Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: II. Comparison with Observation, Clump Properties, and Scaling to Physical Units

Abstract

Ambipolar diffusion is important in redistributing magnetic flux and in damping Alfven waves in molecular clouds. The importance of ambipolar diffusion on a length scale $\ell$ is governed by the ambipolar diffusion Reynolds number, $\rad=\ell/\lad$, where $\lad$ is the characteristic length scale for ambipolar diffusion. The logarithmic mean of the AD Reynolds number in a sample of 15 molecular clumps with measured magnetic fields (Crutcher 1999) is 17, comparable to the theoretically expected value. We identify several regimes of ambipolar diffusion in a turbulent medium, depending on the ratio of the flow time to collision times between ions and neutrals; the clumps observed by Crutcher (1999) are all in the standard regime of ambipolar diffusion, in which the neutrals and ions are coupled over a flow time. We have carried out two-fluid simulations of ambipolar diffusion in isothermal, turbulent boxes for a range of values of $\rad$. The mean Mach numbers were fixed at $\calm=3$ and $\ma=0.67$; self-gravity was not included. We study the properties of overdensities--i.e., clumps--in the simulation and show that the slope of the higher-mass portion of the clump mass spectrum increases as $\rad$ decreases, which is qualitatively consistent with Padoan et al. (2007)'s finding that the mass spectrum in hydrodynamic turbulence is significantly steeper than in ideal MHD turbulence. For a value of $\rad$ similar to the observed value, we find a slope that is consistent with that of the high-mass end of the Initial Mass Function for stars. However, the value we find for the spectral index in our ideal MHD simulation differs from theirs, presumably because our simulations have different initial conditions. This suggests that the mass spectrum of the clumps in the Padoan et al. (2007) turbulent fragmentation model for the IMF depends on the environment, which would conflict with evidence ...