An efficient pipeline for searches of supermassive binary black holes with pulsar timing arrays using gradient-based sampling methods

The pulsar timing array (PTA) community has found evidence for a correlated stochastic signal following the Hellings-Downs pattern indicative of an isotropic stochastic gravitational-wave background (GWB). The most likely source of such a background is a population of supermassive black hole binaries, and particularly loud individual sources could be detected in future datasets. Searching for these single continuous gravitational wave (CW) sources adds additional computational complexity to an already time-intensive analysis. This increases the already large number of parameters needed to be sampled concurrently and introduces strong covariance into the model, namely between binaries emitting at low frequencies and the GWB. We present a pipeline for efficiently performing joint Bayesian searches for both the GWB and CW sources. The pipeline utilizes particular Markov Chain Monte Carlo methods, namely the Hamiltonian Monte Carlo algorithm, which use sample proposals based in the gradient of the model likelihood to fully explore the high-dimensional covariant parameter space. We explore this method's capability at accurately recovering both the GWB and CW sources and present computational scaling arguments for this algorithm against the current prescriptions for PTA analyses.