A Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE). XV. The Halpha luminosity function of the Virgo cluster

We use a complete set of deep narrow-band imaging data for 384 galaxies gathered during the VESTIGE survey to derive the first Halpha luminosity function (LF) of the Virgo cluster within R200. The data allow us to cover the whole dynamic range of the Halpha LF (10^36<LHa<10^42 erg s^-1). After they are corrected for [NII] contamination and dust attenuation, the data are used to derive the SFR function in the range 10^-4<SFR<10 Mo yr^-1. These LF are compared to those derived at other frequencies or using different tracers of star formation in Virgo, in other nearby and high-z clusters, in the field, and to those predicted by the IllustrisTNG cosmological hydrodynamical simulations. The Halpha LF of the Virgo cluster is fairly flat (a=-1.07) in the range 10^38.5<LHa<10^40.5 erg s^-1, and it abruptly decreases at lower luminosities. When compared to those derived for other nearby clusters and for the field, the slope and the characteristic luminosity of the Schechter function change as a function of the dynamical mass of the system, of the temperature of the X-rays gas, and of the dynamical pressure exerted on the interstellar medium of galaxies moving at high velocity within the intracluster medium. All these trends can be explained in a scenario in which the activity of SF is reduced in massive clusters due to their hydrodynamical interaction with the surrounding medium, suggesting once again that ram-pressure stripping is the dominant mechanism affecting galaxy evolution in local clusters of dynamical mass M200>10^14 Mo. The comparison with the IllustrisTNG cosmological hydrodynamical simulations shows a more pronounced decrease at the faint end of the distribution. If Virgo is representative of typical nearby clusters of similar mass, this difference suggests that the stripping process in simulated galaxies in these environments is more efficient than observed.