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Magnetorotational instability (MRI) has a potential to generate the vigorous turbulence in protoplanetary disks, although its turbulence strength and accretion stress remains debatable because of the uncertainty of MRI with low ionization fraction. We focus on the heating of electrons by strong electric fields which amplifies nonideal magnetohydrodynamic effects. The heated electrons frequently collide with and stick to dust grains, which in turn decreases the ionization fraction and is expected to weaken the turbulent motion driven by MRI. In order to quantitatively investigate the nonlinear evolution of MRI including the electron heating, we perform magnetohydrodynamical simulation with the unstratified shearing box. We introduce a simple analytic resistivity model depending on the current density by mimicking resistivity given by the calculation of ionization. Our simulation confirms that the electron heating suppresses magnetic turbulence when the electron heating occurs with low current density. We find a clear correlation between magnetic stress and its current density, which means that the magnetic stress is proportional to the squared current density. When the turbulent motion is completely suppressed, laminar accretion flow is caused by ordered magnetic field. We give an analytical description of the laminar state by using a solution of linear perturbation equations with resistivity. We also propose a formula that successfully predicts the accretion stress in the presence of the electron heating.
The magnetorotational instability (MRI) drives vigorous turbulence in a region of protoplanetary disks where the ionization fraction is sufficiently high. It has recently been shown that the electric field induced by the MRI can heat up electrons and
The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary disks (PPDs). While there is extensive literature on the VSI in the hydrodynamic limit, PPDs are expected to be magnetized and their extremely low ionization fra
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 i
The gas temperature in protoplanetary disks (PPDs) is determined by a combination of irradiation heating and accretion heating, with the latter conventionally attributed to turbulent dissipation. However, recent studies have suggested that the inner
We present a new instability driven by a combination of coagulation and radial drift of dust particles. We refer to this instability as ``coagulation instability and regard it as a promising mechanism to concentrate dust particles and assist planetes