A Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE).XIV. The main sequence relation in a rich environment down to M_star ~ 10^6 Mo

Using a compilation of Halpha fluxes for 384 star forming galaxies detected during the VESTIGE survey, we study several important scaling relations for a complete sample of galaxies in a rich environment. The extraordinary sensitivity of the data allows us to sample the whole dynamic range of the Halpha luminosity function, from massive (M*~10^11 Mo) to dwarf systems (M*~10^6 Mo). This extends previous works to a dynamic range in stellar mass and star formation rate (10^-4<SFR<10 Mo yr^-1) never explored so far. The main sequence (MS) relation derived for all star forming galaxies within one virial radius of the Virgo cluster has a slope comparable to that observed in other nearby samples of isolated objects, but has a dispersion ~3 times larger. The dispersion is tightly connected to the available amount of HI gas, with gas-poor systems located far below objects of similar stellar mass but with a normal HI content. When measured on unperturbed galaxies with a normal HI gas content, the relation has a slope a=0.92, an intercept b=-1.57, and a scatter ~0.40. We compare these observational results to the prediction of models. The observed scatter in the MS relation can be reproduced only after a violent and active stripping process such as ram-pressure that removes gas from the disc and quenches star formation on short (<1 Gyr) timescales. This rules out milder processes such as starvation. This interpretation is also consistent with the position of galaxies of different star formation activity and gas content within the phase-space diagram. We also show that the star forming regions formed in the stripped material outside perturbed galaxies are located well above the MS relation drawn by unperturbed systems. These HII regions, which might be at the origin of compact sources typical in rich environments, are living a starburst phase lasting only <50 Myr, later becoming quiescent systems.