CO-to-H$_2$ conversion factor and grain size distribution through the analysis of $\alpha_\mathrm{CO}$-$q_\mathrm{PAH}$ relation

TL;DR

This study investigates how the CO-to-H$_2$ conversion factor varies with dust grain size distribution and metallicity in nearby galaxies, revealing complex relationships and limitations in current models.

Contribution

It introduces an analytical model linking grain size distribution, metallicity, and $eta_ ext{CO}$, and compares it with resolved galaxy observations to understand their interdependence.

Findings

Observed $q_ ext{PAH}$ aligns with diffuse-gas-dominated dust shattering models.

$eta_ ext{CO}$ anti-correlates with metallicity in observations and models.

Discrepancies exist between observed and modeled $eta_ ext{CO}$ correlations with $q_ ext{PAH}$.

Abstract

The CO-to-H$_2$ conversion factor ($\alpha_\mathrm{CO}$) is expected to vary with dust abundance and grain size distribution through the efficiency of shielding gas from CO-dissociation radiation. We present a comprehensive analysis of $\alpha_\mathrm{CO}$ and grain size distribution for nearby galaxies, using the PAH fraction ($q_\mathrm{PAH}$) as an observable proxy of grain size distribution. We adopt the resolved observations at 2-kpc resolution in 42 nearby galaxies, where $\alpha_\mathrm{CO}$ is derived from measured metallicity and surface densities of dust and HI assuming a fixed dust-to-metals ratio. We use an analytical model for the evolution of H$_2$ and CO, in which the evolution of grain size distribution is controlled by the dense gas fraction ($\eta$). We find that the observed level of $q_\mathrm{PAH}$ is consistent with the diffuse-gas-dominated model ($\eta=0.2$) where dust shattering is more efficient. Meanwhile, the slight decreasing trend of observed $q_\mathrm{PAH}$ with metallicity is more consistent with high-$\eta$ predictions, likely due to the more efficient loss of PAHs by coagulation. We discuss how grain size distribution (indicated by $q_\mathrm{PAH}$) and metallicity impact $\alpha_\mathrm{CO}$; we however did not obtain conclusive evidence that the grain size distribution affects $\alpha_\mathrm{CO}$. Observations and model predictions show similar anti-correlation between $\alpha_\mathrm{CO}$ and 12+log(O/H). Meanwhile, there is a considerable difference in how resolved $\alpha_\mathrm{CO}$ behaves with $q_\mathrm{PAH}$. The observed $\alpha_\mathrm{CO}$ has a positive correlation with $q_\mathrm{PAH}$, while the model-predicted $\alpha_\mathrm{CO}$ does not have a definite correlation with $q_\mathrm{PAH}$. This difference is likely due to the limitation of one-zone treatment in the model.