2010ApJ...720.1612M

Ambipolar diffusion (AD) is important in redistributing magnetic flux and in damping Alfvén waves in molecular clouds. The importance of AD on a length scale ℓ is governed by the AD Reynolds number, R_AD= ℓ/ℓ_AD, where ℓ_AD is the characteristic length scale for AD. The logarithmic mean of the AD Reynolds number in a sample of 15 molecular clumps with measured magnetic fields is 17, comparable to the theoretically expected value. We identify several regimes of AD in a turbulent medium, depending on the ratio of the flow time to collision times between ions and neutrals; the clumps observed by Crutcher in 1999 are all in the standard regime of AD, in which the neutrals and ions are coupled over a flow time. We have carried out two-fluid simulations of AD in isothermal, turbulent boxes for a range of values of R_AD. The mean Mach numbers were fixed at {M=3} and {{M_A}=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 R_ADdecreases, which is qualitatively consistent with Padoan et al.'s finding that the mass spectrum in hydrodynamic turbulence is significantly steeper than in ideal MHD turbulence. For a value of R_AD similar to the observed value, we find a slope that is consistent with that of the high-mass end of the initial mass function (IMF) 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. turbulent fragmentation model for the IMF depends on the environment, which would conflict with evidence for a universal IMF. In addition, we give a general discussion of how the results of simulations of magnetized, turbulent, isothermal boxes can be scaled to physical systems. Each physical process that is introduced into the simulation, such as AD, introduces a dimensionless parameter, such as R_AD, which must be fixed for the simulation, thereby reducing the number of scaling parameters by one. We show that the importance of self-gravity is fixed in any simulation of AD; it is not possible to carry out a simulation in which self-gravity and AD are varied independently unless the ionization is a free parameter. We show that our simulations apply to small regions in molecular clouds, generally with ℓ₀≲ 0.4 pc and M ≲ 25 M_☉. A general discussion of the scaling relations for magnetized, isothermal, turbulent boxes, including self-gravitating systems, is given in the appendix.