Pulse profile modelling of accreting millisecond X-ray pulsars

Pulse profile modelling (PPM) is the relativistic ray-tracing technique to compute X-ray pulse profiles of millisecond pulsars. Using modern sampling techniques, this technique is used to infer posterior probability distributions of neutron star (NS) parameters. In particular, accurate measurements of mass and radius are important, because these constrain the properties of poorly-understood dense matter in NS cores. Whereas PPM has so far been successful in its application to rotation-powered millisecond pulsars (RMPs), this thesis applies the technique to another class: accretion-powered millisecond pulsars (AMPs). Powered by accretion, this class of pulsars are more variable and necessitate modelling of an accretion disc, making them altogether harder to constrain. In including them, the goal is to improve overall mass and radius measurement statistics, and to better understand the NS population and evolution. In this thesis, we adapt an RMP model to AMPs by adding the appropriate hotspot atmosphere and accretion disc, and test the analysis on simulated data. One important finding is that the disc and non-pulsed radiation from NS hot spots can be difficult to disentangle, making it harder to constrain parameters. Following this, we analyse data of two AMPs, in one case including polarimetric data. We infer various parameters but find results are sometimes not robust, being dependent on modelling choices. In the future, we expect that the combination of high and low energy X-ray data, as well as polarimetric data, is a promising avenue that will lead to tighter parameter constraints.