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Interdependence of Electric Discharge and The Magnetorotational Instability in Protoplanetary Disks

We study how the magnetorotational instability (MRI) in protoplanetary disks is affected by the electric discharge caused by the electric field in the resistive MHD. We have performed three-dimensional shearing box simulations with various values of plasma beta and electrical breakdown models. We find the self-sustainment of the MRI in spite of the high resistivity. The instability gives rise to the large electric field that causes the electrical breakdown, and the breakdown maintains the high ionization degree required for the instability. The condition for this self-sustained MRI is set by the balance between the energy supply from the shearing motion and the energy consumed by the Ohmic dissipation. We apply the condition to various disk models and study where the active, self-sustained, and dead zones of MRI are. In the fiducial minimum-mass solar nebula (MMSN) model, the newly-found sustained zone occupies only the limited volume of the disk. In the late-phase gas-depleted disk models, however, the sustained zone occupies larger volume of the disk.