Peering into neutron stars Rays, relativity, and rapid inference

Neutron stars, the ultradense compact remnants of supernova explosions, serve as natural laboratories for exploring fundamental physics, particularly the behaviour of matter and fundamental forces under extreme densities. A key challenge in astrophysics is understanding the internal structure of these compact objects, which dictates their Equation of State (EoS), a relation between their internal pressure and density. The EoS directly governs the macroscopic observables, mass and radius, of a neutron star. This thesis focuses on utilising pulse profile modelling, a technique that exploits relativistic effects on X-rays emitted from the hot magnetic polar caps on the surface of rapidly rotating neutron stars (i.e., pulsars) to precisely measure their properties, including their masses and radii. Specifically, the research develops a robust, open-source software framework for neutron star X-ray pulse profile modelling, incorporating advances in computational methods and astrophysical theory. The software framework, X-PSI, employs relativistic ray tracing to develop neutron star models capable of accurately simulating observed pulse profiles, enabling Bayesian inference of stellar parameters. We then proceed to apply this framework to state-of-the-art data of the millisecond pulsar PSR J0437–4715 from NASA's Neutron Star Interior Composition Explorer (NICER) mission, leading to one of the most precise mass and radius measurements to date. In light of the heavy computational load incurred by such analyses and the anticipated improvements in methodology and data quality, we also explore the possibility of accelerating inference via simulation-based inference techniques and lay the foundations for further research.