Effect of Ambipolar Diffusion on the Non-linear Evolution of Magnetorotational Instability in Weakly Ionized Disks

TL;DR

This study investigates how ambipolar diffusion influences the non-linear development of magnetorotational instability in weakly ionized protoplanetary disks through simulations, revealing dependencies on magnetic flux and ion-neutral collision frequency.

Contribution

It provides the first comprehensive simulation-based analysis of ambipolar diffusion effects on MRI turbulence saturation levels across various magnetic geometries and ion-neutral collision rates.

Findings

Turbulence saturation depends on magnetic flux and geometry.

Maximum turbulent stress decreases with lower Am.

A tight correlation exists between turbulent stress and plasma beta.

Abstract

We study the role of ambipolar diffusion (AD) on the non-linear evolution of the MRI in protoplanetary disks using the strong coupling limit, which applies when the electron recombination time is much shorter than the orbital time. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency of which neutral particles collide with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the MRI turbulence depends on the magnetic geometry and increases with the net magnetic flux. There is an upper limit to the net flux for sustained turbulence, corresponding to the requirement that the most unstable vertical wavelength be less than the disk scale height. Correspondingly, at a given Am, there exists a maximum value of the turbulent stress alpha_max. For Am<1, the largest stress is associated with a field geometry that has both net vertical and toroidal flux. In this case, we confirm the results of linear analyses that show the fastest growing mode has a non-zero radial wave number with growth rate exceeding the pure vertical field case. We find there is a very tight correlation between the turbulent stress (alpha) and the plasma beta=P_gas/P_mag~1/(2alpha) at the saturated state of the MRI turbulence regardless of field geometry, and alpha_max rapidly decreases with decreasing Am. In particular, we quote alpha_max~0.007 for Am=1 and alpha_max~0.0006 for Am=0.1.