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Register a new userHall-effect Mediated Magnetic Flux Transport in Protoplanetary Disks
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The global evolution of protoplanetary disks (PPDs) has recently been shown to be largely controlled by the amount of poloidal magnetic flux threading the disk, which is further controlled by the poorly understood process of magnetic flux transport. In weakly ionized gas as in PPDs, magnetic flux is largely frozen in the electron fluid, except when resistivity is large. When the disk is largely laminar, we show that the relative drift between the electrons and ions (the Hall-drift), and the ions and neutral fluids (ambipolar-drift) can play a dominant role on the transport of magnetic flux. Using two-dimensional simulations that incorporate the Hall effect and ambipolar diffusion (AD) with prescribed diffusivities, we show that when large-scale poloidal field is aligned with disk rotation, the Hall effect rapidly drags magnetic flux inward at the midplane region, while it slowly pushes flux outward above/below the midplane. This leads to a highly radially elongated field configuration as a global manifestation of the Hall-shear instability. This field configuration further promotes rapid outward flux transport by AD at the midplane, leading to instability saturation. In quasi-steady state, magnetic flux is transported outward at approximately the same rate at all heights, and the rate is comparable to the Hall-free case. For anti-aligned field polarity, the Hall effect consistently transports magnetic flux outward, leading to a largely vertical field configuration in the midplane region. The field lines in the upper layer first bend radially inward and then outward to launch a disk wind. Overall, the net rate of outward flux transport is about twice faster than the aligned case. In addition, the rate of flux transport increases with increasing disk magnetization. The absolute rate of transport is sensitive to disk microphysics which remains to be explored in future studies.
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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.
It has recently been shown that the inner region of protoplanetary disks (PPDs) is governed by wind-driven accretion, and the resulting accretion flow showing complex vertical profiles. Such complex flow structures are further enhanced due to the Hall effect, especially when the background magnetic field is aligned with disk rotation. We investigate how such flow structures impact global dust transport via Monte-Carlo simulations, focusing on two scenarios. In the first scenario, the toroidal magnetic field is maximized in the miplane, leading to accretion and decretion flows above and below. In the second scenario, the toroidal field changes sign across the midplane, leading to an accretion flow at the disk midplane, with decretion flows above and below. We find that in both cases, the contribution from additional gas flows can still be accurately incorporated into the advection-diffusion framework for vertically-integrated dust transport, with enhanced dust radial diffusion up to an effective $alpha^{rm eff}sim10^{-2}$ for strongly coupled dust, even when background turbulence is weak $alpha<10^{-4}$. Dust radial drift is also modestly enhanced in the second scenario. We provide a general analytical theory that accurately reproduces our simulation results, thus establishing a framework to model global dust transport that realistically incorporates vertical gas flow structures. We also note that the theory is equally applicable to the transport of chemical species.
We perform 3D stratified shearing-box MHD simulations on the gas dynamics of protoplanetary disks threaded by net vertical magnetic field Bz. All three non-ideal MHD effects, Ohmic resistivity, the Hall effect and ambipolar diffusion are included in a self-consistent manner based on equilibrium chemistry. We focus on regions toward outer disk radii, from 5-60AU, where Ohmic resistivity tends to become negligible, ambipolar diffusion dominates over an extended region across disk height, and the Hall effect largely controls the dynamics near the disk midplane. We find that around R=5AU, the system launches a laminar/weakly turbulent magnetocentrifugal wind when the net vertical field Bz is not too weak, as expected. Moreover, the wind is able to achieve and maintain a configuration with reflection symmetry at disk midplane. The case with anti-aligned field polarity (Omega. Bz<0) is more susceptible to the MRI when Bz drops, leading to an outflow oscillating in radial directions and very inefficient angular momentum transport. At the outer disk around and beyond R=30AU, the system shows vigorous MRI turbulence in the surface layer due to far-UV ionization, which efficiently drives disk accretion. The Hall effect affects the stability of the midplane region to the MRI, leading to strong/weak Maxwell stress for aligned/anti-aligned field polarities. Nevertheless, the midplane region is only very weakly turbulent. Overall, the basic picture is analogous to the conventional layered accretion scenario applied to the outer disk. In addition, we find that the vertical magnetic flux is strongly concentrated into thin, azimuthally extended shells in most of our simulations beyond 15AU. This is a generic phenomenon unrelated to the Hall effect, and leads to enhanced zonal flow. Observational and theoretical implications, as well as future prospects are briefly discussed.
Global evolution and dispersal of protoplanetary disks (PPDs) is governed by disk angular momentum transport and mass-loss processes. Recent numerical studies suggest that angular momentum transport in the inner region of PPDs is largely driven by magnetized disk wind, yet the wind mass-loss rate remains unconstrained. On the other hand, disk mass loss has conventionally been attributed to photoevaporation, where external heating on the disk surface drives a thermal wind. We unify the two scenarios by developing a 1D model of magnetized disk winds with a simple treatment of thermodynamics as a proxy for external heating. The wind properties largely depend on 1) the magnetic field strength at the wind base, characterized by the poloidal Alfven speed $v_{Ap}$, 2) the sound speed $c_s$ near the wind base, and 3) how rapidly poloidal field lines diverge (achieve $R^{-2}$ scaling). When $v_{Ap}gg c_s$, corotation is enforced near the wind base, resulting in centrifugal acceleration. Otherwise, the wind is accelerated mainly by the pressure of the toroidal magnetic field. In both cases, the dominant role played by magnetic forces likely yields wind outflow rates that well exceed purely hydrodynamical mechanisms. For typical PPD accretion-rate and wind-launching conditions, we expect $v_{Ap}$ to be comparable to $c_s$ at the wind base. The resulting wind is heavily loaded, with total wind mass loss rate likely reaching a considerable fraction of wind-driven accretion rate. Implications for modeling global disk evolution and planet formation are also discussed.
The planet-forming region of protoplanetary disks is cold, dense, and therefore weakly ionized. For this reason, magnetohydrodynamic (MHD) turbulence is thought to be mostly absent, and another mechanism has to be found to explain gas accretion. It has been proposed that magnetized winds, launched from the ionized disk surface, could drive accretion in the presence of a large-scale magnetic field. The efficiency and the impact of these surface winds on the disk structure is still highly uncertain. We present the first global simulations of a weakly ionized disk that exhibits large-scale magnetized winds. We also study the impact of self-organization, which was previously demonstrated only in non-stratified models. We perform numerical simulations of stratified disks with the PLUTO code. We compute the ionization fraction dynamically, and account for all three non-ideal MHD effects: ohmic and ambipolar diffusions, and the Hall drift. Simplified heating and cooling due to non-thermal radiation is also taken into account in the disk atmosphere. We find that disks can be accreting or not, depending on the configuration of the large-scale magnetic field. Magnetothermal winds, driven both by magnetic acceleration and heating of the atmosphere, are obtained in the accreting case. In some cases, these winds are asymmetric, ejecting predominantly on one side of the disk. The wind mass loss rate depends primarily on the average ratio of magnetic to thermal pressure in the disk midplane. The non-accreting case is characterized by a meridional circulation, with accretion layers at the disk surface and decretion in the midplane. Finally, we observe self-organization, resulting in axisymmetric rings of density and associated pressure bumps. The underlying mechanism and its impact on observable structures are discussed.
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