Distance biases in the estimation of the physical properties of Hi-GAL compact sources-I. Clump properties and the identification of high-mass star forming candidates

The degradation of spatial resolution in star-forming regions observed at large distances ($d\gtrsim1$ kpc) with Herschel,can lead to estimates of the physical parameters of the detected compact sources (clumps) which do not necessarily mirror the properties of the original population of cores. This paper aims at quantifying the bias introduced in the estimation of these parameters by the distance effect. To do so, we consider Herschel maps of nearby star-forming regions taken from the Herschel-Gould-Belt survey, and simulate the effect of increased distance to understand what amount of information is lost when a distant star-forming region is observed with Herschel resolution. In the maps displaced to different distances we extract compact sources, and we derive their physical parameters as if they were original Hi-GAL maps of the extracted source samples. In this way, we are able to discuss how the main physical properties change with distance. In particular, we discuss the ability of clumps to form massive stars: we estimate the fraction of distant sources that are classified as high-mass stars-forming objects due to their position in the mass vs radius diagram, that are only "false positives". We give also a threshold for high-mass star-formation $M>1282 \ \left(\frac{r}{[\mathrm{pc}]}\right)^{1.42} M_{\odot}$. In conclusion, this paper provides the astronomer dealing with Herschel maps of distant star-forming regions with a set of prescriptions to partially recover the character of the core population in unresolved clumps.