Sérsic profile

A Sérsic profile (or Sérsic model or Sérsic law) is a relation describing the relative surface brightness of a galaxy (i.e., a surface brightness profile), 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.

         R1/n
I(R) ∝ e

or

log I(R) = c1 - c2R1/n

• R - distance from brightest point.
• I(R) - brightness(intensity) at R.
• n - Sérsic index.
• c₁ and c₂ - constants (often stated in terms of particular values).

Some particular galaxy (or type of galaxy) might be well-described by a Sérsic profile (with some Sérsic index), while others won't. The Sérsic profile is a generalized such relation for which once instance is the de Vaucouleurs' profile (Sérsic profile with an index of 4) and another the exponential profile (index of 1).