We study the effect of the non-linear process of ambipolar diffusion (joint transport of magnetic flux and charged particles relative to neutral particles) on the long-term behavior of a non-uniform magnetic field in a one-dimensional geometry. Our main focus is the dissipation of magnetic energy inside neutron stars(particularly magnetars), but our results have a wider application, particularly to the interstellar medium and the loss of magnetic flux from collapsing molecular cloud cores. Our system is a weakly ionized plasma in which neutral and charged particles can be converted into each other through nuclear beta decays (or ionization-recombination processes). In the "weak-coupling" limit of infrequent inter-particle interactions, the evolution of the magnetic field is controlled by the beta decay rate and can be described by a non-linear partial integro-differential equation. In the opposite, "strong-coupling" regime, the evolution is controlled by the inter-particle collisions and can be modelled through a non-linear diffusion equation. We show numerically that, in both regimes, ambipolar diffusion tends to spread out the magnetic flux, but, contrary to the normal Ohmic diffusion, it produces sharp magnetic field gradients with associated current sheets around those regions where the magnetic field is weak.
The lower solar atmosphere consists of partially ionized turbulent plasmas harbouring velocity field, magnetic field and current density fluctuations. The correlations amongst these small scale fluctuations give rise to large scale flows and magnetic fields which decisively affect all transport processes. The three fluid system consisting of electrons, ions and neutral particles supports nonideal effects such as the Hall effect and the ambipolar diffusion. Here, we study magnetic transport by ambipolar diffusion and compare the characteristic timescales of the laminar and the turbulent ambipol…
Magnetohydrodynamic (MHD) simulations of the solar atmosphere are often performed under the assumption that the plasma is fully ionized. However, in the lower solar atmosphere a reduced temperature often results in only the partial ionization of the plasma. The interaction between the decoupled neutral and ionized components of such a partially ionized plasma produces ambipolar diffusion. To investigate the role of ambipolar diffusion in propagating wave characteristics in the photosphere and chromosphere, we employ the Mancha3D numerical code to model magnetoacoustic waves propagating through…
We show that the ambipolar-diffusion--initiated fragmentation of molecular clouds leads simply and naturally to an initial core mass function (CMF) which is very similar to the initial stellar mass function (IMF) and in excellent agreement with existing observations. This agreement is robust provided that the three (input) free parameters remain within their range of values suggested by observations. Other, observationally testable, predictions are made.
In partially ionised plasmas, the magnetic field can become decoupled from the neutral gas and diffuse through it in a process known as ambipolar diffusion. Although ambipolar diffusion has been implemented in several grid codes, we here provide an implementation in smoothed particle magnetohydrodynamics (SPMHD). We use the strong coupling approximation in which the ion density is negligible, allowing a single fluid approach. The equations are derived to conserve energy, and to provide a positive definite contribution to the entropy. We test the implementation in both a simple 1D SPMHD code an…
The heating of the chromosphere in internetwork regions remains one of the foremost open questions in solar physics. In the present study we tackle this old problem by using a very high spatial-resolution simulation of quiet-Sun conditions performed with radiative MHD numerical models and IRIS observations. We have expanded a previously existing 3D radiative MHD numerical model of the solar atmosphere, which included self-consistently locally driven magnetic amplification in the chromosphere, by adding ambipolar diffusion and time-dependent non-equilibrium hydrogen ionization to the model. The…
Ambipolar diffusion is important in redistributing magnetic flux and in damping Alfven waves in molecular clouds. The importance of ambipolar diffusion on a length scale $\ell$ is governed by the ambipolar diffusion Reynolds number, $\rad=\ell/\lad$, where $\lad$ is the characteristic length scale for ambipolar diffusion. The logarithmic mean of the AD Reynolds number in a sample of 15 molecular clumps with measured magnetic fields (Crutcher 1999) is 17, comparable to the theoretically expected value. We identify several regimes of ambipolar diffusion in a turbulent medium, depending on the ra…
The chromosphere is a partially ionized layer of the solar atmosphere, the transition between the photosphere where the gas motion is determined by the gas pressure and the corona dominated by the magnetic field. We study the effect of partial ionization for 2D wave propagation in a gravitationally stratified, magnetized atmosphere with properties similar to the solar chromosphere. We adopt an oblique uniform magnetic field in the plane of propagation with strength suitable for a quiet sun region. The theoretical model used is a single fluid magnetohydrodynamic approximation, where ion-neutral…
In this paper we reconsider the problem of magnetic field diffusion in neutron star cores. We model the star as consisting of a mixture of neutrons, protons and electrons, and allow for particle reactions and binary collisions between species. Our analysis is in much the same spirit as that of Goldreich & Reisenegger (1992), and we content ourselves with rough estimates of magnetic diffusion timescales, rather than solving accurately for some particular field geometry. However, our work improves upon previous treatments in one crucial respect: we allow for superfluidity in the neutron star mat…
Ambipolar diffusion is a physical mechanism related to the drift between charged and neutral particles in a partially ionized plasma that is key in many different astrophysical systems. However, understanding its effects is challenging due to basic uncertainties concerning relevant microphysical aspects and the strong constraints it imposes on the numerical modeling. Our aim is to introduce a numerical tool that allows us to address complex problems involving ambipolar diffusion in which, additionally, departures from ionization equilibrium are important or high resolution is needed. The prima…
Magnetic flux emergence has been shown to be a key mechanism for unleashing a wide variety of solar phenomena. However, there are still open questions concerning the rise of the magnetized plasma through the atmosphere, mainly in the chromosphere, where the plasma departs from local thermodynamic equilibrium (LTE) and is partially ionized. We aim to investigate the impact of the nonequilibrium (NEQ) ionization and recombination and molecule formation of hydrogen, as well as ambipolar diffusion, on the dynamics and thermodynamics of the flux emergence process. Using the Bifrost code, we perform…
We propose a mechanism for efficient heating of the solar chromosphere, based on non-ideal plasma effects. Three ingredients are needed for the work of this mechanism: (1) presence of neutral atoms; (2) presence of a non-potential magnetic field; (3) decrease of the collisional coupling of the plasma. Due to decrease of collisional coupling, a net relative motion appears between the neutral and ionized components, usually referred to as "ambipolar diffusion". This results in a significant enhancement of current dissipation as compared to the classical MHD case. We propose that the current diss…
Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds yields information about length scales involved in star formation. Combining these length scales with various distributions of other environmental variables, (i.e., column density and mass-to-flux ratio) and applying Monte Carlo methods allow us to produce synthetic core mass functions (CMFs) for different environmental conditions. Our analysis shows that the shape of the CMF is directly dependent on the physical conditions of the cloud. Specifically, magnetic fields act to broaden the mass function a…
We analyze the properties of steady and time-dependent C shocks under conditions prevailing in giant molecular clouds. For steady C shocks, we show that ionization equilibrium holds and use numerical integrations to obtain the shock thickness mediated by ambipolar diffusion as a function of density, inflow velocity, magnetic field, and ionization fraction in the cloud. Our formula also agrees with an analytic estimate based on ion-neutral momentum exchange. Using time-dependent numerical simulations, we show that C shocks have a transient stage when the neutrals are compressed much more strong…
In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution during prestellar core collapse by including resistive terms in the magnetohydrodynamics (MHD) equations. We focus more particularly on the impact of ambipolar diffusion. We use the adaptive mesh refinement code RAMSES to carry out such calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral and grain species. The inclusion of ambipolar diffusion leads to the formation of a magnetic diffusion ba…
We investigate the stability of partially ionised, differentially rotating, diffusive disc threaded by both azimuthal and vertical magnetic field. The general stability criterion of such a disc in the presence of axisymmetric fluctuations can be stated purely in terms of ambipolar and Hall diffusivities. It is shown that the disc is magnetorotationally unstable if the sum of scaled ambipolar and Hall diffusivities are larger than some numerical constant determined by the rotation profile of the disc. This criterion suggests that the diffusive discs are always unstable to almost radial fluctuat…
This paper presents the results of the analysis of 3D simulations of solar magneto-convection that include the joint action of the ambipolar diffusion and the Hall effect. Three simulation-runs are compared: one including both ambipolar diffusion and Hall effect; one including only ambipolar diffusion; and one without any of these two effects. The magnetic field is amplified from initial field to saturation level by the action of turbulent local dynamo. In each of these cases, we study 2 hours of simulated solar time after the local dynamo reaches the saturation regime. We analyze the power sp…
We investigate the roles of magnetic fields and ambipolar diffusion during prestellar core formation in turbulent giant molecular clouds (GMCs), using three-dimensional numerical simulations. Our simulations focus on the shocked layer produced by a converging flow within a GMC, and survey varying ionization and angle between the upstream flow and magnetic field. We also include ideal magnetohydrodynamic (MHD) and hydrodynamic models. From our simulations, we identify hundreds of self-gravitating cores that form within 1 Myr, with masses M ~ 0.04 - 2.5 solar-mass and sizes L ~ 0.015 - 0.07 pc, …
We study ambipolar diffusion in strongly magnetised neutron stars, with special focus on the effects of neutrino reaction rates and the impact of a superfluid/superconducting transition in the neutron star core. For axisymmetric magnetic field configurations, we determine the deviation from $β-$equilibrium induced by the magnetic force and calculate the velocity of the slow, quasi-stationary, ambipolar drift. We study the temperature dependence of the velocity pattern and clearly identify the transition to a predominantly solenoidal flow. For stars without superconducting/superfluid constituen…
The temperature of the gas in molecular clouds is a key determinant of the characteristic mass of star formation. Ambipolar diffusion (AD) is considered one of the most important heating mechanisms in weakly ionized molecular clouds. In this work, we study the AD heating rate using 2-fluid turbulence simulations and compare it with the overall heating rate due to turbulent dissipation. We find that for observed molecular clouds, which typically have Alfven Mach numbers of ~1 (Crutcher 1999) and AD Reynolds numbers of ~20 (McKee et al. 2010), about 70% of the total turbulent dissipation is in t…
The partial ionization of the solar plasma causes several nonideal effects such as the ambipolar diffusion, the Hall effect, and the Biermann battery effect. Here we report on the first three-dimensional realistic simulations of solar local dynamo where all three effects were taken into account. The simulations started with a snapshot of already saturated battery-seeded dynamo, where two new series were developed: one with solely ambipolar diffusion and another one also taking into account the Hall term in the generalized Ohm's law. The simulations were then run for about 4 hours of solar time…
We employ the three-dimensional magnetohydrodynamic simulation including ambipolar diffusion to study the gravitationally-driven fragmentation of subcritical molecular clouds, in which the gravitational fragmentation is stabilized as long as magnetic flux-freezing applies. The simulations show that the cores in an initially subcritical cloud generally develop gradually over an ambipolar diffusion time, which is about a few $\times 10^7$ years in a typical molecular cloud. On the other hand, the formation of collapsing cores in subcritical clouds is accelerated by supersonic nonlinear flows. Ou…
Magnetic fields play a role in the dynamics of many astrophysical processes, but they are hard to detect. In a partially ionized plasma, a magnetic field works directly on the ionized medium but not on the neutral medium, which gives rise to a velocity drift between them: ambipolar diffusion. This process is suggested to be important in the process of star formation, but has never been directly observed. We introduce a method that could be used to detect ambipolar diffusion and the magnetic field that gives rise to it, where we exploit the velocity drift between the charged and neutral medium.…
Though flux freezing is a good approximation frequently assumed for molecular clouds, ambipolar diffusion (AD) is inevitable at certain scales. The scale at which AD sets in can be a crucial parameter for turbulence and the star formation process. However, both observation and simulation of AD are very challenging and our knowledge of it is very limited. We proposed earlier (Li and Houde 2008) that the difference between ion and neutral velocity spectra is a signature of turbulent AD and can be used to estimate the AD scales and magnetic field strength. Here we present observational evidence s…
Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β=0.1) and mildly supersonic turbulence (M=3, corresponding to an Alfven mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominate…
We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test and the Alfven wave test. For the latte…
We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion-neutral interaction effects using the Generalized Ohm's Law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere and transition region partially ionized. Our simulations reveal that the interactions between ionized parti…
Over the last decades, realistic 3D radiative-MHD simulations have become the dominant theoretical tool for understanding the complex interactions between the plasma and the magnetic field on the Sun. Most of such simulations are based on approximations of magnetohydrodynamics, without directly considering the consequences of the very low degree of ionization of the solar plasma in the photosphere and bottom chromosphere. The presence of large amount of neutrals leads to a partial decoupling of the plasma and the magnetic field. As a consequence of that, a series of non-ideal effects (ambipola…
The solar chromosphere is weakly ionized and interactions between ionized particles and neutral particles likely have significant consequences for the thermodynamics of the plasma. We investigate the importance of introducing neutral particles using numerical 2.5D radiative MHD simulations obtained with the Bifrost code. The models span from the upper layers of the convection zone to the low corona, and solve the full MHD equations with non-grey and NLTE radiative transfer, and thermal conduction. The effects of partial ionization are implemented using the generalized Ohm's law. The approximat…
Disks are essential to the formation of both stars and planets, but how they form in magnetized molecular cloud cores remains debated. This work focuses on how the disk formation is affected by turbulence and ambipolar diffusion (AD), both separately and in combination, with an emphasis on the protostellar mass accretion phase of star formation. We find that a relatively strong, sonic turbulence on the core scale strongly warps but does not completely disrupt the well-known magnetically-induced flattened pseudodisk that dominates the inner protostellar accretion flow in the laminar case, in ag…
In this paper, we study the heating of the magnetized solar chromosphere induced by the large fraction of neutral atoms present in this layer. The presence of neutrals, together with the decrease with height of the collisional coupling, leads to deviations from the classical MHD behavior of the chromospheric plasma. A relative net motion appears between the neutral and ionized components, usually referred to as ambipolar diffusion. The dissipation of currents in the chromosphere is enhanced orders of magnitude due to the action of ambipolar diffusion, as compared to the standard ohmic diffusio…
Ambipolar diffusion is a process occurring in partially ionised astrophysical systems that imparts a complicated mathematical and physical nature to Ohm's law. The numerical codes that solve the magnetohydrodynamic (MHD) equations have to be able to deal with the singularities that are naturally created in the system by the ambipolar diffusion term. The global aim is to calculate a set of theoretical self-similar solutions to the nonlinear diffusion equation with cylindrical symmetry that can be used as tests for MHD codes which include the ambipolar diffusion term. First, following the genera…
Context: Ideal MHD simulations have revealed catastrophic magnetic braking (MB) in the protostellar phase, which prevents the formation of a centrifugal disk around a nascent protostar. Aims: We determine if non-ideal MHD, including the effects of ambipolar diffusion and Ohmic dissipation determined from a detailed chemical network model, allows for disk formation at the earliest stages of star formation (SF). Methods: We employ the axisymmetric thin-disk approximation in order to resolve a dynamic range of 9 orders of magnitude in length and 16 in density, while also calculating partial ioniz…
Ambipolar diffusion likely plays a pivotal role in the formation and evolution of dense cores in weakly-ionized molecular clouds. Linear analyses show that the evolutionary times and fragmentation scales are significantly greater than the hydrodynamic (Jeans) values even for clouds with mildly supercritical mass-to-flux ratio. We utilize values of fragmentation scales and growth times that correspond to typical ionization fractions within a molecular cloud, and apply to the context of the observed estimated lifetime of prestellar cores as well as the observed number of such embedded cores form…
We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma $β$ of the centre of the first core becomes large, $β>10^4$. Thus, proper treatment of first core phase is crucial in investigating the formation of protostar and disc. On the other hand, in an ideal simulation, $β\sim 10$ at the centre of the first core. The simu…
Simulations generally show that non-self-gravitating clouds have a lognormal column density ($Σ$) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynam…
We study mass accretion and ejection in the vicinity of massive star forming cores using high-resolution (5 au) 3D AMR numerical simulations. We investigate the mechanisms at the origin of outflows and characterise the properties of the disc forming around massive protostars. We include both protostellar radiative feedback via PMS evolutionary tracks and magnetic ambipolar diffusion. We studied 3 different cases: purely hydrodynamical, ideal MHD, and ambipolar diffusion. In the resistive models, we investigate the effects the initial amplitude of both magnetic field and rotation have on the pr…
In a previous paper we formulated the problem of the formation and evolution of fragments (or cores) in magnetically-supported, self-gravitating molecular clouds in axisymmetric geometry, accounting for the effects of ambipolar diffusion and Ohmic dissipation, grain chemistry and dynamics, and radiative transfer. Here we present results of star formation simulations that accurately track the evolution of a protostellar fragment over eleven orders of magnitude in density (from 300 cm^-3 to \approx 10^14 cm^-3), i.e., from the early ambipolar-diffusion--initiated fragmentation phase, through the…
Protoplanetary discs are poorly ionised due to their low temperatures and high column densities, and are therefore subject to three "non-ideal" magnetohydrodynamic effects: Ohmic dissipation, ambipolar diffusion, and the Hall effect. The existence of magnetically driven turbulence in these discs has been a central question since the discovery of the magnetorotational instability. Early models considered Ohmic diffusion only and led to a scenario of layered accretion, in which a magnetically "dead" zone in the disc midplane is embedded within magnetically "active" surface layers at distances ~1…
The transport of angular momentum is capital during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. We investigate the impact of including resistive MHD in simulations of the gravitational collapse of a 1 solar mass gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. We used the AMR code RAMSES to perform two 3D simulati…
In a weakly ionized plasma, the evolution of the magnetic field is described by a "generalized Ohm's law" that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the viscous, the resistive and the ambipolar dissipation mechanisms. The plasma, depending on its properties and the energy injection rate, may preferentially select one of the these dissipation scales. thus det…
MHD turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into radial structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. The strong sedimentation of millimetre dust measured in…
We use local numerical simulations to investigate the strength and nature of magnetohydrodynamic (MHD) turbulence in the outer regions of protoplanetary disks, where ambipolar diffusion is the dominant non-ideal MHD effect. The simulations include vertical stratification and assume zero net vertical magnetic flux. We employ a super time-stepping technique to ameliorate the Courant restriction on the diffusive time step. We find that in idealized stratified simulations, with a spatially constant ambipolar Elsasser number Am, turbulence driven by the magnetorotational instability (MRI) behaves i…
(Abridged) Context. Massive stars form in magnetized and turbulent environments, and are often located in stellar clusters. Their accretion mechanism, as well as the origin of their system's stellar multiplicity are poorly understood. Aims. We study the influence of both magnetic fields and turbulence on the accretion mechanism of massive protostars and their multiplicity. Methods. We present a series of four Radiation-MHD simulations of the collapse of a massive magnetized, turbulent core of 100 $M_\odot$ with the AMR code Ramses, including a hybrid radiative transfer method for stellar irrad…
We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (Ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheet-like cloud or disk. Our results show that there is a…
We investigate differences in the molecular abundances between magnetically super- and sub-critical prestellar cores, performing three-dimensional non-ideal magnetohydrodynamical (MHD) simulations with varying densities and magnetic field strengths, and post-processing the results with a time-dependent gas-grain chemical code. Most molecular species show significantly more central depletion in subcritical models, due to the longer duration of collapse. However, the directly observable quantities - the molecule to hydrogen column density ratios - are generally too similar for observational data…
We investigate the formation and evolution of giant molecular clouds (GMCs) by the collision of convergent warm neutral medium (WNM) streams in the interstellar medium, in the presence of magnetic fields and ambipolar diffusion (AD), focusing on the evolution of the star formation rate (SFR) and efficiency (SFE), as well as of the mass-to-magnetic-flux ratio (M2FR) in the forming clouds. We find that: 1) Clouds formed by supercritical inflow streams proceed directly to collapse, while clouds formed by subcritical streams first contract and then re-expand, oscillating on the scale of tens of My…
We study the role of ambipolar diffusion (AD) on the non-linear evolution of the MRI in protoplanetary disks using the strong coupling limit, which applies when the electron recombination time is much shorter than the orbital time. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency of which neutral particles collide with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the …
In the present-day universe, magnetic fields play such essential roles in star formation as angular momentum transport and outflow driving, which control circumstellar disc formation/fragmentation and also the star formation efficiency. While only a much weaker field has been believed to exist in the early universe, recent theoretical studies find that strong fields can be generated by turbulent dynamo during the gravitational collapse. Here, we investigate the gravitational collapse of a cloud core ($\sim 10^{3}\ \rm cm^{-3}$) up to protostar formation ($\sim 10^{20}\ \rm cm^{-3}$) by non-ide…
(Abridged) Most massive protostars exhibit bipolar outflows. Nonetheless, there is no consensus regarding the mechanism at the origin of these outflows, nor on the cause of the less-frequently observed monopolar outflows. We aim to identify the origin of early massive protostellar outflows, focusing on the combined effects of radiative transfer and magnetic fields in a turbulent medium. We use four state-of-the-art radiation-magnetohydrodynamical simulations following the collapse of massive 100 Msun pre-stellar cores with the Ramses code. Turbulence is taken into account via initial velocity …
