Unifying the dynamical classification of early-type galaxies: kinematic deficits in IllustrisTNG versus observations

We conduct a comparative analysis of galaxy kinematics using IllustrisTNG simulations and integral-field spectroscopy (IFS) observations. We identify 2,342 early-type galaxies (ETGs) from the TNG100 simulation and 236 ETGs from the TNG50 simulation, comparing them with observations from MaNGA and ATLAS$^{3D}$. For these systems, we measure key kinematic parameters: the intrinsic spin parameter $\lambda_{R,\mathrm{intr}}$ (measured edge-on), the cylindrical rotational energy fraction $\kappa_{\mathrm{rot}}$, and structural mass ratios including the spheroid mass fraction $f_{\mathrm{spheroid}}$ and stellar halo mass fraction $f_{\mathrm{halo}}$. Our study reveals that standard classifiers--the $\lambda_{R}(R_e)=0.31\sqrt{\varepsilon}$ relation and $\overline{k_5}$ coefficient (higher-order Fourier term of velocity fields)--fail to align with observed kinematic bimodality. We propose revised thresholds: $\lambda_{R,\mathrm{intr}} \sim 0.4$, $\kappa_{\mathrm{rot}} \sim 0.5$, and $f_{\mathrm{spheroid}} \sim 0.6$, which classify galaxies into rotation-dominated (fast rotators) and random motion-dominated (slow rotators). Scaling relations from TNG enable observational estimates of $\kappa_{\mathrm{rot}}$ and $f_{\mathrm{spheroid}}$. The simulations exhibit a bimodality deficit, characterized by a lack of fast rotators and suppressed $\lambda_{R,\mathrm{intr}}$, attributed to excess galaxies with intermediate rotation and high spheroid/stellar halo mass. We introduce a novel method to estimate $f_{\mathrm{halo}}$ from IFS kinematics, though uncertainties remain.