A Search for Larson-Type Relations in Numerical Simulations of the ISM. Evidence for Non-Constant 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 $dN(M)\mathrm{/}dM\sim M^{-1.44\pm 0.1}$ and a velocity dispersion-size relation $\mathrm{\Delta }v\sim R^{0.41\pm 0.08}$. However, the clouds do {\it 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 $R_{\mathrm{m}\mathrm{a}\mathrm{x}}\sim {\rho }^{\alpha }$, with $\alpha =-0.81\pm .15$, although numerical effects cannot be ruled out as responsible for the latter correlation. Clouds span a range of column densities $N$ of two orders of magnitude, supporting the suggestion that the observational density-size relation may be an artifact of survey limitations. In this case, the $\mathrm{\Delta }v$–$R$ relation can be interpreted as a direct consequence of a $k^{-2}$ turbulent spectrum, characteristic of a field of shocks, verified in the simulations, rather than of virial equilibrium of clouds with a $\rho \propto R^{-1}$ law. 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 $Deltav$–$R$ relation, and of 100 in the density-size relation, according to the equilibrium relation $\mathrm{\Delta }v\sim (NR{)}^{1\mathrm{/}2}$. Finally, we compare these results with observational data. We propose a simple model suggesting that recent results finding 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.