Kinematics of simulated galaxies – I. Connecting dynamical and morphological properties of early-type galaxies at different redshifts

State-of-the-art integral field surveys like $\mathrm{ATLAS^{3D}}$, SLUGGS, CALIFA, SAMI, and MaNGA provide large data sets of kinematical observations of early-type galaxies (ETGs), yielding constraints on the formation of ETGs. Using the cosmological hydrodynamical \textit{Magneticum Pathfinder} simulations, we investigate the paradigm of fast and slow rotating ETGs in a fully cosmological context. We show that the ETGs within the \textit{Magneticum} simulation are in remarkable agreement with the observations, revealing fast and slow rotators quantified by the angular momentum proxy $\lambda_{\mathrm{R}}$ and the flattening $\epsilon$ with the observed prevalence. Taking full advantage of the three-dimensional data, we demonstrate that the dichotomy between fast and slow rotating galaxies gets enhanced, showing an upper and lower population separated by an underpopulated region in the edge-on $\lambda_{\mathrm{R}}$-$\epsilon$ plane. Following the evolution of the $\lambda_{\mathrm{R}}$-$\epsilon$ plane through cosmic time, we find that, while the upper population is already in place at $z=2$, the lower population gets statistically significant below $z=1$ with a gradual increase. At least $50\%$ of the galaxies transition from fast to slow rotators on a short timescale, in most cases associated to a significant merger event. Furthermore, we connect the $M_{*}$-$j_{*}$ plane, quantified by the $b$-value, with the $\lambda_{\mathrm{R}}$-$\epsilon$ plane, revealing a strong correlation between the position of a galaxy in the $\lambda_{\mathrm{R}}$-$\epsilon$ plane and the $b$-value. Going one step further, we classify our sample based on features in their velocity map, finding all five common kinematic groups, also including the recently observed group of prolate rotators, populating distinct regions in the $\lambda_{\mathrm{R}}$-$b$ plane.