Super-Eddington accretion discs with advection and outflows around magnetized neutron stars.

We present a model for a super-Eddington accretion disc around a magnetized neutron star taking into account advection of heat and the mass loss by the wind. The model is semi-analytical and predicts radial profiles of all the basic physical characteristics of the accretion disc. The magnetospheric radius is found as an eigenvalue of the problem. When the inner disc is in radiation-pressure-dominated regime but does not reach its local Eddington limit, advection is mild, and the radius of the magnetosphere depends weakly on the accretion rate. Once it approaches the local Eddington limit the disc becomes advection-dominated, and the scaling for the magnetospheric radius with the mass accretion rate is similar to the classical Alfven relation. Allowing for the mass loss in a wind leads to an increase in the magnetospheric radius. Our model can be applied to a wide variety of magnetized neutron stars accreting close to or above their Eddington limits: ultra-luminous X-ray pulsars, Be/X-ray binaries in outbursts, and other systems. In the context of our model we discuss the observational properties of NGC5907 X-1, the brightest ultra-luminous pulsar currently known, and NGC300 ULX1, which is apparently a Be/X-ray binary experiencing a very bright super-Eddington outburst.