The shape of rotating neutron stars and systematic errors in pulse profile observations parameter estimation

The Neutron star Interior Composition Explorer (NICER) is currently observing the pulse profiles produced by hotspots on the surface of rotating neutron stars (NSs), allowing us to measure their radii with unprecedented precision in the very near-future, helping solve the long standing problem of determining the equation of state (EOS) at supranuclear densities found in the interior of these stars. In the standard approach to model these pulse profiles, photons are assumed to propagate in a Schwarzschild background despite being emitted by an oblate surface. This oblateness (due to rotation) is described by analytic formulas, obtained by fitting catalogs of rotating NS models (covering a large sample of EOSs and spin frequencies) to some prescribed shape function. However, this smearing over EOSs, introduces a systematic error when estimating e.g. the star's radius, as the star's actual shape is determined by a single, underlying EOS. The question then arises: are the shape functions currently in use by NICER accurate enough to keep this error under control? How large it? Can we improve these formulas to tame this error? We present a first step in tackling this issue and present new, accurate formulas to model the shape of rotating NSs.