Local Simulations of the Magneto-rotational Instability in Core-Collapse Supernovae

TL;DR

This study uses 3D local shearing box simulations to analyze the nonlinear behavior of the magneto-rotational instability in proto-neutron stars, revealing a power-law relation between turbulent stress and shear-vorticity ratio, with implications for core-collapse supernova mechanisms.

Contribution

It provides a systematic analysis of MRI turbulence scaling in proto-neutron stars and explores its impact on supernova energy dissipation and explosion mechanisms.

Findings

Turbulent stress scales as g_q^{0.5} with shear-vorticity ratio.

Magnetic energy and Maxwell stress follow similar power-law scaling.

MRI turbulence can significantly influence energy dissipation in core-collapse supernovae.

Abstract

Bearing in mind the application to core-collapse supernovae, we study nonlinear properties of the magneto-rotational instability (MRI) by means of three- dimensional simulations in the framework of a local shearing box approximation. By changing systematically the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear- vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress ($<< w_{\rm tot}>>$) and the shear- vorticity ratio ($g_q$) as $<<w_{\rm tot}>> \propto g_q^{\delta}$ with its index $\delta \sim 0.5$. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has slightly smaller power-law index ($\sim 0.36$). By modeling the effect of viscous heating rates due to the MRI turbulence, we show that the stronger magnetic fields or the larger shear rates initially imposed lead to the higher dissipation rates. For a rapidly rotating PNS with the spin period in milliseconds and with strong magnetic fields of $10^{15}$ G, the energy dissipation rate is estimated to exceed $10^{51} {\rm erg\ sec^{-1}}$. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by the MRI-driven turbulence, which we speculate, on one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface, on the other hand the energy deposition there might be potentially favorable for the working of the neutrino-heating mechanism.