Accretion disc backflow in resistive MHD simulations

TL;DR

This study uses resistive MHD and hydrodynamic simulations to analyze accretion disc flow patterns, revealing that midplane backflow is a persistent feature influenced by magnetic Prandtl number and other parameters.

Contribution

It demonstrates that midplane backflow exists in both hydrodynamic and MHD accretion discs, extending previous analytic results to more complex magnetic scenarios.

Findings

Midplane backflow exists in hydrodynamic simulations matching analytic solutions.

In MHD simulations, backflow persists below a critical magnetic Prandtl number.

Backflow exhibits quasiperiodic oscillations near the critical Prandtl number.

Abstract

We investigate accretion onto a central star, with the size, rotation rate, and magnetic dipole of a young stellar object, to study the flow pattern (velocity and density) of the fluid within and outside of the disc. We perform resistive MHD simulations of thin $\alpha$-discs, varying the parameters such as the stellar rotation rate and magnetic field, and (anomalous) coefficients of viscosity and resistivity in the disc. To provide a benchmark for the results and to compare with known analytic results, we also perform purely hydrodynamic simulations (HD) for the same problem. Although obtained for a different situation with differing inner boundary condition, the disc structure in the HD simulations closely follows the analytic solution of Klu\'zniak and Kita (2000) -- in particular a region of "midplane" backflow exists in the right range of radii, depending on the viscosity parameter. In the MHD solutions, whenever the magnetic Prandtl number does not exceed a certain critical value, the midplane backflow exists throughout the accretion disc, extending all the way down to the inner transition zone where the disc transitions to a magnetic funnel flow. For values of the magnetic Prandtl number close to the critical value the backflow and the inner disc undergo a quasiperiodic radial oscillation, otherwise the backflow is steady, as is the disc solution. From our results, supplemented by our reading of the literature, we conclude that midplane backflow is a real feature of at least some accretion discs, whether HD $\alpha$-discs or MHD discs, including ones driven by MRI turbulence.