Electron Heating and Saturation of Self-regulating Magnetorotational Instability in Protoplanetary Disks

Abstract

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.

arXiv comment12 pages, 12 figures, accepted for publication in ApJ

References in corpus (33)

• Streaming Instabilities in Protoplanetary Disks
• First Results from High Angular Resolution ALMA Observations Toward the HL Tau Region
• Athena: A New Code for Astrophysical MHD
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration
• Dust and Gas in the disc of HL Tauri: Surface density, dust settling, and dust-to-gas ratio
• Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation
• Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability
• Weak Turbulence in the HD 163296 Protoplanetary Disk Revealed by ALMA CO Observations
• A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO${}^{+}$
• Thanatology in Protoplanetary Discs: the combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones
• How to form planetesimals from mm-sized chondrules and chondrule aggregates
• The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks
• Effect of Ambipolar Diffusion on the Non-linear Evolution of Magnetorotational Instability in Weakly Ionized Disks
• Dependence of inner accretion disk stress on parameters: the Schwarzschild case
• Dust settling in local simulations of turbulent protoplanetary disks
• The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: II. Saturation Level and Critical Magnetic Reynolds Number
• Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics
• Two-Component Secular Gravitational Instability in a Protoplanetary Disk: A Possible Mechanism for Creating Ring-Like Structures
• Magnetically driven accretion in protoplanetary discs
• Implementation of the Shearing Box Approximation in Athena
• Turbulence and Steady Flows in 3D Global Stratified MHD Simulations of Accretion Disks
• Magnetic self-organisation in Hall-dominated magnetorotational turbulence
• Wind-driven Accretion in Protoplanetary Disks --- II: Radial Dependence and Global Picture
• Global MHD simulations of stratified and turbulent protoplanetary discs. II. Dust settling
• Dust Transport in Protostellar Disks Through Turbulence and Settling
• An Origin of Multiple Ring Structure and Hidden Planets in HL Tau: A Unified Picture by Secular Gravitational Instability
• Self-Sustained Ionization and Vanishing Dead Zones in Protoplanetary Disks
• Dust Transport in MRI Turbulent Disks: Ideal and Non-ideal MHD with Ambipolar Diffusion
• Diffusion coefficient of a passive contaminant in a local MHD model of a turbulent accretion disc
• Self-organisation in protoplanetary disks: global, non-stratified Hall-MHD simulations
• Interdependence of Electric Discharge and The Magnetorotational Instability in Protoplanetary Disks
• The Nonlinear Ohm's Law: Plasma Heating by Strong Electric Fields and its Effects on the Ionization Balance in Protoplanetary Disks
• Electron Heating in the Magnetorotational Instability: Implications for Turbulence Strength in Outer Regions of Protoplanetary Disks

Cited by in corpus (8)

• Temperature Structure in the Inner Regions of Protoplanetary Disks: Inefficient Accretion Heating Controlled by Nonideal Magnetohydrodynamics
• Formation of rocky and icy planetesimals inside and outside the snow line: Effects of diffusion, sublimation and back-reaction
• Planetesimal formation around the snow line. II. Dust or pebbles?
• A "no-drift" runaway pile-up of pebbles in protoplanetary disks in which midplane turbulence increases with radius
• Collisional Elongation: Possible Origin of Extremely Elongated Shape of 1I/`Oumuamua
• The Generalized Nonlinear Ohm's Law: How a Strong Electric Field Influences Non-ideal MHD Effects in Dusty Protoplanetary Disks
• Radiative Nonideal MHD Simulations of Inner Protoplanetary Disks: Temperature Structures, Asymmetric Winds, and Episodic Surface Accretion
• MHD in a cylindrical shearing box II: Intermittent Bursts and Substructures in MRI Turbulence