Viscosity and Rotation in Core-Collapse Supernovae

Abstract

We construct models of core-collapse supernovae in one spatial dimension, including rotation, angular momentum transport, and viscous dissipation employing an alpha-prescription. We compare the evolution of a fiducial 11 M_sun non-rotating progenitor with its evolution including a wide range of imposed initial rotation profiles (1.25<P_0<8 s, where P_0 is the initial, approximately solid-body, rotation period of the iron core). This range of P_0 covers the region of parameter space from where rotation begins to modify the dynamics (P_0~8 s) to where angular velocities at collapse approach Keplerian (P_0~1 s). Assuming strict angular momentum conservation, all models in this range leave behind neutron stars with spin periods <10 ms, shorter than those of most radio pulsars, but similar to those expected theoretically for magnetars at birth. A fraction of the gravitational binding energy of collapse is stored in the free energy of differential rotation. This energy source may be tapped by viscous processes, providing a mechanism for energy deposition that is not strongly coupled to the mass accretion rate through the stalled supernova shock. This effect yields qualitatively new dynamics in models of supernovae. We explore several potential mechanisms for viscosity in the core-collapse environment: neutrino viscosity, turbulent viscosity caused by the magnetorotational instability (MRI), and turbulent viscosity by entropy- and composition-gradient-driven convection. We argue that the MRI is the most effective. We find that for rotation periods in the range P_0<~5 s, and a range of viscous stresses, that the post-bounce dynamics is significantly effected by the inclusion of this extra energy deposition mechanism; in several cases we obtain strong supernova explosions.