On criteria for the magnetospheric accretion in X-ray binary systems

We consider the accretion process in the X-ray binary systems with neutron stars as relativistic components. We focus our investigation at the question of magnetospheres formation in the process of mass accretion onto the neutron stars in these systems. We note that the answer to this question depends, in particular, on the geometry and physical parameters of the accretion flow. We show that magnetospheres are the most likely to form in the systems with spherical (quasi-spherical) accretion. Formation of a magnetosphere is less likely in the case of accretion through the Keplerian disk or in the MAD-accretion scenario. This findings should be taken into account in the estimation of expected number of accreting X-ray pulsars in the low-mass X-ray binaries.