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'''[[de Vaucouleurs]]' law''' (also called the '''de Vaucouleurs profile''') describes how the surface brightness <math>I</math> of an [[elliptical galaxy]] varies as a function of apparent distance <math>R</math> from the center:<ref>[http://adsabs.harvard.edu/abs/1948AnAp...11..247D  Recherches sur les Nebuleuses Extragalactiques]</ref>

:<math>
\ln I(R) = \ln I_{0} - k R^{1/4}.
</math>

By defining ''R<sub>e</sub>'' as the radius of the [[Contour_line#Other_phenomena|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:

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

or

:<math>
I(R) = I_{e} e^{-7.669 \left[ (\frac{R}{R_{e}})^{1/4} - 1 \right]}
</math>

where ''I<sub>e</sub>'' is the surface brightness at ''R<sub>e</sub>''. This can be confirmed by noting

:<math>
\int^{R_e}_0 I(R) r dr = \frac{1}{2} \int^{\infty}_0 I(R) r dr  .
</math>

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 profile|Jaffe's model]] and [[Dehnen profile|Dehnen's model]].

== References ==

{{reflist}}

==External links==
* [http://scienceworld.wolfram.com/astronomy/deVaucouleursLaw.html Eric Weisstein's World of Astronomy entry]

[[Category:Astrophysics]]


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