The spectral correlation function of molecular clouds: A statistical test for theoretical models

We compute the spectral correlation function (SCF) of (CO)-C-13 J=1-0 maps of molecular cloud complexes. The SCF is a power law over approximately an order of magnitude in spatial separation in every map. The power-law slope of the SCF, alpha, its normalization, S-0(1 pc), and the spectral line width averaged over the whole map, sigma(v), are computed for all the observational maps. The values of alpha, S-0(1 pc), and sigma(v) are combined to obtain empirical correlations to be used as tests for theoretical models of molecular clouds. Synthetic spectral maps are computed from different theoretical models, including solutions of the magnetohydrodynamic (MHD) equations with different values of the rms Mach number of the flow and stochastic models with different power spectra of the velocity field. In order to compute the radiative transfer from the MHD models, it is necessary to assign the models a physical scale and a physical density. When these assignments are made according to Larson-type relations, the best fit to the observational correlations is obtained. Unphysical stochastic models are instead ruled out by the empirical correlations. MHD models with equipartition of magnetic and kinetic energy of turbulence do not reproduce the observational data when their average magnetic field is oriented approximately parallel to the line of sight.