Modelling 3D galactic gaseous discs with non-isothermal vertical distributions

The vertical structure of galactic gaseous discs plays a relevant role in various astrophysical contexts, however observing it is difficult, so theoretical models are often used to study them. For simplicity, a vertical isothermal distribution is usually assumed; in this thesis, I aim to model thick galactic gaseous discs disregarding this assumption, so I assume a generic velocity dispersion that depends on both the radial (R) and vertical (z) coordinate. I derive the theoretical formalism for these models, and present the numerical approach I developed to build the models. I show two different illustrative models to highlight the effects that arise from assuming a generic non-isothermal vertical distribution. I find that for a decreasing vertical profile of the velocity dispersion I can have the peak of the vertical density profile can shift from z=0. Moreover, I can have a negative vertical gradient of the specific entropy, which may violate the Solberg-Høiland criterion for stability. Finally, I model the HI disc of the Milky Way, using four different radial and vertical profiles of the velocity dispersion. I compare my results to the observed flaring shown in Kalberla et al. (2007), managing to reproduce the profile up to R≈22 kpc without the need for a DM ring, which was the solution adopted by Kalberla et al. (2007). However, I can only reproduce the sharp increase in the flaring from R≈22 kpc using a very complex radial profile for the velocity dispersion that is only partially based on observational constraints.