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The stellar velocity ellipsoid (SVE) in galaxies can provide importantinformation on the processes that participate in the dynamical heating of theirdisc components (e.g. giant molecular clouds, mergers, spiral density waves,bars). Earlier findings suggested a strong relation between the shape of thedisc SVE and Hubble type, with later-type galaxies displaying more anisotropicellipsoids and early-types being more isotropic. In this paper, we revisit thestrength of this relation using an exhaustive compilation of observationalresults from the literature on this issue. We find no clear correlation betweenthe shape of the disc SVE and morphological type, and show that galaxies withthe same Hubble type display a wide range of vertical-to-radial velocitydispersion ratios. The points are distributed around a mean value and scatterof $\sigma_z/\sigma_R=0.7\pm 0.2$. With the aid of numerical simulations, weargue that different mechanisms might influence the shape of the SVE in thesame manner and that the same process (e.g. mergers) does not have the sameimpact in all the galaxies. The complexity of the observational picture isconfirmed by these simulations, which suggest that the vertical-to-radial axisratio of the SVE is not a good indicator of the main source of disc heating.Our analysis of those simulations also indicates that the observed shape of thedisc SVE may be affected by several processes simultaneously and that thesignatures of some of them (e.g. mergers) fade over time.

Revisiting the Stellar Velocity Ellipsoid - Hubble type relation: observations versus simulations