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 that the magnetospheric radius R₀ does not represent the true inner edge R_in of the disk, but controversies exist in the literature concerning the relation between R₀ and R_in. In the model of Ghosh & Lamb, the width of the boundary layer is given by δ=R₀-R_in≪R₀, or R_in≃R₀, while Li & Wickramasinghe recently argued that R_in could be significantly smaller than R₀ in the case of a slow rotator. Here we show that if the star is able to absorb the angular momentum of the disk plasma at R₀, appropriate for binary X-ray pulsars, the inner disk radius can be constrained by 0.8≲R_in/R₀≲1, and the star reaches spin equilibrium with a relatively large value of the fastness parameter (~0.7-0.95). For accreting neutron stars in low-mass X-ray binaries (LMXBs), R₀ is generally close to the stellar radius, R_s, 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 R_in is still near R₀.