Hall Effect in Magnetic Braking

As a molecular cloud core collapses to form a rotationally supported protostellar disk, various non-ideal MHD effects associated with the characteristically low ionization fraction become important at different stages of the contraction. The most significant of these effects in many disks at intermediate densities is the Hall effect. The magnetic braking of a rotating cylindrical disk is studied analytically using the Hall MHD equations and, in the limits of large and small Hall diffusion, the solution is compared with numerical simulations performed using the Idefix code. It is found that the Hall effect couples the magnetic flux through a protostellar disk with its angular momentum and can significantly increase the braking time of the disk.