It is established that the formation of rotationally supported disks during the main accretion phase of star formation is suppressed by a moderately strong magnetic field in the ideal MHD limit. Non-ideal MHD effects are expected to weaken the magnetic braking, perhaps allowing the disk to reappear. We concentrate on one such effect, ambipolar diffusion, which enables the field lines to slip relative to the bulk neutral matter. We find that the slippage does not sufficiently weaken the braking to allow rotationally supported disks to form for realistic levels of cloud magnetization and cosmic ray ionization rate; in some cases, the magnetic braking is even enhanced. Only in dense cores with both exceptionally weak fields and unreasonably low ionization rate do such disks start to form in our simulations. We conclude that additional processes, such as Ohmic dissipation or Hall effect, are needed to enable disk formation. Alternatively, the disk may form at late times when the massive envelope that anchors the magnetic brake is dissipated, perhaps by a protostellar wind.
Recent high-resolution studies of the L1544 protostellar core by Tafalla et al. and Williams et al. reveal the structure and kinematics of the gas. The observations of this prestellar core provide a natural test for theoretical models of core formation and evolution. Based on their results, the above authors claim a discrepancy with the implied infall motions from ambipolar diffusion models. In this paper, we reexamine the earlier ambipolar diffusion models, and conclude that the L1544 core can be understood to be a magnetically supercritical core undergoing magnetically diluted collapse. We a…
Magnetic fields are usually considered dynamically important in star formation when the dimensionless mass-to-flux ratio is close to, or less than, unity (lambda<~1). We show that, in disk formation, the requirement is far less stringent. This conclusion is drawn from a set of 2D (axisymmetric) simulations of the collapse of rotating, magnetized, singular isothermal cores. We find that a weak field corresponding to 1ambda~100 can begin to disrupt the rotationally supported disk through magnetic braking, by creating regions of rapid, supersonic collapse in the disk. These regions are separated …
We extend our earlier work on ambipolar diffusion induced formation of protostellar cores in isothermal sheet-like magnetic interstellar clouds, by studying nonaxisymmetric collapse for the physically interesting regime of magnetically critical and supercritical model clouds ($\mui \geq 1$, where $\mui$ is the initial mass-to-magnetic flux ratio in units of the critical value for gravitational collapse). Cores that form in model simulations are effectively triaxial, with shapes that are typically closer to being oblate, rather than prolate. Infall velocities in the critical model ($\mui = 1$) …
Recent WMAP observations indicate that the primordial abundance of lithium should have been 2-4 times higher than the value measured in low-metallicity stars. We show that this discrepancy can be explained by the process of ambipolar diffusion in protostellar clouds, which leads to depletion of elements with low ionization potential, such as lithium and sodium. In high-metallicity stars, [Fe/H]>~-1, the depletion of lithium due to this process is found to be negligible, but for [Fe/H]<~-1.5 the lithium abundance falls by a factor of ~3, consistent with WMAP observations.
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…
We revisit the problem of the formation of dense protostellar cores due to ambipolar diffusion within magnetically supported molecular clouds, and derive an analytical expression for the core formation timescale. The resulting expression is similar to the canonical expression = t_{ff}^2/t_{ni} ~ 10 t_{ni} (where t_{ff} is the free-fall time and t_{ni} is the neutral-ion collision time), except that it is multiplied by a numerical factor C(μ_{c0}), where μ_{c0} is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C(μ_{c0}) is typically ~ 1 in hi…
Improving our understanding of the earliest stages of star formation is crucial to gain insight into the origin of stellar masses, multiple systems, and protoplanetary disks. We discuss recent advances made in this area thanks to detailed mapping observations at infrared and (sub)millimeter wavelengths. Although ambipolar diffusion appears to be too slow to play a direct role in the formation of dense cores, there is nevertheless good evidence that the gravitational collapse of isolated protostellar cores is strongly magnetically controlled. We also argue that the beginning of protostellar col…
This paper reviews current theoretical work on the various stages of accretion in protostars, and the relationship of these ideal stages to the spectral classes of observed protostellar systems. I discuss scaling relationships that have been obtained for models of pre-stellar cores as they evolve by ambipolar diffusion toward a central singularity, and expectations for the dynamical evolution as the cores collapse radially to form a rotating disk. I summarize work that suggests accretion in T Tauri systems may be limited by ionization to disk surface layers, and implications for the variation …
Angular momentum in protostellar discs can be transported either radially, through turbulence induced by the magnetorotational instability (MRI), or vertically, through the torque exerted by a large-scale magnetic field. We present a model of steady-state discs where these two mechanisms operate at the same radius and derive approximate criteria for their occurrence in an ambipolar diffusion dominated disc. We obtain "weak field'' solutions - which we associate with the MRI channel modes in a stratified disc - and transform them into accretion solutions with predominantly radial angular-moment…
Newly formed stars are often observed to possess circumstellar disks, from which mass continues to be accreted onto the star and fed into outflowing jets, and which eventually may evolve into dusty debris disks and planetary systems. Recent modeling developments have made it possible, for the first time, to study the formation and early evolution of rotationally supported protostellar disks in the context of a realistic scenario of star formation in weakly ionized, magnetic, molecular cloud cores. The derived semianalytic solutions incorporate ambipolar diffusion and magnetic braking and may b…
Under ideal MHD conditions the magnetic field strength should be correlated with density in the interstellar medium (ISM). However, observations indicate that this correlation is weak. Ambipolar diffusion can decrease the flux-to-mass ratio in weakly ionized media; however, it is generally thought to be too slow to play a significant role in the ISM except in the densest molecular clouds. Turbulence is often invoked in astrophysical problems to increase transport rates above the (very slow) laminar values predicted by kinetic theory. We describe a series of numerical experiments addressing the…
We follow the ambipolar-diffusion--driven formation and evolution of a fragment in a magnetically supported molecular cloud, until a hydrostatic protostellar core forms at its center. This problem was formulated in Paper I. We determine the density, velocity and magnetic field as functions of space and time, and the contribution of ambipolar diffusion and Ohmic dissipation to the resolution of the magnetic flux problem of star formation. The issue of whether the magnetic field ever decouples from the (neutral) matter is also addressed. We also find that the electrons do not decouple from the f…
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…
The breakdown of flux-freezing in molecular clouds and protostellar discs is usually approximated by ambipolar diffusion at low densities or by resistive diffusion at high densities. Here I discuss an intermediate regime in which the Hall term in the conductivity tensor is significant, and the vector evolution of the magnetic field -- and therefore the evolution of the system under consideration -- is dramatically altered. Calculations of charged particle abundances in dense gas in molecular clouds and protostellar discs demonstrate that Hall diffusion is important over a surprisingly broad ra…
We present self-similar solutions that describe the gravitational collapse of rotating, isothermal, magnetic molecular-cloud cores, relevant to the formation of rotationally supported protostellar disks. This work focuses on the evolution after a point mass first forms at the center and generalizes previous results by Contopoulos, Ciolek, & Konigl that did not include rotation. Our model includes ambipolar diffusion and magnetic braking and allows us to examine the full range of expected behaviors and their dependence on the physical parameters. For typical parameter values, the inflow first p…
Angular momentum transport in protostellar discs can take place either radially, through turbulence induced by the magnetorotational instability (MRI), or vertically, through the torque exerted by a large-scale magnetic field that threads the disc. Using semi-analytic and numerical results, we construct a model of steady-state discs that includes vertical transport by a centrifugally driven wind as well as MRI-induced turbulence. We present approximate criteria for the occurrence of either one of these mechanisms in an ambipolar diffusion-dominated disc. We derive ``strong field'' solutions in…
We formulate the problem of the formation and collapse of nonaxisymmetric protostellar cores in weakly ionized, self-gravitating, magnetic molecular clouds. In our formulation, molecular clouds are approximated as isothermal, thin (but with finite thickness) sheets. We present the governing dynamical equations for the multifluid system of neutral gas and ions, including ambipolar diffusion, and also a self-consistent treatment of thermal pressure, gravitational, and magnetic (pressure and tension) forces. The dimensionless free parameters characterizing model clouds are discussed. The response…
Interstellar magnetic fields influence all stages of the process of star formation, from the collapse of molecular cloud cores to the formation of protostellar jets. This requires us to have a full understanding of the physical properties of magnetized plasmas of different degrees of ionization for a wide range of densities and temperatures. We derive general equations governing the magneto-hydrodynamic evolution of a three-fluid medium of arbitrary ionization, also including the possibility of charged dust grains as the main charge carriers. In a companion paper (Pinto & Galli 2007), we compl…
MHD in protostellar discs is modified by the Hall current when the ambipolar diffusion approximation breaks down. Here I examine the Balbus-Hawley (magnetorotational) instability of a weak, vertical magnetic field within a weakly-ionized disc. Vertical stratification is neglected, and a linear analysis is undertaken for the case that the wave vector of the perturbation is parallel to the magnetic field. The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel ca…
We formulate the problem of the formation and subsequent evolution of fragments (or cores) in magnetically-supported, self-gravitating molecular clouds in two spatial dimensions. The six-fluid (neutrals, electrons, molecular and atomic ions, positively-charged, negatively-charged, and neutral grains) physical system is governed by the radiative, nonideal magnetohydrodynamic (RMHD) equations. The magnetic flux is not assumed to be frozen in any of the charged species. Its evolution is determined by a newly-derived generalized Ohm's law, which accounts for the contributions of both elastic and i…
We use magnetic collapse models to place some constraints on the formation and angular momentum evolution of circumstellar disks which are embedded in magnetized cloud cores. Previous models have shown that the early evolution of a magnetized cloud core is governed by ambipolar diffusion and magnetic braking, and that the core takes the form of a nonequilibrium flattened envelope which ultimately collapses dynamically to form a protostar. In this paper, we focus on the inner centrifugally-supported disk, which is formed only after a central protostar exists, and grows by dynamical accretion fr…
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 …
The problem of the late accretion phase of the evolution of an axisymmetric, isothermal magnetic disk surrounding a forming star has been formulated in a companion paper. The "central sink approximation" is used to circumvent the problem of describing the evolution inside the opaque central region for densities greater than 10^11 cm^-3 and radii smaller than a few AUs. Only the electrons are assumed to be attached to the magnetic field lines, and the effects of both negatively and positively charged grains are accounted for. After a mass of 0.1 solar mass accumulates in the central cell (formi…
