Pulse profile modelling of thermonuclear burst oscillations

Neutron star cores provide a unique window into fundamental interactions under extreme conditions, with their composition tightly linked to mass and radius through the equation of state. Pulse Profile Modeling (PPM)—a relativistic ray-tracing technique—is a leading method for inferring neutron star mass, radius, and surface properties. To date, most PPM efforts have focused on rotation-powered millisecond pulsars, which are "relatively" less complex to model. This thesis investigates methods to extend PPM to thermonuclear burst oscillation sources, where pulsations arise during thermonuclear explosions triggered by nuclear runaways. These sources offer several advantages but also introduce significant challenges. Chief among these is the high computational demand driven by relativistic ray tracing and the large number of free parameters, which becomes even more pronounced due to the short-timescale variabilities. In Chapter I, we investigate whether mass and radius estimations remain accurate when time variability is ignored for computational efficiency. We show that neglecting variability introduces biases in these estimates. In Chapter II, we address this challenge by segmenting bursts into shorter intervals where variability is minimal and jointly fitting these segments. This approach mitigates the biases, reducing systematic uncertainties on mass and radius to within the range of statistical uncertainties. In Chapter IV, we apply the method developed in Chapter II to XTE J1814-338, constraining its properties. In Chapter V, we extend the analysis to the superburst oscillation source 4U 1636-536. For both sources, we find that the inferred properties are sensitive to assumptions about the accretion contribution to the burst.