Non-ideal MHD Effects Research Articles

Fragmentation of dense rotation-dominated structures fed by collapsing gravo-magneto-sheetlets and origin of misaligned 100 au-scale binaries and multiple systems

ABSTRACT The majority of stars are in binary/multiple systems. How such systems form in turbulent, magnetized cores of molecular clouds in the presence of non-ideal magnetohydrodynamic (MHD) effects remains relatively underexplored. Through athena++-based non-ideal MHD adaptive mesh refinement simulations with ambipolar diffusion, we show that the collapsing protostellar envelope is dominated by dense gravo-magneto-sheetlets, a turbulence-warped version of the classic pseudodisc produced by anisotropic magnetic resistance to the gravitational collapse, in agreement with previous simulations of turbulent, magnetized single-star formation. The sheetlets feed mass, magnetic fields, and angular momentum to a Dense ROtation-Dominated (DROD) structure, which fragments into binary/multiple systems. This DROD fragmentation scenario is a more dynamic variant of the traditional disc fragmentation scenario for binary/multiple formation, with dense spiral filaments created by inhomogeneous feeding from the highly structured larger-scale sheetlets rather than the need for angular momentum transport, which is dominated by magnetic braking. Provided that the local material is sufficiently demagnetized, with a plasma-$\beta$ of 10 or more, collisions between the dense spiralling filaments play a key role in facilitating gravitational collapse and stellar companion formation by pushing the local magnetic Toomre parameter $Q_\mathrm{m}$ below unity. This mechanism can naturally produce in situ misaligned systems on the 100-au scale, often detected with high-resolution Atacama Large Millimeter Array (ALMA) observations. Our simulations also highlight the importance of non-ideal MHD effects, which affect whether fragmentation occurs and, if so, the masses and orbital parameters of the stellar companions formed.

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.

Smoothed particle magnetohydrodynamics

Smoothed particle magnetohydrodynamics has reached a level of maturity that enables the study of a wide range of astrophysical problems. In this review, the numerical details of the modern SPMHD method are described. The three fundamental components of SPMHD are methods to evolve the magnetic field in time, calculate accelerations from the magnetic field, and maintain the divergence-free constraint on the magnetic field (no monopoles). The connection between these three requirements in SPMHD will be highlighted throughout. The focus of this review is on the methods that work well in practice, with discussion on why they work well and other approaches do not. Numerical instabilities will be discussed, as well as strategies to overcome them. The inclusion of non-ideal MHD effects will be presented. A prospective outlook on possible avenues for further improvements will be discussed.

Turbulent Transport of Dust Particles in Protostellar Disks: The Effect of Upstream Diffusion

We study the long-term radial transport of micron to millimeter-size grains in protostellar disks (PSDs) based on diffusion and viscosity coefficients measured from 3D global stratified-disk simulations with a Lagrangian hydrodynamic method. While gas drag tends to transport dust species radially inwards, stochastic diffusion can spread a considerable fraction of dust radially outwards (upstream) depending on the nature of turbulence. In gravitationally unstable disks, we measure a high radial diffusion coefficient D r ∼ H 2Ω with little dependence on altitude. This leads to strong and vertically homogeneous upstream diffusion in early PSDs. In the solar nebula, the robust upstream diffusion of micron to millimeter-size grains not only efficiently transports highly refractory micron-size grains (such as those identified in the samples of comet 81P/Wild 2) from their regions of formation inside the snow line out to the Kuiper Belt, but can also spread millimeter-size calcium–aluminum-rich inclusions formed close to the Sun to distances where they can be assimilated into chondritic meteorites. In disks dominated by magnetorotational instability, the upstream diffusion effect is generally milder, with a separating feature due to diffusion being stronger in the surface layer than in the midplane. This variation becomes much more pronounced if we additionally consider a quiescent midplane with lower turbulence and larger characteristic dust size due to nonideal MHD effects. This segregation scenario helps to account for the dichotomy of the spatial distribution of two dust populations as observed in scattered light and Atacama Large Millimeter/submillimeter Array images.

Effective dust growth in laminar circumplanetary discs with magnetic wind-driven accretion

ABSTRACT It has been considered that large satellites around gas planets form in situ circumplanetary discs (CPDs). However, dust particles supplied into CPDs drift toward the central planets before they grow into satellitesimals, building blocks of the satellites. We investigate the dust growth in laminar CPDs with magnetic wind-driven accretion. In such laminar discs, dust particles can settle on to the mid-plane and grow large by mutual collision more efficient than in classical turbulent CPDs. First, we carry out 3D local MHD simulations of a CPD including all the non-ideal MHD effects (Ohmic resistivity, Hall effect, and ambipolar diffusion). We investigate if the disc accretion can be governed by magnetic wind-driven accretion and how laminar the disc can be, in a situation where the magnetic disc wind can be launched from the disc. Secondly, we model 1D steady CPDs consistent with the results of the MHD simulations and calculate the steady radial distributions of the dust profiles in the modelled discs, taking account of the collisional growth, radial drift, fragmentation, and vertical stirring by the Kelvin–Helmholtz instability. We show that satellitesimals can form in such CPDs if the dust-to-gas mass ratio of the inflow to the discs is larger than 0.02, which is 50 times smaller than the critical value in turbulent CPDs. This condition can be satisfied when enough amount of dust piles up at the gas pressure bump created by the planets. This result shows that satellitesimals would form in laminar CPDs with magnetic wind-driven accretion.

No Impact of Core-scale Magnetic Field, Turbulence, or Velocity Gradient on Sizes of Protostellar Disks in Orion A

Abstract We compared the sizes and fluxes of a sample of protostellar disks in Orion A measured with the Atacama Large Millimeter/submillimeter Array 0.87 mm continuum data from the VLA/ALMA Nascent Disk and Multiplicity survey with the physical properties of their ambient environments on the core scale of 0.6 pc estimated with the Green Bank Ammonia Survey data and the legacy catalog datasets of the polarimeter for the Submillimeter Common-User Bolometer Array. We did not find any significant dependence of the disk radii and continuum fluxes on a single parameter on the core scale, such as nonthermal line width, magnetic field orientation and strength, or magnitude and orientation of the velocity gradient. Among these parameters, we only found a positive correlation between the magnitude of the velocity gradient and the nonthermal line width. Thus, the observed velocity gradients are more likely related to turbulent motion but not large-scale rotation. Our results of no clear dependence of the disk radii on these parameters are more consistent with the expectation from nonideal MHD simulations of disk formation in collapsing cores, where the disk size is self-regulated by magnetic braking and diffusion, compared to other simulations that only include turbulence and/or a magnetic field misaligned with the rotational axis. Therefore, our results could hint that the nonideal MHD effects play a more important role in the disk formation. Nevertheless, we cannot exclude the influences on the observed disk size distribution by dynamical interaction in a stellar cluster or amounts of angular momentum on the core scale, which cannot be probed with the current data.

Slow-Mode Magnetoacoustic Waves in Coronal Loops

Rapidly decaying long-period oscillations often occur in hot coronal loops of active regions associated with small (or micro-) flares. This kind of wave activity was first discovered with the SOHO/SUMER spectrometer from Doppler velocity measurements of hot emission lines, thus also often called "SUMER" oscillations. They were mainly interpreted as global (or fundamental mode) standing slow magnetoacoustic waves. In addition, increasing evidence has suggested that the decaying harmonic type of pulsations detected in light curves of solar and stellar flares are likely caused by standing slow-mode waves. The study of slow magnetoacoustic waves in coronal loops has become a topic of particular interest in connection with coronal seismology. We review recent results from SDO/AIA and Hinode/XRT observations that have detected both standing and reflected intensity oscillations in hot flaring loops showing the physical properties (e.g., oscillation periods, decay times, and triggers) in accord with the SUMER oscillations. We also review recent advances in theory and numerical modeling of slow-mode waves focusing on the wave excitation and damping mechanisms. MHD simulations in 1D, 2D and 3D have been dedicated to understanding the physical conditions for the generation of a reflected propagating or a standing wave by impulsive heating. Various damping mechanisms and their analysis methods are summarized. Calculations based on linear theory suggest that the non-ideal MHD effects such as thermal conduction, compressive viscosity, and optically thin radiation may dominate in damping of slow-mode waves in coronal loops of different physical conditions. Finally, an overview is given of several important seismological applications such as determination of transport coefficients and heating function.

Generalized General Relativistic Magnetohydrodynamic Equations for Plasmas of Active Galactic Nuclei in the Era of the Event Horizon Telescope

Abstract The generalized general relativistic magnetohydrodynamic (generalized GRMHD) equations have been used to study specific relativistic plasma phenomena, such as relativistic magnetic reconnection or wave propagation modified by nonideal MHD effects. However, the Θ term in the generalized Ohm’s law, which expresses the energy exchange between two fluids composing a plasma, has yet to be determined in these equations. In this paper, we determine the Θ term based on the generalized relativistic Ohm’s law itself. This provides closure of the generalized GRMHD equations, yielding a closed system of the equations of relativistic plasma. According to this system of equations, we reveal the characteristic scales of nonideal MHD phenomena and clarify the applicable condition of the ideal GRMHD equations. We evaluate the characteristic scales of the nonideal MHD phenomena in the M87* plasma using the Event Horizon Telescope observational data.

Nonideal MHD Simulation of HL Tau Disk: Formation of Rings

Abstract Recent high-resolution observations unveil ring structures in circumstellar disks. The origin of these rings has been widely investigated under various theoretical scenarios. In this work we perform global 3D nonideal MHD simulations including effects from both ohmic resistivity and ambipolar diffusion (AD) to model the HL Tau disk. The nonideal MHD diffusion profiles are calculated based on the global dust evolution calculation including sintering effects. Disk ionization structure changes dramatically across the snow line due to the change of dust size distribution close to the snow line of major volatiles. We find that accretion is mainly driven by disk wind. Gaps and rings can be quickly produced from different accretion rates across the snow line. Furthermore, AD leads to highly preferential accretion at the midplane, followed by magnetic reconnection. This results in a local zone of decretion that drains the mass in the field reconnection area, which leaves a gap and an adjacent ring just outside of it. Overall, under favorable conditions, both snow lines and nonideal MHD effects can lead to gaseous gaps and rings in protoplanetary disks.

Gravitoturbulent dynamos in astrophysical discs

The origin of large-scale and coherent magnetic fields in astrophysical discs is an important and long standing problem. Researchers commonly appeal to a turbulent dynamo, sustained by the magneto-rotational instability (MRI), to supply the large-scale field. But research over the last decade in particular has demonstrated that various non-ideal MHD effects can impede or extinguish the MRI, especially in protoplanetary disks. In this paper we propose a new scenario, by which the magnetic field is generated and sustained via the gravitational instability (GI). We use 3D stratified shearing box simulations to characterise the dynamo and find that it works at low magnetic Reynolds number (from unity to ~100) for a wide range of cooling times and boundary conditions. The process is kinematic, with a relatively fast growth rate ($< 0.1 \Omega$), and it shares some properties of mean field dynamos. The magnetic field is generated via the combination of differential rotation and spiral density waves, the latter providing compressible horizontal motions and large-scale vertical rolls. At greater magnetic Reynolds numbers the build up of large-scale field is diminished and instead small-scale structures emerge from the breakdown of twisted flux ropes. We propose that GI may be key to the dynamo engine not only in young protoplanetary discs but also in some AGN and galaxies.

The impact of non-ideal effects on the circumstellar disk evolution and their observational signatures

AbstractIt has been recognized that non-ideal MHD effects (Ohmic diffusion, Hall effect, ambipolar diffusion) play crucial roles for the circumstellar disk formation and evolution. Ohmic and ambipolar diffusion decouple the gas and the magnetic field, and significantly reduces the magnetic torque in the disk, which enables the formation of the circumstellar disk (e.g., Tsukamoto et al. 2015b). They set an upper limit to the magnetic field strength of ∼ 0.1 G around the disk (Masson et al. 2016). The Hall effect notably changes the magnetic torques in the envelope around the disk, and strengthens or weakens the magnetic braking depending on the relative orientation of magnetic field and angular momentum. This suggests that the bimodal evolution of the disk size possibly occurs in the early disk evolutionary phase (Tsukamoto et al. 2015a, Tsukamoto et al. 2017). Hall effect and ambipolar diffusion imprint the possibly observable characteristic velocity structures in the envelope of Class 0/I YSOs. Hall effect forms a counter-rotating envelope around the disk. Our simulations show that counter rotating envelope has the size of 100–1000 au and a recent observation actually infers such a structure (Takakuwaet al. 2018). Ambipolar diffusion causes the significant ion-neutral drift in the envelopes. Our simulations show that the drift velocity of ion could become 100-1000 ms–1.

Kinematics of neutral and ionzied gas in the candidate protostar with efficient magnetic braking B335

AbstractAmbipolar diffusion can cause a velocity drift between ions and neutrals. This is one of the non-ideal MHD effects proposed to enable the formation of large Keplerian disks with sizes of tens of au (Zhao et al. 2018). To observationally study ambipolar diffusion in collapsing protostellar envelopes, we analyzed the ALMA H13CO+ (3–2) and C18O (2–1) data of the protostar B335, which is a candidate source with efficient magnetic braking (Yen et al. 2015). We constructed kinematical models to fit the velocity structures observed in H13CO+ and C18O. With our kinematical models, the infalling velocities in H13CO+ and C18O are both measured to be 0.85 ± 0.2 km s−1 at a radius of 100 au, suggesting that the velocity drift between the ionized and neutral gas is at most 0.3 km s−1 at a radius of 100 au in B335. The Hall parameter for H13CO+ is estimated to be ≫1 on a 100 au scale in B335, so that H13CO+ is expected to be attached to the magnetic field. Our non-detection or upper limit of the velocity drift between the ionized and neutral gas could suggest that the magnetic field remains rather well coupled to the bulk neutral material on a 100 au scale in B335, and that any significant field-matter decoupling, if present, likely occurs only on a smaller scale, leading to an accumulation of magnetic flux and thus efficient magnetic braking in the inner envelope in B335.

Effect of grain size on differential desorption of volatile species and on non-ideal MHD diffusivity

We developed a chemical network for modeling the chemistry and non-ideal MHD effects from the collapsing dense molecular clouds to protostellar disks. First, we re-formulated the cosmic-ray desorption rate by considering the variations of desorption rate over the grain size distribution. We find that the differential desorption of volatile species is amplified by the grains larger than 0.1 $\mu$m, because larger grains are heated to a lower temperature by cosmic-rays and hence more sensitive to the variations in binding energies. As a result, atomic nitrogen N is $\sim$2 orders of magnitude more abundant than CO; N$_2$H$^+$ also becomes a few times more abundant than HCO$^+$ due to the increased gas-phase N$_2$. However, the changes in ionization fraction due to freeze-out and desorption only have minor effects on the non-ideal MHD diffusivities. Our chemical network confirms that the very small grains (VSGs: below a few 100 $\AA$) weakens the efficiency of both ambipolar diffusion and Hall effect. In collapsing dense cores, a maximum ambipolar diffusion is achieved when truncating the MRN size distribution at 0.1 $\mu$m, and for a maximum Hall effect, the truncation occurs at 0.04 $\mu$m. We conclude that the grain size distribution is crucial to the differential depletion between CO and N$_2$ related molecules, as well as to the non-ideal MHD diffusivities in dense cores.

Convection Enhances Magnetic Turbulence in AM CVn Accretion Disks

Abstract We present the results of local, vertically stratified, radiation magnetohydrodynamic shearing-box simulations of magnetorotational instability (MRI) turbulence for a (hydrogen poor) composition applicable to accretion disks in AM CVn type systems. Many of these accreting white dwarf systems are helium analogs of dwarf novae (DNe). We utilize frequency-integrated opacity and equation-of-state tables appropriate for this regime to accurately portray the relevant thermodynamics. We find bistability of thermal equilibria in the effective-temperature, surface-mass-density plane typically associated with disk instabilities. Along this equilibrium curve (i.e., the S-curve), we find that the stress to thermal pressure ratio α varied with peak values of ∼0.15 near the tip of the upper branch. Similar to DNe, we found enhancement of α near the tip of the upper branch caused by convection; this increase in α occurred despite our choice of zero net vertical magnetic flux. Two notable differences we find between DN and AM CVn accretion disk simulations are that AM CVn disks are capable of exhibiting persistent convection in outburst, and ideal MHD is valid throughout quiescence for AM CVns. In contrast, DNe simulations only show intermittent convection, and nonideal MHD effects are likely important in quiescence. By combining our previous work with these new results, we also find that convective enhancement of the MRI is anticorrelated with mean molecular weight.

On the effects of ion-neutral interactions in solar plasmas

Solar photosphere and chromosphere are composed of weakly ionized plasma for which collisional coupling decreases with height. This implies a breakdown of some hypotheses underlying magnetohydrodynamics at low altitudes and gives rise to non-ideal MHD effects such as ambipolar diffusion, Hall effect, etc. Recently, there has been progress in understanding the role of these effects for the dynamics and energetics of the solar atmosphere. There are evidences that phenomena such as wave propagation and damping, magnetic reconnection, formation of stable magnetic field concentrations, magnetic flux emergence, etc can be affected. This paper reviews the current state-of-the-art of multi-fluid MHD modeling of the coupled solar atmosphere.

MAGNETICALLY SELF-REGULATED FORMATION OF EARLY PROTOPLANETARY DISKS

ABSTRACT The formation of protoplanetary disks during the collapse of molecular dense cores is significantly influenced by angular momentum transport, notably by the magnetic torque. In turn, the evolution of the magnetic field is determined by dynamical processes and non-ideal MHD effects such as ambipolar diffusion. Considering simple relations between various timescales characteristic of the magnetized collapse, we derive an expression for the early disk radius, where M is the total disk plus protostar mass, is the ambipolar diffusion coefficient, and B z is the magnetic field in the inner part of the core. This is significantly smaller than the disks that would form if angular momentum was conserved. The analytical predictions are confronted against a large sample of 3D, non-ideal MHD collapse calculations covering variations of a factor 100 in core mass, a factor 10 in the level of turbulence, a factor 5 in rotation, and magnetic mass-to-flux over critical mass-to-flux ratios 2 and 5. The disk radius estimates are found to agree with the numerical simulations within less than a factor 2. A striking prediction of our analysis is the weak dependence of circumstellar disk radii upon the various relevant quantities, suggesting weak variations among class-0 disk sizes. In some cases, we note the onset of large spiral arms beyond this radius.

Outbursts in ultracompact X-ray binaries

Very faint X-ray binaries appear to be transient in many cases with peak luminosities much fainter than that of usual soft X-ray transients, but their nature still remains elusive. We investigate the possibility that this transient behaviour is due to the same thermal/viscous instability which is responsible for outbursts of bright soft X-ray transients, occurring in ultracompact binaries for adequately low mass-transfer rates. More generally, we investigate the observational consequences of this instability when it occurs in ultracompact binaries. We use our code for modelling the thermal-viscous instability of the accretion disc, assumed here to be hydrogen poor. We also take into account the effects of disc X-ray irradiation, and consider the impact of the mass-transfer rate on the outburst brightness. We find that one can reproduce the observed properties of both the very faint and the brighter short transients (peak luminosity, duration, recurrence times), provided that the viscosity parameter in quiescence is slightly smaller (typically a factor of between two and four) than in bright soft X-ray transients and normal dwarf nova outbursts, the viscosity in outburst being unchanged. This possibly reflects the impact of chemical composition on non-ideal MHD effects affecting magnetically driven turbulence in poorly ionized discs.

Protostellar disc formation enabled by removal of small dust grains

It has been shown that a realistic level of magnetization of dense molecular cloud cores can suppress the formation of a rotationally supported disk (RSD) through catastrophic magnetic braking in the axisymmetric ideal MHD limit. In this study, we present conditions for the formation of RSDs through non-ideal MHD effects computed self-consistently from an equilibrium chemical network. We find that removing from the standard MRN distribution the large population of very small grains (VSGs) of ~10 $\AA$ to few 100 $\AA$ that dominate the coupling of the bulk neutral matter to the magnetic field increases the ambipolar diffusivity by ~1--2 orders of magnitude at densities below 10$^{10}$ cm$^{-3}$. The enhanced ambipolar diffusion (AD) in the envelope reduces the amount of magnetic flux dragged by the collapse into the circumstellar disk-forming region. Therefore, magnetic braking is weakened and more angular momentum can be retained. With continuous high angular momentum inflow, RSDs of tens of AU are able to form, survive, and even grow in size, depending on other parameters including cosmic-ray ionization rate, magnetic field strength, and rotation speed. Some disks become self-gravitating and evolve into rings in our 2D (axisymmetric) simulations, which have the potential to fragment into (close) multiple systems in 3D. We conclude that disk formation in magnetized cores is highly sensitive to chemistry, especially to grain sizes. A moderate grain coagulation/growth to remove the large population of VSGs, either in the prestellar phase or during free-fall collapse, can greatly promote AD and help formation of tens of AU RSDs.

VISCOUS INSTABILITY TRIGGERED BY LAYERED ACCRETION IN PROTOPLANETARY DISKS

Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate ($\dot{M}$), while the disk midplane where MRIs are generally quenched ends up with a low value of $\dot{M}$. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of $\alpha$ in 1D disk models. To this end, we obtain a new expression of $\alpha$ by utilizing an empirical formula that is derived from recent MHD simulations of stratified disks with Ohmic diffusion. It is interesting that this new formulation can be regarded as a general extension of the classical $\alpha$. Armed with the new $\alpha$, we perform a linear stability analysis of protoplanetary disks that undergo layered accretion, and find that a viscous instability can occur around the outer edge of dead zones. Disks become stable in using the classical $\alpha$. We identify that the difference arises from $\Sigma-$dependence of $\dot{M}$; whereas $\Sigma$ is uniquely determined for a given value of $\dot{M}$ in the classical approach, the new approach leads to $\dot{M}$ that is a multi-valued function of $\Sigma$. We confirm our finding both by exploring a parameter space as well as by performing the 1D, viscous evolution of disks. We finally discuss other non-ideal MHD effects that are not included in our analysis, but may affect our results.

Theory of Protostellar Disk Formation

AbstractHow large, 100-AU scale, rotationally supported disks form around protostars remains unsettled, both observationally and theoretically. In this contribution, we discuss the theoretical difficulties with disk formation in the presence of a dynamically significant magnetic field and their possible resolutions. These difficulties are caused by the concentration of magnetic field lines close to the forming star by protostellar collapse, and the strong magnetic braking associated with the concentrated field. Possible resolutions include magnetic field-rotation axis misalignment, non-ideal MHD effects, and turbulence. The field-rotation misalignment has been shown to promote disk formation, especially when the field is relatively weak and the misalignment angle is relatively large. Non-ideal MHD effects can enable the formation of small disks at early times. How such disks grow at later times remains to be fully quantified. Turbulence has been found to enable disk formation in a number of simulations, but the exact reason for its beneficial effect is debated.