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 cod
e 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.
We present our recent results on the properties of the outskirts of disk galaxies. In particular, we focus on spiral galaxies with stellar disk truncations in their radial surface brightness profiles. Using SDSS, UDF and GOODS data we show how the po
sition of the break (i.e., a direct estimator of the size of the stellar disk) evolves with time since z~1. Our findings agree with an evolution on the radial position of the break by a factor of 1.3+/-0.1 in the last 8 Gyr for galaxies with similar stellar masses. We also present radial color gradients and how they evolve with time. At all redshift we find a radial inside-out bluing reaching a minimum at the position of the break radius, this minimum is followed by a reddening outwards. Our results constrain several galaxy disk formation models and favour a scenario where stars are formed inside the break radius and are relocated in the outskirts of galaxies through secular processes.
