VERTICO IV: Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals

We measure the molecular-to-atomic gas ratio, $R_{\rm mol}$, and the star formation rate (SFR) per unit molecular gas mass, SFE$_{\rm mol}$, in 38 nearby galaxies selected from the Virgo Environment Traced in CO (VERTICO) survey. We determine their scale-lengths for the molecular and stellar components and find a roughly 3:5 ratio between them compared to $\sim$1:1 in field galaxies, indicating that the CO emission is more centrally concentrated than the stars. We compute $R_{\rm mol}$ as a function of different physical quantities. While the spatially-resolved $R_{\rm mol}$ on average decreases with increasing radius, we find that the mean molecular-to-atomic gas ratio within the stellar effective radius $R_{\rm e}$, $R_{\rm mol}(r<R_{\rm e})$, shows a systematic increase with the level of H$_{\rm I}$, truncation and/or asymmetry (H$_{\rm I}$ perturbation). Analysis of the molecular- and the atomic-to-stellar mass ratios within $R_{\rm e}$, $R^{\rm mol}_{\star}(r<R_{\rm e})$ and $R^{\rm atom}_{\star}(r<R_{\rm e})$, shows that VERTICO galaxies have increasingly lower $R^{\rm atom}_{\star}(r<R_{\rm e})$ for larger levels of H$_{\rm I}$perturbation (compared to field galaxies matched in stellar mass), but no significant change in $R^{\rm mol}_{\star}(r<R_{\rm e})$. We also measure a clear systematic decrease of the SFE$_{\rm mol}$ within $R_{\rm e}$, SFE$_{\rm mol}(r<R_{\rm e})$, with increasingly perturbed H$_{\rm I}$. Therefore, compared to galaxies from the field, VERTICO galaxies are more compact in CO emission in relation to their stellar distribution, but increasingly perturbed atomic gas increases their $R_{\rm mol}$ and decreases the efficiency with which their molecular gas forms stars. (abridged)