Properties of Hi-GAL clumps in the inner Galaxy]{The Hi-GAL compact source catalogue. I. The physical properties of the clumps in the inner Galaxy ($-71.0^{\circ}< \ell < 67.0^{\circ}$)

Hi-GAL is a large-scale survey of the Galactic plane, performed with Herschel in five infrared continuum bands between 70 and 500 $\mu$m. We present a band-merged catalogue of spatially matched sources and their properties derived from fits to the spectral energy distributions (SEDs) and heliocentric distances, based on the photometric catalogs presented in Molinari et al. (2016a), covering the portion of Galactic plane $-71.0^{\circ}< \ell < 67.0^{\circ}$. The band-merged catalogue contains 100922 sources with a regular SED, 24584 of which show a 70 $\mu$m counterpart and are thus considered proto-stellar, while the remainder are considered starless. Thanks to this huge number of sources, we are able to carry out a preliminary analysis of early stages of star formation, identifying the conditions that characterise different evolutionary phases on a statistically significant basis. We calculate surface densities to investigate the gravitational stability of clumps and their potential to form massive stars. We also explore evolutionary status metrics such as the dust temperature, luminosity and bolometric temperature, finding that these are higher in proto-stellar sources compared to pre-stellar ones. The surface density of sources follows an increasing trend as they evolve from pre-stellar to proto-stellar, but then it is found to decrease again in the majority of the most evolved clumps. Finally, we study the physical parameters of sources with respect to Galactic longitude and the association with spiral arms, finding only minor or no differences between the average evolutionary status of sources in the fourth and first Galactic quadrants, or between "on-arm" and "inter-arm" positions.