Pinning down the ram-pressure-induced halt of star formation in the Virgo cluster spiral galaxy NGC 4388: A joint inversion of spectroscopic and photometric data

Context. In a galaxy cluster, the evolution of spiral galaxies depends on their cluster environment. Ram pressure due to the rapid motion of a spiral galaxy within the hot intracluster medium removes the galaxy's interstellar medium from the outer disk. Once the gas has left the disk, star formation stops. The passive evolution of the stellar populations should be detectable in optical spectroscopy and multi-wavelength photometry. Aims. The goal of our study is to recover the stripping age of the Virgo spiral galaxy NGC 4388, i.e. the time elapsed since the halt of star formation in the outer galactic disk using a combined analysis of optical spectra and photometry. Methods. We performed VLT FORS2 long-slit spectroscopy of the inner star-forming and outer gas-free disk of NGC 4388. We developed a non-parametric inversion tool that allows us to reconstruct the star formation history of a galaxy from spectroscopy and photometry. The tool was tested on a series of mock data using Monte Carlo simulations. The results from the non-parametric inversion were refined by applying a parametric inversion method. Results. The star formation history of the unperturbed galactic disk is flat. The non-parametric method yields a rapid decline of star formation less than or similar to 200 Myr ago in the outer disk. The parametric method is not able to distinguish between an instantaneous and a long-lasting star formation truncation. We find that 190 +/- 30 Myr ago the star formation reached half of its pre-stripping value. Conclusions. We are able to give a precise stripping age that is consistent with revised dynamical models.