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A Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE).XI. Two dimensional H$α$ kinematics of the edge-on ram pressure stripped galaxy NGC 4330

Using the VESTIGE survey, a deep narrow-band H$α$ imaging survey of the Virgo cluster carried on at the CFHT with MegaCam, we discovered a long diffuse tail of ionised gas in the edge-on late-type galaxy NGC 4330. This peculiar feature witnesses an ongoing ram pressure stripping (RPS) event able to remove the gas in the outer disc region. Tuned hydrodynamic simulations suggest that the RPS event is occurring almost face-on, making NGC 4330 the ideal candidate to study the effects of the perturbation in the direction perpendicular to the disc plane. We present here two new independent sets of Fabry-Perot observations (R$\simeq$10000) in order to understand the effects of the RPS process on the ionised gas kinematics. Despite their limited sensitivity to the diffuse gas emission, the data allowed us to measure the velocity and the velocity dispersion fields over the galaxy disc and in several features at the edges or outside the stellar disc formed after the RPS event. We have constructed the position-velocity diagrams and the rotation curves of the galaxy using three different techniques. The data show, consistent with the hydrodynamic simulations, that the galaxy has an inner solid-body rotation up to $\sim$2.4 kpc, with non-circular streaming motions outwards the disc and in the several external features formed during the interaction of the galaxy with the surrounding intracluster medium. The data also indicate a decrease of the rotational velocity of the gas with increasing distance from the galaxy disc along the tails, suggesting a gradual but not linear loss of angular momentum in the stripped gas. Consistent with a RPS scenario, the $i$-band image shows a boxy shape at the southwest edge of the disc, where the stellar orbits might have been perturbed by the modification of the gravitational potential well of the galaxy due to the displacement of the gas in the $z$-direction.