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

## TL;DR

This paper introduces a semi-analytical model for super-Eddington accretion discs around magnetized neutron stars, accounting for heat advection and wind-driven mass loss, predicting physical profiles and magnetospheric radius behavior.

## Contribution

It provides a novel semi-analytical framework for super-Eddington accretion discs with advection and outflows, including the magnetospheric radius as an eigenvalue, applicable to various neutron star systems.

## Key findings

- Magnetospheric radius depends weakly on accretion rate when advection is mild.
- Approaching the Eddington limit, the disc becomes advection-dominated with classical Alfven scaling.
- Mass loss via wind increases the magnetospheric radius.

## Abstract

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 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 approaching 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 of the magnetospheric radius. Our model may be applied to a large 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 NGC 5907~X-1, the brightest ultra-luminous pulsar known so far, and NGC 300~ULX-1 which is apparently a Be/X-ray binary experiencing a very bright super-Eddington outburst.