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 [1], 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.

Expected properties of the first gravitational wave signal detected with pulsar timing arrays

“…Second, throughout the paper we adopted a conservative definition of GWB (isotropic, stochastic, Gaussian, unpolarised, and stationary); the true signal produced by the superposition of GWs coming from the ensemble of SBHBs might well be dominated by a handful of signals, therefore significantly departing from isotropy and/or Gaussianity. The development of detection algorithms targeting multiple individual sources (Babak & Sesana 2012;Petiteau et al 2013) as well as certain types of anisotropic signals (Gair et al 2014) might prove to be a 'more optimal' strategy than searching for a GWB with the aforementioned properties.…”

Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

“…Individually resolvable binaries can be subtracted from the data, and are treated separately from the stochastic background. An individual source can be efficiently searched for with matched filtering techniques [32][33][34][35]. Therefore, we expect the power necessary to detect a single SMBH binary to be significantly less than the power necessary to measure a stochastic background.…”

A Bayesian analysis pipeline for continuous GW sources in the PTA band

“…There are several ways that we could improve this step such as choosing a more suitable starting jump proposal distribution before starting adaptation or even starting adaptation sooner, however for the purpose of this work we believe that this is sufficient as the algorithm can still collect ∼ 2 × 10 6 samples with 8 chains in about 4 hours running on a 2.7 GHz quad core MacBook Pro. It is also important to note that in practice we will have carried out a simpler search algorithm such as an F-statistic [17,18,19] search prior to this Bayesian analysis. If any signal is detected, then we will have a very good idea of the frequency of the GW source and can therefore seed our MCMC algorithm much closer to the true value.…”

“…[16] developed a Bayesian framework aimed at the detection of GW memory in PTAs; however, the authors mention that the methods presented could be used for continuous GW sources as well. Most recently, a maximized likelihood based approach has been developed by [17,18] and was later extended to include multiple resolvable sources in [19].…”