# Sersic profile

## Description

The Sérsic profile (or Sérsic model or Sérsic’s law) is a mathematical function that describes how the intensity I of a galaxy varies with distance R from its center. It is a generalization of de Vaucouleurs’ law. José Luis Sérsic first published his law in 1963.

The Sérsic profile has the shown form, where the smaller the value of n, the less centrally concentrated the profile is and the shallower (steeper) the logarithmic slope at small (large) radii is

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.

Related formulas## Variables

I(R) | galaxy intensity at distance R (W*sr^{-1}*m^{-2}) |

I_{0} | intensity at R=0 (W*sr^{-1}*m^{-2}) |

k | constant (dimensionless) |

R | distance from the galaxy center, m (dimensionless) |

n | Sérsic index (dimensionless) |