The Eddington limit and supercritical accretion. I - Time-independent calculations

Spherically symmetric, steady state accretion of an ionized hydrogen plasma onto a neutron star is considered for accretion rates which exceed a critical rate at which the Eddington limiting luminosity is produced. The coupled hydrodynamic and frequency integrated, radiative transfer equations are solved for accretion rates up to 10 times the nominal limit. Steady state solutions are presented that imply a multiplicity of different luminosity solutions for a single accretion rate in this 'supercritical' regime.