Analyzing The Gravitational Wave Background using Pulsar Timing Arrays

Abstract

Pulsar timing arrays (PTAs) use neutron stars with stable spins to measure the effectof gravitational waves (GWs) passing between the earth and pulsar line-of-sight in the nanohertz frequency range. The combined effect of GWs from all sources gives rise to the gravitational wave background (GWB). The main contribution of the GWB in this frequency regime is thought to be supermassive black hole binaries (SMBHBs) which exist in the centers of merged galaxies. In this dissertation we discuss methods and statistics to analyze and characterize the signal of the GWB. In Chapters 1 and 2 we introduce the concepts of gravitational wave radiation and pulsar responses to the GWs. In Chapter 3 we present a generalized form of the frequentist optimal statistic (OS) to measure the signature of the GWB from the pulsar pair cross-correlations. The Hellings- Downs curve is the expected cross-correlation signature between timing residuals of pairs of pulsars as a function of their angular separation. However to detect sources of corre- lated noise or test for alternative polarizations of GWs, we must construct a statistic that is modular, and able to search over multiple signatures simultaneously. We show that this method is useful for ruling out absent correlations that may bias our analyses. In Chapter 4 how it can be used to search for alternative polarizations in . In Chapter 5, we use the Bayesian analysis t-process method to detect anisotropy in the background as a function of frequency. Deviations from a power law in the GWB might arise from the population of SMBHBs, the astrophysics of the binaries, or a breakdown of stochasticity. We show that the t-process is able to recover both an idealized pure power-law background, as well as a background that has deviations from the theoretical power-law prescription of the GWB. In Chapter 6, we improve our frequentist Fp statistic for the detection of determinis- tic signals produced from an individual SMBHB by marginalizing it over multiple noise realizations. We show that this method is able to better detect the presence or absence of a continuous signal. Using noise-marginalization allows us to create distributions over each frequency bin rather than a single distribution marginalized across all frequencies. In Chapter 7, we conclude by summarizing our findings for each of the projects and discuss future prospects for PTA detections and analyses.