Neutrino-Driven Convection in Core-Collapse Supernovae: High-Resolution Simulations

Abstract

We present results from high-resolution semi-global simulations of neutrino-driven convection in core-collapse supernovae. We employ an idealized setup with parametrized neutrino heating/cooling and nuclear dissociation at the shock front. We study the internal dynamics of neutrino-driven convection and its role in re-distributing energy and momentum through the gain region. We find that even if buoyant plumes are able to locally transfer heat up to the shock, convection is not able to create a net positive energy flux and overcome the downwards transport of energy from the accretion flow. Turbulent convection does, however, provide a significant effective pressure support to the accretion flow as it favors the accumulation of energy, mass and momentum in the gain region. We derive an approximate equation that is able to explain and predict the shock evolution in terms of integrals of quantities such as the turbulent pressure in the gain region or the effects of non-radial motion of the fluid. We use this relation as a way to quantify the role of turbulence in the dynamics of the accretion shock. Finally, we investigate the effects of grid resolution, which we change by a factor 20 between the lowest and highest resolution. Our results show that the shallow slopes of the turbulent kinetic energy spectra reported in previous studies are a numerical artefact. Kolmogorov scaling is progressively recovered as the resolution is increased.

General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

“…As some of us found in the parameterized 3D simulations of Abdikamalov et al (2015), lower resolution appears to be more favorable for shock runaway for simulations near the threshold of explosion (cf. Radice et al 2016). At low resolution, imposing octant symmetry does not have a large effect on the dynamics in Figure 1.…”

“…The large variation of shock evolution with resolution suggests that the postshock hydrodynamics in our models are unconverged (Radice et al 2016). Although our highest-resolution simulation is the highest-resolution unconstrained neutrino radiation-hydrodynamics simulation performed to date, it is still likely to be severely underresolved.…”

“…This is many orders of magnitude lower than the physical Reynolds number in these systems (although there is no one-to-one correspondence between physical and numerical viscosity; Radice et al 2015). Clearly, convectively driven turbulence will behave differently at this low Reynolds number relative to what would happen at the physical Reynolds number (Abdikamalov et al 2015;Radice et al 2016). Abdikamalov et al (2015) suggested that altering the resolution changes the numerical viscosity and alters the spectrum of turbulence.…”

“…We neglect regions that lie outside of the shock. Although we do not plot it here, we find the well-known result that neutrino-driven turbulence is anisotropic on large scales with~q q ff R R R 2 2 rr (e.g., Murphy et al 2013;Radice et al 2016). At all times before shock runaway, the Reynolds stress of s27FL tracks the Reynolds stress of s27FH below ∼100 km.…”

“…Nevertheless, there are many other differences between our simulation and theirs, so we caution against drawing definitive conclusions. The results of Radice et al (2016) are an important caveat. They carried out parameterized neutrino-driven convection simulations over a large range of resolutions.…”