Radius of the neutron star magnetosphere during disk accretion

The dependence of the spin frequency derivative $\dot{\nu}$ of accreting neutron stars with a strong magnetic field (X-ray pulsars) on the mass accretion rate (bolometric luminosity, $L_{bol}$) has been investigated for eight transient pulsars in binary systems with Be stars. Using data from the Fermi/GBM and Swift/BAT telescopes, we have shown that for seven of the eight systems the dependence $\dot{\nu}$ can be fitted by the model of angular momentum transfer through an accretion disk, which predicts the relation $\dot{\nu}\sim L^{6/7}_{bol}$. Hysteresis in the dependence $\dot{\nu}(L_{bol})$ has been confirmed in the system V 0332+53 and has been detected for the first time in the systems KS 1947+300, GRO J1008-57, and 1A 0535+26. The radius of the neutron star magnetosphere in all of the investigated systems have been estimated. We show that this quantity varies from pulsar to pulsar and depends strongly on the analytical model and the estimates for the neutron star and binary system parameters.