Circular velocity at the stellar half-mass radius, V_c, e as a function of the stellar line-of-sight velocity dispersion, averaged within the effective radius, R_e. All galaxies categorized as early-type in EAGLE (open circles) and TNG (filled circles) are shown. (See Appendix A for details on the morphological classification procedure.) The thick black solid line indicates the model of Wolf et al. (2010). The solid and dashed red lines are simple power-law fits to the EAGLE and TNG data, respectively. For fits of the form V_c, e = V₀ (σ_e/km s⁻¹)ⁿ, the best fit parameters are (V₀, n) = (2.37 km s⁻¹, 0.94) for EAGLE and (V₀, n) = (7.03 km s⁻¹, 0.73) for TNG.