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

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The role of star formation in luminous and ultraluminous infrared galaxies (LIRGs, L IR ! 10 11 L ; ULIRGs, L IR ! 10 12 L ) is a hotly debated issue: while it is clear that starbursts play a large role in powering the IR luminosity in these galaxies, the relative importance of possible enshrouded AGNs is unknown. It is therefore important to better understand the role of star-forming gas in contributing to the infrared luminosity in IR-bright galaxies. The J ¼ 3 level of 12 CO lies 33 K above ground and has a critical density of $1:5 ; 10 4 cm À3 . The 12 CO J ¼ 3 2 line serves as an effective tracer for warm, dense molecular gas heated by active star formation. Here we report on 12 CO J ¼ 3 2 observations of 17 starburst spiral galaxies, LIRGs, and ULIRGs, which we obtained with the Heinrich Hertz Submillimeter Telescope on Mount Graham, Arizona. Our main results are as follows. (1) We find a nearly linear relation between the infrared luminosity and warm, dense molecular gas such that the infrared luminosity increases as the warm, dense molecular gas to the power 0.92; we interpret this to be roughly consistent with the recent results of Gao & Solomon. (2) We find L IR /M H 2 warm; dense ratios ranging from $38 to $482 L /M using a modified CO-H 2 conversion factor of 8:3 ; 10 19 cm À2 (K km s À1 ) À1 derived in this paper.

We assess the impact of starburst and AGN feedback-driven winds on the CO emission from galaxy mergers, and, in particular, search for signatures of these winds in the simulated CO morphologies and emission line profiles. We do so by combining a 3D non-LTE molecular line radiative transfer code with smoothed particle hydrodynamics (SPH) simulations of galaxy mergers that include prescriptions for star formation, black hole growth, a multiphase interstellar medium (ISM), and the winds associated with star formation and black hole growth. Our main results are: (1) Galactic winds can drive outflows of masses ~10^8-10^9 Msun which may be imaged via CO emission line mapping. (2) AGN feedback-driven winds are able to drive imageable CO outflows for longer periods of time than starburst-driven winds owing to the greater amount of energy imparted to the ISM by AGN feedback compared to star formation. (3) Galactic winds can control the spatial extent of the CO emission in post-merger galaxies, and may serve as a physical motivation for the sub-kiloparsec scale CO emission radii observed in local advanced mergers. (4) Secondary emission peaks at velocities greater than the circular velocity are seen in the CO emission lines in all models. In models with winds, these high velocity peaks are seen to preferentially correspond to outflowing gas entrained in winds, which is not the case in the model without winds. The high velocity peaks seen in models without winds are typically confined to velocity offsets (from the systemic) < 1.7 times the circular velocity, whereas the models with AGN feedback-driven winds can drive high velocity peaks to ~2.5 times the circular velocity.Comment: Accepted by ApJ; Minor revisions; Resolution tests include

We study the effects of feedback from active galactic nuclei (AGNs) on emission from molecular gas in galaxy mergers by combining hydrodynamic simulations that include black holes with a three-dimensional, non-local thermodynamic equilibrium (LTE) radiative transfer code. We find that molecular clouds entrained in AGN winds produce an extended CO morphology with significant off-nuclear emission, which may be detectable via contour mapping. Furthermore, kinematic signatures of these molecular outflows are visible in emission-line profiles when the outflow has a large line-of-sight velocity. Our results can help interpret current and upcoming observations of luminous infrared galaxies, as well as provide a detailed test of subresolution prescriptions for supermassive black hole growth in galaxy-scale hydrodynamic simulations.