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 ~ M -1.44±0.1 and a velocity dispersion-size relation Δ v ~ 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 ~ ρ α , with α = -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 Δ v - 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 ρ ∝ 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 Δ v - R relation, and of 100 in the density-size relation, according to the equilibrium relation Δ v ~ ( 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.