We study the star formation quenching mechanism in cluster galaxies by fitting the SED of the Herschel Reference Survey, a complete volume-limited K-band-selected sample of nearby galaxies including objects in different density regions, from the core of the Virgo cluster to the general field. The SED are fitted using the CIGALE SED modelling code. The truncated activity of cluster galaxies is parametrised using a specific SFH with 2 free parameters, the quenching age QA and the quenching factor QF. These 2 parameters are crucial for the identification of the quenching mechanism which acts on long timescales if starvation while rapid and efficient if ram pressure. To be sensitive to an abrupt and recent variation of the star formation activity, we combine in a new way 20 UV to FIR photometric bands with 3 age-sensitive Balmer line absorption indices extracted from available medium-resolution integrated spectroscopy and with Halpha narrow band imaging data. The use of a truncated SFH significantly increases the quality of the fit in those objects whose atomic gas content has been removed during the interaction with the hostile cluster environment. The typical QA of the perturbed late-type galaxies is QA < 300 Myr whenever the activity of star formation is reduced by 50% < QF <= 80% and QA < 500 Myr for QF > 80%, while that of the quiescent early-types is QA ~ 1-3 Gyr. The fraction of late-types with a star formation activity reduced by QF > 80% and with an HI-deficiency parameter HI-def > 0.4 drops by a factor of ~ 5 from the inner half virial radius of the Virgo cluster, where the hot diffuse X-ray emitting gas of the cluster is located, to the outer regions. The efficient quenching of the star formation activity observed in Virgo suggests that the dominant stripping process is ram pressure. We discuss the implication of this result in the cosmological context of galaxy evolution.
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