Water emission tracing active star formation from the Milky Way to high-z galaxies

Context. The question of how most stars in the Universe form remains open. While star formation predominantly takes place in young massive clusters, the current framework focuses on isolated star formation. This poses a problem when trying to constrain the initial stellar mass and the core mass functions, both in the local and distant Universe.Aims. One way to access the bulk of protostellar activity within star-forming clusters is to trace signposts of active star formation with emission from molecular outflows. These outflows are bright (e.g., in water emission), which is observable throughout cosmological times, providing a direct observational link between nearby and distant galaxies. We propose to utilize the in-depth knowledge of local star formation as seen with molecular tracers, such as water, to explore the nature of star formation in the Universe.Methods. We present a large-scale statistical galactic model of emission from galactic active star-forming regions. Our model is built on observations of well-resolved nearby clusters. By simulating emission from molecular outflows, which is known to scale with mass, we create a proxy that can be used to predict the emission from clustered star formation on galactic scales. In particular, the para-H2O 2(02) - 1(11) line is well suited for this purpose as it is one of the brightest transitions observed toward Galactic star-forming regions and is now routinely observed toward distant galaxies.Results. We evaluated the impact of the most important global star formation parameters (i.e., initial stellar mass function, molecular cloud mass distribution, star formation efficiency, and free-fall time efficiency) on simulation results. We observe that for emission from the para-H2O 2(02) - 1(11) line, the initial mass function and molecular cloud mass distribution have a negligible impact on the emission, both locally and globally, whereas the opposite holds for star formation efficiency and free