Non-ideal Magnetohydrodynamic Simulations Research Articles

Co-evolution of dust grains and protoplanetary disks. II. Structure and evolution of protoplanetary disks: An analytical approach

Abstract In our previous study (Tsukamoto et al. 2023b, PASJ, 75, 835), we investigated the formation and early evolution of protoplanetary disks with 3D non-ideal magnetohydrodynamics simulations considering dust growth, and found that the modified equations of the conventional steady accretion disk model that consider magnetic braking, dust growth, and ambipolar diffusion reproduce the disk structure (such as density and vertical magnetic field) obtained from simulations very well. In this paper, as a sequel to our previous study, we analytically investigate the structure and evolution of protoplanetary disks corresponding to Class 0/I young stellar objects using the modified steady accretion disk model combining an analytical model of envelope accretion. We estimate that the disk radius is several astronomical units at the disk formation epoch and increases to several hundred astronomical units at the end of the accretion phase. The disk mass is estimated to be $0.01 \lesssim M_{\rm disk} \lesssim 0.1 \, M_\odot$ for a disk with a radius of several tens of astronomical units and a mass accretion rate of $\dot{M}_{\rm disk} \sim 10^{-6} \, M_\odot \,\, {\rm yr^{-1}}$. These estimates seems to be consistent with recent observations. We also found that, with typical disk ionization rates (ζ ≳ 10−19 s−1) and a moderate mass accretion rate ($\dot{M}_{\rm disk}\gtrsim 10^{-8} \, M_\odot \,\, {\rm yr^{-1}}$), magnetorotational instability is suppressed in the disk because of low plasma β and efficient ambipolar diffusion. We argue that the radial profile of specific angular momentum (or rotational velocity) at the disk outer edge should be continuously connected to that of the envelope if the disk evolves by magnetic braking, and should be discontinuous if the disk evolves by an internal angular momentum transport process such as gravitational instability or magnetorotational instability. Future detailed observations of the specific angular momentum profile around the disk outer edge are important for understanding the angular momentum transport mechanism of protoplanetary disks.

Dynamics near the inner dead-zone edges in a proprotoplanetary disk

Abstract We perform three-dimensional global non-ideal magnetohydrodynamic simulations of a protoplanetary disk containing the inner dead-zone edge. We take into account realistic diffusion coefficients of the Ohmic resistivity and ambipolar diffusion based on detailed chemical reactions with single-size dust grains. We found that the conventional dead zone identified by the Elsässer numbers of the Ohmic resistivity and ambipolar diffusion is divided into two regions: “the transition zone” and “the coherent zone.” The coherent zone has the same properties as the conventional dead zone, and extends outside of the transition zone in the radial direction. Between the active and coherent zones, we discover the transition zone, the inner edge of which is identical to that of the conventional dead zone. The transition zone extends out over the regions where thermal ionization determines diffusion coefficients. The transition zone has completely different physical properties than the conventional dead zone, the so-called undead zone, and the zombie zone. The combination of amplification of the radial magnetic field owing to the ambipolar diffusion and a steep radial gradient of the Ohmic diffusivity causes the efficient evacuation of the net vertical magnetic flux from the transition zone within several rotations. Surface gas accretion occurs in the coherent zone but not in the transition zone. The presence of the transition zone prohibits mass and magnetic flux transport from the coherent zone to the active zone. Mass accumulation occurs at both edges of the transition zone as a result of mass supply from the active and coherent zones.

Outflows Driven from a Magnetic Pseudodisk

Outflows play a pivotal role in star formation as one of its most visible markers and a means of transporting mass, momentum, and angular momentum from the infalling gas into the surrounding molecular cloud. Their wide reach (at least thousands of astrnomical units) is a contrast to typical disk sizes (∼10–100 au). We employ high-resolution three-dimensional nested-grid nonideal magnetohydrodynamic (MHD) simulations to study outflow properties in the Class 0 phase. We find that no disk wind is driven from the extended centrifugal disk that has weak magnetic coupling. The low-velocity winds emerge instead from the infalling magnetic pseudodisk. Much of the disk actually experiences an infall of matter rather than outflowing gas. Some of the pseudodisk wind (PD-wind) moves inward to regions above the disk and either falls onto the disk or proceeds upward. The upward flow gives the impression of a disk wind above a certain height even if the gas is originally emerging from the pseudodisk. The PD-wind has the strongest flow coming from a disk interaction zone that lies just outside the disk and is an interface between the inwardly advected magnetic field of the pseudodisk and the outwardly diffusing magnetic field of the disk. The low-velocity wind exhibits the features of a flow driven by the magnetic pressure gradient force in some regions and those of a magnetocentrifugal wind in other regions. We interpret the structure and dynamics of the outflow zone in terms of the basic physics of gravity, angular momentum, magnetic fields, and nonideal MHD.

Formation of Unipolar Outflow and Protostellar Rocket Effect in Magnetized Turbulent Molecular Cloud Cores

Observed protostellar outflows exhibit a variety of asymmetrical features, including remarkable unipolar outflows and bending outflows. Revealing the formation and early evolution of such asymmetrical protostellar outflows, especially the unipolar outflows, is essential for a better understanding of the star and planet formation because they can dramatically change the mass accretion and angular momentum transport to the protostars and protoplanetary disks. Here we perform three-dimensional nonideal magnetohydrodynamics simulations to investigate the formation and early evolution of the asymmetrical protostellar outflows in magnetized turbulent isolated molecular cloud cores. We find, for the first time to our knowledge, that the unipolar outflow forms even in the single low-mass protostellar system. The results show that the unipolar outflow is driven in the weakly magnetized cloud cores with the dimensionless mass-to-flux ratios of μ = 8 and 16. Furthermore, we find the protostellar rocket effect of the unipolar outflow, which is similar to the launch and propulsion of a rocket. The unipolar outflow ejects the protostellar system from the central dense region to the outer region of the parent cloud core, and the ram pressure caused by its ejection suppresses the driving of additional new outflows. In contrast, the bending bipolar outflow is driven in the moderately magnetized cloud core with μ = 4. The ratio of the magnetic to turbulent energies of a parent cloud core may play a key role in the formation of asymmetrical protostellar outflows.

Co-evolution of dust grains and protoplanetary disks

Abstract We propose a new evolutionary process for protoplanetary disks, the co-evolution of dust grains and protoplanetary disks, revealed by dust–gas two-fluid non-ideal magnetohydrodynamics simulations considering the growth of dust grains and associated changes in magnetic resistivity. We found that the dust growth significantly affects disk evolution by changing the coupling between the gas and the magnetic field. Moreover, once the dust grains grow sufficiently large and the adsorption of charged particles on to them becomes negligible, the physical quantities (e.g., density and magnetic field) of the disk are well described by characteristic power laws. In this disk structure, the radial profile of density is steeper and the disk mass is smaller than those of the model ignoring dust growth. We analytically derive these power laws from the basic equations of non-ideal magnetohydrodynamics. The analytical power laws are determined only by observable physical quantities, e.g., central stellar mass and mass accretion rate, and do not include difficult-to-determine parameters, e.g., the viscous parameter α. Therefore, our model is observationally testable and this disk structure is expected to provide a new perspective for future studies on protostar and disk evolution.

Magnetically activated accretion outbursts of pre-main-sequence discs

ABSTRACT We investigate whether triggering of the magnetorotational instability (MRI) in protoplanetary discs can account for the wide diversity of observed accretion outbursts. We show that short-lived, relatively low accretion rate events probably result from triggering in the inner disc and can occur at low surface densities, comparable to or smaller than the minimum mass solar nebula, and thus are very unlikely to result from MRI triggering by gravitational instability. We develop time-dependent accretion disc models using an α-viscosity approach and calculate light curves to compare with observations. Our modelling indicates that the lag time between infrared and optical bursts seen in Gaia 17bpi can be explained with an outside-in propagation with an α ∼ 0.1 in the MRI-active region, consistent with other estimates. While outbursts in inner discs can show time delays of a few yr between infrared and optical light curves, our models indicate that large, FU Ori-like bursts can exhibit infrared precursors decades before optical bursts. Detecting such precursors could enable analysis of the central star before it is overwhelmed by the rapid accreting material, as well as constraining outburst physics. Our results emphasize the importance of near-infrared monitoring of young stellar objects in addition to optical surveys. In addition, our findings emphasize the need for more sophisticated, three-dimensional, non-ideal magnetohydrodynamic simulations to fully exploit observational results.

The Roles of Dust Growth in the Temperature Evolution and Snow Line Migration in Magnetically Accreting Protoplanetary Disks

The temperature structure of protoplanetary disks provides an important constraint on where in the disks rocky planets like our own form. Recent nonideal magnetohydrodynamical (MHD) simulations have shown that the internal Joule heating associated with magnetically driven disk accretion is inefficient at heating the disk midplane. A disk temperature model based on the MHD simulations predicts that in a disk around a solar-mass young star, the water snow line can move inside the current Earth’s orbit within 1 Myr after disk formation. However, the efficiency of the internal Joule heating depends on the disk’s ionization and opacity structures, both of which are governed by dust grains. In this study, we investigate these effects by combining the previous temperature model for magnetically accreting disks with a parameterized model for the grain size and vertical distribution. Grain growth enhances the gas ionization fraction and thereby allows Joule heating to occur closer to the midplane. However, growth beyond 10 μm causes a decrease in the disk opacity, leading to a lower midplane temperature. The combination of these two effects results in the midplane temperature being maximized when the grain size is in the range 10–100 μm. Grain growth to millimeter sizes can also delay the snow line’s migration to the 1 au orbit by up to a few million years. We conclude that accounting for dust growth is essential for accurately modeling the snow line evolution and terrestrial planet formation in magnetically accreting protoplanetary disks.

Cosmic ray ionization rate versus dust fraction: Which plays a crucial role in the early evolution of the circumstellar disc?

ABSTRACTWe study the formation and early evolution of young stellar objects (YSOs) using three-dimensional non-ideal magnetohydrodynamic (MHD) simulations to investigate the effect of cosmic ray ionization rate and dust fraction (or amount of dust grains) on circumstellar disc formation. Our simulations show that a higher cosmic ray ionization rate and a lower dust fraction lead to (i) a smaller magnetic resistivity of ambipolar diffusion, (ii) a smaller disc size and mass, and (iii) an earlier timing of outflow formation and a greater angular momentum of the outflow. In particular, at a high cosmic ray ionization rate, the discs formed early in the simulation are dispersed by magnetic braking on a time-scale of about 104 yr. Our results suggest that the cosmic ray ionization rate has particularly a large impact on the formation and evolution of discs, while the impact of the dust fraction is not significant.

Three-dimensional Global Simulations of Type-II Planet–Disk Interaction with a Magnetized Disk Wind. I. Magnetic Flux Concentration and Gap Properties

Giant planets embedded in protoplanetary disks (PPDs) can create annulus density gaps around their orbits in the type-II regime, potentially responsible for the ubiquity of annular substructures observed in PPDs. Although a substantial amount of works studying type-II planetary migration and gap properties have been published, they have almost exclusively all been conducted under the viscous accretion disk framework. However, recent studies have established magnetized disk winds as the primary mechanism driving disk accretion and evolution, which can coexist with turbulence from the magnetorotational instability (MRI) in the outer PPDs. We conduct a series of 3D global nonideal magnetohydrodynamic (MHD) simulations of type-II planet–disk interactions applicable to the outer PPDs. Our simulations properly resolve the MRI turbulence and accommodate the MHD disk wind. We found that the planet triggers the poloidal magnetic flux concentration around its orbit. The concentrated magnetic flux strongly enhances angular momentum removal in the gap, which is along the inclined poloidal field through a strong outflow emanating from the disk surface outward to the planet gap. The resulting planet-induced gap shape is more similar to an inviscid disk, while being much deeper, which can be understood from a simple inhomogeneous wind torque prescription. The corotation region is characterized by a fast trans-sonic accretion flow that is asymmetric in azimuth about the planet and lacking the horseshoe turns, and the meridional flow is weakened. The torque acting on the planet generally drives inward migration, though the migration rate can be affected by the presence of neighboring gaps through stochastic, planet-free magnetic flux concentration.

Non-ideal magnetohydrodynamic simulations of the first star formation: the effect of ambipolar diffusion

ABSTRACT In the present-day universe, magnetic fields play such essential roles in star formation as angular momentum transport and outflow driving, which control circumstellar disc formation/fragmentation and also the star formation efficiency. While only a much weaker field has been believed to exist in the early universe, recent theoretical studies find that strong fields can be generated by turbulent dynamo during the gravitational collapse. Here, we investigate the gravitational collapse of a cloud core ($\sim 10^{3}\ \rm cm^{-3}$) up to protostar formation ($\sim 10^{20}\ \rm cm^{-3}$) by non-ideal magnetohydrodynamic simulations considering ambipolar diffusion (AD), the dominant non-ideal effects in the primordial-gas. We systematically study rotating cloud cores either with or without turbulence and permeated with uniform fields of different strengths. We find that AD can slightly suppress the field growth by dynamo especially on scales smaller than the Jeans-scale at the density range $10^{10}\!-\!10^{14}\ \rm cm^{-3}$, while we could not see the AD effect on the temperature evolution, since the AD heating rate is always smaller than compression heating. The inefficiency of AD makes the field as strong as $10^{3}\!-\!10^{5} \rm \ G$ near the formed protostar, much stronger than in the present-day cases, even in cases with initially weak fields. The magnetic field affects the inflow motion when amplified to the equipartition level with turbulence on the Jeans-scale, although disturbed fields do not launch winds. This might suggest that dynamo amplified fields have smaller impact on the dynamics in the later accretion phase than other processes such as ionization feedback.

Turbulence in outer protoplanetary discs: MRI or VSI?

ABSTRACT The outer protoplanetary discs (PPDs) can be subject to the magnetorotational instability (MRI) and the vertical shear instability (VSI). While both processes can drive turbulence in the disc, existing numerical simulations have studied them separately. In this paper, we conduct global 3D non-ideal magnetohydrodynamic (MHD) simulations for outer PPDs, with ambipolar diffusion and instantaneous cooling, and hence conductive to both instabilities. Given the range of ambipolar Elsässer numbers (Am) explored, it is found that the VSI turbulence dominates over the MRI when ambipolar diffusion is strong (Am = 0.1); the VSI and MRI can co-exist for Am = 1; and the VSI is overwhelmed by the MRI when ambipolar diffusion is weak (Am = 10). Angular momentum transport process is primarily driven by MHD winds, while viscous accretion due to MRI and/or VSI turbulence makes a moderate contribution in most cases. Spontaneous magnetic flux concentration and formation of annular substructures remain robust in strong ambipolar diffusion-dominated discs (Am ≤ 1) with the presence of the VSI. Ambipolar diffusion is the major contributor to the magnetic flux concentration phenomenon rather than advection.

Turbulent Dust-trapping Rings as Efficient Sites for Planetesimal Formation

Recent observations of protoplanetary disks (PPDs) at submillimeter wavelengths have revealed the ubiquity of annular substructures that are indicative of pebble-sized dust particles trapped in turbulent ringlike gas pressure bumps. This major paradigm shift also challenges the leading theory of planetesimal formation from such pebbles by means of the streaming instability, which operates in a pressure gradient and can be suppressed by turbulence. Here, we conduct 3D local shearing box nonideal magnetohydrodynamic simulations of dust trapping in enforced gas pressure bumps, including dust backreaction. Under a moderate level of turbulence generated by the magnetorotational instability with ambipolar diffusion, which is suitable for outer disk conditions, we achieve quasi-steady states of dust trapping balanced by turbulent diffusion. We find strong dust clumping in all simulations near the gas pressure maxima, reaching a maximum density well above the threshold for triggering gravitational collapse to form planetesimals. A strong pressure bump concentrates dust particles toward the bump’s center. With a weak pressure bump, dust can also concentrate in secondary filaments off the bump’s center, due to dust backreaction, but strong clumping still occurs mainly in the primary ring around the bump’s center. Our results reveal dust-trapping rings to be robust locations for planetesimal formation in outer PPDs, while they may possess diverse observational properties.

Synthetic Polarization Maps of an Outflow Zone from Magnetohydrodynamic Simulations

The canonical theory of star formation in a magnetized environment predicts the formation of hourglass-shaped magnetic fields during the prestellar collapse phase. In protostellar cores, recent observations reveal complex and strongly distorted magnetic fields in the inner regions that are sculpted by rotation and outflows. We conduct resistive, nonideal magnetohydrodynamic simulations of a protostellar core and employ the radiative transfer code POLARIS to produce synthetic polarization segment maps. A comparison of our mock-polarization maps based on the toroidal-dominated magnetic field in the outflow zone with the observed polarization vectors of SiO lines in Orion Source I shows a reasonable agreement when the magnetic axis is tilted at an angle θ = 15° with respect to the plane of the sky and if the SiO lines have a net polarization parallel to the local magnetic field. Although the observed polarization is from SiO lines and our synthetic maps are due to polarized dust emission, a comparison is useful and allows us to resolve the ambiguity of whether the line polarization is parallel or perpendicular to the local magnetic field direction.

Revealing the Drag Instability in One-fluid Nonideal Magnetohydrodynamic Simulations of a 1D Isothermal C-shock

C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in nonideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density fluctuation with a constant frequency. The perturbations clearly grow after entering the C-shock region until they start being damped at the transition to the post-shock region. We show that the profiles of a predominant Fourier mode extracted locally from the simulated growing perturbation match those of the growing mode derived from the linear analysis. Moreover, the local growth rate and wave frequency derived from the predominant mode generally agree with those from the linear theory. Therefore, we confirm the presence of the drag instability in simulated 1D isothermal C-shocks. We also explore the nonlinear behavior of the instability by imposing larger-amplitude perturbations to the simulation. We find that the drag instability is subject to wave steepening, leading to saturated perturbation growth. Issues concerning local analysis, nonlinear effects, one-fluid approach, and astrophysical applications are discussed.

The initial magnetic criticality of pre-stellar cores

ABSTRACT Direct observational measurements of the magnetic field strength in pre-stellar cores typically find supercritical mass-to-flux ratios, suggesting that the magnetic field is insufficient to prevent gravitational collapse. These measurements suffer from significant uncertainties; an alternative approach is to utilize the sensitivity of pre-stellar chemistry to the evolutionary history, and indirectly constrain the degree of magnetic support. We combine non-ideal magnetohydrodynamic simulations of pre-stellar cores with time-dependent chemistry and radiative transfer modelling, producing synthetic observations of the model cores in several commonly observed molecular lines. We find that molecules strongly affected by freeze-out, such as CS and HCN, typically have much lower line intensities in magnetically subcritical models compared to supercritical ones, due to the longer collapse time-scales. Subcritical models also produce much narrower lines for all species investigated. Accounting for a range of core properties, ages, and viewing angles, we find that supercritical models are unable to reproduce the distribution of CS and N2H+ line strengths and widths seen in an observational sample, whereas subcritical models are in good agreement with the available data. This suggests that despite presently having supercritical mass-to-flux ratios, pre-stellar cores form as magnetically subcritical objects.

The Magnetic Field versus Density Relation in Star-forming Molecular Clouds

Abstract We study the magnetic field to density (B–ρ) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density ρ T between the relatively flat low-density regime and a power-law regime at higher densities. We present an analytic theory for ρ T based on the interplay of the magnetic field, turbulence, and gravity. The break density ρ T scales with the strength of the initial Alfvén Mach number  A 0 for sub-Alfvénic (  A 0 < 1 ) and trans-Alfvénic (  A 0 ∼ 1 ) clouds. We fit the variation of ρ T for model clouds as a function of  A 0 , set by different values of initial sonic Mach number  0 and the initial ratio of gas pressure to magnetic pressure β 0. This implies that ρ T, which denotes the transition in mass-to-flux ratio from the subcritical to the supercritical regime, is set by the initial turbulent compression of the molecular cloud.

Steady-state accretion in magnetized protoplanetary disks

Context. The transition between magnetorotational instability (MRI)-active and magnetically dead regions corresponds to a sharp change in the disk turbulence level, where pressure maxima may form, hence potentially trapping dust particles and explaining some of the observed disk substructures. Aims. We aim to provide the first building blocks toward a self-consistent approach to assess the dead zone outer edge as a viable location for dust trapping, under the framework of viscously driven accretion. Methods. We present a 1+1D global magnetically driven disk accretion model that captures the essence of the MRI-driven accretion, without resorting to 3D global nonideal magnetohydrodynamic (MHD) simulations. The gas dynamics is assumed to be solely controlled by the MRI and hydrodynamic instabilities. For given stellar and disk parameters, the Shakura–Sunyaev viscosity parameter, α, is determined self-consistently under the adopted framework from detailed considerations of the MRI with nonideal MHD effects (Ohmic resistivity and ambipolar diffusion), accounting for disk heating by stellar irradiation, nonthermal sources of ionization, and dust effects on the ionization chemistry. Additionally, the magnetic field strength is numerically constrained to maximize the MRI activity. Results. We demonstrate the use of our framework by investigating steady-state MRI-driven accretion in a fiducial protoplanetary disk model around a solar-type star. We find that the equilibrium solution displays no pressure maximum at the dead zone outer edge, except if a sufficient amount of dust particles has accumulated there before the disk reaches a steady-state accretion regime. Furthermore, the steady-state accretion solution describes a disk that displays a spatially extended long-lived inner disk gas reservoir (the dead zone) that accretes a few times 10−9 M⊙ yr−1. By conducting a detailed parameter study, we find that the extent to which the MRI can drive efficient accretion is primarily determined by the total disk gas mass, the representative grain size, the vertically integrated dust-to-gas mass ratio, and the stellar X-ray luminosity. Conclusions. A self-consistent time-dependent coupling between gas, dust, stellar evolution models, and our general framework on million-year timescales is required to fully understand the formation of dead zones and their potential to trap dust particles.

Global Non-ideal Magnetohydrodynamic Simulations of Protoplanetary Disks with Outer Truncation

Abstract It has recently been established that the evolution of protoplanetary disks is primarily driven by magnetized disk winds, requiring a large-scale magnetic flux threading the disks. The size of such disks is expected to shrink with time, as opposed to the conventional scenario of viscous expansion. We present the first global 2D non-ideal magnetohydrodynamic simulations of protoplanetary disks that are truncated in the outer radius, aiming to understand the interaction of the disk with the interstellar environment, as well as the global evolution of the disk and magnetic flux. We find that as the system relaxes, the poloidal magnetic field threading the disk beyond the truncation radius collapses toward the midplane, leading to a rapid reconnection. This process removes a substantial amount of magnetic flux from the system and forms closed poloidal magnetic flux loops encircling the outer disk in quasi-steady state. These magnetic flux loops can drive expansion beyond the truncation radius, corresponding to substantial mass loss through a magnetized disk outflow beyond the truncation radius analogous to a combination of viscous spreading and external photoevaporation. The magnetic flux loops gradually shrink over time, the rates of which depend on the level of disk magnetization and the external environment, which eventually governs the long-term disk evolution.

The impact of non-ideal magnetohydrodynamic processes on discs, outflows, counter-rotation, and magnetic walls during the early stages of star formation

ABSTRACT Non-ideal magnetohydrodynamic (MHD) processes – namely Ohmic resistivity, ambipolar diffusion, and the Hall effect – modify the early stages of the star formation process and the surrounding environment. Collectively, they have been shown to promote disc formation and promote or hinder outflows. But which non-ideal process has the greatest impact? Using three-dimensional smoothed particle radiation non-ideal MHD simulations, we model the gravitational collapse of a rotating, magnetized cloud through the first hydrostatic core phase to shortly after the formation of the stellar core. We investigate the impact of each process individually and collectively. Including any non-ideal process decreases the maximum magnetic field strength by at least an order of magnitude during the first core phase compared to using ideal MHD, and promotes the formation of a magnetic wall. When the magnetic field and rotation vectors are anti-aligned and the Hall effect is included, rotationally supported discs of r ≳ 20 au form; when only the Hall effect is included and the vectors are aligned, a counter-rotating pseudo-disc forms that is not rotationally supported. Rotationally supported discs of r ≲ 4 au form if only Ohmic resistivity or ambipolar diffusion are included. The Hall effect suppresses first core outflows when the vectors are anti-aligned and suppresses stellar core outflows independent of alignment. Ohmic resistivity and ambipolar diffusion each promote first core outflows and delay the launching of stellar core outflows. Although each non-ideal process influences star formation, these results suggest that the Hall effect has the greatest influence.

Global three-dimensional simulations of outer protoplanetary discs with ambipolar diffusion

ABSTRACT The structure and evolution of protoplanetary discs (PPDs) are largely governed by disc angular momentum transport, mediated by magnetic fields. In the most observable outer disc, ambipolar diffusion is the primary non-ideal magnetohydrodynamic (MHD) effect. In this work, we study the gas dynamics in outer PPDs by conducting a series of global three-dimensional non-ideal MHD simulations with ambipolar diffusion and net poloidal magnetic flux, using the Athena++ MHD code, with resolution comparable to local simulations. Our simulations demonstrate the coexistence of magnetized disc winds and turbulence driven by the magneto-rotational instability (MRI). While MHD winds dominate disc angular momentum transport, the MRI turbulence also contributes significantly. We observe that magnetic flux spontaneously concentrates into axisymmetric flux sheets, leading to radial variations in turbulence levels, stresses, and accretion rates. Annular substructures arise as a natural consequence of magnetic flux concentration. The flux concentration phenomena show diverse properties with different levels of disc magnetization and ambipolar diffusion. The disc generally loses magnetic flux over time, though flux sheets could prevent the leak of magnetic flux in some cases. Our results demonstrate the ubiquity of disc annular substructures in weakly MRI turbulent outer PPDs and imply a stochastic nature of disc evolution.