Ambipolar Diffusion and Star Formation: Formation and Contraction of Axisymmetric Cloud Cores. II. Results

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Abstract

The problem of the formation and contraction of fragments (or cores) in magnetically supported parent molecular clouds was formulated in a previous paper. Three dimensionless free parameters appear in the evolution equations: the initial ratio of the free-fall and neutral-ion collision times (in the uniform reference state), ν_ff,0, the exponent κ in the relation between the ion and neutral densities n_i ∝ nk_n, and the initial ratio of the magnetic and thermal pressures, α₀. The initial central mass-to-flux ratio in units of the critical value for gravitational collapse, μ₀ enters through the initial conditions. We follow both the quasistatic and dynamic phases of contraction and demonstrate that ambipolar diffusion leads to self-initiated protostar formation ("quasistatic" meaning motion with negligible acceleration). A typical cloud core forms and contracts quasi- statically on the flux-loss time scale until the central mass-to-flux ratio (dM/dΦ_B)_c exceeds the critical value. During quasistatic contraction, the magnetic field lines are essentially "held in place" as the neutrals contract through them, and the field strength increases by less than a factor of 2. Despite subsequent dynamic contraction perpendicular to magnetic field lines, thermal pressure continues to balance gravity along field lines, thereby enforcing quasistatic contraction in this direction. We follow the contraction until the central density n_c increases by a factor of 106 (typically from 3 × 102 to 3 × 108 cm-3). The envelope remains magnetically supported. The results from our parameter study show that decreasing ν_ff,0 speeds up ambipolar diffusion, shortens the quasistatic phase of contraction, and causes (dM/dΦ_B)_c to increase by a greater amount above the critical value. The enhancement of the central magnetic field B_c, however, is not sensitive to the value of ν_ff,0. A smaller κ leads to progressively more rapid ambipolar diffusion as n_c increases. Reducing μ₀ lengthens the duration of the quasistatic phase and results in a larger reduction of a core's magnetic flux, but the dynamic phase of contraction is independent of μ₀. The value of (dM/dΦ_B)_c in our models is initially 1.9-16.3 times smaller than the critical value, but increases (because of ambipolar diffusion) by a factor of 10-50 by the time n_c has increased by a factor ≡106. The value of α₀ mainly affects the relaxation of clouds from their initial states into the corresponding equilibrium states under flux-freezing, in which α is related to μ₀ by &alpha_;c,eqμ2₀ ≍ constant.

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