Deep Effelsberg 100-m HI observations of 5 HI deficient Virgo spiral galaxies are presented. No new extended HI tail is found in these galaxies. The already known HI tail north of NGC 4388 does not significantly extend further than a WSRT image has shown. Based on the absence of HI tails in a sample of 6 Virgo spiral galaxies and a balance of previous detections of extraplanar gas in the targeted galaxies we propose a global picture where the outer gas disk (beyond the optical radius R_25) is removed much earlier than expected by the classical ram pressure criterion. Based on the two-phase nature of atomic hydrogen located in a galactic disk, we argue that the warm diffuse HI in the outer galactic disk is evaporated much more rapidly than the cold dense HI. Therefore, after a ram pressure stripping event we can only observe atomic hydrogen which was cold and dense before it was removed from the galactic disk. This global picture is consistent with all available observations. We detect between 0.3% and 20% of the stripped mass assuming an initially non-deficient galaxy and between 3% and 70% of the stripped mass assuming an initially HI deficient galaxy (def=0.4). Under the latter assumption we estimate an evaporation rate by dividing the missing mass by the estimated time to peak ram pressure from dynamical simulations. We find evaporation rates between 10 and 100 M_solar/yr.
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