Non-ideal Magnetohydrodynamics Research Articles

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.

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 ($ sim 10$s\,au) and high sensitivity, which has resulted in only a handful of MHD disk wind candidates to date. In this work we present high angular resolution sim 30$\,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 sim 0.9$\,mm) has a radius of sim 23$\,au. Rotating infall signatures in H13CO$^+$ indicate a central mass of $0.4 0.1$\,M$_ and a centrifugal radius similar to the dust disk radius. Above the disk, we identify rotation signatures in the outflow traced by H13CN, CH$_3$OH, and SO lines and find a kinematical structure consistent with theoretical predictions for MHD disk winds. This is the first detection of an MHD disk wind candidate in H13CN and CH$_3$OH. The wind launching region estimated from cold MHD wind theory extends out to the disk edge. The magnetic lever arm parameter would be $ phi 1.7$, in line with recent non-ideal MHD disk models. The estimated mass-loss rate is approximately four times the protostellar accretion rate ($ M acc M_ odot /yr$) and suggests that the rotating wind could carry enough angular momentum to drive disk accretion.

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

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. 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. We postprocessed $2 $ 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. 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 (iCOMs) such as methyl formate, acetaldehyde, and formamide are formed during the warm-up process. Grain size in the hot corino $(n_ H )$ increases forty-fold during the last 30 kyr, with negligible effects on its chemical composition. At moderate densities $(10^ <n_ H )$ and cool temperatures $15<T<50$ K, increasing grain sizes delay molecular depletion. At low densities $(n_ H )$, 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. 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.

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.

Star-forming environments in smoothed particle magnetohydrodynamics simulations II: Re-simulating isolated clumps to determine equivalence of extracted clumps and parent simulations

Abstract What is the numerical reproducibility of a stellar system (including its discs) when evolving only a sub-set of (partially-evolved) smoothed particle hydrodynamics (SPH) particles? To investigate this, we modelled the evolution of 29 star forming clumps that were extracted from our previous simulations that investigated the formation and early evolution of low-mass star clusters. These clumps were evolved using a three-dimensional smoothed particle radiation magnetohydrodynamics code, where we included or excluded non-ideal magnetohydrodynamics to match the cluster simulation. While star formation proceeded as expected, we were unable to identically reproduce any of the systems present at the end of the cluster simulations. However, the final distributions of stellar mass, stellar system mass, disc mass, and disc radii were reproduced statistically; unfortunately, the distribution of average magnetic field strengths in the discs was not reproduced statistically, but this may be a result of our updated algorithms governing the evolution of the magnetic field. Therefore, given that our clumps yield stellar masses that are statistically similar to those in the original low-mass star clusters, we have demonstrated that we can statistically reproduce systems (aside from their magnetic field strength) by evolving a subset of SPH particles. Therefore, clumps such as these can be used as initial conditions to investigate the formation of isolated stars from less-contrived initial environments.

Generalized χ and η Cross-Helicities in Non-Ideal Magnetohydrodynamics

We study the generalized χ and η cross-helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). χ and η, the additional label translation symmetry group, are used to generalize cross-helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behavior in non-ideal MHD, we calculate the time derivative of both helicities using non-ideal MHD equations in which viscosity, finite resistivity, and heat conduction are taken into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that χ and η cross-helicities are not strict constants of motion in non-ideal MHD and show a rate of dissipation that is comparable to the dissipation of other topological constants of motion.

Generalized cross-helicity in non-ideal magnetohydrodynamics

The objective of the present paper is to investigate the constancy of the topological invariant, denoted the non-barotropic generalized cross-helicity in the case of non-ideal magnetohydrodynamics (MHD). Existing work considers only ideal barotropic MHD and ideal non-barotropic MHD. Here, we consider dissipative processes in the form of thermal conduction, finite electrical conductivity and viscosity and the effect of these processes on the cross-helicity conservation. An analytical approach has been adopted to obtain the mathematical expressions for the time derivative of the cross-helicity. Obtained results show that the generalized cross-helicity is not conserved in the non-ideal MHD limit and indicate which processes affect the helicity and which do not. Furthermore, we indicate the configurations in which this topological constant is conserved despite the dissipative processes. Some examples and applications are also given.

Non-ideal magnetohydrodynamics on a moving mesh II: Hall effect

ABSTRACT In this work, we extend the non-ideal magnetohydrodynamics (MHD) solver in the moving-mesh code arepo to include the Hall effect. The core of our algorithm is based on an estimation of the magnetic field gradients by a least-squares reconstruction on the unstructured mesh, which we also used in the companion paper for Ohmic and ambipolar diffusion. In an extensive study of simulations of a magnetic shock, we show that without additional magnetic diffusion our algorithm for the Hall effect becomes unstable at high resolution. We can however stabilize it by artificially increasing the Ohmic resistivity, ηOR, so that it satisfies the condition ηOR ≥ ηH/5, where ηH is the Hall diffusion coefficient. Adopting this solution, we find second-order convergence for the C-shock and are also able to accurately reproduce the dispersion relation of the whistler waves. As a first application of the new scheme, we simulate the collapse of a magnetized cloud with constant Hall parameter ηH and show that, depending on the sign of ηH, the magnetic braking can either be weakened or strengthened by the Hall effect. The quasi-Lagrangian nature of the moving-mesh method used here automatically increases the resolution in the forming core, making it well suited for more realistic studies with non-constant magnetic diffusivities in the future.

Non-ideal magnetohydrodynamics on a moving mesh I: ohmic and ambipolar diffusion

ABSTRACT Especially in cold and high-density regions, the assumptions of ideal magnetohydrodynamics (MHD) can break down, making first order non-ideal terms such as ohmic and ambipolar diffusion as well as the Hall effect important. In this study, we present a new numerical scheme for the first two resistive terms, which we implement in the moving-mesh code arepo using the single-fluid approximation combined with a new gradient estimation technique based on a least-squares fit per interface. Through various test calculations including the diffusion of a magnetic peak, the structure of a magnetic C-shock, and the damping of an Alfvén wave, we show that we can achieve an accuracy comparable to the state-of-the-art code athena++ . We apply the scheme to the linear growth of the magnetorotational instability and find good agreement with the analytical growth rates. By simulating the collapse of a magnetized cloud with constant magnetic diffusion, we show that the new scheme is stable even for large contrasts in the spatial resolution. Thanks to the Lagrangian nature of the moving mesh method the new scheme is thus well suited for intended future applications where a high resolution in the dense cores of collapsing protostellar clouds needs to be achieved. In a forthcoming work, we will extend the scheme to include the Hall effect.

Simulations of dynamo action in slowly rotating M dwarfs: Dependence on dimensionless parameters

Aims. The aim of this study is to explore the magnetic and flow properties of fully convective M dwarfs as a function of rotation period Prot and magnetic Reynolds ReM and Prandlt numbers PrM. Methods. We performed three-dimensional simulations of fully convective stars using a star-in-a-box set-up. This set-up allows global dynamo simulations in a sphere embedded in a Cartesian cube. The equations of non-ideal magnetohydrodynamics were solved with the PENCIL CODE. We used the stellar parameters of an M5 dwarf with 0.21 M⊙ at three rotation rates corresponding to rotation periods (Prot) of 43, 61, and 90 days, and varied the magnetic Prandtl number in the range from 0.1 to 10. Results. We found systematic differences in the behaviour of the large-scale magnetic field as functions of rotation and PrM. For the simulations with Prot = 43 days and PrM ≤ 2, we found cyclic large-scale magnetic fields. For PrM > 2, the cycles vanish and the field shows irregular reversals. In the simulations with Prot = 61 days for PrM ≤ 2, the cycles are less clear and the reversal are less periodic. In the higher PrM cases, the axisymmetric mean field shows irregular variations. For the slowest rotation case with Prot = 90 days, the field has an important dipolar component for PrM ≤ 5. For the highest PrM the large-scale magnetic field is predominantly irregular at mid-latitudes, with quasi-stationary fields near the poles. For the simulations with cycles, the cycle period length slightly increases with increasing ReM.

Magnetorotational instability in a swirling partially ionized gas

ABSTRACT The magnetorotational instability (MRI) has been proposed as the method of angular momentum transport that enables accretion in astrophysical discs. However, for weakly ionized discs, such as protoplanetary discs, it remains unclear whether the combined non-ideal magnetohydrodynamic (MHD) effects of Ohmic resistivity, ambipolar diffusion, and the Hall effect make these discs MRI stable. While much effort has been made to simulate non-ideal MHD MRI, these simulations make simplifying assumptions and are not always in agreement with each other. Furthermore, it is difficult to directly observe the MRI astrophysically because it occurs on small scales. Here, we propose the concept of a swirling gas experiment of weakly ionized argon gas between two concentric cylinders threaded with an axial magnetic field that can be used to study non-ideal MHD MRI. For our proposed experiment, we derive the hydrodynamic equilibrium flow and a dispersion relation for MRI that includes the three non-ideal effects. We solve this dispersion relation numerically for the parameters of our proposed experiment. We find it should be possible to produce a non-ideal MRI in such an experiment because of the Hall effect, which increases the MRI growth rate when the vertical magnetic field is anti-aligned with the rotation axis. As a proof of concept, we also present experimental results for a hydrodynamic flow in an unmagnetized prototype. We find that our prototype has a small, but non-negligible, α-parameter that could serve as a baseline for comparison to our proposed magnetized experiment, which could be subject to additional turbulence from the MRI.

On the importance of disc chemistry in the formation of protoplanetary disc rings

ABSTRACT Radial substructures have now been observed in a wide range of protoplanetary discs (PPDs), from young to old systems; however, their formation is still an area of vigorous debate. Recent magnetohydrodynamic (MHD) simulations have shown that rings and gaps can form naturally in PPDs when non-ideal MHD effects are included. However, these simulations employ ad hoc approximations to the magnitudes of the magnetic diffusivities in order to facilitate ring growth. We replace the parametrization of these terms with a simple chemical network and grain distribution model to calculate the non-ideal effects in a more self-consistent way. We use a range of grain distributions to simulate grain formation for different disc conditions. Including ambipolar diffusion, we find that large grain populations (>1 $\mu$m), and those including a population of very small polyaromatic hydrocarbons (PAHs) facilitate the growth of periodic, stable rings, while intermediate-sized grains suppress ring formation. Including Ohmic diffusion removes the positive influence of PAHs, with only large grain populations still producing periodic ring and gap structures. These results relate closely to the degree of coupling between the magnetic field and the neutral disc material, quantified by the non-dimensional Elsasser number Λ (the ratio of magnetic forces to Coriolis force). For both the ambipolar-only and ambipolar-ohmic cases, if the total Elsasser number is initially of the order of unity along the disc mid-plane, ring and gap structures may develop.

IDEFIX: A versatile performance-portable Godunov code for astrophysical flows

Context. The exascale super-computers becoming available rely on hybrid energy-efficient architectures that involve an accelerator such as a graphics processing unit (GPU). Leveraging the computational power of these machines often means a significant rewrite of the numerical tools each time a new architecture becomes available. Aims. We present IDEFIX, a new code for astrophysical flows that relies on the KOKKOS meta-programming library to guarantee performance portability on a wide variety of architectures while keeping the code as simple as possible to the user. Methods. IDEFIX is based on a Godunov finite-volume method that solves the nonrelativistic hydrodynamical (HD) and magnetohy-drodynamical (MHD) equations on various grid geometries. IDEFIX includes a large choice of solvers and several additional modules (constrained transport, orbital advection, nonideal MHD), allowing users to address complex astrophysical problems. Results. IDEFIX has been successfully tested on Intel and AMD CPUs (up to 131 072 CPU cores on Irene-Rome at TGCC) as well as NVidia and AMD GPUs (up to 1024 GPUs on Adastra at CINES). IDEFIX achieves more than 108 cell s−1 in MHD on a single NVidia V100 GPU and 3 × 1011 cell s−1 on 256 Adastra nodes (1024 GPUs) with 95% parallelization efficiency (compared to single node). For the same problem, IDEFIX is up to six times more energy efficient on GPUs compared to Intel Cascade Lake CPUs. Conclusions. IDEFIX is now a mature exascale-ready open-source code that can be used on a large variety of astrophysical and fluid dynamics applications.

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.

Dust dynamics in current sheets within protoplanetary disks

Context.Chondrules originate from the reprocessing of dust grains. They are key building blocks of telluric planets, yet their formation, which must happen in strongly localized regions of high temperature, remains poorly understood.Aims.We examine the dust spatial distribution near regions of strong local heating produced by current sheets, as a step toward exploring a potential path for chondrule formation. We further aim to investigate current sheet formation under various conditions in protoplanetary disks in the presence of ambipolar diffusion and Ohmic resistivity and the effect of current sheet morphology on dust dynamics in their vicinity.Methods.We used the RAMSES code including modules for nonideal magnetohydrodynamics and the solution of the dynamics of multiple sizes of dust grains to compute unstratified shearing box simulations of current sheet formation. Through seven models, we investigated the effect of the ambipolar diffusion and Ohmic resistivity strength, the initial density, and magnetic field, as well as the resolution and box size.Results.We find that current sheets form in all our models, with typical widths of 10−3–10−2AU, and that strong dust fraction variations occur for millimeter-sized grains. These variations are typically of an order of magnitude and up to two orders of magnitude for the most favorable cases. We also show that the box size and resolution has a strong impact on the current sheet distribution and intensity.Conclusions.The formation of current sheets that can intensely heat their surroundings near strong dynamical dust fraction variations could have important implications for chondrule formation, as it appears likely to happen in regions with a large dust fraction.

Non-ideal MHD growth of current interchange tearing modes at plasma edge and response to externally-imposed flow

Current interchange tearing modes (CITMs) have been proposed to explain an intermittent eruption of electric current toward a divertor at an edge region of a tokamak device. Extended magnetohydrodynamic (MHD) simulations combined with the Scrape-Off-Layer diffusion model, which has been developed by the authors [Miura et al., Phys. Plasmas 24, 092111 (2017)], are carried out in order to study the growth of a CITM under influences of two-fluid and gyro-viscous effects, or non-ideal MHD effects. Numerical simulations both with and without an externally imposed azimuthal flow show that the growth of a CITM is observed for a relatively small flow velocity, and that a CITM can be a candidate mechanism for the intermittent eruption of the current in a tokamak, whether the growth is under influences of non-ideal MHD effects or not. The growth can be suppressed when an externally imposed azimuthal flow is sufficiently large to cause a finite radial displacement because such a displacement prevents a transition from an interchange to a tearing mode that is the key process of a CITM. Furthermore, it is also found that a stripe pattern similar to so-called streamers is formed in the course of the CITM growth. The basic nature of this streamer-like structure is also presented.

Smoothed particle hydrodynamics method for pinch plasma simulation with non-ideal MHD model

When plasma is compressed by magnetic forces, a pinch phenomenon is observed. Pinch plasma has received significant attention as an efficient source of radiation and a way for high-density plasma physics analysis. In this study, a non-ideal magnetohydrodynamics (MHD) model is applied to a smoothed particle hydrodynamics (SPH) framework to analyze pinch plasmas whose local resistivity varies with temperature and pressure. The proposed SPH model incorporates several numerical treatments, such as a correction term to satisfy the ∇·B constraint and some artificial dissipation terms to govern the shock wave. Moreover, it includes the evaluation of a novel SPH discretization for non-ideal MHD terms, including current density calculations. Furthermore, the proposed model is validated with three benchmark cases: (1) Brio and Wu shock tube (ideal MHD), (2) resistive MHD shock simulation, and (3) magnetized Noh Z-pinch problem. The simulation results are compared with the results of some reference Eulerian MHD simulations and analytical solutions. The simulations agree well with the reference data, and the introduced numerical treatments are effective. Finally, X-pinch simulations are performed using the proposed model. The simulations well produce the micro Z-pinch and jet shapes, which are important X-pinch features. Overall, the proposed SPH model has extensive potential for studying the complex pinch plasma phenomena.