Re. I. Understanding galaxy sizes, associated luminosity densities, and the artificial division of the early-type galaxy population
Abstract For decades, the deceptive simplicity of the radius 
$R_{\rm e}$
 , enclosing an arbitrary 50% of a galaxy’s light, has hamstrung the understanding of early-type galaxies (ETGs). Half a century ago, using these ‘effective half-light’ radii from de Vaucouleurs’ 
$R^{1/4}$
 model, Sérsic reported that bright ETGs follow the relation 
$\mathfrak{M}_B\propto2.5\log R_{\rm e}$
 ; and consequently, one has that 
$\langle\mu\rangle_{\rm e}\propto2.5\log R_{\rm e}$
 and 
$\mu_{\rm e}\propto2.5\log R_{\rm e}$
 , where 
$\mu_{\rm e}$
 and 
$\langle\mu\rangle_{\rm e}$
 are the effective surface brightness at 
$R_{\rm e}$
 and the mean effective surface brightness within 
$R_{\rm e}$
 , respectively. Sérsic additionally observed an apparent transition which led him to advocate for a division between what he called dwarf and giant ETGs; a belief frequently restated to occur at 
$\mathfrak{M}_B \approx -18$
 mag or 
$n\approx 2.5$
 . Here, the location of this false dichotomy in diagrams using ‘effective’ parameters is shown to change by more than 3 mag simply depending on the arbitrary percentage of light used to quantify a galaxy’s size. A range of alternative radii are explored, including where the projected intensity has dropped by a fixed percentage plus a battery of internal radii, further revealing that the transition at 
$\mathfrak{M}_B
\approx -18$
 mag is artificial and does not demark a boundary between different physical processes operating on the ETG population. The above understanding surrounding the effective radius 
$R_{\rm e}$
 is of further importance because quantities such as dynamical mass 
$\sigma^2R/G$
 , gravitational-binding energy 
$GM^2/R$
 , acceleration 
$GM/R^2$
 , and the ‘Fundamental Plane’ also depend on the arbitrary percentage of light used to define R, with implications for dark matter estimates, galaxy formation theories, compact massive galaxies, studies of peculiar velocity flows, and more. Finally, some of the vast literature which has advocated for segregating the ETG population at 
$\mathfrak{M}_B \approx -18$
 mag ( 
$M\approx1$
 – 
$2\times10^{10}\,{\rm M}_{\odot}$
 ) is addressed, and it is revealed how this pervasive mindset has spilled over to influence both the classical bulge versus pseudobulge debate and recently also correlations involving supermassive black hole masses.