Mass-radius constraints from a pulse shape model for Hercules X-1

An accretion column model is applied to reproduce the pulse shape of Her X-1. The motivation for the model is the observed 35 day sequence of pulse shape changes, which imply a pencil beam from the near pole and a fan beam from the far pole. The pulse shape depends on the beam pattern, which is calculated for an emitting surface in the shape of a filled cone. The calculation has a parameterized emissivity function and includes gravitational light-bending and shadowing effects. Least-squares fitting of the model to the observed pulse profile yields best-fit parameters and statistical uncertainties for the viewing geometry, the geometry of the accretion column, and the mass-to-radius ratio of the neutron star. The derived mass-to-radius ratio is 0.121-0.128 M-circle dot km(-1) (3 sigma statistical range). Combined with the mass determined from analysis of the orbit of Her X-1, several recent equations of state for dense matter are excluded for the neutron star in Her X-1.