# Sersic profile (in terms of the half-light radius, Re)

## 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.

Today, it is more common to write this function in terms of the half-light radius, Re, and the intensity at that radius, Ie, as shown. 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.

It can be shown that bn satisfies γ(2n;b_{n})=0.5Γ(2n) , where Γ and γ are respectively the Gamma function and lower incomplete Gamma function. Many related expressions, in terms of the surface brightness, also exist.

## Variables

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

I_{e} | intensity at the half-light radius Re (W*sr^{-1}*m^{-2}) |

b_{n} | constant (dimensionless) |

R | distance from the galaxy center (m) |

R_{e} | half-light radius (m) |

n | the Sérsic index (dimensionless) |