Authors: Alister W. Graham
Abstract:For decades, the deceptive simplicity of the radius Re, enclosing an arbitrary 50 percent 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' R1/4 model, Sérsic reported that bright ETGs follow the relation MB∝2.5log Re; and consequently one has that ⟨μ⟩e∝2.5 log Re and ⟨μ⟩e∝2.5 log Re, where μe and ⟨μ⟩e are the effective surface brightness at Re and the mean effective surface brightness within Re, 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 MB ≈ -18 mag or n≈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 MB ≈ -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 Re is of further importance because quantities such as dynamical mass σ2R/G, gravitational binding energy GM2/R, acceleration GM/R2, 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 MB ≈ -18 mag (Mass ≈ 1—2×1010 M☉) 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.