Empirical relation between angular momentum transport and thermal-to-magnetic pressure ratio in shearing box simulations

Abstract

By combining data from different published 3-D simulations of Keplerian shearing boxes unstable to the magnetorotational instability (MRI), we highlight tight anti-correlations between the total effective inferred angular momentum transport parameter, ${\alpha }_{tot}$, its separate Maxwell and Reynolds contributions ${\alpha }_{mag}$ and ${\alpha }_{kin}$, and the kinetic to magnetic pressure ratio $\beta$, defined with the initial or saturated (when available) thermal pressure. Plots of $Log({\alpha }_{kin}),Log({\alpha }_{mag})$, and $Log({\alpha }_{tot})$ vs $Log(\beta )$ are well fit by straight lines even as ${\alpha }_{kin}$, ${\alpha }_{mag}$,and ${\alpha }_{tot}$ vary by four orders of magnitude over the simulations included. The ratio ${\alpha }_{kin}/{\alpha }_{mag}$ and the product ${\alpha }_{tot}\beta$ are quite constant and largely independent of the presence or absence of weak mean fields, the choice of initial and boundary conditions, and the resolution. In short, simulations have more strongly constrained the product ${\alpha }_{tot}\beta$ than ${\alpha }_{tot}$ itself.

22 pages (includes 10 tables and 3 figs.), accepted by New Astronomy

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