Dense, star-forming, cores of molecular clouds are observed to be significantly magnetized. A realistic magnetic field of moderate strength has been shown to suppress, through catastrophic magnetic braking, the formation of a rotationally supported disk during the protostellar accretion phase of low-mass star formation in the ideal MHD limit. We address, through 2D (axisymmetric) simulations, the question of whether realistic levels of nonideal effects, computed with a simplified chemical network including dust grains, can weaken the magnetic braking enough to enable a rotationally supported disk to form. We find that ambipolar diffusion, the dominant nonideal MHD effect over most of the density range relevant to disk formation, does not enable disk formation, at least in 2D. The reason is that ambipolar diffusion allows the magnetic flux that would be dragged into the central stellar object in the ideal MHD limit to pile up instead in a small circumstellar region, where the magnetic field strength (and thus the braking efficiency) is greatly enhanced. We also find that, on the scale of tens of AU or more, a realistic level of Ohmic dissipation does not weaken the magnetic braking enough for a rotationally supported disk to form, either by itself or in combination with ambipolar diffusion. The Hall effect, the least explored of these three nonideal MHD effects, can spin up the material close to the central object to a significant, supersonic rotation speed, even when the core is initially non-rotating, although the spun-up material remains too sub-Keplerian to form a rotationally supported disk. The problem of catastrophic magnetic braking that prevents disk formation in dense cores magnetized to realistic levels remains unresolved. Possible resolutions of this problem are discussed.
It is widely believed that T Tauri winds are driven magnetocentrifugally from accretion disks close to the central stars. The exact launching conditions are uncertain. We show that a general relation exists between the poloidal and toroidal velocity components of a magnetocentrifugal wind at large distances and the rotation rate of the launching surface, independent of the uncertain launching conditions. We discuss the physical basis of this relation and verify it by using a set of numerically determined large-scale wind solutions. Both velocity components are in principle measurable from spatially resolved spectra, as has been done for the extended lowvelocity component (LVC) of the DG Tauri wind by Bacciotti et al. For this particular source, we infer that the spatially resolved LVC originates from a region on the disk extending from ∼0.3 to ∼4.0 AU from the star, which is consistent with, and a refinement over, the rough estimate of Bacciotti et al.
We present self-similar solutions that describe the gravitational collapse of rotating, isothermal, magnetic molecular-cloud cores. These solutions make it possible, for the first time, to study the formation of rotationally supported protostellar disks of the type detected around many young stellar objects in the context of a realistic scenario of star formation in magnetically supported, weakly ionized, molecular cloud cores. This work focuses on the evolution after a point mass first forms at the center and generalizes previous results by Contopoulos, Ciolek, & Königl that did not include rotation. Our semianalytic scheme incorporates ambipolar diffusion and magnetic braking and allows us to examine the full range of expected behaviors and their dependence on the physical parameters. We find that, for typical parameter values, the inflow first passes through an ambipolar-diffusion shock (at a radius r a ), where the magnetic flux decouples from the matter, and subsequently through a centrifugal shock (at r c ), inward of which a rotationally supported disk (of mass M d ) is established. By the time (∼ 10 5 yr) that the central mass M c grows to ∼ 1 M ⊙ , r a 10 3 AU, r c 10 2 AU, and M d /M c 0.1. The derived disk properties are consistent with data on T Tauri systems, and our results imply that protostellar disks may well be Keplerian also during earlier phases of their evolution. We demonstrate that the disk is likely to drive centrifugal outflows that transport angular momentum and mass, and we show how the radially self-similar wind solution of Blandford & Payne can be naturally incorporated into the disk model. We further verify that gravitational torques and magnetorotational instability-induced turbulence typically do not play an important role in the angular momentum transport. For completeness, we also present solutions for the limiting cases of fast rotation (where the collapse results in a massive disk with such a large outer radius that it traps the ambipolar-diffusion front) and strong braking (where no disk is formed and the collapse resembles that of a nonrotating core at small radii), as well as solutions describing the rotational collapse of ideal-MHD and of nonmagnetic model cores.
It has been shown that a realistic level of magnetization of dense molecular cloud cores can suppress the formation of a rotationally supported disk (RSD) through catastrophic magnetic braking in the axisymmetric ideal MHD limit. In this study, we present conditions for the formation of RSDs through non-ideal MHD effects computed self-consistently from an equilibrium chemical network. We find that removing from the standard MRN distribution the large population of very small grains (VSGs) of ∼10 Å to few 100 Å that dominate the coupling of the bulk neutral matter to the magnetic field increases the ambipolar diffusivity by ∼1-2 orders of magnitude at densities below 10 10 cm −3 . The enhanced ambipolar diffusion (AD) in the envelope reduces the amount of magnetic flux dragged by the collapse into the circumstellar disk-forming region. Therefore, magnetic braking is weakened and more angular momentum can be retained. With continuous high angular momentum inflow, RSDs of tens of AU are able to form, survive, and even grow in size, depending on other parameters including cosmic-ray ionization rate, magnetic field strength, and rotation speed. Some disks become self-gravitating and evolve into rings in our 2D (axisymmetric) simulations, which have the potential to fragment into (close) multiple systems in 3D. We conclude that disk formation in magnetized cores is highly sensitive to chemistry, especially to grain sizes. A moderate grain coagulation/growth to remove the large population of VSGs, either in the prestellar phase or during free-fall collapse, can greatly promote AD and help formation of tens of AU RSDs.
We present ALMA 1.3 mm continuum, 12 CO, C 18 O, and SO data for the Class 0 protostars, Lupus 3 MMS, IRAS 15398−3559, and IRAS 16253−2429 at resolutions of ∼100 AU. By measuring a rotational profile in C 18 O, a 100 AU Keplerian disk around a 0.3 M ⊙ protostar is observed in Lupus 3 MMS. No 100 AU Keplerian disks are observed in IRAS 15398−3559 and IRAS 16253−2429. Nevertheless, embedded compact (<30 AU) continuum components are detected. The C 18 O emission in IRAS 15398−3559 shows signatures of infall with a constant angular momentum. IRAS 16253−2429 exhibits signatures of infall and rotation, but its rotational profile is unresolved. By fitting the C 18 O data with our kinematic models, the protostellar masses and the disk radii are inferred to be 0.01 M ⊙ and 20 AU in IRAS 15398−3559, and 0.03 M ⊙ and 6 AU in IRAS 16253−2429. By comparing the specific angular momentum profiles from 10,000 to 100 AU in 8 Class 0 and I protostars, we find that the evolution of envelope rotation can be described with conventional inside-out collapse models. In comparison with a sample of 18 protostars with known disk radii, our results reveal signs of disk growth, with the disk radius increasing as M * 0.8±0.14 or t 1.09±0.37 in the Class 0 stage, where M * is the protostellar mass and t is the age. The disk growth rate slows down in the Class I stage. Besides, we find a hint that the mass accretion rate declines as t −0.26±0.04 from the Class 0 to I stages.
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