terms is critical toremove such a bias; (iii) in the case of strong detections (withsignal-to-noise ratio $\gtrsim$ 30), it may be possible to improve pulsardistance estimation through GW measurements.

Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms