Observations of molecular gas in high-z star-forming galaxies typically rely on emission from CO lines arising from states with rotational quantum numbers J > 1. Converting these observations to an estimate of the CO J=1-0 intensity, and thus inferri
ng H2 gas masses, requires knowledge of the CO excitation ladder, or spectral line energy distribution (SLED). The few available multi-J CO observations of galaxies show a very broad range of SLEDs, even at fixed galaxy mass and star formation rate, making the conversion to J=1-0 emission and hence molecular gas mass highly uncertain. Here, we combine numerical simulations of disk galaxies and galaxy mergers with molecular line radiative transfer calculations to develop a model for the physical parameters that drive variations in CO SLEDs in galaxies. An essential feature of our model is a fully self-consistent computation of the molecular gas temperature and excitation structure. We find that, while the shape of the SLED is ultimately determined by difficult-to-observe quantities such as the gas density, temperature, and optical depth distributions, all of these quantities are well-correlated with the galaxys mean star formation rate surface density (Sigma_SFR), which is observable. We use this result to develop a model for the CO SLED in terms of Sigma_SFR, and show that this model quantitatively reproduces the SLEDs of galaxies over a dynamic range of ~200 in SFR surface density, at redshifts from z=0-6. This model should make it possible to significantly reduce the uncertainty in deducing molecular gas masses from observations of high-J CO emission.
I present a model for the star formation properties of z~2 starburst galaxies. Here, I discuss models for the formation of high-z Submillimeter Galaxies, as well as the CO-H2 conversion factor for these systems. I then apply these models to literatur
e observations. I show that when using a functional form for XCO that varies smoothly with the physical properties in galaxies, galaxies at both local and high-z lie on a unimodal Kennicutt-Schmidt star formation law, with power-law index of ~2. The inferred gas fractions of these galaxies are large (fgas ~ 0.2-0.4), though a factor ~2 lower than most literature estimates that utilize locally-calibrated CO-H2 conversion factors.
We consider the effects of different star formation criteria on galactic scales, in high-resolution simulations with explicitly resolved GMCs and stellar feedback. We compare: (1) a self-gravity criterion (based on the local virial parameter and the
assumption that self-gravitating gas collapses to high density in a free-fall time), (2) a fixed density threshold, (3) a molecular-gas law, (4) a temperature threshold, (5) a Jeans-instability requirement, (6) a criteria that cooling times be shorter than dynamical times, and (7) a convergent-flow criterion. We consider these both MW-like and high-density (starburst) galaxies. With feedback present, all models produce identical integrated star formation rates (SFRs), in agreement with the Kennicutt relation. Without feedback all produce orders-of-magnitude excessive SFRs. This is totally dependent on feedback and independent of the SF law. However, the spatial and density distribution of SF depend strongly on the SF criteria. Because cooling rates are generally fast and gas is turbulent, criteria (4)-(7) are weak and spread SF uniformly over the disk (above densities n~0.01-0.1 cm^-3). A molecular criterion (3) localizes to higher densities, but still a wide range; for Z Z_solar, it is similar to a density threshold at n~1 cm^-3 (well below mean densities in the MW center or starbursts). Fixed density thresholds (2) can always select the highest densities, but must be adjusted for simulation resolution and galaxy properties; the same threshold that works in a MW-like simulation will select nearly all gas in a starburst. Binding criteria (1) tend to adaptively select the largest over-densities, independent of galaxy model or resolution, and automatically predict clustered SF. We argue that this SF model is most physically-motivated and presents significant numerical advantages in large-dynamic range simulations.
We examine the cosmic evolution of a stellar initial mass function (IMF) in galaxies that varies with the Jeans mass in the interstellar medium, paying particular attention to the K-band stellar mass to light ratio (M/L_K) of present-epoch massive ga
laxies. We calculate the typical Jeans mass using high-resolution hydrodynamic simulations coupled with a fully radiative model for the ISM, which yields a parameterisation of the IMF characteristic mass as a function of galaxy star formation rate (SFR). We then calculate the star formation histories of galaxies utilising an equilibrium galaxy growth model coupled with constraints on the star formation histories set by abundance matching models. We find that at early times, energetic coupling between dust and gas drive warm conditions in the ISM, yielding bottom-light/top- heavy IMFs associated with large ISM Jeans masses for massive star-forming galaxies. Owing to the remnants of massive stars that formed during the top-heavy phases at early times, the resultant M/L_K(sigma) in massive galaxies at the present epoch is increased relative to the non- varying IMF case. At late times, lower cosmic ray fluxes allow for cooler ISM temperatures in massive galaxies, and hence newly formed clusters will exhibit bottom-heavy IMFs, further increasing M/L_K(sigma). Our central result is hence that a given massive galaxy may go through both top-heavy and bottom-heavy IMF phases during its lifetime, though the bulk of the stars form during a top-heavy phase. Qualitatively, the variations in M/L_K(sigma) with galaxy mass are in agreement with observations, however, our model may not be able to account for bottom-heavy mass functions as indicated by stellar absorption features.
The CO-H2 conversion factor (Xco; otherwise known as the X-factor) is observed to be remarkably constant in the Milky Way and in the Local Group (aside from the SMC). To date, our understanding of why Xco should be so constant remains poor. Using a c
ombination of extremely high resolution (~ 1 pc) galaxy evolution simulations and molecular line radiative transfer calculations, we suggest that Xco displays a narrow range of values in the Galaxy due to the fact that molecular clouds share very similar physical properties. In our models, this is itself a consequence of stellar feedback competing against gravitational collapse. GMCs whose lifetimes are regulated by radiative feedback show a narrow range of surface densities, temperatures and velocity dispersions with values comparable to those seen in the Milky Way. As a result, the X-factors from these clouds show reasonable correspondence with observed data from the Local Group, and a relatively narrow range. On the other hand, feedback-free clouds collapse to surface densities that are larger than those seen in the Galaxy, and hence result in X-factors that are systematically too large compared to the Milky Ways. We conclude that radiative feedback within GMCs can generate cloud properties similar to those observed in the Galaxy, and hence a roughly constant Milky Way X-factor in normal, quiescent clouds.
CO measurements of z~1-4 galaxies have found that their baryonic gas fractions are significantly higher than galaxies at z=0, with values ranging from 20-80 %. Here, we suggest that the gas fractions inferred from observations of star-forming galaxie
s at high-z are overestimated, owing to the adoption of locally-calibrated CO-H2 conversion factors (Xco). Evidence from both observations and numerical models suggest that Xco varies smoothly with the physical properties of galaxies, and that Xco can be parameterised simply as a function of both gas phase metallicity and observed CO surface brightness. When applying this functional form, we find fgas ~10-40 % in galaxies with M*=10^10-10^12 Msun at high-z. Moreover, the scatter in the observed fgas-M* relation is lowered by a factor of two. The lower inferred gas fractions arise physically because the interstellar media of high-z galaxies have higher velocity dispersions and gas temperatures than their local counterparts, which results in an Xco that is lower than the z=0 value for both quiescent discs and starbursts. We further compare these gas fractions to those predicted by cosmological galaxy formation models. We show that while the canonically inferred gas fractions from observations are a factor of 2-3 larger at a given stellar mass than predicted by models, our rederived Xco values for z=1-4 galaxies results in revised gas fractions that agree significantly better with the simulations.
We show that the mass fraction of GMC gas (n>100 cm^-3) in dense (n>>10^4 cm^-3) star-forming clumps, observable in dense molecular tracers (L_HCN/L_CO(1-0)), is a sensitive probe of the strength and mechanism(s) of stellar feedback. Using high-resol
ution galaxy-scale simulations with pc-scale resolution and explicit models for feedback from radiation pressure, photoionization heating, stellar winds, and supernovae (SNe), we make predictions for the dense molecular gas tracers as a function of GMC and galaxy properties and the efficiency of stellar feedback. In models with weak/no feedback, much of the mass in GMCs collapses into dense sub-units, predicting L_HCN/L_CO(1-0) ratios order-of-magnitude larger than observed. By contrast, models with feedback properties taken directly from stellar evolution calculations predict dense gas tracers in good agreement with observations. Changing the strength or timing of SNe tends to move systems along, rather than off, the L_HCN-L_CO relation (because SNe heat lower-density material, not the high-density gas). Changing the strength of radiation pressure (which acts efficiently in the highest density gas), however, has a much stronger effect on L_HCN than on L_CO. We predict that the fraction of dense gas (L_HCN/L_CO(1-0)) increases with increasing GMC surface density; this drives a trend in L_HCN/L_CO(1-0) with SFR and luminosity which has tentatively been observed. Our results make specific predictions for enhancements in the dense gas tracers in unusually dense environments such as ULIRGs and galactic nuclei (including the galactic center).
We investigate the relationship between the star formation rate (SFR) and dense molecular gas mass in the nuclei of galaxies. To do this, we utilize the observed 850 micron luminosity as a proxy for the infrared luminosity and SFR, and correlate this
with the observed CO (J=3-2) luminosity. We find tentative evidence that the LIR-CO (J=3-2) index is similar to the Kennicutt-Schmidt (KS) index (N ~ 1.5) in the central ~1.7 kpc of galaxies, and flattens to a roughly linear index when including emission from the entire galaxy. This result may imply that the volumetric Schmidt relation is the underlying driver behind the observed SFR-dense gas correlations, and provides tentative confirmation for recent numerical models. While the data exclude the possibility of a constant LIR-CO (J=3-2) index for both galaxy nuclei and global measurements at the ~80% confidence level, the considerable error bars cannot preclude alternative interpretations.
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 com
bining 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.
We investigate the nature of CO emission from z~6 quasars by combining non-LTE radiative transfer calculations with merger-driven models of z~6 quasar formation that arise naturally in LCDM cosmological simulations. We consider four model quasars for
med in 10^12-10^13 M_sun halos from different merging histories. Our main results follow. Owing to massive starbursts and funneling of dense gas into the nuclear regions of merging galaxies, the CO is highly excited and the flux density peaks between J=5-8. The CO morphology of z~6 quasars often exhibits multiple emission peaks which arise from H2 concentrations which have not yet fully coalesced. Quasars at z~6 display a large range of sightline dependent line widths such that the lines are narrowest when the rotating H2 gas associated with the quasar is viewed face-on (when L_B is largest), and broadest when the gas is seen edge-on (when L_B is lowest). Thus for all models selection effects exist such that quasars selected for optical luminosity are preferentially face-on which may result in detected CO line widths narrower than the median. The sightline averaged line width is reflective of the circular velocity (V_c) of the host halo, and ranges from sigma~300-650 km/s. For optically selected QSOs, 10-25% (halo-mass dependant) of sightlines have narrow line widths compatible with the sole CO detection at z>6, J1148+5251. When accounting for both the temporal evolution of CO line widths, as well as the redshift evolution of halo V_c, these models self-consistently account for the CO line widths of both z~2 sub-mm galaxies and QSOs. Finally, the dynamical mass derived from the sightline averaged line widths provides a good estimate of the total mass, and allows for a stellar bulge and SMBH consistent with the local M_BH-M_bulge relation. [abridged]
