Accurate neutron star models in the Hartle-Thorne approach

Inferences from future X-ray observations with NICER and LOFT, along with gravitational-wave detections, require accurate neutron star models. In this talk, I will present the development of highly accurate solutions for slowly rotating neutron stars, extending the Hartle-Thorne approximation to seventh-order in a slow-rotation expansion. This level of approximation enables us to extract second-, fourth-, and sixth-order spin corrections to the Tolman-Oppenheimer-Volkoff (TOV) mass, radius, and moment of inertia, as well as higher multipole moments with their spin corrections. We found that such corrections depend on higher-order susceptibilities, which can provide new information about the nuclear structure of matter. In addition, we obtained expressions for the mass and mass-current multipole moments and their spin corrections in terms of Geroch-Hansen invariant multipoles, which were verified using Thorne's ACMC approach. This allows us to obtain additional three-hair relations that can be useful to break parameter degeneracies in future observations. Finally, we provide error estimates for each multipole at every truncation order and for different spin frequencies, which can be used to obtain accurate X-ray profile models for upcoming observations.