Non-ideal Magnetohydrodynamics Research Articles

Rossby wave instability in magnetized protoplanetary disks. I. azimuthal or vertical B-fields

Abstract Rossby wave instability (RWI) is considered the underlying mechanism to crescent-shaped azimuthal asymmetries, discovered in (sub-)millimeter dust continuum of many protoplanetary disks. Previous works on linear theory were conducted in the hydrodynamic limit. Nevertheless, protoplanetary disks are likely magnetized and weakly ionized. We examine the influence of magnetic fields and non-ideal magnetohydrodynamic (MHD) effects - namely, Ohmic resistivity, Hall drift, and ambipolar diffusion - on the RWI unstable modes. We perform radially global linear analyses, employing constant azimuthal (Bφ) or vertical (Bz) background magnetic fields. It is found that, in the ideal MHD regime, magnetism can either enhance or diminish RWI growth. Strong non-ideal MHD effects cause RWI growth rates to recover hydrodynamic results. The sign of Hall Elsässer number slightly complicates the results. Vertical wavenumbers can diminish growth rates.

3D Gap opening in non-ideal MHD protoplanetary disks: Asymmetric accretion, meridional vortices, and observational signatures

Abstract Recent high-angular resolution ALMA observations have revealed rich information about protoplanetary disks, including ubiquitous substructures and three-dimensional gas kinematics at different emission layers. One interpretation of these observations is embedded planets. Previous 3-D planet-disk interaction studies are either based on viscous simulations, or non-ideal magnetohydrodynamics (MHD) simulations with simple prescribed magnetic diffusivities. This study investigates the dynamics of gap formation in 3-D non-ideal MHD disks using non-ideal MHD coefficients from the look-up table that is self-consistently calculated based on the thermo-chemical code. We find a concentration of the poloidal magnetic flux in the planet-opened gap (in agreement with previous work) and enhanced field-matter coupling due to gas depletion, which together enable efficient magnetic braking of the gap material, driving a fast accretion layer significantly displaced from the disk midplane. The fast accretion helps deplete the gap further and is expected to negatively impact the planet growth. It also affects the corotation torque by shrinking the region of horseshoe orbits on the trailing side of the planet. Together with the magnetically driven disk wind, the fast accretion layer generates a large, persistent meridional vortex in the gap, which breaks the mirror symmetry of gas kinematics between the top and bottom disk surfaces. Finally, by studying the kinematics at the emission surfaces, we discuss the implications of planets in realistic non-ideal MHD disks on kinematics observations.

Sparsified time-dependent Fourier neural operators for fusion simulations

This paper presents a sparsified Fourier neural operator for coupled time-dependent partial differential equations (ST-FNO) as an efficient machine learning surrogate for fluid and particle-based fusion codes such as NIMROD (Non-Ideal Magnetohydrodynamics with Rotation - Open Discussion) and GTC (Gyrokinetic Toroidal Code). ST-FNO leverages the structures in the governing equations and utilizes neural operators to represent Green's function-like numerical operators in the corresponding numerical solvers. Once trained, ST-FNO can rapidly and accurately predict dynamics in fusion devices compared with first-principle numerical algorithms. In general, ST-FNO represents an efficient and accurate machine learning surrogate for numerical simulators for multi-variable nonlinear time-dependent partial differential equations, with the proposed architectures and loss functions. The efficacy of ST-FNO has been demonstrated using quiescent H-mode simulation data from NIMROD and kink-mode simulation data from GTC. The ST-FNO H-mode results show orders of magnitude reduction in memory and central processing unit usage in comparison with the numerical solvers in NIMROD when computing fields over a selected poloidal plane. The ST-FNO kink-mode results achieve a factor of 2 reduction in the number of parameters compared to baseline FNO models without accuracy loss.

Protostellar Disk Formation Regimes: Angular Momentum Conservation versus Magnetic Braking

Protostellar disks around young protostars exhibit diverse properties, with their radii ranging from less than ten to several hundred astronomical units. To investigate the mechanisms shaping this disk radius distribution, we compiled a sample of 27 Class 0 and I single protostars with resolved disks and dynamically determined protostellar masses from the literature. Additionally, we derived the radial profile of the rotational-to-gravitational-energy ratio in dense cores from the observed specific angular momentum profiles in the literature. Using these observed protostellar masses and rotational energy profile, we computed theoretical disk radii from the hydrodynamic and nonideal magnetohydrodynamic (MHD) models in Y.-N. Lee et al. and generated synthetic samples to compare with the observations. In our theoretical model, the disk radii are determined by hydrodynamics when the central protostar+disk mass is low. After the protostars and disks grow and exceed certain masses, the disk radii become regulated by magnetic braking and nonideal MHD effects. The synthetic disk radius distribution from this model matches well with the observations. This result suggests that hydrodynamics and nonideal MHD can be dominant in different mass regimes (or evolutionary stages), depending on the rotational energy and protostar+disk mass. This model naturally explains the rarity of large (>100 au) disks and the presence of very small (<10 au) disks. It also predicts that the majority of protostellar disks have radii of a few tens of astronomical units, as observed.

Turbulent Diffuse Molecular Media with Nonideal Magnetohydrodynamics and Consistent Thermochemistry: Numerical Simulations and Dynamic Characteristics

Turbulent diffuse molecular clouds can exhibit complicated morphologies caused by the interactions among radiation, chemistry, fluids, and fields. We performed full 3D simulations for turbulent diffuse molecular interstellar media, featuring time-dependent nonequilibrium thermochemistry coevolved with magnetohydrodynamics (MHD). Simulation results exhibit the relative abundances of key chemical species (e.g., C, CO, OH) vary by more than one order of magnitude for the “premature” epoch of chemical evolution (t ≲ 2 × 105 yr). Various simulations are also conducted to study the impacts of physical parameters. Nonideal MHD effects are essential in shaping the behavior of gases, and strong magnetic fields (∼10 μG) tend to inhibit vigorous compressions and thus reduce the fraction of warm gases (T ≳ 102 K). Thermodynamical and chemical conditions of the gas are sensitive to modulation by dynamic conditions, especially the energy injection by turbulence. Chemical features, including ionization (cosmic ray and diffuse interstellar radiation), would not directly affect the turbulence power spectra. Nonetheless, their effects are prominent in the distribution profiles of temperatures and gas densities. Comprehensive observations are necessary and useful to eliminate the degeneracies of physical parameters and constrain the properties of diffuse molecular clouds with confidence.

Discs are born eccentric

Context. Recent observations have begun probing the early phases of disc formation, but little data yet exists on disc structure and morphology of Class 0 objects. Using simulations, we are able to lay out predictions of disc morphologies expected in future surveys of young discs. Based on detailed simulations of ab initio star formation by core collapse, we predict that early discs must be eccentric. Aims. In this Letter, we study the morphology and, in particular, the eccentricity of discs formed in non-ideal magnetohydrodynamic (MHD) collapse simulations. We attempt to show that discs formed by cloud collapse are likely to be eccentric. Methods. We ran non-ideal MHD collapse simulations in the adaptive mesh refinement code RAMSES with radiative transfer. We used state-of-the-art analysis methods to measure the disc eccentricity. Results. We find that despite no asymmetry in the initial conditions, the discs formed are eccentric, with eccentricities on the order of 0.1. Conclusions. These results may have important implications for protoplanetary disc dynamics and planet formation. The presence of eccentricity in young discs that is not seen at later stages of disc evolution is in tension with current viscous eccentricity damping models. This implies that there may be an as-yet undiscovered circularisation mechanism in circumstellar discs.

Nonideal Magnetohydrodynamic Instabilities in Protoplanetary Disks: Vertical Modes and Reflection Asymmetry

Magnetized disk winds and wind-driven accretion are an essential and intensively studied dispersion mechanism of protoplanetary disks (PPDs). However, the stability of these mechanisms has yet to be adequately examined. This paper employs semi-analytic linear perturbation theories under nonideal magnetohydrodynamics, focusing on disk models whose magnetic diffusivities vary by a few orders of magnitude from the disk midplane to its surface. Linear modes are distinguished by their symmetry with respect to the midplane. These modes have qualitatively different growth rates: symmetric modes almost always decay, while at least one antisymmetric mode always has a positive growth rate. This growth rate decreases faster than the Keplerian angular velocity with cylindrical radius R in the disk and scales steeper than R −5/2 in the fiducial disk model. The growth of antisymmetric modes breaks the reflection symmetry across the disk equatorial plane, and may occur even in the absence of the Hall effect. In the disk regions where fully developed antisymmetric modes occur, accretion flows appear only on one side of the disk, while disk winds occur only on the other. This may explain the asymmetry of some observed PPD outflows.

Rossby wave instability and substructure formation in 3D non-ideal MHD wind-launching discs

ABSTRACT Rings and gaps are routinely observed in the dust continuum emission of protoplanetary discs (PPDs). How they form and evolve remains debated. Previous studies have demonstrated the possibility of spontaneous gas rings and gaps formation in wind-launching discs. Here, we show that such gas substructures are unstable to the Rossby wave instability (RWI) through numerical simulations. Specifically, shorter wavelength azimuthal modes develop earlier, and longer wavelength ones dominate later, forming elongated (arc-like) anticyclonic vortices in the rings and (strongly magnetized) cyclonic vortices in the gaps that persist until the end of the simulation. Highly elongated vortices with aspect ratios of 10 or more are found to decay with time in our non-ideal magnetohydrodynamic (MHD) simulation, in contrast with the hydro case. This difference could be caused by magnetically induced motions, particularly strong meridional circulations with large values of the azimuthal component of the vorticity, which may be incompatible with the columnar structure preferred by vortices. The cyclonic and anticyclonic RWI vortices saturate at moderate levels, modifying but not destroying the rings and gaps in the radial gas distribution of the disc. In particular, they do not shut-off the poloidal magnetic flux accumulation in low-density regions and the characteristic meridional flow patterns that are crucial to the ring and gap formation in wind-launching discs. Nevertheless, the RWI and their associated vortices open up the possibility of producing non-axisymmetric dust features observed in a small fraction of PPDs through non-ideal MHD, although detailed dust treatment is needed to explore this possibility.

On the existence of simple waves for two-dimensional non-ideal magneto-hydrodynamics

Abstract In this article, a method called characteristic decomposition is used to show the presence of simple waves for the two-dimensional compressible flow in a non-ideal magneto-hydrodynamics system. Here, a steady and pseudo-steady state magneto-hydrodynamics system is considered, and we provide a characteristic decomposition of the flow equations in both systems. This decomposition ensures the presence of a simple wave adjacent to a region of constant state for the system under consideration. Further, this result is extended as an application of the characteristic decomposition in a pseudo-steady state, and we prove the existence of a simple wave in a full magneto-hydrodynamics system by taking the vorticity and the entropy to be constant along the pseudo-flow characteristics. These results extend the fundamental theorem proposed by Courant and Friedrichs for a reducible system (R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, New York, Interscience Publishers, Inc., 1948, p. 464). A motivational work was carried out for an ideal gas by Li et al. (“Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations,” Commun. Math. Phys. Math. Phys., vol. 267, no. 1, pp. 1–12, 2006) and for a non-ideal gas by Zafar and Sharma (“Characteristic decomposition of compressible Euler equations for a non-ideal gas in two-dimensions,” J. Math. Phys., vol. 55, no. 9, pp. 093103–093112, 2014], [M. Zafar, “A note on characteristic decomposition for two-dimensional euler system in van der waals fluids,” Int. J. Non-Linear Mech., vol. 86, pp. 33–36, 2016].

Effect of Magnetic Diffusion in the Chromosphere on the Solar Wind

We investigate nonideal magnetohydrodynamical (MHD) effects in the chromosphere on the solar wind by performing MHD simulations for Alfvén-wave-driven winds, explicitly including ohmic and ambipolar diffusion. We find that MHD waves are significantly damped in the chromosphere by ambipolar diffusion so that the Alfvénic Poynting flux that reaches the corona is substantially reduced. As a result, the coronal temperature and the mass-loss rate of the solar wind are considerably reduced, compared with those obtained from an ideal MHD case, which is indicative of the great importance of the nonideal MHD effects in the solar atmosphere. However, the temperature and the mass-loss rate are recovered by a small increase in the convection-originated velocity perturbation at the photosphere because of the sensitive dependence of the ambipolar diffusion and reflection of Alfvén waves on the physical properties of the chromosphere. We also find that density perturbations in the corona are reduced by the ambipolar diffusion of Alfvén waves in the chromosphere because the nonlinear generation of compressible perturbations is suppressed.

Cloud Dissipation and Disk Wind in the Late Phase of Star Formation

We perform a long-term simulation of star and disk formation using three-dimensional nonideal magnetohydrodynamics. The simulation starts from a prestellar cloud and proceeds through the long-term evolution of the circumstellar disk until ∼1.5 × 105 yr after protostar formation. The disk has size ≲50 au and little substructure in the main accretion phase because of the action of magnetic braking and the magnetically driven outflow to remove angular momentum. The main accretion phase ends when the outflow breaks out of the cloud, causing the envelope mass to decrease rapidly. The outflow subsequently weakens as the mass accretion rate also weakens. While the envelope-to-disk accretion continues, the disk grows gradually and develops transient spiral structures, due to gravitational instability. When the envelope-to-disk accretion ends, the disk becomes stable and reaches a size ≳300 au. In addition, about 30% of the initial cloud mass has been ejected by the outflow. A significant finding of this work is that after the envelope dissipates a revitalization of the wind occurs, and there is mass ejection from the disk surface that lasts until the end of the simulation. This mass ejection (or disk wind) is generated because the magnetic pressure significantly dominates both the ram pressure and thermal pressure above and below the disk at this stage. Using the angular momentum flux and mass-loss rate estimated from the disk wind, the disk dissipation timescale is estimated to be ∼106 yr.

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.

ALMA view of the L1448-mm protostellar system on disk scales: CH3OH and H13CN as new disk wind tracers

Protostellar disks are known to accrete; however, the exact mechanism that extracts the angular momentum and drives accretion in the low-ionization “dead” region of the disk is under debate. In recent years, magnetohydrodynamic (MHD) disk winds have become a popular solution. Even so, observations of these winds require both high spatial resolution (~10 s au) and high sensitivity, which has resulted in only a handful of MHD disk wind candidates to date. In this work we present high angular resolution (~30 au) ALMA observations of the emblematic L1448-mm protostellar system and find suggestive evidence for an MHD disk wind. The disk seen in dust continuum (~0.9 mm) has a radius of ~23 au. Rotating infall signatures in H13CO+ indicate a central mass of 0.4 ± 0.1 M⊙ and a centrifugal radius similar to the dust disk radius. Above the disk, we identify rotation signatures in the outflow traced by H13CN, CH3OH, and SO lines and find a kinematical structure consistent with theoretical predictions for MHD disk winds. This is the first detection of an MHD disk wind candidate in H13CN and CH3OH. The wind launching region estimated from cold MHD wind theory extends out to the disk edge. The magnetic lever arm parameter would be λϕ ≃ 1.7, in line with recent non-ideal MHD disk models. The estimated mass-loss rate is approximately four times the protostellar accretion rate (Ṁacc ≃ 2 × 10−6M⊙ yr−1) and suggests that the rotating wind could carry enough angular momentum to drive disk accretion.

The First Estimation of the Ambipolar Diffusivity Coefficient from Multi-scale Observations of the Class 0/I Protostar, HOPS-370

Protostars are born in magnetized environments. As a consequence, the formation of protostellar disks can be suppressed by the magnetic field, efficiently removing the angular momentum of the infalling material. Nonideal MHD effects are proposed as one way to allow protostellar disks to form. Thus, it is important to understand their contributions to observations of protostellar systems. We derive an analytical equation to estimate the ambipolar diffusivity coefficient at the edge of the protostellar disk in the Class 0/I protostar, HOPS-370, for the first time, under the assumption that the disk radius is set by ambipolar diffusion. Using previous results of the protostellar mass, disk mass, disk radius, density and temperature profiles, and magnetic field strength, we estimate the ambipolar diffusivity coefficient to be 1.7−1.4+1.5×1019cm2s−1 . We quantify the contribution of ambipolar diffusion by estimating its dimensionless Elsässer number to be ∼1.7−1.0+1.0 , indicating its dynamical importance in this region. We compare our results to those of the chemical calculations of the ambipolar diffusivity coefficient using the Non-Ideal Magnetohydrodynamics Coefficients and Ionization Library, which are consistent with our results. In addition, we compare our derived ambipolar diffusivity coefficient to the diffusivity coefficients for ohmic dissipation and the Hall effect, and find ambipolar diffusion is dominant in our density regime. These results demonstrate a new methodology to understand nonideal MHD effects in observations of protostellar disks. More detailed modeling of the magnetic field, envelope, and microphysics, along with a larger sample of protostellar systems, is needed to further understand the contributions of nonideal MHD.

Grain growth and its chemical impact in the first hydrostatic core phase

Context. The first hydrostatic core (FHSC) phase is a brief stage in the protostellar evolution that is difficult to detect. Its chemical composition determine that of later evolutionary stages. Numerical simulations are the tool of choice to study these objects. Aims. Our goal is to characterize the chemical evolution of gas and dust during the formation of the FHSC. Moreover, we are interested in analyzing, for the first time with 3D magnetohydrodynamic (MHD) simulations, the role of grain growth in its chemistry. Methods. We postprocessed 2 × 105 tracer particles from a RAMSES non-ideal MHD simulation using the codes NAUTILUS and SHARK to follow the chemistry and grain growth throughout the simulation. Results. Gas-phase abundances of most of the C, O, N, and S reservoirs in the hot corino at the end of the simulation match the ice-phase abundances from the prestellar phase. Interstellar complex organic molecules such as methyl formate, acetaldehyde, and formamide are formed during the warm-up process. Grain size in the hot corino (nH &gt; 1011 cm−3) increases forty-fold during the last 30 kyr, with negligible effects on its chemical composition. At moderate densities (1010 &lt; nH &lt; 1011 cm−3) and cool temperatures 15 &lt; T &lt; 50 K, increasing grain sizes delay molecular depletion. At low densities (nH ~ 107 cm−3), grains do not grow significantly. To assess the need to perform chemo-MHD calculations, we compared our results with a two-step model that reproduces well the abundances of C and O reservoirs, but not the N and S reservoirs. Conclusions. The chemical composition of the FHSC is heavily determined by that of the parent prestellar core. Chemo-MHD computations are needed for an accurate prediction of the abundances of the main N and S elemental reservoirs. The impact of grain growth in moderately dense areas delaying depletion permits the use of abundance ratios as grain growth proxies.

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.

Dust Dynamics in Hall-effected Protoplanetary Disks. I. Background Drift Hall Instability

Recent studies have shown that the large-scale gas dynamics of protoplanetary disks (PPDs) are controlled by nonideal magnetohydrodynamics (MHD), but how this influences dust dynamics is not fully understood. To this end, we investigate the stability of dusty, magnetized disks subject to the Hall effect, which applies to planet-forming regions of PPDs. We find a novel background drift Hall instability (BDHI) that may facilitate planetesimal formation in Hall-effected disk regions. Through a combination of linear analysis and nonlinear simulations, we demonstrate the viability and characteristics of BDHI. We find it can potentially dominate over the classical streaming instability (SI) and standard MHD instabilities at low dust-to-gas ratios and weak magnetic fields. We also identify magnetized versions of the classic SI, but these are usually subdominant. We highlight the complex interplay between magnetic fields and dust-gas dynamics in PPDs, underscoring the need to consider nonideal MHD like the Hall effect in the broader narrative of planet formation.

Mancha3D Code: Multipurpose Advanced Nonideal MHD Code for High-Resolution Simulations in Astrophysics

The Mancha3D code is a versatile tool for numerical simulations of magnetohydrodynamic (MHD) processes in solar/stellar atmospheres. The code includes nonideal physics derived from plasma partial ionization, a realistic equation of state and radiative transfer, which allows performing high-quality realistic simulations of magnetoconvection, as well as idealized simulations of particular processes, such as wave propagation, instabilities or energetic events. The paper summarizes the equations and methods used in the Mancha3D (Multifluid (-purpose -physics -dimensional) Advanced Non-ideal MHD Code for High resolution simulations in Astrophysics 3D) code. It also describes its numerical stability and parallel performance and efficiency. The code is based on a finite difference discretization and a memory-saving Runge–Kutta (RK) scheme. It handles nonideal effects through super-time-stepping and Hall diffusion schemes, and takes into account thermal conduction by solving an additional hyperbolic equation for the heat flux. The code is easily configurable to perform different kinds of simulations. Several examples of the code usage are given. It is demonstrated that splitting variables into equilibrium and perturbation parts is essential for simulations of wave propagation in a static background. A perfectly matched layer (PML) boundary condition built into the code greatly facilitates a nonreflective open boundary implementation. Spatial filtering is an important numerical remedy to eliminate grid-size perturbations enhancing the code stability. Parallel performance analysis reveals that the code is strongly memory bound, which is a natural consequence of the numerical techniques used, such as split variables and PML boundary conditions. Both strong and weak scalings show adequate performance up to several thousands of processors (CPUs).

Protoplanetary Disk Size under Nonideal Magnetohydrodynamics: A General Formalism with Inclined Magnetic Field

Many mechanisms have been proposed to alleviate the magnetic catastrophe, which prevents the Keplerian disk from forming inside a collapsing magnetized core. Such propositions include inclined field and nonideal magnetohydrodynamics effects, and have been supported with numerical experiments. Models have been formulated for typical disk sizes when a field threads the rotating disk, parallel to the rotation axis, while observations at the core scales do not seem to show evident correlation between the directions of angular momentum and the magnetic field. In the present study, we propose a new model that considers both vertical and horizontal fields and discuss their effects on the protoplanetary disk size.