A search for Larson-type relations in numerical simulations of the ISM: Evidence for nonconstant column densities

We present results from a statistical study of clouds in two-dimensional numerical simulations of the interstellar medium. The clouds in the simulations exhibit a differential mass spectrum dN(M)/dM similar to M(-1.44+/-0.1) and a velocity dispersion-size relation Delta nu similar to R(0.41+/-0.08). However, the clouds do not exhibit a clear density-size relation. At a given mean density, clouds span a range of sizes from the smallest resolved scales up to a maximum given by a Larson-type relation R(max) similar to p(alpha), with alpha = -0.81 +/- 0.15, although numerical effects cannot be ruled out as being responsible for the latter correlation. The clouds additionally span a range of column densities N of 2 orders of magnitude, supporting the suggestion that the observational density-size relation may be an artifact of survey limitations. In this case, the Delta nu-R relation can be interpreted as a direct consequence of a k(-2) turbulent spectrum rather than of virial equilibrium of clouds that satisfy a p proportional to R(-1) law. The k(-2) spectrum is verified in the simulations and is characteristic of a field of shocks. However, we also discuss the possibility that the clouds are in balance between self-gravity and turbulence but with a scatter of at least a factor of 10 in the Delta nu-R relation, and of 100 in the density-size relation, according to the equilibrium relation Delta nu similar to (NR)(1/2). In addition, we compare these results with recent observational data. We propose a simple model suggesting that recent results that find nearly constant column densities for dark IRAS clouds may be an artifact of a temperature gradient within the clouds induced by external radiative heating. As a consequence, we emphasize that IRAS surface brightness maps are not appropriate for measuring column densities.