### Numerical Experiments in Core-Collapse Supernova Hydrodynamics

### Rodrigo A. Fernandez

Doctor of Philosophy 2009

Graduate Department of Astronomy and Astrophysics, University of Toronto
The explosion of massive stars involves the formation of a shock
wave. In stars that develop iron cores, this shock wave stalls on its
way out due to neutrino emission and the breakup of heavy nuclei
flowing through the shock. For the explosion to succeed, a fraction of
the gravitational binding energy of the collapsed core that is
radiated in neutrinos needs to be absorbed by the material below the
shock. How much energy is needed depends on the interplay between
non-spherical hydrodynamic instabilities, neutrino heating, and
nuclear dissociation. This thesis seeks to understand this interplay
through numerical experiments that model the key physical components
of the system and separate them out to examine their individual
effects. Specifically, one- and two dimensional time-dependent
hydrodynamic simulations are performed to study the effects of
non-spherical shock oscillations, neutrino-driven convection, and
alpha particle recombination on the dynamics of the system and the
critical heating rate for explosion.

We find that nuclear dissociation has a significant effect on the
linear stability and saturation amplitude of shock oscillations. At
the critical neutrino heating rate for an explosion, convection due to
a negative entropy gradient plays a major role in driving dipolar
shock motions. One dimensional explosions are due to a global
instability involving the advection of entropy perturbations from the
shock to the region where the accretion flow cools due to neutrino
emission. Large scale shock expansions in two-dimensions are due to a
finite amplitude instability involving the balance between buoyancy
forces and the ram pressure of the flow upstream of the shock. During
these expansions, a significant amount of energy is released when
nucleons recombine into alpha particles, constituting a significant
last step in the transition to explosion. The critical neutrino
heating rate for an explosion depends sensitively on the starting
radius of the shock relative to the radius at which the binding energy
of an alpha particle is comparable to the gravitational binding
energy.