A MegaCam Survey of Outer Halo Satellites. VII. A Single S\'ersic Index v/s Effective Radius Relation for Milky Way Outer Halo Satellites

In this work we use structural properties of Milky Way's outer halo ($R_G > 25\,\mathrm{kpc}$) satellites (dwarf spheroidal galaxies, ultra-faint dwarf galaxies and globular clusters) derived from deep, wide-field and homogeneous data, to present evidence of a correlation in the S\'ersic index v/s effective radius plane followed by a large fraction of outer halo globular clusters and satellite dwarf galaxies. We show that this correlation can be entirely reproduced by fitting empirical relations in the central surface brightness v/s absolute magnitude and S\'ersic index v/s absolute magnitude parameter spaces, and by assuming the existence of two types of outer halo globular clusters: one of high surface brightness (HSB group), with properties similar to inner halo clusters; and another of low surface brightness (LSB group), which share characteristics with dwarf spheroidal and ultra-faint dwarf galaxies. Given the similarities of LSB clusters with dwarf spheroidal and ultra-faint dwarf galaxies, we discuss the possibility that outer halo clusters also originated inside dark matter halos and that tidal forces from different galaxy host's potentials are responsible for the different properties between HSB and LSB clusters.