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

We analyse the bulge/spheroid size-(stellar mass), $R_{\rm e,Sph}-M_{\rm *,Sph}$, relation and spheroid structural parameters for 202 local (predominantly $\lesssim 110~\rm Mpc$) galaxies spanning $ M_*\sim 3\times10^{9}-10^{12}~\rm M_{\odot}$ 0.1 \lesssim R_{\rm e, Sph}\lesssim32~\rm kpc$ from multicomponent decomposition. The correlations between S\'ersic index ($n_{\rm Sph}$), central surface brightness ($\mu_{\rm 0, effective half-light radius ($R_{\rm absolute magnitude ($\mathfrak{M}_{\rm Sph}$) stellar mass ($M_{\rm *,Sph}$) are explored. also investigate consequences of using different scale radii, $R_{z,\rm Sph}$, encapsulating a fraction ($z$, 0 to 1) total luminosity. correlation strengths projected densities, $\Sigma_z$ $\langle \Sigma \rangle_z$, vary significantly with choice $z$. Spheroid size z, strongly correlated all light fractions find: $\log(R_{\rm e,Sph}/\rm kpc) = 0.88\log(M_{\rm *,Sph}/\rm M_{\odot})-9.15$ small scatter $\Delta_{rms} 0.24~\rm dex$. This result is discussed relative \textit{curved} size-mass early-type due their discs yielding larger galaxy radii at lower masses. Moreover, slope our factor $\sim3$, steeper than reported bulge relations, sizes $M_{\rm *,sph}\sim 3\times10^9~M_\odot$ which 2 3 times smaller. Finally, we show that spheroids align well quiescent $z\sim1.25$--$2.25$. In essence, high-$z$ appear structurally similar, likely dictated by virial theorem.