## GNU Astronomy Utilities

#### 8.1.1.4 Galaxies

Today, most practitioners agree that the flux of galaxies can be modeled with one or a few generalized de Vaucouleur’s (or Sérsic) profiles.

$$I(r) = I_e \exp \left ( -b_n \left[ \left( r \over r_e \right)^{1/n} -1 \right] \right )$$

Gérard de Vaucouleurs (1918-1995) was first to show in 1948 that this function resembles the galaxy light profiles, with the only difference that he held $$n$$ fixed to a value of 4. Twenty years later in 1968, J. L. Sérsic showed that $$n$$ can have a variety of values and does not necessarily need to be 4. This profile depends on the effective radius ($$r_e$$) which is defined as the radius which contains half of the profile’s 2-dimensional integral to infinity (see Profile magnitude). $$I_e$$ is the flux at the effective radius. The Sérsic index $$n$$ is used to define the concentration of the profile within $$r_e$$ and $$b_n$$ is a constant dependent on $$n$$. MacArthur et al.211 show that for $$n>0.35$$, $$b_n$$ can be accurately approximated using this equation:

$$b_n=2n - {1\over 3} + {4\over 405n} + {46\over 25515n^2} + {131\over 1148175n^3}-{2194697\over 30690717750n^4}$$

#### Footnotes

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MacArthur, L. A., S. Courteau, and J. A. Holtzman (2003). “Structure of Disk-dominated Galaxies. I. Bulge/Disk Parameters, Simulations, and Secular Evolution”. In: ApJ 582, pp. 689—722.