Bearing in mind the application of core-collapse supernovae, we study the nonlinear properties of the magnetorotational instability (MRI) by means of three-dimensional simulations in the framework of a local shearing box approximation. By systematically changing 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 tot) and the shear-vorticity ratio (gq ) as w tot∝g δ q with an index of δ ~ 0.5. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has a slightly smaller power-law index (~0.36). By modeling the effect of viscous heating rates from MRI turbulence, we show that the stronger magnetic fields, or the larger shear rates initially imposed, lead to higher dissipation rates. For a rapidly rotating PNS with a spin period in milliseconds and with strong magnetic fields of 1015 G, the energy dissipation rate is estimated to exceed 1051 erg s–1. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by MRI-driven turbulence, which we speculate, on the one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface; or, on the other hand, its energy deposition might be potentially favorable for the working of the neutrino-heating mechanism.
展开▼
