The size–mass and other structural parameter (n, μ z , Rz) relations for local bulges/spheroids from multicomponent decompositions

We analyse the bulge/spheroid size–(stellar mass), Re, Sph–M*, Sph, relation and spheroid structural parameters for 202 local (predominantly ≲110 Mpc⁠) galaxies spanning M* ∼ 3 × 109–1012 M⊙ and 0.1≲Re,Sph≲32 kpc from multicomponent decomposition. The correlations between the spheroid Sérsic index (nSph), central surface brightness (μ0, Sph), effective half-light radius (Re, Sph), absolute magnitude (⁠MSph⁠) and stellar mass (M*, Sph) are explored. We also investigate the consequences of using different scale radii, Rz,Sph⁠, encapsulating a different fraction (z, from 0 to 1) of the total spheroid luminosity. The correlation strengths for projected mass densities, Σz and 〈Σ〉z, vary significantly with the choice of z. Spheroid size (⁠Rz,Sph⁠) and mass (M*, Sph) are strongly correlated for all light fractions z. We find: log(Re,Sph/kpc)=0.88log(M∗,Sph/M⊙)−9.15 with a small scatter of Δrms=0.24 dex in the log (Re, Sph) direction. This result is discussed relative to the curved size–mass relation for early-type galaxies due to their discs yielding larger galaxy radii at lower masses. Moreover, the slope of our spheroid size–mass relation is a factor of ∼3, steeper than reported bulge size–mass relations, and with bulge sizes at M*, sph ∼ 3 × 109 M⊙ which are 2 to 3 times smaller. Our spheroid size–mass relation present no significant flattening in slope in the low-mass end (M*, sph ∼ 109–1010 M⊙⁠). Instead of treating galaxies as single entities, future theoretical and evolutionary models should also attempt to recreate the strong scaling relations of specific galactic components. Additional scaling relations, such as log (nSph)–log (M*, Sph), log (Σ0, Sph)–log (nSph), and log (nSph)–log (Re, Sph), are also presented. Finally, we show that the local spheroids align well with the size-mass distribution of quiescent galaxies at z ∼ 1.25–2.25. In essence, local spheroids and high-z quiescent galaxies appear structurally similar, likely dictated by the virial theorem.