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-pressuredominated 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 Alfvén 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.

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 Alfvén radius times a dimensionless factor ξ 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 Alfvén 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.

Some modern models of neutron star evolution predict that initially large magnetic fields rapidly decay down to some saturation value ∼ few × 10 13 G and weaker magnetic fields do not decay significantly (Pons et al., 2009). It is difficult to check the predictions of this model for initially highly magnetized objects on the time scale of a few million years. We propose to use Be/X-ray binaries for this purpose. We apply several methods to estimate magnetic fields of neutron stars in these accreting systems using the data obtained by the RXTE satellite (Galache et al., 2008). Only using the most modern approach for estimating the magnetic field strengths of long period NSs as proposed by Shakura et al. (2011) we are able to obtain a field distribution compatible with predictions of the theoretical model of field decay of Pons et al. (2009).

We have performed a series of numerical experiments aimed at studying the activation of Kerr black holes (BHs) by advection of small scale magnetic fields. Such configurations may potentially give rise to the formation of quasi-striped Blandford-Znajek jets. It can also lead to enhanced dissipation and generation of plasmoids in current sheets formed in the vicinity of the BH horizon, which may constitute a mechanism to power the hard X-ray emission seen in many accreting BH systems (a la lamppost models). Our analysis suggests that formation of quasi-striped jets with significant power may be possible provided loops with alternating polarity having sizes larger than ∼10rg or so can be maintained (either form sporadically or advected from outside) at a radius ≲ 102rg. This conclusion is consistent with recent results of general relativistic force-free simulations. We also find that the accretion dynamics exhibits cyclic behaviour in MAD states, alternating between high accretion phases and quenched accretion phases during which the magnetosphere becomes force-free out to radii ≳ 10rg. We suggest that such a behaviour should lead to notable variations of the observed luminosity and image of the inner disc (BH shadow image). Finally, we find that the transition between accreted loops on the BH gives rise to the formation of current sheets and energetic plasmoids on the jet boundary during intermittent periods when the jet becomes inactive, in addition to an equatorial current sheet that forms during peaks in the jet activity.

Standard accretion disc model relies upon several assumptions, the most important of which is geometrical thinness. Whenever this condition is violated, new physical effects become important such as radial energy advection and mass loss from the disc. These effects are important, for instance, for large mass accretion rates when the disc approaches its local Eddington limit. In this work, we study the upper limits for standard accretion disc approximation and find the corrections to the standard model that should be considered in any model aiming on reproducing the transition to super-Eddington accretion regime. First, we find that for thin accretion disc, taking into account relativistic corrections allows to increase the local Eddington limit by about a factor of two due to stronger gravity in General Relativity (GR). However, violation of the local Eddington limit also means large disc thickness. To consider consequently the disc thickness effects, one should make assumptions upon the twodimensional rotation law of the disc. For rotation frequency constant on cylinders r sin θ = const, vertical gravity becomes stronger with height on spheres of constant radius. On the other hand, effects of radial flux advection increase the flux density in the inner parts of the disc and lower the Eddington limit. In general, the effects connected to disc thickness tend to increase the local Eddington limit even more. The efficiency of accretion is however decreased by advection effects by about a factor of several.

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Black holes are spun up by accreting matter and possibly spun-down by magnetic fields. In our work we consider the effect on black hole rotation of the two electromagnetic processes, Blandford-Znajek and Direct Magnetic Link, that differ in their magnetic field configuration. The efficiency of these processes varies with mass accretion rate and accretion regime and generally result in an equilibrium spin parameter in the range from 0.35 to ∼ 0.98. Magnetic field loses its energy while being accreted that may lead to an increase in equilibrium Kerr parameter for the case of advection-dominated disc. We find magnetic field decay decay can decrease electromagnetic term significantly thus increasing the Kerr parameter. We have performed Monte-Carlo simulations for a supermassive black hole population. Our simulations show broad distributions in Kerr parameter (0.1 a 0.98) with a peak at a ∼ 0.6. To explain the high observational Kerr parameter values of a 0.9, episodes of supercritical accretion are required. This implication does not however take into account black hole mergers (that play an important role for supermassive black hole evolution).

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