A cautionary note about composite Galactic star formation relations
  We explore the pitfalls which affect the comparison of the star-formation
(SF) relation for nearby molecular clouds with that for distant compact
molecular clumps. We show that both relations behave differently in the
($\Sigma_{gas}$, $\Sigma_{SFR}$) space, where $\Sigma_{gas}$ and $\Sigma_{SFR}$
are, respectively, the gas and SF rate surface densities, even when the physics
of star formation is the same. This is because the SF relation of nearby clouds
relates gas and star surface densities measured locally, that is, within a
given interval of gas surface density, or at a given protostar location. We
refer to such measurements as local measurements, and the corresponding SF
relation as the local relation. In contrast, the stellar content of a distant
molecular clump remains unresolved. Only the mean SF rate can be obtained from
e.g. the clump infrared luminosity. One clump therefore provides one single
point to the ($\Sigma_{gas}$, $\Sigma_{SFR}$) space, that is, its mean gas
surface density and SF rate surface density. We refer to this SF relation as a
global relation since it builds on the global properties of molecular clumps.
Its definition therefore requires an ensemble of cluster-forming clumps. We
show that, although the local and global relations have different slopes, this
per se cannot be taken as evidence for a change in the physics of SF with gas
surface density. It therefore appears that great caution should be taken when
physically interpreting a composite SF relation, that is, a relation combining
together local and global measurements.
