A COHERENT METHOD FOR THE DETECTION AND PARAMETER ESTIMATION OF CONTINUOUS GRAVITATIONAL WAVE SIGNALS USING A PULSAR TIMING ARRAY

The use of a high precision pulsar timing array is a promising approach to detecting gravitational waves in the very low frequency regime (10(-6)-10(-9) Hz) that is complementary to ground-based efforts (e. g., LIGO, Virgo) at high frequencies (similar to 10-10(3) Hz) and space-based ones (e. g., LISA) at low frequencies (10(-4)-10(-1) Hz). One of the target sources for pulsar timing arrays is individual supermassive black hole binaries which are expected to form in galactic mergers. In this paper, a likelihood-based method for detection and parameter estimation is presented for a monochromatic continuous gravitational wave signal emitted by such a source. The so-called pulsar terms in the signal that arise due to the breakdown of the long-wavelength approximation are explicitly taken into account in this method. In addition, the method accounts for equality and inequality constraints involved in the semianalytical maximization of the likelihood over a subset of the parameters. The remaining parameters are maximized over numerically using Particle Swarm Optimization. Thus, the method presented here solves the monochromatic continuous wave detection and parameter estimation problem without invoking some of the approximations that have been used in earlier studies.