Analysis of the galaxy size versus stellar mass relation
  The scatter in the galaxy size versus stellar mass (Mstar) relation gets
largely reduced when, rather than the half-mass radius Re, the size at a fixed
surface density is used. Here we address why this happens. We show how a
reduction is to be expected because any two galaxies with the same Mstar have
at least one radius with identical surface density, where the galaxies have
identical size. However, the reason why the scatter is reduced to the observed
level is not trivial, and we pin it down to the galaxy surface density profiles
approximately following Sersic profiles with their Re and Sersic index (n)
anti-correlated (i.e., given Mstar, n increases when Re decreases). Our
analytical results describe very well the behavior of the observed galaxies as
portrayed in the NASA Sloan Atlas (NSA), which contains more than half a
million local objects with 7 < log(Mstar/Msun) < 11.5. The comparison with NSA
galaxies also allows us to find the optimal values for the mass surface density
(2.4m0.9p1.3 Msun/pc2) and surface brightness (r-band 24.7pm0.5 mag/arcsec2)
that minimize the scatter, although the actual values depend somehow on the
subset of NSA galaxies used for optimization. The physical reason for the
existence of optimal values is unknown but, as Trujillo+20 point out, they are
close to the gas surface density threshold to form stars and thus may trace the
physical end of a galaxy. Our NSA-based size--mass relation agrees with theirs
on the slope as well as on the magnitude of the scatter. As a by-product of the
narrowness of the size--mass relation (only 0.06 dex), we propose to use the
size of a galaxy to measure its stellar mass. In terms of observing time, it is
not more demanding than the usual photometric techniques and may present
practical advantages in particular cases.
