2025A&A...696A.217R

Molecular clouds are astrophysical objects whose complex nonlinear dynamics are reflected in their complex morphological features. Many studies investigating the bridge between higher-order statistics and physical properties have highlighted the value of non-Gaussian morphological features in capturing physical information. Yet, as this bridge is usually characterized in the supervised world of simulations, transferring it to observations can be hazardous, especially when the discrepancy between simulations and observations remains unknown. In this paper, we aim to evaluate, directly from the observation data, the discriminating ability of a set of statistics. To do so, we developed a test that allowed us to compare the informative power of two sets of summary statistics for a given unlabeled dataset. Contrary to supervised approaches, this test does not require knowledge of any class label or parameter associated with the data. Instead, it evaluates and compares the degeneracy levels of the summary statistics based on a notion of statistical compatibility. We applied this test to column density maps of 14 nearby molecular clouds observed by Herschel and iteratively compared different sets of typical summary statistics. We show that a standard Gaussian description of these clouds is highly degenerate but can be substantially improved when being estimated on the logarithm of the maps. This illustrates that low-order statistics, when properly used, remain a very powerful tool. We further show that such descriptions still exhibit a small quantity of degeneracies, some of which are lifted by the higher-order statistics provided by reduced wavelet scattering transforms. These degeneracies quantitatively differ between observations and state-of-the-art simulations of dense molecular cloud collapse, and they are not present for log-fractional Brownian motion models. Finally, we show how the summary statistics identified can be cooperatively used to build a morphological distance, which is evaluated visually and gives convincing results.