We present results from an extensive set of simulations of gravitational fragmentation in the presence of magnetic fields and ambipolar diffusion. The average fragmentation spacing in the nonlinear phase of evolution is in excellent agreement with the prediction of linear perturbation theory. The time scale for nonlinear growth and runaway of the first core is $\approx 10$ times the calculated growth time $\taugm$ of the eigenmode with minimum growth time, when starting from a uniform background state with small-amplitude white-noise perturbations. Subcritical and transcritical models typically evolve on a significantly longer time scale than the supercritical models. Infall motions in the nonlinear fully-developed contracting cores are subsonic on the core scale in subcritical and transcritical clouds, but are somewhat supersonic in supercritical clouds. Core mass distributions are sharply peaked with a steep decline to large masses, consistent with the existence of a preferred mass scale for each unique set of dimensionless free parameters. However, a sum total of results for various initial mass-to-flux ratios yields a broad distribution reminiscent of observed core mass distributions. Based on our results, we conclude that fragmentation spacings, magnitude of infall motions, core shapes, and, especially, the curvature of magnetic field morphology, may serve as indirect observational means of determining a cloud's ambient mass-to-flux ratio.
We investigate numerically the combined effects of supersonic turbulence, strong magnetic fields and ambipolar diffusion on cloud evolution leading to star formation. We find that, in clouds that are initially magnetically subcritical, supersonic turbulence can speed up star formation, through enhanced ambipolar diffusion in shocks. The speedup overcomes a major objection to the standard scenario of low-mass star formation involving ambipolar diffusion, since the diffusion time scale at the average density of a molecular cloud is typically longer than the cloud life time. At the same time, the…
We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion-neutral friction in regulating gravitationally-driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infall speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (\ga 0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent w…
We revisit the modeling of ion-neutral (or ambipolar) diffusion with two fluid smoothed particle hydrodynamics, as discussed by Hosking & Whitworth. Some parts of the technique are optimized to testify the pioneer works on behavior of the ambipolar diffusion in an isothermal self-gravitating layer. The frictional heating by ambipolar diffusion is examined, and its effect on fragmentation of the layer is studied. The results are compared to the thermal phases of instability as obtained by Nejad-Asghar.
We present a parameter study of simulations of fragmentation regulated by gravity, magnetic fields, ambipolar diffusion, and nonlinear flows. The thin-sheet approximation is employed with periodic lateral boundary conditions, and the nonlinear flow field ("turbulence") is allowed to freely decay. In agreement with previous results in the literature, our results show that the onset of runaway collapse (formation of the first star) in subcritical clouds is significantly accelerated by nonlinear flows in which a large-scale wave mode dominates the power spectrum. In addition, we find that a power…
We demonstrate that the formation of collapsing cores in subcritical clouds is accelerated by nonlinear flows, by performing three-dimensional non-ideal MHD simulations. An initial random supersonic (and trans-Alfvenic) turbulent-like flow is input into a self-gravitating gas layer that is threaded by a uniform magnetic field (perpendicular to the layer) such that the initial mass-to-flux ratio is subcritical. Magnetic ambipolar diffusion occurs very rapidly initially due to the sharp gradients introduced by the turbulent flow. It subsequently occurs more slowly in the traditional near-quasist…
Until recently, many of the dozens of quantitative predictions of the ambipolar-diffusion theory of gravitational fragmentation (or core formation) of molecular clouds have been confirmed by observations and, just as importantly, no prediction has been contradicted by any observation. A recent paper, however, claims that measurements of the variation of the mass-to-flux ratio from envelopes to cores in four clouds {\it de}creases, in direct contrast to a prediction of the theory but in agreement with turbulent fragmentation (in the absence of gravity) and, therefore, the ambipolar-diffusion th…
We simulate fragmentation and gravitational collapse of cold, magnetized molecular clouds. We explore the nonlinear development of an instability mediated by ambipolar diffusion, in which the collapse rate is intermediate to fast gravitational collapse and slow quasistatic collapse. Initially uniform stable clouds fragment into elongated clumps with masses largely determined by the cloud temperature, but substantially larger than the thermal Jeans mass. The clumps are asymmetric, with significant rotation and vorticity, and lose magnetic flux as they collapse. The clump shapes, intermediate co…
The collapse and fragmentation of initially filamentary, magnetic molecular clouds is calculated in three dimensions with a gravitational, radiative hydrodynamics code. The code includes magnetic field effects in an approximate manner: magnetic pressure, tension, braking, and ambipolar diffusion are all modelled. Three types of outcomes are observed: direct collapse and fragmentation into a multiple protostar system, periodic contraction and expansion without collapse, or periodic contraction and expansion leading eventually to collapse. While the models begin their evolution at rest except fo…
Isolated low-mass stars are formed in dense cores of molecular clouds. In the standard picture, the cores are envisioned to condense out of strongly magnetized clouds through ambipolar diffusion. Most previous calculations based on this scenario are limited to axisymmetric cloud evolution leading to a single core, which collapses to form an isolated star or stellar system at the center. These calculations are here extended to the nonaxisymmetric case under thin-disk approximation, which allows for a detailed investigation into the process of fragmentation, fundamental to binary, multiple syste…
We study the non-axisymmetric evolution of magnetized clouds, using a 2D MHD code based on the physically motivated thin-disk approximation. We found that such clouds become unstable to non-axisymmetric perturbations after the supercritical cores are formed due to ambipolar diffusion. We show that for a wide range of initial cloud parameters, the $m=2$ mode grows nonlinearly into a bar during the isothermal collapse after the supercritical core formation. The supercritical core can break up into fragments during or after the isothermal phase of cloud evolution. The outcome of fragmentation dep…
We carry out three-dimensional MHD simulations of star formation in turbulent, magnetized clouds, including ambipolar diffusion and feedback from protostellar outflows. The calculations focus on relatively diffuse clouds threaded by a strong magnetic field capable of resisting severe tangling by turbulent motions and retarding global gravitational contraction in the cross-field direction. They are motivated by observations of the Taurus molecular cloud complex (and, to a lesser extent, Pipe Nebula), which shows an ordered large-scale magnetic field, as well as elongated condensations that are …
We have begun a systematic numerical study of the nonlinear growth of nonaxisymmetric perturbations during the ambipolar diffusion-driven evolution of initially magnetically subcritical molecular clouds, with an eye on the formation of binaries, multiple stellar systems and small clusters. In this initial study, we focus on the $m=2$ (or bar) mode, which is shown to be unstable during the dynamic collapse phase of cloud evolution after the central region has become magnetically supercritical. We find that, despite the presence of a strong magnetic field, the bar can grow fast enough that for a…
We study numerically the ambipolar diffusion-driven evolution of non-rotating, magnetically subcritical, disk-like molecular clouds, assuming axisymmetry. Previous similar studies have concentrated on the formation of single magnetically supercritical cores at the cloud center, which collapse to form isolated stars. We show that, for a cloud with many Jeans masses and a relatively flat mass distribution near the center, a magnetically supercritical ring is produced instead. The supercritical ring contains a mass well above the Jeans limit. It is expected to break up, through both gravitational…
In the standard scenario of isolated low-mass star formation, strongly magnetized molecular clouds are envisioned to condense gradually into cores, driven by ambipolar diffusion. Once the cores become magnetically supercritical, they collapse to form stars. Most previous studies based on this scenario are limited to axisymmetric calculations leading to single supercritical core formation. The assumption of axisymmetry has precluded a detailed investigation of cloud fragmentation, generally thought to be a necessary step in the formation of binary and multiple stars. In this contribution, we de…
The existence of quasars at redshift z > 5 indicates that supermassive black holes were present since the very early times. If they grew by accretion, the seeds of mass ~ 10^5 Msun must have formed at z ~ 9. These seed black holes may result from the collapse and dissipation of primordial gas during the early stages of galaxy formation. I discuss the effects of magnetic fields on the fragmentation of cold gas clouds embedded into a hot diffuse phase and a virialized dark matter halo. The field of 10^-4 G ejected by supernova remnants can halt cloud break-up at 10^4 Msun. High star formation ra…
We review theoretical models of the early stages of star formation, in which gravitational collapse is strongly regulated by magnetic fields and the associated process of ambipolar diffusion. We discuss results of numerical simulations and analytical studies of core formation and collapse, which can be directly tested against observation. We also focus on recent data which are relevant to this theory of star formation, such as: observations of extended infall in protostellar cores, estimates of evolutionary timescales ~ 1 Myr for cores, measured mass-to-flux ratios of cores, and the relative a…
Improving our understanding of the initial conditions and earliest stages of star formation is crucial to gain insight into the origin of stellar masses, multiple systems, and protoplanetary disks. We review the properties of low-mass dense cores as derived from recent millimeter/submillimeter observations of nearby molecular clouds and discuss them in the context of various contemporary scenarios for cloud core formation and evolution. None of the extreme scenarios can explain all observations. Pure laminar ambipolar diffusion has relatively long growth times for typical ionization levels and…
X-ray emission from hot (T = 10^7 K) interstellar gas in massive elliptical galaxies indicates that 10^{10} M_sun has cooled over a Hubble time, but optical and radio evidence for this cold gas is lacking. We provide detailed theoretical support for the hypothesis that this gas has formed into low luminosity stars. Within several kpc of the galactic center, interstellar gas first cools to T = 10^4 K where it is heated by stellar UV and emits the observed diffuse optical line emission. This cooling occurs at a large number (10^6) of isolated sites. After less than a solar mass of gas has accumu…
In the context of star formation through fragmentation of an extremely metal-deficient protogalactic cloud, the gravitational collapse of filamentary gas clouds is explored with 1D numerical hydrodynamics coupled with non-equilibrium chemistry of H$_2$ and HD. It is found that the cloud evolution is governed mainly by the initial central density ($n_{\rm c,0}$) and H$_2$ abundance ($x_{\rm H_2,0}$). In particular, the evolution of low-density filaments bifurcates at a threshold H$_2$ abundance of $x_{\rm H_2,cr}\simeq 3 \times 10^{-3}$, beyond which HD cooling overwhelms H$_2$ cooling. The con…
Magnetic fields are proposed to play an important role in the formation and support of self-gravitating clouds and the formation and evolution of protostars in such clouds. We use R-band linear polarimetry collected for about 12000 stars in 46 fields with lines of sight toward the Pipe nebula to investigate the properties of the polarization across this dark cloud complex. Mean polarization vectors show that the magnetic field is locally perpendicular to the large filamentary structure of the Pipe nebula (the `stem'), indicating that the global collapse may have been driven by ambipolar diffus…
