Turbulence in Core-Collapse Supernovae

TL;DR

This study systematically compares three turbulence definitions (SSA, LSA, and a Spectral method) in four 3D CCSN simulations with the ELEPHANT code to determine how measurement choices shape conclusions about turbulence's role in explosions. While all methods capture a qualitative growth of turbulent energy in the gain region, SSA yields substantially larger turbulent energies and stronger correlations with explosion outcomes than LSA or Spectral, which align more closely with enstrophy. The analysis shows that SSA can overemphasize convective plumes, biasing the inferred turbulent contribution to shock revival, whereas LSA and Spectral provide more consistent pictures of small-scale turbulence. The turbulent and effective adiabatic indices likewise depend on the turbulence definition, with SSA predicting larger, time-stable increases in $\gamma_{\rm eff}$; overall, the work emphasizes the need for careful, multi-faceted turbulence diagnostics in CCSN studies and suggests enstrophy-consistent measures as robust benchmarks.

Abstract

It is understood in a general sense that turbulent fluid motion below the shock front in a core-collapse supernova stiffens the effective equation of state of the fluid and aids in the revival of the explosion. However, when one wishes to be precise and quantify the amount of turbulence in a supernova simulation, one immediately encounters the problem that turbulence is difficult to define and measure. Using the 3D magnetohydrodynamic code ELEPHANT, we study how different definitions of turbulence change one's conclusions about the amount of turbulence in a supernova and the extent to which it helps the explosion. We find that, while all the definitions of turbulence we use lead to a qualitatively similar growth pattern over time of the turbulent kinetic energy in the gain region, the total amount of turbulent kinetic energy, and especially the ratios of turbulent to total kinetic energy, distinguish them. Some of the definitions appear to indicate turbulence is a necessary contributor to the explosion, and others indicate it is not. The different definitions also produce turbulence maps with different correlations with maps of the enstrophy, a quantity widely regarded as also indicating the presence of turbulence. We also compute the turbulent adiabatic index and observe that in regions of low enstrophy, this quantity is sensitive to the definition used. As a consequence, the effective adiabatic index depends upon the method used to measure the turbulence and thus alter one's conclusions regarding the impact of turbulence within the supernova.

Figures (16)

• Figure 1: Average shock radii (lines), together with the minimum and maximum shock radii (shaded bands) as a function of the post-bounce time for all four simulations. The simulations end when the shock radius reaches the boundary of the largest (500 km) 3D domain. Note that the s23 simulation does not undergo a successful shock revival during the simulation time.
• Figure 2: Entropy maps in the $xy$-plane for the s15 (top), s20 (second row), s23 (third row), and s27 (bottom row) simulations at $\sim 100$ ms (first column), $\sim 150$ ms (second column), $\sim 195$ ms (third column) post bounce, and at the final simulation time (last column). Note the smaller spatial scale and entropy scale for s23.
• Figure 3: Ratio of the transverse energy to the total kinetic energy in the gain region as a function of the post-bounce time for the s15 (solid), s20 (dashed), s23 (dot-dashed), and s27 (dotted) simulations.
• Figure 4: The ratio of advection timescale to heating timescale as a function of the post-bounce time for all four simulations. The gray dotted line marks where the ratio equals unity.
• Figure 5: Difference between the mass accretion rate through the shock front ($\dot{M}_{\mathrm{shock}}$) and the mass accretion rate onto the PNS ($\dot{M}_{\mathrm{PNS}}$) as a function of the post-bounce time for all four simulations. The data is smoothed over a 5 ms window.