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Resolved Profiles of Stellar Mass, Star Formation Rate, and Predicted CO-to-H$_2$ Conversion Factor Across Thousands of Local Galaxies

Jiayi Sun, Yu-Hsuan Teng, I-Da Chiang, Adam K. Leroy, Karin Sandstrom, Jakob den Brok, Alberto D. Bolatto, Jeremy Chastenet, Ryan Chown, Annie Hughes, Eric W. Koch, Thomas G. Williams

TL;DR

This work delivers spatially resolved predictions for the CO-to-H2 conversion factor, $\alpha_{CO}$, across thousands of local galaxies by combining GALEX UV and WISE infrared data to derive stellar mass and star formation rate surface densities. It implements a state-of-the-art three-term prescription (CO-dark gas, CO emissivity, and CO excitation) to compute $\alpha_{CO}$ for both CO(1-0) and CO(2-1) on kiloparsec scales, and validates these predictions against a wide body of literature measurements. The results show that metallicity-driven CO-dark gas dominates $\alpha_{CO}$ variations in low-mass galaxies, while emissivity and excitation effects become central in high-mass or highly star-forming systems; global trends indicate that $t_{dep}$ must also vary with stellar mass to reconcile observed $SFR/L'^CO$ trends. The authors provide extensive data products and a Python package to enable broad use of spatially varying $\alpha_{CO}$ in interpreting CO surveys, underscoring the need to account for $\alpha_{CO}$ variability in studies of molecular gas and star formation across galaxies.

Abstract

We present radial profiles of surface brightness in UV and IR bands, estimate stellar mass surface density ($Σ_\star$) and star formation rate surface density ($Σ_\mathrm{SFR}$), and predict the CO-to-H$_2$ conversion factor ($α_\mathrm{CO}$) for over 5,000 local galaxies with stellar mass $M_\star\,{\geq}\,10^{9.3}\rm\,M_\odot$. We build these profiles and measure galaxy half-light radii using GALEX and WISE images from the $z$0MGS program, with special care given to highly inclined galaxies. From the UV and IR surface brightness profiles, we estimate $Σ_\star$ and $Σ_\mathrm{SFR}$ and use them to predict $α_\mathrm{CO}$ with state-of-the-art empirical prescriptions. We validate our (kpc-scale) $α_\mathrm{CO}$ predictions against observational estimates, finding the best agreement when accounting for CO-dark gas as well as CO emissivity and excitation effects. The CO-dark correction plays a primary role in lower-mass galaxies, whereas CO emissivity and excitation effects become more important in higher-mass and more actively star-forming galaxies, respectively. We compare our estimated $α_\mathrm{CO}$ to observed galaxy-integrated SFR to CO luminosity ratio as a function of $M_\star$. A large compilation of literature data suggests that star-forming galaxies with $M_\star = 10^{9.5{-}11}\,M_\odot$ show strong anti-correlations of SFR/$L^\prime_\mathrm{CO(1{-}0)} \propto M_\star^{-0.29}$ and SFR/$L^\prime_\mathrm{CO(2{-}1)} \propto M_\star^{-0.40}$. The estimated $α_\mathrm{CO}$ trends, when combined with a constant molecular gas depletion time $t_\mathrm{dep}$, can only explain ${\approx}1/3$ of these SFR/$L^\prime_\mathrm{CO}$ trends. This suggests that $t_\mathrm{dep}$ being systematically shorter in lower-mass star-forming galaxies is the main cause of the observed SFR/$L^\prime_\mathrm{CO}$ variations. (Abridged)

Resolved Profiles of Stellar Mass, Star Formation Rate, and Predicted CO-to-H$_2$ Conversion Factor Across Thousands of Local Galaxies

TL;DR

This work delivers spatially resolved predictions for the CO-to-H2 conversion factor, , across thousands of local galaxies by combining GALEX UV and WISE infrared data to derive stellar mass and star formation rate surface densities. It implements a state-of-the-art three-term prescription (CO-dark gas, CO emissivity, and CO excitation) to compute for both CO(1-0) and CO(2-1) on kiloparsec scales, and validates these predictions against a wide body of literature measurements. The results show that metallicity-driven CO-dark gas dominates variations in low-mass galaxies, while emissivity and excitation effects become central in high-mass or highly star-forming systems; global trends indicate that must also vary with stellar mass to reconcile observed trends. The authors provide extensive data products and a Python package to enable broad use of spatially varying in interpreting CO surveys, underscoring the need to account for variability in studies of molecular gas and star formation across galaxies.

Abstract

We present radial profiles of surface brightness in UV and IR bands, estimate stellar mass surface density () and star formation rate surface density (), and predict the CO-to-H conversion factor () for over 5,000 local galaxies with stellar mass . We build these profiles and measure galaxy half-light radii using GALEX and WISE images from the 0MGS program, with special care given to highly inclined galaxies. From the UV and IR surface brightness profiles, we estimate and and use them to predict with state-of-the-art empirical prescriptions. We validate our (kpc-scale) predictions against observational estimates, finding the best agreement when accounting for CO-dark gas as well as CO emissivity and excitation effects. The CO-dark correction plays a primary role in lower-mass galaxies, whereas CO emissivity and excitation effects become more important in higher-mass and more actively star-forming galaxies, respectively. We compare our estimated to observed galaxy-integrated SFR to CO luminosity ratio as a function of . A large compilation of literature data suggests that star-forming galaxies with show strong anti-correlations of SFR/ and SFR/. The estimated trends, when combined with a constant molecular gas depletion time , can only explain of these SFR/ trends. This suggests that being systematically shorter in lower-mass star-forming galaxies is the main cause of the observed SFR/ variations. (Abridged)

Paper Structure

This paper contains 20 sections, 12 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Data & Methods
  3. UV and IR Images
  4. UV and IR Surface Brightness Profiles
  5. Galaxy Half-light Radii
  6. From Observed Quantities to Physical Properties
  7. Conversion Factor Prescriptions
  8. Comparisons to Conversion Factor Measurements in the Literature
  9. CO(1-0) Conversion Factor
  10. CO(2-1) Conversion Factor
  11. Path to Better Conversion Factor Recipes
  12. Conversion Factor Variations
  13. Conversion Factor Radial Profiles
  14. Galaxy Global Conversion Factors
  15. Implications for the Molecular Gas Depletion Time
  16. ...and 5 more sections

Figures (9)

  • Figure 1: Our data processing workflow, from reduced GALEX and WISE images to $\alpha_\mathrm{CO}$ predictions. Methodological details for the three major steps (image processing and radial profile creation, physical property estimation, and conversion factor prescription) are described in Sections \ref{['sec:method:data']}-\ref{['sec:method:radprof']}, \ref{['sec:method:phys']}, and \ref{['sec:method:alphaCO']} respectively.
  • Figure 2: The WISE1 band image (left & middle panels) and surface brightness radial profiles (right panel) for PGC 40153 (a.k.a. NGC 4321, $i=27^\circ$), as an example of our radial profile construction techniques. A set of elliptical rings (orange dotted lines) in the left panel represent galactocentric radius ($r_\mathrm{gal}$) bins, in which we directly compute the mean/median surface brightness. A set of long stripes (red rectangles) in the middle panel represent the regions used for "stripe integral" Warmels_1988, an alternative method for deriving radial profiles that is applicable to even edge-on galaxies (see \ref{['sec:method:radprof']}). For visual clarity, the densities of bins/stripes are reduced by a factor of eight in both panels. Both methods account for masked area due to foreground stars or other galaxies (white ellipses). As shown by the right panel, the radial profiles derived with both methods agree well out to large $r_\mathrm{gal}$, even after the stripe integral-based results drop below 3$\sigma$ significance (red dotted curve).
  • Figure 3: Comparing four versions of $\mathrm{CO}\,(1\text{--}0)$-to-H$_2$ conversion factor predictions ($x$-axes) with observational estimates from the literature ($y$-axis). The latter include dust-based estimates across many galaxies presented in denBrok_etal_2023, Yasuda_etal_2023, and Chiang_etal_2024, as well as CO multi-line modeling (i.e., LVG) by Teng_etal_2023 and carbon budget accounting by Israel_2020 in galaxy centers. Note that the blue contours and downward triangles separately show measurements in galaxy disks and centers from Chiang_etal_2024; the filled and open stars show two versions of results from Teng_etal_2023 assuming CO/$\mathrm{H}_2$ abundance ratios of $1.5{\times}10^{-4}$ and $3{\times}10^{-4}$, respectively. Top left: The metallicity-dependent CO-dark term $f(Z)$ alone only spans a limited dynamic range, thus failing to match low $\alpha_\mathrm{CO(1{-}0)}$ values from observational estimates in galaxy centers. Top right: A combination of the $f(Z)$ term and a $\Sigma_\star$-dependent emissivity term $g(\Sigma_\star)$ matches dust-based and LVG-based estimates well but still disagrees with carbon budget accounting results Israel_2020. Bottom left: Adopting an alternative emissivity term $g(\Sigma_\star)_\mathrm{B13}$Bolatto_etal_2013 results in lower $\alpha_\mathrm{CO(1{-}0)}$ than most estimates for galaxy centers though still moderately higher than those from Israel_2020. Bottom right: An alternative CO-dark term $f(Z)_\mathrm{G20}$Gong_etal_2020 yields similar results as the fiducial choice (top right), though the weaker metallicity dependence in $f(Z)_\mathrm{G20}$ leads to slightly more underestimated $\alpha_\mathrm{CO}$ at the high end (i.e., in outer galaxy disks).
  • Figure 4: Comparing three versions of $\mathrm{CO}\,(2\text{--}1)$-to-H$_2$ conversion factor predictions ($x$-axes) with observational estimates from the literature ($y$-axis). The latter include a similar set of literature results as \ref{['fig:alphaCO10']}, except omitting $\alpha_\mathrm{CO(1{-}0)}$ estimates by Yasuda_etal_2023 and adding $\alpha_\mathrm{CO(2{-}1)}$ from Sandstrom_etal_2013. Left & middle: Assuming a constant line ratio of $R_\mathrm{21,\,const}=0.65$, the CO-dark and emissivity terms in combination can provide a wider range of $\alpha_\mathrm{CO(2{-}1)}$ values and better agreements with observational results than the CO-dark term alone. Right: Including a $\Sigma_\mathrm{SFR}$-dependent line ratio term on top of the CO-dark and emissivity terms further improves the agreement with observations at both low and high $\alpha_\mathrm{CO(2{-}1)}$ ends.
  • Figure 5: Median $\alpha_\mathrm{CO}$ radial profiles for galaxies grouped by stellar mass ($M_\star$) and offset from the star-forming main sequence ($\Delta\mathrm{MS}$; \ref{['eq:DeltaMS']}). The $x$-axis represents galactocentric radius in units of $r_\mathrm{50}$ in WISE1 band. In lower-mass galaxies ($M_\star<10^{10}\,\mathrm{M_\odot}$, dotted lines), the radial profile of $\alpha_\mathrm{CO(1{-}0)}$ (top panel) is effectively set by the CO-dark term $f(Z)$ alone. In higher-mass galaxies ($M_\star>10^{10}\,\mathrm{M_\odot}$, solid lines) the radial profile of $\alpha_\mathrm{CO(1{-}0)}$ steepens at $r \lesssim r_\mathrm{50}$ as the emissivity term $g(\Sigma_\star)$ plays a significant role. While the $\alpha_\mathrm{CO(1{-}0)}$ radial profiles barely vary with $\Delta\mathrm{MS}$ (color-coded), the $\alpha_\mathrm{CO(2{-}1)}$ radial profiles (bottom panel) clearly do depend on this quantity. We predict lower $\alpha_\mathrm{CO(2{-}1)}$ in galaxies with higher $\Delta\mathrm{MS}$ (due to a higher line ratio $R_{21}$).
  • ...and 4 more figures