Funnel Flows from Disks to Magnetized Stars

Abstract

This work considers flows from an accretion disk corotating with the aligned dipole magnetic field of a rotating star. Ideal magnetohydrodynamics (MHD) is assumed with the pressure and density related as p ∝ ρ γ and with ρv2 ≪ B2/4ψ, where v is the flow velocity. Transonic flows, which go from subsonic motion near the disk to supersonic inflow near the star, are shown to be possible only for a range of Rd∼ rc = (GM/Ω2)1/3, where Rd the radius at which the dipole field line intersects the disk, rc is the corotation radius, M is the mass of the star, and Ω is its angular rotation rate. Over a larger range of Rd ≲ r c, subsonic flows from the disk to the star are possible. The transonic flows have very different behaviors for 7 > 7/5 and γ < 7/5. In both cases, the plasma flow velocity v (which is parallel to B) increases with decreasing distance R from the star. However, for γ > 7/5, the Mach number script capital M sign ≡ |v|/cs (with cs the sound speed) initially increases to values ≫ 1 with R decreasing from Rd, but for R decreasing from ≈0.22Rd (for γ = 5/3) the Mach number decreases while still being ≫ 1. In the other limit, γ < 7/5, script capital M sign increases monotonically with decreasing R. Application of these results is made to funnel flows to magnetized neutron stars and young stellar objects, We argue that the rotation needs to be included in the calculation of emission-line profiles of young stellar objects.