Magnetospheric flows in X-ray pulsars - I Instability at super-Eddington regime of accretion

Within the magnetospheric radius, the geometry of accretion flow in X-ray pulsars is shaped by a strong magnetic field of a neutron star. Starting at the magnetospheric radius, accretion flow follows field lines and reaches the stellar surface in small regions located close to the magnetic poles of a star. At low mass accretion rates, the dynamics of the flow is determined by gravitational attraction and rotation of the magnetosphere due to the centrifugal force. At the luminosity range close to the Eddington limit and abo v e it, the flow is additionally affected by the radiative force. We construct a model simulating accretion flow dynamics o v er the magnetosphere, assuming that the flo w strictly follo ws field lines and is af fected by gravity, radiati ve, and centrifugal forces only. The magnetic field of a neutron star is taken to be dominated by the dipole component of arbitrary inclination with respect to the accretion disc plane. We show that accretion flow becomes unstable at high mass accretion rates and tends to fluctuate quasi-periodically with a typical period comparable to the free-fall time from the inner disc radius. The inclination of a magnetic dipole with respect to the disc plane and strong anisotropy of X-ray radiation stabilize the mass accretion rate at the poles of a star, but the surface density of material co v ering the magnetosphere fluctuates even in this case.