Disk Accretion onto Magnetized Neutron Stars: The Inner Disk Radius and Fastness Parameter

Abstract

It is well known that the accretion disk around a magnetized compact star can penetrate inside the magnetospheric boundary, so the magnetospheric radius \ro does not represent the true inner edge \rin of the disk; but controversies exist in the literature concerning the relation between \ro and \rin. In the model of Ghosh & Lamb, the width of the boundary layer is given by \delta=\ro-\rin\ll\ro, or \rin\simeq\ro, while Li & Wickramasinghe recently argued that \rin could be significantly smaller than \ro in the case of a slow rotator. Here we show that if the star is able to absorb the angular momentum of disk plasma at \ro, appropriate for binary X-ray pulsars, the inner disk radius can be constrained by 0.8\lsim \rin/\ro\lsim 1, and the star reaches spin equilibrium with a relatively large value of the fastness parameter ($\sim 0.7-0.95$). For accreting neutron stars in low-mass X-ray binaries (LMXBs), \ro is generally close to the stellar radius \rs so that the toroidal field cannot transfer the spin-up torque efficiently to the star. In this case the critical fastness parameter becomes smaller, but \rin is still near \ro.Comment: 7 pages, 2 figures, to appear in Ap