Low-frequency Gravitational Wave Searches and Data Analysis with Hamiltonian Sampling

Abstract

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), opening up a new area of gravitational wave astrophysics in the low-frequency regime. 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. In this dissertation we discuss the development of data analysis methods aimed at addressing the computational roadblocks facing PTA science. We focus on the implementation of the Hamiltonian Monte Carlo (HMC) sampling algorithm, which uses sample proposals based on the gradient of the model likelihood to more efficiently explore the high-dimensional covariant parameter spaces compared to the random-walk techniques currently employed. The HMC method was originally introduced for the studies of quantum chromodynamics but this marks the first time it is broadly adapted for methods of nanohertz GW detection. We present an end-to-end pipeline for performing joint Bayesian searches for both a GWB and CW sources using Hamiltonian sampling, and produce a collection of benchmarking and consistency tests to display its improvements over current methods. In particular, we show that our work will scale more favorably towards future PTA datasets in terms of computational cost saved, as we continue to add more pulsars to our array and increase our data volume. Lastly we shift our focus to yet another area of GW astrophysics, the millihertz frequency regime that will be analyzed by the Laser Interferometer Space Antenna (LISA). We begin to explore whether a Hamiltonian sampling pipeline can aid in the inference of extreme mass ratio inspiral sources, an as of yet unsolved problem for LISA data science.