The Hi-GAL catalogue of dusty filamentary structures in the Galactic Plane

The recent data collected by {\it Herschel} have confirmed that interstellar structures with filamentary shape are ubiquitously present in the Milky Way. Filaments are thought to be formed by several physical mechanisms acting from the large Galactic scales down to the sub-pc fractions of molecular clouds, and they might represent a possible link between star formation and the large-scale structure of the Galaxy. In order to study this potential link, a statistically significant sample of filaments spread throughout the Galaxy is required. In this work we present the first catalogue of $32,059$ candidate filaments automatically identified in the Hi-GAL survey of the entire Galactic Plane. For these objects we determined morphological (length, $l^{a}$, and geometrical shape) and physical (average column density, $N_{\rm H_{2}}$, and average temperature, $T$) properties. We identified filaments with a wide range of properties: 2$'$\,$\leq l^{a}\leq$\, 100$'$, $10^{20} \leq N_{\rm H_{2}} \leq 10^{23}$\,cm$^{-2}$ and $10 \leq T\leq$ 35\,K. We discuss their association with the Hi-GAL compact sources, finding that the most tenuous (and stable) structures do not host any major condensation and we also assign a distance to $\sim 18,400$ filaments for which we determine mass, physical size, stability conditions and Galactic distribution. When compared to the spiral arms structure, we find no significant difference between the physical properties of on-arm and inter-arm filaments. We compared our sample with previous studies, finding that our Hi-GAL filament catalogue represents a significant extension in terms of Galactic coverage and sensitivity. This catalogue represents an unique and important tool for future studies devoted to understanding the filament life-cycle.