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Register a new userMolecular Star Formation Rate Indicators in Galaxies
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Desika Narayanan
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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.
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What else can be said about star formation rate indicators that has not been said already many times over? The `coming of age of large ground-based surveys and the unprecedented sensitivity, angular resolution and/or field-of-view of infrared and ultraviolet space missions have provided extensive, homogeneous data on both nearby and distant galaxies, which have been used to further our understanding of the strengths and pitfalls of many common star formation rate indicators. The synergy between these surveys has also enabled the calibration of indicators for use on scales that are comparable to those of star-forming regions, thus much smaller than an entire galaxy. These are being used to investigate star formation processes at the sub-galactic scale. I review progress in the field over the past decade or so.
In this paper, we investigate the relevance of using the $^{12}$CO line emissions as indicators of star formation rates (SFR). For the first time, we present this study for a relatively large number of $^{12}$CO transitions (12) as well as over a large interval in redshift (from z$sim$0 to z$sim$6). For the nearby sources (D$leq$10 Mpc), we have used homogeneous sample of $^{12}$CO data provided by Bayet et al. (2004, 2006), mixing observational and modelled line intensities. For higher-z sources (z $geq$ 1), we have collected $^{12}$CO observations from various papers and have completed the data set of line intensities with model predictions which we also present in this paper. Finally, for increasing the statistics, we have included recent $^{12}$CO(1-0) and $^{12}$CO(3-2) observations of intermediate-z sources. Linear regressions have been calculated for identifying the tightest SFR-$^{12}$CO line luminosity relationships. We show that the emph{total} $^{12}$CO, the $^{12}$CO(5-4), the $^{12}$CO(6-5) and the $^{12}$CO(7-6) luminosities are the best indicators of SFR (as measured by the far-infrared luminosity). Comparisons with theoretical approaches from Krumholz and Thompson (2007) and Narayanan et al. (2008) are also performed in this paper. Although in general agreement, the predictions made by these authors and the observational results we present here show small and interesting discrepancies. In particular, the slope of the linear regressions, for J$_{upper}geq$ 4 $^{12}$CO lines are not similar between theoretical studies and observations. On one hand, a larger high-J $^{12}$CO data set of observations might help to better agree with models, increasing the statistics. On the other hand, theoretical studies extended to high redshift sources might also reduce such discrepancies.
As images and spectra from ISO and Spitzer have provided increasingly higher-fidelity representations of the mid-infrared (MIR) and Polycyclic Aromatic Hydrocarbon (PAH) emission from galaxies and galactic and extra-galactic regions, more systematic efforts have been devoted to establishing whether the emission in this wavelength region can be used as a reliable star formation rate indicator. This has also been in response to the extensive surveys of distant galaxies that have accumulated during the cold phase of the Spitzer Space Telescope. Results so far have been somewhat contradictory, reflecting the complex nature of the PAHs and of the mid-infrared-emitting dust in general. The two main problems faced when attempting to define a star formation rate indicator based on the mid-infrared emission from galaxies and star-forming regions are: (1) the strong dependence of the PAH emission on metallicity; (2) the heating of the PAH dust by evolved stellar populations unrelated to the current star formation. I review the status of the field, with a specific focus on these two problems, and will try to quantify the impact of each on calibrations of the mid-infrared emission as a star formation rate indicator.
The star formation rate (SFR) is a fundamental property of galaxies and it is crucial to understand the build-up of their stellar content, their chemical evolution, and energetic feedback. The SFR of galaxies is typically obtained by observing the emission by young stellar populations directly in the ultraviolet, the optical nebular line emission from gas ionized by newly-formed massive stars, the reprocessed emission by dust in the infrared range, or by combining observations at different wavelengths and fitting the full spectral energy distributions of galaxies. In this brief review we describe the assumptions, advantages and limitations of different SFR indicators, and we discuss the most promising SFR indicators for high-redshift studies.
The Sloan Digital Sky Survey (SDSS) first data release provides a database of 106000 unique galaxies in the main galaxy sample with measured spectra. A sample of star-forming (SF) galaxies are identified from among the 3079 of these having 1.4 GHz luminosities from FIRST, by using optical spectral diagnostics. Using 1.4 GHz luminosities as a reference star formation rate (SFR) estimator insensitive to obscuration effects, the SFRs derived from the measured SDSS Halpha, [OII] and u-band luminosities, as well as far-infrared luminosities from IRAS, are compared. It is established that straightforward corrections for obscuration and aperture effects reliably bring the SDSS emission line and photometric SFR estimates into agreement with those at 1.4 GHz, although considerable scatter (~60%) remains in the relations. It thus appears feasible to perform detailed investigations of star formation for large and varied samples of SF galaxies through the available spectroscopic and photometric measurements from the SDSS. We provide herein exact prescriptions for determining the SFR for SDSS galaxies. The expected strong correlation between [OII] and Halpha line fluxes for SF galaxies is seen, but with a median line flux ratio F_[OII]/F_Halpha=0.23, about a factor of two smaller than that found in the sample of Kennicutt (1992). This correlation, used in deriving the [OII] SFRs, is consistent with the luminosity-dependent relation found by Jansen et al. (2001). The median obscuration for the SDSS SF systems is found to be A_Halpha=1.2 mag, while for the radio detected sample the median obscuration is notably higher, 1.6 mag, and with a broader distribution.
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