ATLASGAL: The HCN-IR star formation relation for the Milky Way

We examine the relation between star formation and dense gas, traced by HCN (1–0), using a sample of 343 Galactic clumps spanning the full range of evolutionary stages representative of high-mass and cluster formation, including quiescent, protostellar, young stellar object (YSO), and H ii regions. Earlier Galactic studies, based primarily on luminous H ii regions, reported a linear correlation between infrared (IR) and HCN luminosities, consistent with extragalactic surveys, and interpreted it as a universal star formation law. Our larger evolutionary sample yields a significantly steeper slope of 1.80 ± 0.08, inconsistent with extragalactic trends. However, we find that each of the star-forming evolutionary stages individually has a shallower slope (~1.2) than that of the full sample, with quiescent clumps showing no correlation. We estimate the Milky Way’s total IR and HCN luminosities from dense clumps by integrating the bolometric luminosities and clump masses of Hi-GAL sources. Both fall significantly below extragalactic values, demonstrating that clumps alone cannot account for the IR–HCN relation. Only ~5–25 percnt of Galactic HCN luminosity arises from dense clumps, implying that most extragalactic HCN traces gas that is not involved in star formation. Additionally, dense clumps contribute only ~2–3 percnt of the Milky Way’s IR luminosity, which is dominated instead by extended H ii regions and PDRs tracing longer star formation timescales. As a result, the observed linear relation in nearby galaxies reflects a nearly constant star formation efficiency averaged over large areas and long timescales, rather than a direct link between SFR and dense gas mass.