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Register a new userTemperature Structure in the Inner Regions of Protoplanetary Disks: Inefficient Accretion Heating Controlled by Nonideal Magnetohydrodynamics
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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.
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The gas dynamics of weakly ionized protoplanetary disks (PPDs) is largely governed by the coupling between gas and magnetic fields, described by three non-ideal magnetohydrodynamical (MHD) effects (Ohmic, Hall, ambipolar). Previous local simulations incorporating these processes have revealed that the inner regions of PPDs are largely laminar accompanied by wind-driven accretion. We conduct 2D axisymmetric, fully global MHD simulations of these regions ($sim1-20$ AU), taking into account all non-ideal MHD effects, with tabulated diffusion coefficients and approximate treatment of external ionization and heating. With net vertical field aligned with disk rotation, the Hall-shear instability strongly amplifies horizontal magnetic field, making the overall dynamics dependent on initial field configuration. Following disk formation, the disk likely relaxes into an inner zone characterized by asymmetric field configuration across the midplane that smoothly transitions to a more symmetric outer zone. Angular momentum transport is driven by both MHD winds and laminar Maxwell stress, with both accretion and decretion flows present at different heights, and modestly asymmetric winds from the two disk sides. With anti-aligned field polarity, weakly magnetized disks settle into an asymmetric field configuration with supersonic accretion flow concentrated at one side of disk surface, and highly asymmetric winds between the two disk sides. In all cases, the wind is magneto-thermal in nature characterized by mass loss rate exceeding the accretion rate. More strongly magnetized disks give more symmetric field configuration and flow structures. Deeper far-UV penetration leads to stronger and less stable outflows. Implications for observations and planet formation are also discussed.
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.
The gas dynamics of protoplanetary disks (PPDs) is largely controlled by non-ideal magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion. Among these the role of the Hall effect is the least explored and most poorly understood. We have included all three non-ideal MHD effects in a self-consistent manner to investigate the role of the Hall effect on PPD gas dynamics using local shearing-box simulations. In this first paper, we focus on the inner region of PPDs, where previous studies excluding the Hall effect have revealed that the inner disk up to ~10 AU is largely laminar, with accretion driven by a magnetocentrifugal wind. We confirm this basic picture and show that the Hall effect introduces modest modifications to the wind solutions, depending on the polarity of the large-scale poloidal magnetic field B_0 threading the disk. When B_0.Omega>0, the horizontal magnetic field is strongly amplified toward the disk interior, leading to a stronger disk wind (by ~50% or less in terms of the wind-driven accretion rate). The enhanced horizontal field also leads to much stronger large-scale Maxwell stress (magnetic braking) that contributes to a considerable fraction of the wind-driven accretion rate. When B_0.Omega<0, the horizontal magnetic field is reduced, leading to a weaker disk wind (by ~20%) and negligible magnetic braking. Moreover, we find that when B_0.Omega>0, the laminar region extends farther to ~15 AU before the magneto-rotational instability sets in, while for B_0.Omega<0, the laminar region extends only to ~3-5 AU for a typical PPD accretion rates. Scaling relations for the wind properties, especially the wind-driven accretion rate, are provided for aligned and anti-aligned field geometries. Issues with the symmetry of the wind solutions and grain abundance are also discussed.
We present a study of the evolution of the inner few astronomical units of protoplanetary disks around low-mass stars. We consider nearby stellar groups with ages spanning from 1 to 11 Myr, distributed into four age bins. Combining PANSTARSS photometry with spectral types, we derive the reddening consistently for each star, which we use (1) to measure the excess emission above the photosphere with a new indicator of IR excess and (2) to estimate the mass accretion rate ($dot{M}$) from the equivalent width of the H$alpha$ line. Using the observed decay of $dot{M}$ as a constrain to fix the initial conditions and the viscosity parameter of viscous evolutionary models, we use approximate Bayesian modeling to infer the dust properties that produce the observed decrease of the IR excess with age, in the range between 4.5 and $24,mu$m. We calculate an extensive grid of irradiated disk models with a two-layered wall to emulate a curved dust inner edge and obtain the vertical structure consistent with the surface density predicted by viscous evolution. We find that the median dust depletion in the disk upper layers is $epsilon sim 3 times 10^{-3}$ at 1.5 Myr, consistent with previous studies, and it decreases to $epsilon sim 3 times 10^{-4}$ by 7.5 Myr. We include photoevaporation in a simple model of the disk evolution and find that a photoevaporative wind mass-loss rate of $sim 1 -3 times 10 ^{-9} , M_{odot}yr^{-1}$ agrees with the decrease of the disk fraction with age reasonably well. The models show the inward evolution of the H$_2$O and CO snowlines.
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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