Dynamics of an alfvn surface in core collapse supernovae

Abstract

We investigate the dynamics of an Alfvén surface (where the Alfvén speed equals the advection velocity) in the context of core collapse supernovae during the phase of accretion on the proto-neutron star. Such a surface should exist even for weak magnetic fields because the advection velocity decreases to zero at the center of the collapsing core. In this decelerated flow, Alfvén waves created by the standing accretion shock instability or convection accumulate and amplify while approaching the Alfvén surface. We study this amplification using one-dimensional MHD simulations with explicit physical dissipation (resistivity and viscosity). In the linear regime, the amplification continues until the Alfvén wavelength becomes as small as the dissipative scale. A pressure feedback that increases the pressure in the upstream flow is created via a nonlinear coupling. We derive analytic formulae for the maximum amplification and the nonlinear coupling and check them with numerical simulations to very good accuracy. Interestingly, these quantities diverge if the dissipation is decreased to zero, scaling as the square root of the Reynolds number, suggesting large effects in weakly dissipative flows. We also characterize the nonlinear saturation of this amplification when compression effects become important, leading to either a change of the velocity gradient, or a steepening of the Alfvén wave. Applying these results to core collapse supernovae shows that the amplification can be fast enough to affect the dynamics if the magnetic field is strong enough for the Alfvén surface to lie in the region of strong velocity gradient just above the neutrinosphere. This requires the presence of a strong magnetic field in the progenitor star, which would correspond to the formation of a magnetar under the assumption of magnetic flux conservation. An extrapolation of our analytic formula (taking into account the nonlinear saturation) suggests that the Alfvén wave could reach an amplitude of B 1015 G, and that the pressure feedback could significantly contribute to the pressure below the shock. © 2011. The American Astronomical Society. All rights reserved.