Luminosity fraction of hot inner stellar halo f_∗,halo versus the spheroid size R_Sph. Left: Compact ETGs selected from TNG50 central galaxies, colour-coded by accreted stellar mass fraction f_∗,accreted as shown in the colour bar. Middle: Compact ETGs selected from TNG50 satellite galaxies, using the same f_∗,accreted colour scheme. Right: The 15 compact ETGs from observations. The vertical dashed line indicates f_∗,halo = 0.15. Spheroid size and f_∗,halo are strongly correlated for both simulated and observed galaxies. The two parameters are similarly effective at tracing the f_∗,accreted of central galaxies.