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 canpenetrate inside the magnetospheric boundary, so the magnetospheric radius$\ro$ does not represent the true inner edge $\rin$ of the disk; butcontroversies exist in the literature concerning the relation between $\ro$ and$\rin$. In the model of Ghosh & Lamb, the width of the boundary layer is givenby $\delta=\ro-\rin\ll\ro$, or $\rin\simeq\ro$, while Li & Wickramasingherecently argued that $\rin$ could be significantly smaller than $\ro$ in thecase of a slow rotator. Here we show that if the star is able to absorb theangular 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 thestar reaches spin equilibrium with a relatively large value of the fastnessparameter ($\sim 0.7-0.95$). For accreting neutron stars in low-mass X-raybinaries (LMXBs), $\ro$ is generally close to the stellar radius $\rs$ so thatthe toroidal field cannot transfer the spin-up torque efficiently to the star.In this case the critical fastness parameter becomes smaller, but $\rin$ isstill near $\ro$.Comment: 7 pages, 2 figures, to appear in Ap