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The Sérsic profile (or Sérsic model or Sérsic's law) is a mathematical function that describes how the intensity
Contents
Definition
The Sérsic profile has the form
where
Applications
Most galaxies are fit by Sérsic profiles with indices in the range 1/2 < n < 10. The best-fit value of n correlates with galaxy size and luminosity, such that bigger and brighter galaxies tend to be fit with larger n. Setting n = 4 gives the de Vaucouleurs profile:
which is a good description of giant elliptical galaxies. Setting n = 1 gives the exponential profile:
which is a good description of spiral galaxy disks and dwarf elliptical galaxies. The correlation of Sérsic index (i.e. galaxy concentration) with galaxy morphology is sometimes used in automated schemes to determine the Hubble type of distant galaxies. Sérsic indices have also been shown to correlate with the mass of the supermassive black hole at the centers of the galaxies.
Sérsic profiles provide the best current description of dark matter halos, and the Sérsic index correlates with halo mass.
Generalizations of the Sérsic profile
The brightest elliptical galaxies often have low-density cores that are not well described by Sérsic's law. The "core-Sérsic" family of models was introduced by A. Graham et al. and Trujillo et al. and further developed by B. Terzić and A. Graham in 2005 to describe such galaxies. Core-Sérsic models have an additional set of parameters that describe the core radius and core density.
Dwarf elliptical galaxies sometimes have pointlike nuclei that are also not well described by Sérsic's law. These galaxies are often fit by a Sérsic model with an added central component representing the nucleus.
The Einasto profile is mathematically identical to the Sérsic profile, except that