Joint search for isolated sources and an unresolved confusion background in pulsar timing array data

Abstract

Supermassive black hole binaries are the most promising source of gravitational-waves in the frequency band accessible to pulsar timing arrays. Most of these binaries will be too distant to detect individually, but together they will form an approximately stochastic background that can be detected by measuring the correlation pattern induced between pairs of pulsars. A small number of nearby and especially massive systems may stand out from this background and be detected individually. Analyses have previously been developed to search for stochastic signals and isolated signals separately. Here we present BayesHopper, an algorithm capable of jointly searching for both signal components simultaneously using transdimensional Bayesian inference. Our implementation uses the Reversible Jump Markov Chain Monte Carlo method for sampling the relevant parameter space with changing dimensionality. We have tested BayesHopper on various simulated datasets. We find that it gives results consistent with fixed-dimensional methods when tested on data with a stochastic background or data with a single binary. For the full problem of analyzing a dataset with both a background and multiple black hole binaries, we find two kinds of interactions between the binary and background components. First, the background effectively increases the noise level, thus making individual binary signals less significant. Second, weak binary signals can be absorbed by the background model due to the natural parsimony of Bayesian inference. Because of its flexible model structure, we anticipate that BayesHopper will outperform existing approaches when applied to realistic data sets produced from population synthesis models.

BayesWave analysis pipeline in the era of gravitational wave observations

“…Looking further afield, the BayesWave approach is being applied to other branches of gravitational wave astronomy, including pulsar timing arrays [39,40] and the future space-based LISA detector [41].…”

Search for Continuous Gravitational Wave Signals in Pulsar Timing Residuals: A New Scalable Approach with Diffusive Nested Sampling

“…For simplicity, we assume the typical timing uncertainty of each pulsar follows a white Gaussian noise with root mean square value of 10 −7 s and it is added to the timing residuals caused by GWs. Other sources of noise, such as pulsar spin noise, dispersion measure variation and stochastic GW background, have complicated correlations in space or time (Tiburzi et al 2016) and could impact CB-SMBH searches in practice (Bécsy & Cornish 2020). As a proof-of-concept of the DNest method, we neglect them here and integrating them into our model will be subjected to a future work.…”

“…Given that assumption, Babak & Sesana (2012) and Petiteau et al (2013) developed a maximum-likelihood-based with an implementation of the genetic algorithm (Holland 1975) to resolve multiple CB-SMBHs. As a further step, Bécsy & Cornish (2020) used trans-dimensional Bayesian inference implemented by reversible jump MCMC (Green 1995) to search for isolate sources and stochastic GW background jointly in PTA data.…”

Iterative time-domain method for resolving multiple gravitational wave sources in Pulsar Timing Array data

“…In [42], which builds on the earlier work in [43], a global fit approach was explored for the multisource resolution problem in which, assuming a certain number of resolvable sources, a fitness function derived from the loglikelihood function of the data (the so-called F-statistic) is maximized over the combined parameter space of the sources using a Genetic Algorithm. A Bayesian alternative to the global fit approach in [44] uses the method of reversible jump Markov chain Monte Carlo (RJMCMC) to obtain the best number of sources. Several simplifying assumptions are made in the above works to reduce the complexity of the multisource resolution problem.…”

“…Several simplifying assumptions are made in the above works to reduce the complexity of the multisource resolution problem. First, the number of resolvable GW sources and the number of array pulsars is limited to ≤ 8 and ≤ 50 in [42], respectively, with the corresponding numbers being 3 and 20 in [44]. Secondly, while the GW signal in the timing residual for any one pulsar contains two contributions [45], called the Earth and pulsar terms, the latter is ignored in both approaches as it results in a simpler, albeit sub-optimal, fitness function.…”