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Register a new userThe collapse of a molecular cloud core to stellar densities using radiation non-ideal magnetohydrodynamics
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We present results from radiation non-ideal magnetohydrodynamics (MHD) calculations that follow the collapse of rotating, magnetised, molecular cloud cores to stellar densities. These are the first such calculations to include all three non-ideal effects: ambipolar diffusion, Ohmic resistivity and the Hall effect. We employ an ionisation model in which cosmic ray ionisation dominates at low temperatures and thermal ionisation takes over at high temperatures. We explore the effects of varying the cosmic ray ionisation rate from $zeta_text{cr}= 10^{-10}$ to $10^{-16}$ s$^{-1}$. Models with ionisation rates $gtrsim 10^{-12}$ s$^{-1}$ produce results that are indistinguishable from ideal MHD. Decreasing the cosmic ray ionisation rate extends the lifetime of the first hydrostatic core up to a factor of two, but the lifetimes are still substantially shorter than those obtained without magnetic fields. Outflows from the first hydrostatic core phase are launched in all models, but the outflows become broader and slower as the ionisation rate is reduced. The outflow morphology following stellar core formation is complex and strongly dependent on the cosmic ray ionisation rate. Calculations with high ionisation rates quickly produce a fast (~14km s$^{-1}$) bipolar outflow that is distinct from the first core outflow, but with the lowest ionisation rate a slower (~3-4 km s$^{-1}$) conical outflow develops gradually and seamlessly merges into the first core outflow.
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We investigate the formation and fragmentation of discs using a suite of three-dimensional smoothed particle radiative magnetohydrodynamics simulations. Our models are initialised as 1M$_odot$ rotating Bonnor-Ebert spheres that are threaded with a uniform magnetic field. We examine the effect of including ideal and non-ideal magnetic fields, the orientation and strength of the magnetic field, and the initial rotational rate. We follow the gravitational collapse and early evolution of each system until the final classification of the protostellar disc can be determined. Of our 105 models, 41 fragment, 21 form a spiral structure but do not fragment, and another 12 form smooth discs. Fragmentation is more likely to occur for faster initial rotation rates and weaker magnetic fields. For stronger magnetic field strengths, the inclusion of non-ideal MHD promotes disc formation, and several of these models fragment, whereas their ideal MHD counterparts do not. For the models that fragment, there is no correlation between our parameters and where or when the fragmentation occurs. Bipolar outflows are launched in only 17 models, and these models have strong magnetic fields that are initially parallel to the rotation axis. Counter-rotating envelopes form in four slowly-rotating, strong-field models -- including one ideal MHD model -- indicating they form only in a small fraction of the parameter space investigated.
We investigate and discuss protostellar discs in terms of where the various non-ideal magnetohydrodynamics (MHD) processes are important. We find that the traditional picture of a magnetised disc (where Ohmic resistivity is dominant near the mid-plane, surrounded by a region dominated by the Hall effect, with the remainder of the disc dominated by ambipolar diffusion) is a great oversimplification. In simple parameterised discs, we find that the Hall effect is typically the dominant term throughout the majority of the disc. More importantly, we find that in much of our parameterised discs, at least two non-ideal processes have coefficients within a factor of 10 of one another, indicating that both are important and that naming a dominant term underplays the importance of the other terms. Discs that were self-consistently formed in our previous studies are also dominated by the Hall effect, and the ratio of ambipolar diffusion and Hall coefficients is typically less than 10, suggesting that both terms are equally important and listing a dominant term is misleading. These conclusions become more robust once the magnetic field geometry is taken into account. In agreement with the literature we review, we conclude that non-ideal MHD processes are important for the formation and evolution of protostellar discs. Ignoring any of the non-ideal processes, especially ambipolar diffusion and the Hall effect, yields an incorrect description of disc evolution.
What cosmic ray ionisation rate is required such that a non-ideal magnetohydrodynamics (MHD) simulation of a collapsing molecular cloud will follow the same evolutionary path as an ideal MHD simulation or as a purely hydrodynamics simulation? To investigate this question, we perform three-dimensional smoothed particle non-ideal magnetohydrodynamics simulations of the gravitational collapse of rotating, one solar mass, magnetised molecular cloud cores, that include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of $a_text{g} = 0.1mu$m, and our free parameter is the cosmic ray ionisation rate, $zeta_text{cr}$. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with $zeta_text{cr}gtrsim10^{-13}$ s$^{-1}$ are indistinguishable from ideal MHD models and the evolution of the model with $zeta_text{cr}=10^{-14}$ s$^{-1}$ matches the evolution of the ideal MHD model within one per cent when considering maximum density, magnetic energy, and maximum magnetic field strength as a function of time; these results are independent of $a_text{g}$. Models with very low ionisation rates ($zeta_text{cr}lesssim10^{-24}$ s$^{-1}$) are required to approach hydrodynamical collapse, and even lower ionisation rates may be required for larger $a_text{g}$. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionisation rate. However, realistic cosmic ray ionisation rates approach neither limit, thus non-ideal MHD cannot be neglected in star formation simulations.
We investigate the effect of non-ideal magnetohydrodynamics (MHD) on the formation of binary stars using a suite of three-dimensional smoothed particle magnetohydrodynamics simulations of the gravitational collapse of one solar mass, rotating, perturbed molecular cloud cores. Alongside the role of Ohmic resistivity, ambipolar diffusion and the Hall effect, we also examine the effects of magnetic field strength, orientation and amplitude of the density perturbation. When modelling sub-critical cores, ideal MHD models do not collapse whereas non-ideal MHD models collapse to form single protostars. In super-critical ideal MHD models, increasing the magnetic field strength or decreasing the initial density perturbation amplitude decreases the initial binary separation. Strong magnetic fields initially perpendicular to the rotation axis suppress the formation of binaries and yield discs with magnetic fields ~10 times stronger than if the magnetic field was initially aligned with the rotation axis. When non-ideal MHD is included, the resulting discs are larger and more massive, and the binary forms on a wider orbit. Small differences in the super-critical cores caused by non-ideal MHD effects are amplified by the binary interaction near periastron. Overall, the non-ideal effects have only a small impact on binary formation and early evolution, with the initial conditions playing the dominant role.
In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfven waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.
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