Super-Eddington accretion on to a magnetized neutron star
Most of ultraluminous X-ray sources are thought to be objects accreting above their Eddington limits. In the recently identified class of ultraluminous X-ray pulsars, accretor is a neutron star and thus has a fairly small mass with a small Eddington limit. The accretion disc structure around such an object affects important observables such as equilibrium period, period derivative and the size of the magnetosphere. We propose a model of a nearly-standard accretion disc interacting with the magnetosphere only in a thin layer near the inner disc rim. Our calculations show that the size of the magnetosphere may be represented as the classical Alfv\'en radius times a dimensionless factor $\xi$ which depends on the disc thickness only. In the case of radiation-pressure-dominated disc, the size of the magnetosphere does not depend on the mass accretion rate. In general, increasing the disc thickness leads to a larger magnetosphere size in units of the Alfv\'en radius. For large enough mass accretion rates and magnetic moments, it is important to take into account not only the pressure of the magnetic field and the radiation pressure inside the disc, but also the pressure of the radiation produced close to the surface of the neutron star in accretion column. The magnetospheric size may increase by up to factor of two as a result of the effects related to the disc thickness and the irradiation from the central source. Accounting for these effects reduces the estimate of the neutron star magnetic moment by a factor of several.