# De Vaucouleurs' law

de Vaucouleurs' law, also known as the de Vaucouleurs profile, describes how the surface brightness ${\displaystyle I}$ of an elliptical galaxy varies as a function of apparent distance ${\displaystyle R}$ from the center:[1]

${\displaystyle \ln I(R)=\ln I_{0}-kR^{1/4}.}$

By defining Re as the radius of the isophote containing half the luminosity (i.e., the radius of the inner disk contributing half the brightness of the galaxy), de Vaucouleurs' law may be written:

${\displaystyle \ln I(R)=\ln I_{e}+7.669\left[1-\left({\frac {R}{R_{e}}}\right)^{1/4}\right]}$

or

${\displaystyle I(R)=I_{e}e^{-7.669\left[({\frac {R}{R_{e}}})^{1/4}-1\right]}}$

where Ie is the surface brightness at Re. This can be confirmed by noting

${\displaystyle \int _{0}^{R_{e}}I(r)2\pi rdr={\frac {1}{2}}\int _{0}^{\infty }I(r)2\pi rdr.}$

de Vaucouleurs' law is a special case of Sersic's law, with Sersic index n=4. A number of density laws that approximately reproduce de Vaucouleurs' law after projection onto the plane of the sky include Jaffe's model and Dehnen's model.

The law is named after Gérard de Vaucouleurs who first formulated it in 1948.[2][3]

## References

1. ^ Recherches sur les Nebuleuses Extragalactiques
2. ^ "Gerard Henri de Vaucouleurs (1918 - 1995)". Bulletin of the American Astronomical Society. 1996.
3. ^ "Gerard De Vaucouleurs". American Institute of Physics. 2015-01-15. Retrieved 2017-06-22.