Toward Connecting Core-Collapse Supernova Theory with Observations

We study the evolution of the collapsing core of a 15 solar mass blue supergiant supernova progenitor from the moment shortly after core bounce until 1.5 seconds later. We present a sample of two- and three-dimensional hydrodynamic models parameterized to match the explosion energetics of supernova SN 1987A. We focus on the characteristics of the flow inside the gain region and the interplay between hydrodynamics, self-gravity, and neutrino heating, taking into account uncertainty in the nuclear equation of state. We characterize the evolution and structure of the flow behind the shock in terms the accretion flow dynamics, shock perturbations, energy transport and neutrino heating effects, and convective and turbulent motions. We also analyze information provided by particle tracers embedded in the flow. Our models are computed with a high-resolution finite volume shock capturing hydrodynamic code. The code includes source terms due to neutrino-matter interactions from a light-bulb neutrino scheme that is used to prescribe the luminosities and energies of the neutrinos emerging from the core of the proto-neutron star. The proto-neutron star is excised from the computational domain, and its contraction is modeled by a time-dependent inner boundary condition. We find the spatial dimensionality of the models to be an important contributing factor in the explosion process. Compared to two-dimensional simulations, our three-dimensional models require lower neutrino luminosities to produce equally energetic explosions. We estimate that the convective engine in our models is $4$% more efficient in three dimensions than in two dimensions. We propose that this is due to the difference of morphology of convection between two- and three-dimensional models. Specifically, the greater efficiency of the convective engine found in three-dimensional simulations might be due to the larger surface-to-volume ratio of convective plumes, which aids in distributing energy deposited by neutrinos. We do not find evidence of the standing accretion shock instability in our models. Instead we identify a relatively long phase of quasi-steady convection below the shock, driven by neutrino heating. During this phase, the analysis of the energy transport in the post-shock region reveals characteristics closely resembling that of penetrative convection. We find that the flow structure grows from small scales and organizes into large, convective plumes on the size of the gain region. We use tracer particles to study the flow properties, and find substantial differences in residency times of fluid elements in the gain region between two-dimensional and three-dimensional models. These appear to originate at the base of the gain region and are due to differences in the structure of convection. We also identify differences in the evolution of energy of the fluid elements, how they are heated by neutrinos, and how they become gravitationally unbound. In particular, at the time when the explosion commences, we find that the unbound material has relatively long residency times in two-dimensional models, while in three dimensions a significant fraction of the explosion energy is carried by particles with relatively short residency times. We conduct a series of numerical experiments in which we methodically decrease the angular resolution in our three-dimensional models. We observe that the explosion energy decreases dramatically once the resolution is inadequate to capture the morphology of convection on large scales. Thus, we demonstrated that it is possible to connect successful, energetic, three-dimensional models with unsuccessful three-dimensional models just by decreasing numerical resolution, and thus the amount of resolved physics. This example shows that the role of dimensionality is secondary to correctly accounting for the basic physics of the explosion. The relatively low spatial resolution of current three-dimensional models allows for only rudimentary insights into the role of turbulence in driving the explosion. However, and contrary to some recent reports, we do not find evidence for turbulence being a key factor in reviving the stalled supernova shock.