VERTICO VII: Environmental quenching caused by suppression of molecular gas content and star formation efficiency in Virgo Cluster galaxies

We study how environment regulates the star formation cycle of 33 Virgo Cluster satellite galaxies on 720 parsec scales. We present the first resolved star-forming main sequence for cluster galaxies, dividing the sample based on their global HI properties and comparing to a control sample of field galaxies. HI-poor cluster galaxies have reduced star formation rate (SFR) surface densities with respect to both HI-normal cluster and field galaxies (0.5 dex), suggesting that mechanisms regulating the global HI content are responsible for quenching local star formation. We demonstrate that the observed quenching in HI-poor galaxies is caused by environmental processes such as ram pressure stripping (RPS) simultaneously reducing molecular gas surface density and star formation efficiency (SFE), compared to regions in HI-normal systems (by 0.38 and 0.22 dex, respectively). We observe systematically elevated SFRs that are driven by increased molecular gas surface densities at fixed stellar mass surface density in the outskirts of early-stage RPS galaxies, while SFE remains unchanged with respect to the field sample. We quantify how RPS and starvation affect the star formation cycle of inner and outer galaxy discs as they are processed by the cluster. We show both are effective quenching mechanisms with the key difference being that RPS acts upon the galaxy outskirts while starvation regulates the star formation cycle throughout disc, including within the truncation radius. For both processes, the quenching is caused by a simultaneous reduction in molecular gas surface densities and SFE at fixed stellar mass surface density.