Degeneracies in X-ray pulse profiles of rotating neutron stars

Abstract

Due to their extremely high density, neutron stars can serve as a "laboratory" for studying exotic physical phenomena which are not observed elsewhere in the universe. To do this, it is essential to be able to simultaneously determine the mass and radius of neutron stars. A possible way is pulse profile modelling: oscillations in the brightness of the star's X-ray emission, which originate from a bright spot on the rotating star surface, encode information about the mass and radius of the star and are compared to theoretical models for the oscillations. Last year, a powerful method was developed by Psaltis et al. (2014) to determine mass and radius via pulse profiles and thus to break the degeneracy between pulse profiles of different star configurations. For this method to work however, it was assumed that an emitting spot is small enough and circular. Possibly, problems arise when differently shaped spots or larger spots are considered as well. Also, additional degeneracies could be introduced by considering stars with two antipodal spots instead of a single spot, since then determining the rotational frequency of the star is no longer trivial.

In this project we use a ray-tracing program to investigate, for various spot shapes and sizes, whether mass-radius measurements still can be done if we make a wrong assumption about the spot shape or size. We find that for small spots the mass and radius of a neutron star can be determined correctly without information about the specific shape of the emitting spot. For large spots however, we show that errors up to ~12% in mass and ~20% in radius can occur in a mass-radius measurement if the shape and size of the hot spot are unknown. Moreover, we report explicit examples of degenerate pulse profiles of stars with a small spot and stars with a large spot, both with a different mass and radius. We also investigate a new method to break the degeneracy between single and double spot configurations. We find that for the wide range of simulations we did, it is possible to separate single and double spot configurations using four observables which can be calculated from pulse profiles. Our results on small spots further confirm the reliability of the method developed by Psaltis et al. (2014). Also, the fact that we were able to break the degeneracy between single and double spot configurations is promising for doing reliable observations. For mass-radius measurements to be reliable though, it is essential to be able to separate pulse profile observations of small spots and large spots. Future investigations should investigate this problem further.