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.
