A cautionary note about composite galactic star formation relations - Parmentier, Geneviève (The astrophysical journal, 2016)
We explore the pitfalls that affect the comparison of the star formation relation for nearby molecular clouds with that for distant compact molecular clumps. We show that both relations behave differently in the ( ##IMG## [http://ej.iop.org/images/0004-637X/826/1/74/apjaa2542ieqn1.gif] $\rmΣ _\rmgas$ , ##IMG## [http://ej.iop.org/images/0004-637X/826/1/74/apjaa2542ieqn2.gif] $\rmΣ _\rmSFR$ ) space, where ##IMG## [http://ej.iop.org/images/0004-637X/826/1/74/apjaa2542ieqn3.gif] $\rmΣ _\rmgas$ and ##IMG## [http://ej.iop.org/images/0004-637X/826/1/74/apjaa2542ieqn4.gif] $\rmΣ _\rmSFR$ are, respectively, the gas and star formation rate surface densities, even when the physics of star formation is the same. This is because the star formation relation of nearby clouds relates the 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 star formation relation as the local relation. In contrast, the stellar content of a distant molecular clump remains unresolved. Only the mean star formation rate can be obtained, e.g., from the clump infrared luminosity. One clump therefore provides one single point to the ( ##IMG## [http://ej.iop.org/images/0004-637X/826/1/74/apjaa2542ieqn5.gif] $\rmΣ _\rmgas$ , ##IMG## [http://ej.iop.org/images/0004-637X/826/1/74/apjaa2542ieqn6.gif] $\rmΣ _\rmSFR$ ) space, that is, its mean gas surface density and star formation rate surface density. We refer to this star formation 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 cannot per se be taken as evidence for a change in the physics of star formation with gas surface density. It therefore appears that great caution should be taken when physically interpreting a composite star formation relation, that is, a relation combining local and global relations.