PREPRINT
EA41EBD2-75A5-4D9E-95D7-4E786D897909

# The size--mass and other structural parameter ($n,{\mu }_{z},{R}_{z}$) relations for local bulges/spheroids from multicomponent decompositions

Dexter S. -H. Hon, Alister W. Graham, Nandini Sahu

Submitted on 4 September 2022

## Abstract

We analyse the bulge/spheroid size-(stellar mass), ${R}_{\mathrm{e},\mathrm{S}\mathrm{p}\mathrm{h}}-{M}_{\ast ,\mathrm{S}\mathrm{p}\mathrm{h}}$, relation and spheroid structural parameters for 202 local (predominantly ) galaxies spanning and from multicomponent decomposition. The correlations between the spheroid S\'ersic index (${n}_{\mathrm{S}\mathrm{p}\mathrm{h}}$), central surface brightness (${\mu }_{0,\mathrm{S}\mathrm{p}\mathrm{h}}$), effective half-light radius (${R}_{\mathrm{e},\mathrm{S}\mathrm{p}\mathrm{h}}$), absolute magnitude (${\mathfrak{M}}_{\mathrm{S}\mathrm{p}\mathrm{h}}$) and stellar mass (${M}_{\ast ,\mathrm{S}\mathrm{p}\mathrm{h}}$) are explored. We also investigate the consequences of using different scale radii, ${R}_{z,\mathrm{S}\mathrm{p}\mathrm{h}}$, encapsulating a different fraction ($z$, from 0 to 1) of the total luminosity. The correlation strengths for projected mass densities, ${\mathrm{\Sigma }}_{z}$ and $⟨\mathrm{\Sigma }{⟩}_{z}$, vary significantly with the choice of $z$. Spheroid size (${R}_{\mathrm{z},\mathrm{S}\mathrm{p}\mathrm{h}}$) and mass (${M}_{\ast ,\mathrm{S}\mathrm{p}\mathrm{h}}$) are strongly correlated for all light fractions $z$. We find: $\mathrm{log}\left({R}_{\mathrm{e},\mathrm{S}\mathrm{p}\mathrm{h}}/\mathrm{k}\mathrm{p}\mathrm{c}\right)=0.88\mathrm{log}\left({\mathrm{M}}_{\ast ,\mathrm{S}\mathrm{p}\mathrm{h}}/{\mathrm{M}}_{\odot }\right)-9.15$ with a small scatter of . This result is discussed relative to the \textit{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 $\sim 3$, steeper than reported bulge size-mass relations, and with bulge sizes at which are 2 to 3 times smaller. Finally, we show that the local spheroids align well with quiescent galaxies at $z\sim 1.25$--$2.25$. In essence, local spheroids and high-$z$ quiescent galaxies appear structurally similar, likely dictated by the virial theorem.

## Preprint

Comment: 19 pages, 15 figures, submitted to MNRAS

Subject: Astrophysics - Astrophysics of Galaxies