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Title: ELECTRON HEATING IN MAGNETOROTATIONAL INSTABILITY: IMPLICATIONS FOR TURBULENCE STRENGTH IN THE OUTER REGIONS OF PROTOPLANETARY DISKS

Abstract

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 thereby affect the ionization balance in the gas. In particular, in a disk where abundant dust grains are present, the electron heating causes a reduction of the electron abundance, thereby preventing further growth of the MRI. By using the nonlinear Ohm's law that takes into account electron heating, we investigate where in protoplanetary disks this negative feedback between the MRI and ionization chemistry becomes important. We find that the “e-heating zone,” the region where the electron heating limits the saturation of the MRI, extends out up to 80 AU in the minimum-mass solar nebula with abundant submicron-sized grains. This region is considerably larger than the conventional dead zone whose radial extent is ∼20 AU in the same disk model. Scaling arguments show that the MRI turbulence in the e-heating zone should have a significantly lower saturation level. Submicron-sized grains in the e-heating zone are so negatively charged that their collisional growth is unlikely to occur. Our present model neglects ambipolar and Hallmore » diffusion, but our estimate shows that ambipolar diffusion would also affect the MRI in the e-heating zone.« less

Authors:
;  [1]
  1. Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152-8551 (Japan)
Publication Date:
OSTI Identifier:
22521661
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 817; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; AMBIPOLAR DIFFUSION; COSMIC DUST; ELECTRIC FIELDS; ELECTRONS; FEEDBACK; HEATING; INSTABILITY; INTERSTELLAR GRAINS; MAGNETOHYDRODYNAMICS; MASS; NONLINEAR PROBLEMS; PROTOPLANETS; SOLAR NEBULA; TURBULENCE; ZONES

Citation Formats

Mori, Shoji, and Okuzumi, Satoshi, E-mail: mori.s@geo.titech.ac.jp. ELECTRON HEATING IN MAGNETOROTATIONAL INSTABILITY: IMPLICATIONS FOR TURBULENCE STRENGTH IN THE OUTER REGIONS OF PROTOPLANETARY DISKS. United States: N. p., 2016. Web. doi:10.3847/0004-637X/817/1/52.
Mori, Shoji, & Okuzumi, Satoshi, E-mail: mori.s@geo.titech.ac.jp. ELECTRON HEATING IN MAGNETOROTATIONAL INSTABILITY: IMPLICATIONS FOR TURBULENCE STRENGTH IN THE OUTER REGIONS OF PROTOPLANETARY DISKS. United States. doi:10.3847/0004-637X/817/1/52.
Mori, Shoji, and Okuzumi, Satoshi, E-mail: mori.s@geo.titech.ac.jp. 2016. "ELECTRON HEATING IN MAGNETOROTATIONAL INSTABILITY: IMPLICATIONS FOR TURBULENCE STRENGTH IN THE OUTER REGIONS OF PROTOPLANETARY DISKS". United States. doi:10.3847/0004-637X/817/1/52.
@article{osti_22521661,
title = {ELECTRON HEATING IN MAGNETOROTATIONAL INSTABILITY: IMPLICATIONS FOR TURBULENCE STRENGTH IN THE OUTER REGIONS OF PROTOPLANETARY DISKS},
author = {Mori, Shoji and Okuzumi, Satoshi, E-mail: mori.s@geo.titech.ac.jp},
abstractNote = {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 thereby affect the ionization balance in the gas. In particular, in a disk where abundant dust grains are present, the electron heating causes a reduction of the electron abundance, thereby preventing further growth of the MRI. By using the nonlinear Ohm's law that takes into account electron heating, we investigate where in protoplanetary disks this negative feedback between the MRI and ionization chemistry becomes important. We find that the “e-heating zone,” the region where the electron heating limits the saturation of the MRI, extends out up to 80 AU in the minimum-mass solar nebula with abundant submicron-sized grains. This region is considerably larger than the conventional dead zone whose radial extent is ∼20 AU in the same disk model. Scaling arguments show that the MRI turbulence in the e-heating zone should have a significantly lower saturation level. Submicron-sized grains in the e-heating zone are so negatively charged that their collisional growth is unlikely to occur. Our present model neglects ambipolar and Hall diffusion, but our estimate shows that ambipolar diffusion would also affect the MRI in the e-heating zone.},
doi = {10.3847/0004-637X/817/1/52},
journal = {Astrophysical Journal},
number = 1,
volume = 817,
place = {United States},
year = 2016,
month = 1
}
  • We use local numerical simulations to investigate the strength and nature of magnetohydrodynamic (MHD) turbulence in the outer regions of protoplanetary disks, where ambipolar diffusion is the dominant non-ideal MHD effect. The simulations include vertical stratification and assume zero net vertical magnetic flux. We employ a super time-stepping technique to ameliorate the Courant restriction on the diffusive time step. We find that in idealized stratified simulations, with a spatially constant ambipolar Elsasser number Am, turbulence driven by the magnetorotational instability (MRI) behaves in a similar manner as in prior unstratified calculations. Turbulence dies away for Am {<=} 1, and becomesmore » progressively more vigorous as ambipolar diffusion is decreased. Near-ideal MHD behavior is recovered for Am {>=} 10{sup 3}. In the intermediate regime (10 {<=} Am {<=} 10{sup 3}) ambipolar diffusion leads to substantial increases in both the period of the MRI dynamo cycle and the characteristic scales of magnetic field structures. To quantify the impact of ambipolar physics on disk accretion, we run simulations at 30 AU and 100 AU that include a vertical Am profile based upon far-ultraviolet (FUV) ionized disk models. These models develop a vertically layered structure analogous to the Ohmic dead zone that is present at smaller radii. We find that, although the levels of surface turbulence can be strong (and consistent with constraints on turbulent line widths at these radii), the inferred accretion rates are at least an order of magnitude smaller than those observed in T Tauri stars. This discrepancy is very likely due to the assumption of zero vertical magnetic field in our simulations and suggests that vertical magnetic fields are essential for MRI-driven accretion in the outer regions of protoplanetary disks.« less
  • We carry out a series of local, vertically stratified shearing box simulations of protoplanetary disks that include ambipolar diffusion and a net vertical magnetic field. The ambipolar diffusion profiles we employ correspond to 30 AU and 100 AU in a minimum mass solar nebula (MMSN) disk model, which consists of a far-ultraviolet-ionized surface layer and low-ionization disk interior. These simulations serve as a follow-up to Simon et al., in which we found that without a net vertical field, the turbulent stresses that result from the magnetorotational instability (MRI) are too weak to account for observed accretion rates. The simulations inmore » this work show a very strong dependence of the accretion stresses on the strength of the background vertical field; as the field strength increases, the stress amplitude increases. For a net vertical field strength (quantified by β{sub 0}, the ratio of gas to magnetic pressure at the disk mid-plane) of β{sub 0} = 10{sup 4} and β{sub 0} = 10{sup 5}, we find accretion rates M-dot ∼10{sup -8}-10{sup –7} M{sub ☉} yr{sup –1}. These accretion rates agree with observational constraints, suggesting a vertical magnetic field strength of ∼60-200 μG and 10-30 μG at 30 AU and 100 AU, respectively, in a MMSN disk. Furthermore, the stress has a non-negligible component due to a magnetic wind. For sufficiently strong vertical field strengths, MRI turbulence is quenched, and the flow becomes largely laminar, with accretion proceeding through large-scale correlations in the radial and toroidal field components as well as through the magnetic wind. In all simulations, the presence of a low-ionization region near the disk mid-plane, which we call the ambipolar damping zone, results in reduced stresses there.« less
  • Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive 'dead zone' of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure of turbulence is well characterized by the vertical magnetic flux andmore » three critical heights derived from the linear analysis of MRI in a stratified disk. In particular, the turbulent structure depends on the resistivity profile only through the critical heights and is insensitive to the details of the resistivity profile. We discover scaling relations between the amplitudes of various turbulent quantities (velocity dispersion, density fluctuation, vertical diffusion coefficient, and outflow mass flux) and vertically integrated accretion stresses. We also obtain empirical formulae for the integrated accretion stresses as a function of the vertical magnetic flux and the critical heights. These empirical relations allow us to predict the vertical turbulent structure of a protoplanetary disk for a given strength of the magnetic flux and a given resistivity profile.« less
  • The radial drift of planetary cores poses a challenge to efficient planet formation in standard disk models. However, the rate of this migration is sensitive to both the surface density and temperature profiles of protoplanetary disks. In this paper, we present a new model to self-consistently calculate the structure of a protoplanetary disk in which the magnetorotational instability (MRI) drives angular momentum transport. In this model, we calculate a quasi-steady-state disk model including a schematic representation involving efficient angular momentum transport in the active region with decreased (but non-zero) angular momentum transport in the dead zone. We find that MRImore » affects not only the surface density distribution but also the temperature profile. In this paper, we present our method and the key novel features evident in our fiducial model. In subsequent papers, we will use this model to study the impact of MRI on the formation and migration of planets.« less
  • Non-ideal MHD effects play an important role in the gas dynamics in protoplanetary disks (PPDs). This paper addresses the influence of non-ideal MHD effects on the magnetorotational instability (MRI) and angular momentum transport in PPDs using the most up-to-date results from numerical simulations. We perform chemistry calculations using a complex reaction network with standard prescriptions for X-ray and cosmic-ray ionizations. We first show that whether or not grains are included, the recombination time is at least one order of magnitude less than the orbital time within five disk scale heights, justifying the validity of local ionization equilibrium and strong couplingmore » limit in PPDs. The full conductivity tensor at different disk radii and heights is evaluated, with the MRI active region determined by requiring that (1) the Ohmic Elsasser number {Lambda} be greater than 1 and (2) the ratio of gas to magnetic pressure {beta} be greater than {beta}{sub min}(Am) as identified in the recent study by Bai and Stone, where Am is the Elsasser number for ambipolar diffusion. With full flexibility as to the magnetic field strength, we provide a general framework for estimating the MRI-driven accretion rate M-dot and the magnetic field strength in the MRI active layer. We find that the MRI active layer always exists at any disk radius as long as the magnetic field in PPDs is sufficiently weak. However, the optimistically predicted M-dot in the inner disk (r = 1-10 AU) appears insufficient to account for the observed range of accretion rates in PPDs (around 10{sup -8} M{sub sun} yr{sup -1}) even in the grain-free calculation, and the presence of solar abundance sub-micron grains further reduces M-dot by one to two orders of magnitude. Moreover, we find that the predicted M-dot increases with radius in the inner disk where accretion is layered, which would lead to runaway mass accumulation if disk accretion is solely driven by the MRI. Our results suggest that stronger sources of ionization and/or additional mechanisms such as magnetized wind are needed to explain the observed accretion rates in PPDs. In contrast, our predicted M-dot is on the order of 10{sup -9} M{sub sun} yr{sup -1} in the outer disk, consistent with the observed accretion rates in transitional disks.« less