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Register a new userElectron Heating in the Magnetorotational Instability: Implications for Turbulence Strength in Outer Regions of Protoplanetary Disks
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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 Ohms 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 $sim20$ 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.
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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 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 disk (a few AU) is largely laminar, with accretion primarily driven by magnetized disk winds, as a result of nonideal magnetohydrodynamic (MHD) effects from weakly ionized gas, suggesting an alternative heating mechanism by Joule dissipation. We perform local stratified MHD simulations including all three nonideal MHD effects (ohmic, Hall, and ambipolar diffusion) and investigate the role of Joule heating and the resulting disk vertical temperature profiles. We find that in the inner disk, as ohmic and ambipolar diffusion strongly suppress electrical current around the midplane, Joule heating primarily occurs at several scale heights above the midplane, making the midplane temperature much lower than that with the conventional viscous heating model. Including the Hall effect, Joule heating is enhanced/reduced when the magnetic fields threading the disks are aligned/anti-aligned with the disk rotation, but it is overall ineffective. Our results further suggest that the midplane temperature in the inner PPDs is almost entirely determined by irradiation heating, unless viscous heating can trigger thermal ionization in the disk innermost region to self-sustain magnetorotational instability turbulence.
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 fractions imply that non-ideal magneto-hydrodynamic (MHD) effects should be properly considered. To this end, we present linear analyses of the VSI in magnetized disks with Ohmic resistivity. We primarily consider toroidal magnetic fields, which are likely to dominate the field geometry in PPDs. We perform vertically global and radially local analyses to capture characteristic VSI modes with extended vertical structures. To focus on the effect of magnetism, we use a locally isothermal equation of state. We find that magnetism provides a stabilizing effect to dampen the VSI, with surface modes, rather than body modes, being the first to vanish with increasing magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic results are recovered. We also briefly consider poloidal fields to account for the magnetorotational instability (MRI), which may develop towards surface layers in the outer parts of PPDs. The MRI grows efficiently at small radial wavenumbers, in contrast to the VSI. When resistivity is considered, we find the VSI dominates over the MRI for Ohmic Els{a}sser numbers $lesssim 0.09$ at plasma beta parameter $beta_Z sim 10^4$.
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.
Mid-infrared molecular line emission detected with the Spitzer Space Telescope is often interpreted using slab models. However, we need to understand the mid-infrared line emission in 2D disk models, such that we gain information about from where the lines are being emitted and under which conditions, such that we gain information about number densities, temperatures, and optical depths in both the radial and vertical directions. In this paper, we introduce a series of 2D thermochemical models of a prototypical T Tauri protoplanetary disk, in order to examine how sensitive the line-emitting regions are to changes in the UV and X-ray fluxes, the disk flaring angle, dust settling, and the dust-to-gas ratio. These all affect the heating of the inner disk, and thus can affect the mid-infrared spectral lines. Using the ProDiMo and FLiTs codes, we produce a series of 2D thermochemical disk models. We find that there is often a significant difference between the gas and dust temperatures in the line emitting regions, and we illustrate that the size of the line emitting regions is relatively robust against changes in the stellar and disk parameters (namely, the UV and X-ray fluxes, the flaring angle, and dust settling). These results demonstrate the potential for localized variations in the line-emitting region to greatly affect the resulting spectra and line fluxes, and the necessity of allowing for such variations in our models.
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