Characterizing the structure of diffuse emission in Hi-GAL maps

We present a study of the structure of the Galactic interstellar medium through the Delta-variance technique, related to the power spectrum and the fractal properties of infrared/sub-mm maps. Through this method, it is possible to provide quantitative parameters which are useful to characterize different morphological and physical conditions, and to better constrain the theoretical models. In this respect, the Herschel Infrared Galactic Plane Survey carried out at five photometric bands from 70 to 500 \mu m constitutes an unique database for applying statistical tools to a variety of regions across the Milky Way. In this paper, we derive a robust estimate of the power-law portion of the power spectrum of four contiguous 2{\deg}x2{\deg} Hi-GAL tiles located in the third Galactic quadrant (217{\deg} < l < 225{\deg}, -2{\deg} < b < 0{\deg}). The low level of confusion along the line of sight testified by CO observations makes this region an ideal case. We find very different values of the power spectrum slope from tile to tile but also from wavelength to wavelength (2 < \beta < 3), with similarities between fields attributable to components located at the same distance. Thanks to the comparison with models of turbulence, an explanation of the determined slopes in terms of the fractal geometry is also provided, and possible relations with the underlying physics are investigated. In particular, an anti-correlation between ISM fractal dimension and star formation efficiency is found for the two main distance components observed in these fields. A possible link between the fractal properties of the diffuse emission and the resulting clump mass function is discussed.