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Polytropes have gained renewed interest because they account for severalseemingly-disconnected observational properties of galaxies. Here we study ifpolytropes are also able to explain the stellar mass distribution withingalaxies. We develop a code to fit surface density profiles using polytropesprojected in the plane of the sky (propols). Sersic profiles are known to begood proxies for the global shapes of galaxies and we find that, ignoringcentral cores, propols and Sersic profiles are indistinguishable withinobservational errors (within 5 % over 5 orders of magnitude in surfacedensity). The range of physically meaningful polytropes yields Sersic indexesbetween 0.4 and 6. The code has been systematically applied to ~750 galaxieswith carefully measured mass density profiles and including all morphologicaltypes and stellar masses (7 < log (Mstar/Msun) < 12). The propol fits aresystematically better than Sersic profiles when log(Mstar/Msun) < 9 andsystematically worst when log(Mstar/Msun) > 10. Although with large scatter,the observed polytropic indexes increase with increasing mass and tend tocluster around m=5. For the most massive galaxies, propols are very good atreproducing their central parts, but they do not handle well cores andoutskirts altogether. Polytropes are self-gravitating systems in thermalmeta-equilibrium as defined by the Tsallis entropy. Thus, the above results arecompatible with the principle of maximum Tsallis entropy dictating the internalstructure in dwarf galaxies and in the central region of massive galaxies.

Physically motivated fit to mass surface density profiles observed in galaxies