X-ray spectra from protons illuminating a neutron star

We consider the interaction of a slowly rotating unmagnetized neutron star with a hot (ion supported, ADAF) accretion ow. The virialized protons of th e ADAF penetrate into the neutron star atmosphere, heating a surface layer. Detailed calculations are presented of the equilibrium between heating by the protons, electron thermal conduction, bremsstrahlung and multiple Compt on scattering in this layer. Its temperature is of the order 40-70 keV. Its optical depth increases with the incident proton energy flux, and is of th e order unity for accretion at 10(-2)-10(-1) of the Eddington rate. At thes e rates, the X-ray spectrum produced by the layer has a hard tail extending to 100 keV, and is similar to the observed spectra of accreting neutron st ars in their hard states. The steep gradient at the base of the heated laye r gives rise to an excess of photons at the soft end of the spectrum (compa red to a blackbody) through an "inverse photosphere effect". The difference s with respect to previous studies of similar problems are discussed, they are due mostly to a more accurate treatment of the proton penetration proce ss and the vertical structure of the heated layer.