Viscosity and rotation in core-collapse supernovae

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-. nonrotating progenitor with its evolution when including a wide range of imposed initial rotation profiles (1.25 s < 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 similar to 8 s) to where angular velocities at collapse approach Keplerian ( P-0 similar to 1 s). Under the assumption of strict angular momentum conservation, all models in this range leave behind neutron stars with spin periods less than or similar to10 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 for rotation periods in the range P-0 less than or similar to 5 s and a range of viscous stresses that the postbounce dynamics is significantly affected by the inclusion of this extra energy deposition mechanism; in several cases we obtain strong supernova explosions.