CO-to-H2 conversion factor and grain size distribution through the analysis of αCO-qPAH relation

The CO-to-H₂ conversion factor (α_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 α_CO and grain size distribution for nearby galaxies, using the PAH fraction (q_PAH) as an observable proxy of grain size distribution. We adopt the resolved observations at 2 kpc resolution in 42 nearby galaxies, where α_CO is derived from measured metallicity and surface densities of dust and H I assuming a fixed dust-to-metals ratio. We use an analytical model for the evolution of H₂ and CO, in which the evolution of grain size distribution is controlled by the dense gas fraction (η). We find that the observed level of q_PAH is consistent with the diffuse-gas-dominated model (η = 0.2) where dust shattering is more efficient. Meanwhile, the slight decreasing trend of observed q_PAH with metallicity is more consistent with high-η predictions, likely due to the more efficient loss of PAHs by coagulation. We discuss how grain size distribution (indicated by q_PAH) and metallicity impact α_CO; we however did not obtain conclusive evidence that the grain size distribution affects α_CO. Observations and model predictions show similar anti-correlation between α_CO and 12+log(O/H). Meanwhile, there is a considerable difference in how resolved α_CO behaves with q_PAH. The observed α_CO has a positive correlation with q_PAH, while the model-predicted α_CO does not have a definite correlation with q_PAH. This difference is likely due to the limitation of one-zone treatment in the model.