Supersonic turbulence in the interstellar medium: Stellar extinction determinations as probes of the structure and dynamics of dark clouds

Lada et al. 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 three-dimensional density held of the gas is well described by a lognormal distribution down to very small scales. 2. The power spectrum and the standard deviation of the three-dimensional density held can be constrained. 3. Such a structure of the density field is likely to be the effect of random supersonic motions present in the gas. In fact, we find a qualitative and quantitative agreement between the predictions based on recent numerical simulations of randomly forced supersonic flows by Nordlund & Padoan and by Padoan, Nordlund, & Jones and the constraints given by the infrared dust extinction measurements.