Fragmentation and Collapse in Magnetic Molecular Clouds: Natural Length Scales and Protostellar Masses

Abstract

Gravity is of course ultimately responsible for fragmentation and star 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 natural “Alfven length scale” (λ A = πv A τni) in the problem which together with a thermal (λT = 1.09 Ca τff) and a magnetic (λ M = 0.62 v A τff) “Jeans length” lead to the formation of fragments (or cores) in otherwise quiescent clouds and determine the sizes and masses of these fragments during the subsequent phases of contraction. (The quantity v A is the Alfven speed, τni the mean neutral-ion collision time, Ca the adiabatic speed of sound, and τff the free fall 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 relation B c ∝ p c κ between the magnetic field strength and the gas density in cloud cores holds with κ = 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 κ ≃ 1/2 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⊙ and a magnetic field ≃ 3 mGauss, and is surrounded by a spatially rapidly decreasing, highly nonspherical (disk-like) density distribution. The amount of mass available for accretion onto the compact core is limited by magnetic forces, and is typically ~ 1 M⊙. These results are built into the detailed scenario for star formation described recently elsewhere.