The limiting luminosity of accreting neutron stars with magnetic fields.

Accretion on to a magnetized neutron star for high accretion rates, when one can no longer ignore the back-reaction of emergent light on the infalling material, is discussed in detail. The equations of hydrodynamics and radiative diffusion are solved analytically in a one-dimensional approximation. The luminosity is evaluated beyond which one should allow for the dynamic effect of emergent light on the infalling material. The limiting X-ray luminosity of accreting magnetized neutron stars is shown to depend crucially on the geometry of the accretion channel. The effects connected with the gas flow along the magnetospheric surface are discussed in detail. The plasma layer on the Alfven surface is shown to be optically thick with respect to Thomson scattering and to reradiate in soft X-rays a considerable fraction of the primary X-ray flux. A necessary condition for the X-ray luminosity to exceed the Eddington limit is a certain degree of asymmetry in the distribution of matter over the Alfven surface.