How non-linear scaling relations unify dwarf and giant elliptical galaxies

Dwarf elliptical galaxies are frequently excluded from bright galaxy samples because they do not follow the same linear relations in diagrams involving effective half light radii R_e or mean effective surface brightnesses _e. However, using two linear relations which unite dwarf and bright elliptical galaxies we explain how these lead to curved relations when one introduces either the half light radius or the associated surface brightness. In particular, the curved _e - R_e relation is derived here. This and other previously misunderstood curved relations, once heralded as evidence for a discontinuity between faint and bright elliptical galaxies at M_B ∼ -18 mag, actually support the unification of such galaxies as a single population whose structure (i.e. stellar concentration) varies continuously with stellar luminosity and mass.