We study the effect of dissipational gas physics on the vertical heating and thickening of disc galaxies during minor mergers. We produce a suite of minor merger simulations for Milky Way-like galaxies. This suite consists of collisionless simulations as well as hydrodynamical runs including a gaseous component in the galactic disc. We find that in dissipationless simulations minor mergers cause the scale height of the disc to increase by up to a factor of ~2. When the presence of gas in the disc is taken into account this thickening is reduced by 25% (50%) for an initial disc gas fraction of 20% (40%), leading to a final scale height z0 between 0.6 and 0.7 kpc, regardless of the initial scale height. We argue that the presence of gas reduces disc heating via two mechanisms: absorption of kinetic impact energy by the gas and/or formation of a new thin stellar disc that can cause heated stars to recontract towards the disc plane. We show that in our simulations most of the gas is consumed during the merger and thus the regrowth of a new thin disc has a negligible impact on the z0 of the post merger galaxy. Final disc scale heights found in our simulations are in good agreement with studies of the vertical structure of spiral galaxies where the majority of the systems are found to have scale heights of 0.4 kpc < z0 < 0.8 kpc. We also found no tension between recent measurements of the scale height of the Milky Way thin disc and results coming from our hydrodynamical simulations. We conclude that the existence of a thin disc in the Milky Way and in external galaxies is not in obvious conflict with the predictions of the CDM model.
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