Evaluating the Fourier Approximation in Pulsar Timing Array Analysis
Zhang, Yongqi
2023-05-29
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This thesis investigates the efficiency and accuracy of the Fourier approximation method employed by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) for detecting gravitational waves (GWs) using millisecond pulsars' time of arrival (TOA) data. NANOGrav utilizes a Python package called "Enterprise" to conduct Bayesian analyses of Gravitational Wave Background (GWB) models. ... read moreThis is computationally intensive, due to the requirement of inverting large covariance matrices, thus leading to the adoption of Fourier approximation for matrix inversion. The primary aim of this thesis is to evaluate the adequacy of the Fourier approximation method used by Enterprise, specifically regarding how this approximation could potentially affect the accuracy of the GW detection process. The analysis includes extending the current Fourier approximation in Enterprise to incorporate more Fourier modes with various frequency spacings, implementing analytic calculation, and a comparison of the likelihood results obtained from different Fourier spacings with the analytic calculation results. Preliminary findings suggest discrepancies between the likelihood results using Fourier approximation and those derived analytically, due to the fact that Fourier approximation only includes a certain range of frequencies. However, how that affects GW detection remains unknown.
Thesis (B.S.)--Tufts University, 2023.
Submitted to the Dept. of Physics and Astronomy.
Adviser: Ken Olum.read less - ID:
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