Formation Of Protoplanetary Disks Research Articles

Thermal processing of primordial pebbles in evolving protoplanetary disks

During protoplanetary disk formation, dust grains located in the outer disk retain their pristine icy composition, while solids in the inner stellar-heated disk undergo volatile loss. This process may have left a fossil record in Solar System material, showing different nucleosynthetic imprints that have been attributed to different degrees of thermal processing. However, it remains unclear how a large mass fraction of thermally processed inner-disk pebbles is produced and how these grains are subsequently transported throughout the disk. In this work we numerically investigate the evolution in time of a two-component pebble disk consisting of both pristine pebbles and those that underwent ice sublimation. We find that stellar outbursts exceeding 1000 times the solar luminosity are efficient in thermally altering, through ice sublimation, a large mass fraction of pebbles (around 80<!PCT!>). After the establishment of this initial radial dust composition gradient throughout the disk, the subsequent mixing and inward drift of pristine outer-disk pebbles alter the inner disk bulk composition from processed to more unprocessed in time. Therefore, if processed pebbles without ice mantles have an isotopic composition similar to ureilite meteorites from the inner Solar System, inner-disk minor bodies forming from the early pebble flux ($<$1Myr) will be isotopically ureilite-like, while later-formed bodies will be increasingly admixed with the signature of the late-incoming, CI chondrite-like unprocessed pebbles. This appears to be largely consistent with the trend seen between the accretion age of different meteoric classes and their different stable isotope composition anomalies (in µ Cr µ Ca µ Si and µ Ni ), but further work may be needed to explain the role of isotopically anomalous refractory inclusions and anomaly trends in other elements. Our findings further support an early thermal processing of ice mantles via stellar outbursts that are common around young Sun-like stars.

Dust growth and pebble formation in the initial stages of protoplanetary disk evolution

Aims. The initial stages of planet formation may start concurrently with the formation of a gas-dust protoplanetary disk. This makes the study of the earliest stages of protoplanetary disk formation crucially important. Here we focus on dust growth and pebble formation in a protoplanetary disk that is still accreting from a parental cloud core. Methods. We have developed an original three-dimensional numerical hydrodynamics code, which computes the collapse of rotating clouds and disk formation on nested meshes using a novel hybrid Coarray Fortran-OpenMP approach for distributed and shared memory parallelization. Dust dynamics and growth are also included in the simulations. Results. We found that the dust growth from ~1 µm to 1–10 mm already occurs in the initial few thousand years of disk evolution but the Stokes number hardly exceeds 0.1 because of higher disk densities and temperatures compared to the minimum mass Solar nebular. The ratio of the dust-to-gas vertical scale heights remains rather modest, 0.2–0.5, which may be explained by the perturbing action of spiral arms that develop in the disk soon after its formation. The dust-to-gas mass ratio in the disk midplane is highly nonhomogeneous throughout the disk extent and is in general enhanced by a factor of several compared to the fiducial 1:100 value. Low St hinders strong dust accumulation in the spiral arms compared to the rest of the disk and the nonsteady nature of the spirals is also an obstacle. The spatial distribution of pebbles in the disk midplane exhibits a highly nonhomogeneous and patchy character. The total mass of pebbles in the disk increases with time and reaches a few tens of Earth masses after a few tens of thousand years of disk evolution. Conclusions. We found that protoplanetary disks with an age ≤20 kyr can possess notable amounts of pebbles and feature dust-togas density enhancements in the disk midplane. Hence, these young disks can already be ripe for the planet formation process to start. Multidimensional numerical models of disk formation that consider the coevolution of gas and dust including dust growth are important to improve our understanding of planet formation.

Influence of protostellar outflows on star and protoplanetary disk formation in a massive star-forming clump

Context. Due to the presence of magnetic fields, protostellar jets or outflows are a natural consequence of accretion onto protostars. They are expected to play an important role in star and protoplanetary disk formation. Aims. We aim to determine the influence of outflows on star and protoplanetary disk formation in star-forming clumps. Methods. Using RAMSES, we performed the first magnetohydrodynamics calculation of massive star-forming clumps with ambipolar diffusion; radiative transfer, including the radiative feedback of protostars; and protostellar outflows while systematically resolving the disk scales. We compared this simulation to a model without outflows. Results. We found that protostellar outflows have a significant impact on both star and disk formation. They provide a significant amount of additional kinetic energy to the clump, with typical velocities of around a few 10 km s−1; impact the clump and disk temperatures; reduce the accretion rate onto the protostars; and enhance fragmentation in the filaments. We found that they promote a more numerous stellar population. They do not impact the low-mass end of the IMF much, which is probably controlled by the mass of the first Larson core; however, they have an influence on its peak and high-mass end. Conclusions. Protostellar outflows appear to have a significant influence on both star and disk formation and should therefore be included in realistic simulations of star-forming environments.

Dust–gas dynamics driven by the streaming instability with various pressure gradients

ABSTRACT The streaming instability, a promising mechanism to drive planetesimal formation in dusty protoplanetary discs, relies on aerodynamic drag naturally induced by the background radial pressure gradient. This gradient should vary in discs, but its effect on the streaming instability has not been sufficiently explored. For this purpose, we use numerical simulations of an unstratified disc to study the non-linear saturation of the streaming instability with mono-disperse dust particles and survey a wide range of gradients for two distinct combinations of the particle stopping time and the dust-to-gas mass ratio. As the gradient increases, we find most kinematic and morphological properties increase but not always in linear proportion. The density distributions of tightly coupled particles are insensitive to the gradient whereas marginally coupled particles tend to concentrate by more than an order of magnitude as the gradient decreases. Moreover, dust–gas vortices for tightly coupled particles shrink as the gradient decreases, and we note higher resolutions are required to trigger the instability in this case. In addition, we find various properties at saturation that depend on the gradient may be observable and may help reconstruct models of observed discs dominated by streaming turbulence. In general, increased dust diffusion from stronger gradients can lower the concentration of dust filaments and can explain the higher solid abundances needed to trigger strong particle clumping and the reduced planetesimal formation efficiency previously found in vertically stratified simulations.

Protoplanetary Disk Formation in a Self-gravitating Molecular Cloud

Protoplanetary Disk Formation in a Self-gravitating Molecular Cloud

An inflationary disk phase to explain extended protoplanetary dust disks

Context. Understanding planetesimal formation is an essential first step towards understanding planet formation. The distribution of these first solid bodies drives the locations where planetary embryos, which eventually form fully-fledged planets, grow. Aims. We seek to understand the parameter space of possible protoplanetary disk formation and evolution models of our Solar System. A good protoplanetary disk scenario for the Solar System must meet at least the following three criteria: (1) It must produce an extended gas and dust disk (e.g. 45 au for the dust); (2) within the disk, the local dust-to-gas ratio in at least two distinct locations must sufficiently increase to explain the early formation of the parent bodies of non-carbonaceous and carbonaceous iron meteorites; and (3) dust particles, which have condensed at high temperatures (i.e. calcium–aluminium-rich inclusions), must be transported to the outer disk. Though current protoplanetary disk models are able to satisfy one or two of these criteria, none have been successful in recreating all three. We aim to find scenarios that satisfy all three. Methods. In this study we used a 1D disk model that tracks the evolution of the gas and dust disks. Planetesimals are formed within the disk at locations where the streaming instability can be triggered. We explored a large parameter space to study the effect of the disk viscosity, the timescale of infall of material into the disk, the distance within which material is deposited into the disk, and the fragmentation threshold of dust particles. Results. We find that scenarios with a large initial disk viscosity (α > 0.05), a relatively short infall timescale (Tinfall < 100–200kyr), and a small centrifugal radius (RC ~ 0.4 au; i.e. the distance within which material falls into the disk) result in disks that satisfy all three criteria needed to represent the protoplanetary disk of the Solar System. The large initial viscosity and short infall timescale result in a rapid initial expansion of the disk, which we dub the ‘inflationary phase’ of the disk. Furthermore, a temperature-dependent fragmentation threshold, which accounts for cold icy particles breaking more easily, results in larger and more massive disks. This, in turn, results in more ‘icy’ than ‘rocky’ planetesimals. Such scenarios are also better in line with our Solar System, which has small terrestrial planets and massive giant planet cores. Finally, we find that scenarios with large RC cannot transport calcium–aluminium-rich inclusions to the outer disk and do not produce planetesimals at two locations within the disk.

Protoplanetary disk formation in rotating, magnetized and turbulent molecular cloud

Protoplanetary disk formation in rotating, magnetized and turbulent molecular cloud

Traveling waves in an evolving interstellar gas cloud

This paper considers the possible emergence of traveling waves within an evolving interstellar gas cloud. To model this evolution, we use Euler–Poisson equations with the additional assumptions that the gas is incompressible, stratified, and self-gravitating. Within this framework, we establish that when the cloud has low density, the speed of these traveling waves is low. We suggest that the self-gravitational coalescence of embedded solid matter in the gas to form larger aggregates, such as cometary nuclei, may occur in the vicinity of wave crests where the mass density is highest. This idea is consistent with the widely agreed mechanism for planetary formation in proto-planetary disks, namely, that the accumulation of solids to form larger planetoids is initiated at the location of pressure maxima in the gas disk.

Propagation of Alfvén waves in the dusty interstellar medium

Context. Alfvén waves are fundamental magnetized modes that play an important role in the dynamics of magnetized flows such as the interstellar medium (ISM). Aims. In a weakly ionized medium, their propagation critically depends on the ionization rate as well as on the charge carriers. Depending on the gas density, these may be ions, electrons, or dust grains. The latter are particularly well known to have a drastic influence on the magnetic resistivities in the dense ISM, such as collapsing dense cores. Yet, in most calculations, for numerical reasons, the grain inertia is usually neglected. Methods. We carried out an analytical investigation of the propagation of Alfvén waves both in a single-size and multi-size grain medium such as the ISM and we obtained exact expressions giving wavenumbers as a function of wave frequencies. These expressions were then solved analytically or numerically by taking into account or neglecting grain inertia. Results. At long wavelengths, neglecting grain inertia is a very good approximation, however, the situation is rather different for wavelengths shorter than a critical value, which broadly scaled as 1/n, with n being the gas density. More precisely, when inertia is neglected, the waves do not propagate at short wavelengths or, due to the Hall effect, they develop for one circular polarization only, namely, a whistler mode such that ℛe(ω) ∝ k2. The other polarization presents a zero group velocity, namely, ℛe(ω) ∝ k0. When grain inertia is accounted for, the propagation of the two polarizations tend to be more symmetrical and the whistler mode is only present at density higher than ≃108 cm−3. At a lower density, it is replaced by a mode having ℛe(ω) ∝ k≃1.2. Interestingly, one of the polarization presents a distribution, instead of a single ω value. Importantly, for short wavelengths, wave damping is considerably reduced when inertia is properly accounted for. Conclusions. To properly handle the propagation of Alfvén waves at short wavelengths, it is necessary to self-consistently treat grain inertia. We discuss the possible consequences this may have in the context of diffuse and dense molecular gas regarding turbulence, magnetic braking, and protoplanetary disk formation as well as cosmic ray propagation in the dense ISM.

Laboratory spectroscopy of theoretical ices: Predictions for JWST and test for astrochemical models

Context. The pre-stellar core L1544 has been the subject of several observations conducted in the past years, complemented by modelling studies focused on its gas and ice-grain chemistry. The chemical composition of the ice mantles reflects the environmental physical changes along the temporal evolution, such as density and temperature. The investigation outcome hints at a layered structure of interstellar ices with abundance of H2O in the inner layers and an increasing concentration of CO near the surface. The morphology of interstellar ice analogues can be investigated experimentally assuming a composition derived from chemical models. Aims. This research presents a new approach of a three-dimensional fit where observational results are first fitted with a gas-grain chemical model predicting the exact ice composition including infrared (IR) inactive species. Then the laboratory IR spectra are recorded for interstellar ice analogues whose compositions reflect the obtained numerical results, in a layered and in a mixed morphology. These results could then be compared with the results of James Webb Space Telescope (JWST) observations. Special attention is paid to the inclusion of IR inactive species whose presence is predicted in the ice, but is typically omitted in the laboratory obtained data. This stands for N2, one of the main possible constituents of interstellar ice mantles, and O2. Methods. Ice analogue spectra were recorded at a temperature of 10 K using a Fourier transform infrared spectrometer. In the case of layered ice we deposited a H2O-CO-N2-O2 mixture on top of a H2O-CH3OH-N2 ice, while in the case of mixed ice we examined a H2O-CH3OH-N2-CO composition. The selected species are the four most abundant ice components predicted by the chemical model. Results. Following the changing composition and structure of the ice, we find differences in the absorption bands for most of the examined vibrational modes. The extent of observed changes in the IR band profiles will allow us to analyse the structure of ice mantles in L1544 from future observations by the JWST. Conclusions. Our spectroscopic measurements of interstellar ice analogues predicted by our well-received gas-grain chemical codes of pre-stellar cores will allow detailed comparison with upcoming JWST observations. This is crucial in order to put stringent constraints on the chemical and physical structure of dust icy mantles just before the formation of stars and protoplanetary disks, and to explain surface chemistry.

A Multifluid Dust Module in Athena++: Algorithms and Numerical Tests

We describe the algorithm, implementation, and numerical tests of a multifluid dust module in the Athena++ magnetohydrodynamic code. The module can accommodate an arbitrary number of dust species interacting with the gas via aerodynamic drag (characterized by the stopping time), with a number of numerical solvers. In particular, we describe two second-order accurate, two-stage, fully implicit solvers that are stable in stiff regimes, including short stopping times and high dust mass loading, and they are paired with the second-order explicit van Leer and Runge–Kutta gas dynamics solvers in Athena++, respectively. Moreover, we formulate a consistent treatment of dust concentration diffusion with dust back-reaction, which incorporates momentum diffusion and ensures Galilean invariance. The new formulation and stiff drag solvers are implemented to be compatible with most of the existing features of Athena++, including different coordinate systems, mesh refinement, and shearing box and orbital advection. We present a large suite of test problems, including the streaming instability in linear and nonlinear regimes, as well as local and global settings, which demonstrate that the code achieves the desired performance. This module will be particularly useful for studies of dust dynamics and planet formation in protoplanetary disks.

Dust coagulation during the early stages of star formation: molecular cloud collapse and first hydrostatic core evolution

ABSTRACT Planet formation in protoplanetary discs requires dust grains to coagulate from the sub-micron sizes that are found in the interstellar medium into much larger objects. For the first time, we study the growth of dust grains during the earliest phases of star formation using three-dimensional hydrodynamical simulations. We begin with a typical interstellar dust grain size distribution and study dust growth during the collapse of a molecular cloud core and the evolution of the first hydrostatic core, prior to the formation of the stellar core. We examine how the dust size distribution evolves both spatially and temporarily. We find that the envelope maintains its initial population of small dust grains with little growth during these phases, except that in the inner few hundreds of au the smallest grains are depleted. However, once the first hydrostatic core forms rapid dust growth to sizes in excess of 100 μm occurs within the core (before stellar core formation). Progressively larger grains are produced at smaller distances from the centre of the core. In rapidly rotating molecular cloud cores, the ‘first hydrostatic core’ that forms is better described as a pre-stellar disc that may be gravitationally unstable. In such cases, grain growth is more rapid in the spiral density waves leading to the larger grains being preferentially found in the spiral waves even though there is no migration of grains relative to the gas. Thus, the grain size distribution can vary substantially in the first core/pre-stellar disc even at these very early times.

Evidence that the Hot Jupiter WASP-77 A b Formed Beyond Its Parent Protoplanetary Disk’s H2O Ice Line

Abstract Idealized protoplanetary disk and giant planet formation models have been interpreted to suggest that a giant planet’s atmospheric abundances can be used to infer its formation location in its parent protoplanetary disk. It has recently been reported that the hot Jupiter WASP-77 A b has subsolar atmospheric carbon and oxygen abundances with a solar C/O abundance ratio. Assuming solar carbon and oxygen abundances for its host star WASP-77 A, WASP-77 A b’s atmospheric carbon and oxygen abundances possibly indicate that it accreted its envelope interior to its parent protoplanetary disk’s H2O ice line from carbon-depleted gas with little subsequent planetesimal accretion or core erosion. We show that the photospheric abundances of carbon and oxygen in WASP-77 A are supersolar with a subsolar C/O abundance ratio, implying that WASP-77 A b’s atmosphere has significantly substellar carbon and oxygen abundances with a superstellar C/O ratio. Our result possibly indicates that WASP-77 A b’s envelope was accreted by the planet beyond its parent protoplanetary disk's H2O ice line. While numerous theoretical complications to these idealized models have now been identified, the possibility of nonsolar protoplanetary disk abundance ratios confound even the most sophisticated protoplanetary disk and giant planet formation models. We therefore argue that giant planet atmospheric abundance ratios can only be meaningfully interpreted relative to the possibly nonsolar mean compositions of their parent protoplanetary disks as recorded in the photospheric abundances of their dwarf host stars.

Impact of local pressure enhancements on dust concentration in turbulent protoplanetary discs

The standard core accretion model for planetesimal formation in protoplanetary discs (PPDs) is subject to a number of challenges. One is related to the vertical settling of dust to the disc mid-plane against turbulent stirring. This is particularly relevant in the presence of the vertical shear instability (VSI), a purely hydrodynamic instability applicable to the outer parts of PPDs, which drives moderate turbulence characterized by large-scale vertical motions. We investigate the evolution of dust and gas in the vicinity of local pressure enhancements (pressure bumps) in a PPD with turbulence sustained by the VSI. Our goal is to determine the morphology of dust concentrations and if dust can concentrate sufficiently to reach conditions that can trigger the streaming instability (SI). We performed a suite of global 2D axisymmetric and 3D simulations of dust and gas for a range of values for Σd∕Σg (ratio of dust-to-gas surface mass densities or metallicity), particle Stokes numbers, τ, and pressure bump amplitude, A. Dust feedback onto the gas is included. For the first time, we use global 3D simulations to demonstrate the collection of dust in long-lived vortices induced by the VSI. These vortices, which undergo a slow radial inward drift, are the dusty analogs of large long-lived vortices found in previous dust-free simulations of the VSI. Without a pressure bump and for solar metallicity Z ≈ 0.01 and Stokes numbers τ ~ 10−2, we find that such vortices can reach dust-to-gas density ratios slightly below unity in the discs’ mid-plane, while for Z ≳ 0.05, long-lived vortices are largely absent. In the presence of a pressure bump, for Z ≈ 0.01 and τ ~ 10−2, a dusty vortex forms that reaches dust-to-gas ratios of a few times unity, such that the SI is expected to develop, before it eventually shears out into a turbulent dust ring. At intermediate metallicities, Z ~ 0.03, this occurs for τ ~ 5 × 10−3, but with a weaker and more short-lived vortex, while for larger τ, only a turbulent dust ring forms. For Z ≳ 0.03, we find that the dust ring becomes increasingly axisymmetric for increasing τ and dust-to-gas ratios reach order unity for τ ≳ 5 × 10−3. Furthermore, the vertical mass flow profile of the disc is strongly affected by dust for Z ≳ 0.03, such that gas is transported inward near the mid-plane and outward at larger heights, which is the reversed situation compared to simulations with zero or small amounts of dust. We find viscous α-values to drop moderately as ~10−3–10−4 for metallicities increasing as Z = 0–0.05. Our results suggest that the VSI can play an active role in the formation of planetesimals through the formation of vortices for plausible values of metallicity and particle size. Also, it may provide a natural explanation for the presence or absence of asymmetries of observed dust rings in PPDs, depending on the background metallicity.

Streaming Instabilities in Accreting and Magnetized Laminar Protoplanetary Disks

Abstract The streaming instability (SI) is one of the most promising pathways to the formation of planetesimals from pebbles. Understanding how this instability operates under realistic conditions expected in protoplanetary disks (PPDs) is therefore crucial to assess the efficiency of planet formation. Contemporary models of PPDs show that magnetic fields are key to driving gas accretion through large-scale, laminar magnetic stresses. However, the effect of such magnetic fields on the SI has not been examined in detail. To this end, we study the stability of dusty, magneftized gas in a protoplanetary disk. We find the SI can be enhanced by passive magnetic torques and even persist in the absence of a global radial pressure gradient. In this case, instability is attributed to the azimuthal drift between dust and gas, unlike the classical SI, which is driven by radial drift. This suggests that the SI can remain effective inside dust-trapping pressure bumps in accreting disks. When a live vertical field is considered, we find the magneto-rotational instability can be damped by dust feedback, while the classic SI can be stabilized by magnetic perturbations. We also find that Alfvén waves can be destabilized by dust–gas drift, but this instability requires nearly ideal conditions. We discuss the possible implications of these results for dust dynamics and planetesimal formation in PPDs.

Rate of formation of caustics in heavy particles advected by turbulence.

The rate of collision and the relative velocities of the colliding particles in turbulent flows are a crucial part of several natural phenomena, e.g. rain formation in warm clouds and planetesimal formation in protoplanetary discs. The particles are often modelled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three-dimensional turbulent flows, we calculate the rate of formation of caustics, [Formula: see text] as a function of the Stokes number ([Formula: see text]). The best approximation to our data is [Formula: see text], in the limit [Formula: see text] where [Formula: see text] is a non-universal constant. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Dust Settling and Clumping in MRI-turbulent Outer Protoplanetary Disks

Abstract Planetesimal formation is a crucial yet poorly understood process in planet formation. It is widely believed that planetesimal formation is the outcome of dust clumping by the streaming instability (SI). However, recent analytical and numerical studies have shown that the SI can be damped or suppressed by external turbulence, and at least the outer regions of protoplanetary disks are likely weakly turbulent due to magneto-rotational instability (MRI). We conduct high-resolution local shearing-box simulations of hybrid particle-gas magnetohydrodynamics (MHD), incorporating ambipolar diffusion as the dominant nonideal MHD effect, applicable to outer disk regions. We first show that dust backreaction enhances dust settling toward the midplane by reducing turbulence correlation time. Under modest level of MRI turbulence, we find that dust clumping is in fact easier than the conventional SI case, in the sense that the threshold of solid abundance for clumping is lower. The key to dust clumping includes dust backreaction and the presence of local pressure maxima, which in our work is formed by the MRI zonal flows overcoming background pressure gradient. Overall, our results support planetesimal formation in the MRI-turbulent outer protoplanetary disks, especially in ring-like substructures.

Formation and early evolution of protoplanetary disk determined by the interaction between magnetic field and weakly ionized plasma

Formation and early evolution of protoplanetary disk determined by the interaction between magnetic field and weakly ionized plasma

Kepler-223 resonance holds information about turbulence during the gas-disk phase

Context. Planet formation remains an open field of research, and many fundamental physical processes regarding planetary formation in protoplanetary disks are still imperfectly understood. It remains to be investigated how different conditions in these protoplanetary disks affect the emergence of different types of observed systems. An elusive phenomenon is the turbulence in these disks. Observations are available of planetary systems and of some protoplanetary disks, which can serve as a starting point for these investigations. The detected systems reveal different architectures of planets. One particularly interesting case to consider is the Kepler-223 system, which contains a rare configuration of four planets in a resonance chain. This implies a certain migration history. Aims. We aim to use the orbital configuration of the Kepler-223 planets to constrain the parameters of the protoplanetary disk that allow the formation of a chain of mean-motion resonances that resembles the resonances of Kepler-223. We primarily investigate the disk viscosity and surface density. Methods. We used the swift_symba N-body integrator with additional dissipative forces to mimic planet-disk interactions. Results. We constrained the surface densities and viscosities that allow the formation of a resonant chain like that of Kepler-223. We find that surface densities of up to a few minimum mass solar nebula surface densities and disk viscosity parameters α of a few × 10−3 up to × 10−2 are most successful at reproducing the architecture of this particular planetary system. We describe the connection of these two quantities with each other, considering the success of reproducing the chain. We find that higher disk surface densities in turn require lower viscosities to build the chain. Conclusions. Our results show that well-characterized observed planetary systems hold information about their formation conditions in the protoplanetary disks and that it is possible to extract this information, namely the initial disk surface density and viscosity. This helps to constrain planet formation.

Universal Protoplanetary Disk Size under Complete Nonideal Magnetohydrodynamics: The Interplay between Ion-neutral Friction, Hall Effect, and Ohmic Dissipation

Abstract The role of nonideal magnetohydrodynamics has been proven critical during the formation of protoplanetary disks, particularly in regulating their sizes. We provide a simple model to predict the disk size under the interplay among ambipolar diffusion, the Hall effect, and ohmic dissipation. The model predicts a small disk size of around 20 au that depends only sublinearly on disk parameters, for a wide range of initial conditions of subsolar mass and moderate magnetization. It is able to explain phenomena manifested in existing numerical simulations, including the bimodal disk behavior under parallel and antiparallel alignment between the rotation and magnetic field. In the parallel configuration, the disk size decreases and eventually disappears. In the antiparallel configuration, the disk has an outer partition (or pseudodisk), which is flat, shrinking, and short-lived, as well as an inner partition, which grows slowly with mass and is long-lived. Even with significant initial magnetization, the vertical field in the disk can only dominate at the early stage when the mass is low, and the toroidal field eventually dominates in all disks.