  The Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE) is a
blind narrow-band H$\alpha$+[NII] imaging survey carried out with MegaCam at
the CFHT. During pilot observations we have observed NGC 4330, an intermediate
mass, edge-on star forming spiral currently falling into the core of the Virgo
cluster. New deep observations revealed a low surface brightness 10 kpc tail
exhibiting a peculiar filamentary structure. The filaments are remarkably
parallel one another and clearly indicate the direction of motion of the galaxy
in the Virgo potential. Motivated by the detection of these features,
indicating ongoing gas stripping, we collected literature photometry in 15
bands from the far-UV to the far-IR and deep optical long slit spectroscopy
using the FORS2 instrument at the ESO Very Large Telescope. Using a newly
developed Monte Carlo code that jointly fits spectroscopy and photometry, we
reconstructed the star formation histories in apertures along the major axis of
the galaxy. Our results have been validated against the output of CIGALE, a
fitting code which has been previously used for similar studies. We found a
clear outside-in gradient with radius of the time when the quenching event
started: the outermost radii have been stripped 500 Myr ago, while the
stripping has reached the inner 5 kpc from the center in the last 100 Myr.
Regions at even smaller radii are currently still forming stars fueled by the
presence of HI and H2 gas. When compared to statistical studies of the
quenching timescales in the local Universe we find that ram pressure stripping
of the cold gas is an effective mechanism to reduce the transformation times
for galaxies falling into massive clusters. Future systematic studies of all
the active galaxies observed by VESTIGE in the Virgo cluster will extend these
results to a robust statistical framework.
