Evolution of the innermost stable orbits around accreting neutron stars

The surface of most neutron stars with 'soft' equations of state lies within the innermost stable circular orbit predicted by general relativity. In disk accretion onto a weakly magnetized neutron star, the disk will reach the stellar surface for 'stiff' equations of state, but for soft equations of state the matter will hit the surface in free fall at an angle of about 0.001 to 0.1 radians. All calculations are carried out through first order in the angular momentum of the star.