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Register a new userThere is no magnetic braking catastrophe: Low-mass star cluster and protostellar disc formation with non-ideal magnetohydrodynamics
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We present results from the first radiation non-ideal magnetohydrodynamics (MHD) simulations of low-mass star cluster formation that resolve the fragmentation process down to the opacity limit. We model 50~M$_odot$ turbulent clouds initially threaded by a uniform magnetic field with strengths of 3, 5 10 and 20 times the critical mass-to-magnetic flux ratio, and at each strength, we model both an ideal and non-ideal (including Ohmic resistivity, ambipolar diffusion and the Hall effect) MHD cloud. Turbulence and magnetic fields shape the large-scale structure of the cloud, and similar structures form regardless of whether ideal or non-ideal MHD is employed. At high densities ($10^6 lesssim n_{rm H} lesssim 10^{11}$~cm$^{-3}$), all models have a similar magnetic field strength versus density relation, suggesting that the field strength in dense cores is independent of the large-scale environment. Albeit with limited statistics, we find no evidence for the dependence of the initial mass function on the initial magnetic field strength, however, the star formation rate decreases for models with increasing initial field strengths; the exception is the strongest field case where collapse occurs primarily along field lines. Protostellar discs with radii $gtrsim 20$~au form in all models, suggesting that disc formation is dependent on the gas turbulence rather than on magnetic field strength. We find no evidence for the magnetic braking catastrophe, and find that magnetic fields do not hinder the formation of protostellar discs.
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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.
Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. In the simplest case of a laminar (non-turbulent) core with the magnetic field aligned with the rotation axis, both analytic considerations and numerical simulations have shown that the formation of a large, $10^2au$-scale, rotationally supported protostellar disk is suppressed by magnetic braking in the ideal MHD limit for a realistic level of core magnetization. This theoretical difficulty in forming protostellar disks is termed magnetic braking catastrophe. A possible resolution to this problem, proposed by citeauthor{HennebelleCiardi2009} and citeauthor{Joos+2012}, is that misalignment between the magnetic field and rotation axis may weaken the magnetic braking enough to enable disk formation. We evaluate this possibility quantitatively through numerical simulations. We confirm the basic result of citeauthor{Joos+2012} that the misalignment is indeed conducive to disk formation. In relatively weakly magnetized cores with dimensionless mass-to-flux ratio $gtrsim 5$, it enabled the formation of rotationally supported disks that would otherwise be suppressed if the magnetic field and rotation axis are aligned. For more strongly magnetized cores, disk formation remains suppressed, however, even for the maximum tilt angle of $90degree$. If dense cores are as strongly magnetized as indicated by OH Zeeman observations (with a mean dimensionless mass-to-flux ratio $sim 2$), it would be difficult for the misalignment alone to enable disk formation in the majority of them. We conclude that, while beneficial to disk formation, especially for the relatively weak field case, the misalignment does not completely solve the problem of catastrophic magnetic braking in general.
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.
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.
(Abridged) The purpose of this paper is to explore and compare the physical and chemical structure of Class I low-mass protostellar sources on protoplanetary disc scales. We present a study of the dust and gas emission towards a representative sample of 12 Class I protostars from the Ophiuchus molecular cloud with the Atacama Large Millimeter/submillimeter Array (ALMA). The continuum at 0.87 mm and molecular transitions from C17O, C34S, H13CO+, CH3OH, SO2 , and C2H were observed at high angular resolution (0.4, ~60 au diameter) towards each source. Disc and stellar masses are estimated from the continuum flux and position-velocity diagrams, and six of the sources show disc-like structures. Towards the more luminous sources, compact emission and large line widths are seen for transitions of SO2 that probe warm gas (Eu ~200 K). In contrast, C17O emission is detected towards the least evolved and less luminous systems. No emission of CH3OH is detected towards any of the continuum peaks, indicating an absence of warm CH3OH gas towards these sources. A power-law relation is seen between the stellar mass and the bolometric luminosity, corresponding to a mass accretion rate of (2.4 +/- 0.6) x 10^-7 Msun/year for the Class I sources. This mass accretion rate is lower than the expected value if the accretion is constant in time and rather points to a scenario of accretion occurring in bursts. The differentiation between C17O and SO2 suggests that they trace different physical components: C17O traces the densest and colder regions of the disc-envelope system, while SO2 may be associated with regions of higher temperature, such as accretion shocks. The lack of warm CH3OH emission suggests that there is no hot-core-like region around any of the sources and that the CH3OH column density averaged over the disc is low.
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