Resolving multiple supermassive black hole binaries with pulsar timing arrays II: genetic algorithm implementation

Abstract: Pulsar timing arrays (PTAs) might detect gravitational waves (GWs) from massive black hole (MBH) binaries within this decade. The signal is expected to be an incoherent superposition of several nearly-monochromatic waves of different strength. The brightest sources might be individually resolved, and the overall deconvolved, at least partially, in its individual components. In this paper we extend the maximum-likelihood based method developed in Babak & Sesana 2012, to search for individual MBH binaries in PTA data. We model the signal as a collection of circular monochromatic binaries, each characterized by three free parameters: two angles defining the sky location, and the frequency. We marginalize over all other source parameters and we apply an efficient multi-search genetic algorithm to maximize the likelihood function and look for sources in synthetic datasets. On datasets characterized by white Gaussian noise plus few injected sources with signal-to-noise ratio (SNR) in the range 10-60, our search algorithm performs well, recovering all the injections with no false positives. Individual source SNRs are estimated within few % of the injected values, sky locations are recovered within few degrees, and frequencies are determined with sub-Fourier bin precision.