Sersic's law

The Sérsic profile (or Sérsic model or Sérsic's law) is a mathematical function that describes how the intensity ${\displaystyle I}$ of a galaxy varies with distance ${\displaystyle R}$ 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 form

where ${\displaystyle I_{0}}$ is the intensity at ${\displaystyle R=0}$. The parameter ${\displaystyle n}$, called the "Sérsic index," controls the degree of curvature of the profile (see figure). The smaller the value of ${\displaystyle n}$, the less centrally concentrated the profile is and the shallower (steeper) the logarithmic slope at small (large) radii is:

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