Magnetic braking, ambipolar diffusion, cloud cores, and star formation - Natural length scales and protostellar masses

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Abstract

Magnetic braking is essential for cloud contraction and star formation. Ambipolar diffusion is unavoidable in self-gravitating, magnetic clouds and leads to single-stage (as opposed to hierarchical) fragmentation (or core formation) and protostar formation. Magnetic forces dominate thermal-pressure and centrifugal forces over scales comparable to molecular cloud radii. Magnetic support of molecular clouds and the imperfect collisional coupling between charged and neutral particles introduce a critical magnetic length scale (λ_M,cr = 0.62υ_Aτ_ff) and an Alfvén length scale ((λ_A = πυ_Aτ_ni), respectively, in the problem which together with a critical thermal length scale (λ_T,cr = 1.09C_aτ_ff) explain naturally the formation of fragments (or cores) in otherwise quiescent clouds and determine the sizes and masses of these fragments during the subsequent stages of contraction. (The quantity υ_A is the Alfvén speed, τ_ni the mean neutral-ion collision time, C_a the adiabatic speed of sound, and τ_ff the free4all time scale.) Numerical calculations based on new adaptive-grid techniques follow the formation of fragments by ambipolar diffusion and their subsequent collapse up to an enhancement in central density above its initial equilibrium value by a factor ≃106 with excellent spatial resolution. The results confirm the existence and relevance of the three length scales and extend the analytical understanding of fragmentation and star formation derived from them. The ultimately bimodal opposition to gravity (by magnetic forces in the envelope and by thermal-pressure forces in the core) introduces a break in the slope of the log p_n -log r profile. The relation B_c ∞ pk_c between the magnetic field strength and the gas density in cloud cores holds with K = 0.4 - 0.5 even in the presence of ambipolar diffusion up to densities ∼109 cm-3 for a wide variety of clouds. The value K ≃ ½ is fairly typical. At the late stages of evolution, for example, at a central density of about 3 × 108 cm-3, a typical core is relatively uniform, contains 0.1 M_sun and a magnetic field ≃ 3 mG, and is surrounded by a spatially rapidly decreasing, highly nonspherical (disklike) density distribution. The amount of mass available for accretion onto the compact core is limited by magnetic forces, and is typically ≃1 M_sun. These results are built into the detailed scenario for star formation described recently elsewhere.

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