Tracing Embedded Stellar Populations in Clusters and Galaxies using Molecular Emission: Methanol as a Signature of the Low-Mass End of the IMF

Most low-mass protostars form in clusters, in particular high-mass clusters; however, how low-mass stars form in high-mass clusters and what the mass distribution is, are still open questions both in our own Galaxy and elsewhere. To access the population of forming embedded low-mass protostars observationally, we propose to use molecular outflows as tracers. Because the outflow emission scales with mass, the effective contrast between low-mass protostars and their high-mass cousins is greatly lowered. In particular, maps of methanol emission at 338.4 GHz (J=7_0 - 6_0 A+) in low-mass clusters illustrate that this transition is an excellent probe of the low-mass population. We here present a model of a forming cluster where methanol emission is assigned to every embedded low-mass protostar. The resulting model image of methanol emission is compared to recent ALMA observations toward a high-mass cluster and the similarity is striking: the toy model reproduces observations to better than a factor of two and suggests that approximately 50\% of the total flux originates in low-mass outflows. Future fine-tuning of the model will eventually make it a tool for interpreting the embedded low-mass population of distant regions within our own Galaxy and ultimately higher-redshift starburst galaxies, not just for methanol emission but also water and high-J CO.