The radius of magnetosphere and the equilibrium radius are not the same!

The process of accretion onto a neutron star with strong magnetic field is discussed. The equilibrium radius, which is defined by equating the pressure of the accreting material with the magnetic pressure due to the dipole magnetic field of the neutron star, is estimated for the cases of a spherical accretion flow and a Keplerian accretion disk. It is emphasized that the magnetospheric radius of an accreting star is defined by equating the mass accretion rate observed in the system with the rate of plasma diffusion into the magnetic field of the neutron star at the magnetospheric boundary. Following this definition we obtained a system of equations, which are the continuity equation and the pressure balance equation. We show that the radius of magnetosphere evaluated in this way significantly differs from the equilibrium radius. In particular, the Alfven radius (which is just the equilibrium radius in a peculiar case of a spherically symmetric accretion flow) under the same conditions exceeds the magnetospheric radius of an accreting neutron star by more than an order of magnitude.