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

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 $\ro$.