Properties of the stellar orbit distributions of simulated galaxies and physical justification of the definition of hot inner stellar halo. Top: probability density distribution in panel a and the average metallicity in panel b, as a function of radius, r, obtained by summing up all the hot orbits with λ_z < 0.5 from a selection of TNG50 galaxies at z = 0, namely those in group g6 of Fig. 1. Each galaxy’s curve is color coded by the galaxy’s stellar ex situ fraction, as indicated by the colorbar. The vertical line indicates the radius r_cut = 3.5 kpc, where both the probability density and metallicity profiles flatten. Middle: distributions of the radii where the probability density distribution of hot orbits peaks, r|_max(phot), for galaxies with M_* > 10^10.3 M_⊙ in the TNG50, TNG100, TNG300, EAGLE, and Illustris simulations. Most galaxies in TNG50 have r|_max(phot) < 1.5 kpc, consistent with real galaxies from the Fornax3D survey. Galaxies in TNG100, TNG300, and EAGLE have slightly larger bulge sizes but still with r|_max(phot) < 3.5 kpc. Bottom: panel d: cumulative distribution function of the hot orbits with λ_z < 0.5, CDF_hot as a function of radius, r, for a selection of TNG50 galaxies. Symbols and selection are the same as in the top panels. The green curve represents the control model constructed by the galaxies with the lowest stellar ex situ fraction. Bottom: panel e: deviation of CDF_hot from the control model, CDF_{hot, control}. The vertical line indicates the radius r_cut = 3.5 kpc, which we adopt throughout as the inner boundary of the hot inner stellar halo.