Physically motivated fit to mass surface density profiles observed in
  galaxies
  Polytropes have gained renewed interest because they account for several
seemingly-disconnected observational properties of galaxies. Here we study if
polytropes are also able to explain the stellar mass distribution within
galaxies. We develop a code to fit surface density profiles using polytropes
projected in the plane of the sky (propols). Sersic profiles are known to be
good proxies for the global shapes of galaxies and we find that, ignoring
central cores, propols and Sersic profiles are indistinguishable within
observational errors (within 5 % over 5 orders of magnitude in surface
density). The range of physically meaningful polytropes yields Sersic indexes
between 0.4 and 6. The code has been systematically applied to ~750 galaxies
with carefully measured mass density profiles and including all morphological
types and stellar masses (7 < log (Mstar/Msun) < 12). The propol fits are
systematically better than Sersic profiles when log(Mstar/Msun) < 9 and
systematically worst when log(Mstar/Msun) > 10. Although with large scatter,
the observed polytropic indexes increase with increasing mass and tend to
cluster around m=5. For the most massive galaxies, propols are very good at
reproducing their central parts, but they do not handle well cores and
outskirts altogether. Polytropes are self-gravitating systems in thermal
meta-equilibrium as defined by the Tsallis entropy. Thus, the above results are
compatible with the principle of maximum Tsallis entropy dictating the internal
structure in dwarf galaxies and in the central region of massive galaxies.
