On the critical ''fastness parameter'' of a rotating star with a magnetically threaded accretion disk

The torque exerted on a rotating, magnetized star by a magnetically threaded accretion disk is dependent on the ''fastness parameter'' omega(s) = (R(o)/R(c))(3/2), where R(o) and R(c) are the inner edge of the accretion disk and the corotation radius of the star respectively. In equilibrium state for which there is no torque on the star, the fastness parameter reaches its critical value omega(c). Recently Wang (1995) obtained that the value of omega(c) lies in the range 0.875 - 0.95. We argue that an uncertainty of a factor of 4 exists in the torque condition at the inner edge of the disk. Together with uncertainties relating to the strength of the toroidal field, we find that the value of omega(c) can range between 0.71 and 0.95. Our results present constraints on the magnetically threaded disk model and seem to be consistent with observations of the binary X-ray pulsar 4U 1626-67.