Supersonic turbulence in the ISM: stellar extinction determinations as probes of the structure and dynamics of dark clouds

Lada et al. (1994) have described a method for studying the distribution of dust in dark clouds using infrared imaging surveys. In particular they show that the method provides some information about the structure of the gas (dust) on scales smaller than their resolution. In the present work we clarify the nature of the information provided by their method. We show that:

1. the 3D density field of the gas is well described by a Log-Normal distribution down to very small scales;
2. the power spectrum and the standard deviation of the 3D density field can be constrained;
3. the origin of such a structure of the density field is likely to be the supersonic turbulence in the gas. In fact we find a qualitative and quantitative agreement between the predictions based on recent numerical simulations of supersonic turbulence (Nordlund and Padoan 1996; Padoan, Nordlund and Jones 1996) and the constraints given by the infrared dust extinction measurements.