Molecular Star Formation Rate Indicators in Galaxies

Abstract

We derive a physical model for the observed relations between star formation rate (SFR) and molecular line (CO and HCN) emission in galaxies, and show how these observed relations are reflective of the underlying star formation law. We do this by combining 3D non-LTE radiative transfer calculations with hydrodynamic simulations of isolated disk galaxies and galaxy mergers. We demonstrate that the observed SFR-molecular line relations are driven by the relationship between molecular line emission and gas density, and anchored by the index of the underlying Schmidt law controlling the SFR in the galaxy. Lines with low critical densities (e.g. CO J=1-0) are typically thermalized and trace the gas density faithfully. In these cases, the SFR will be related to line luminosity with an index similar to the Schmidt law index. Lines with high critical densities greater than the mean density of most of the emitting clouds in a galaxy (e.g. CO J=3-2, HCN J=1-0) will have only a small amount of thermalized gas, and consequently a superlinear relationship between molecular line luminosity and mean gas density. This results in a SFR-line luminosity index less than the Schmidt index for high critical density tracers. One observational consequence of this is a significant redistribution of light from the small pockets of dense, thermalized gas to diffuse gas along the line of sight, and prodigious emission from subthermally excited gas. At the highest star formation rates, the SFR-Lmol slope tends to the Schmidt index, regardless of the molecular transition. The fundamental relation is the Kennicutt-Schmidt law, rather than the relation between SFR and molecular line luminosity. We use these results to make imminently testable predictions for the SFR-molecular line relations of unobserved transitions.Comment: ApJ Accepted - Results remain same as previous version. Content clarified with Referee's comment

Dusty star-forming galaxies at high redshift

“…Models that relate the index of the SFR-line luminosity index for various dense gas tracers to the gas density PDF in galaxies were developed by Krumholz & Thompson (2007) (utilizing analytic models for GMC structure), and Narayanan et al (2008c) (utilizing hydrodynamic models for galaxies in evolution). In this picture, the principle driver behind the power-law index, β in the SFR-L β mol volumetric (gas mass-based) star formation law is the relationship between the gas density distribution and the effective density of the emitting dense gas tracer.…”

“…Gao et al (2007) studied HCN (J=1-0) in a sample of high-z SMGs and quasars, finding a relationship between the FIR luminosity in these systems and HCN luminosity, though offset from the local one (such that the high-z points lie above the local linear relation). It is unclear whether this owes to higher gas density PDFs (e.g Krumholz & Thompson, 2007;Narayanan et al, 2008c), or contribution to the FIR luminosity by AGN. Further evidence for a nonlinear FIR-HCN trend in dense, high-z systems was provided by Greve et al (2006) and Riechers et al (2007).…”

A Total Molecular Gas Mass Census in Z ∼ 2–3 Star-Forming Galaxies: Low-J Co Excitation Probes of Galaxies’ Evolutionary States

“…While there is theoretical motivation for the SchmidtKennicutt index to change with the excitation of the gas phase tracer (e.g., Narayanan et al 2008bNarayanan et al , 2011, 18 the observed lack of difference in the index of the integrated Schmidt-Kennicutt relation when using CO(1-0) and CO(3-2) as the tracers is consistent with some previous analyses (e.g., Greve et al 2014), but not all (e.g., Yao et al 2003;Bayet et al 2009; see also Kamenetzky et al 2015). The lack of excitation difference is best demonstrated by looking for a correlation between the FIR luminosity and the low-J CO excitation ( Figure 11).…”

“…Gao & Solomon 2004;Daddi et al 2010;Genzel et al 2010;Tacconi et al 2013) leadto significant uncertainties in the relation's characteristics (such as the index of the power law) and interpretation. Different molecular emission lines are sensitive to different density regimes in the ISM (Krumholz & Thompson 2007;Narayanan et al 2008bNarayanan et al , 2011, making the observed index of the Schmidt-Kennicutt relation dependent on the gas physical conditions. How the Schmidt-Kennicutt index varies between gas tracers with different critical densities therefore probes the underlying volumetric star-formation relation (the Schmidt law) set by the physics of star formation.…”

Dense molecular gas towards W49A: a template for extragalactic starbursts?

“…This dense gas is much more closely related to star formation activity than CO, as shown by the tighter correlation of L(HCN 1−0) with L(far-IR) (Gao & Solomon 2004). However, factors other than the mass of dense gas presumably affect the HCN emission, and high-J CO lines may trace the star forming activity as well as or even better than HCN 1−0 (Krumholz & Thompson 2007;Narayanan et al 2008;Bayet et al 2009b). …”