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A Sérsic Profile (or Sérsic Model or Sérsic Law) is an equation describing the relative Surface Brightness of a Galaxy, stating that the log of the surface brightness falls off exponentially with distance from the center. The Sérsic Index is the reciprocal of the exponent: i.e., if the exponent is 1/n, then n is the Sérsic index.
The Sérsic profile is a generalization of de Vaucouleurs' Profile, which amounts to an Sérsic profile with an index of 4.