astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

, de Vaucouleurs's law, also known as the de Vaucouleurs profile or de Vaucouleurs model, describes how the surface brightness

I

of an elliptical galaxy varies as a function of apparent distance

R

from the center of the galaxy:

\ln I(R) = \ln I_ - k R^.

By defining ''R_e'' as the radius of the isophote containing half of the total luminosity of the galaxy, the

half-light radius Galaxy effective radius or half-light radius (R_e) is the radius at which half of the total light of a galaxy is emitted. This assumes the galaxy has either intrinsic circular symmetry, spherical symmetry or is at least circularly symmetric as vi ...

, de Vaucouleurs profile may be expressed as:

\ln I(R) = \ln I_ + 7.669 \left 1 - \left( \frac \right)^ \right

I(R) = I_ e^

where ''I_e'' is the surface brightness at ''R_e''. This can be confirmed by noting

\int^_0 I(r)2\pi r \, dr = \frac \int^_0 I(r)2\pi r \, dr  .

De Vaucouleurs model is a special case of Sersic's model, with a Sersic index of . A number of (internal) density profiles that approximately reproduce de Vaucouleurs's law after projection onto the plane of the sky include Jaffe's model and Dehnen's model. The model is named after Gérard de Vaucouleurs who first formulated it in 1948. Although an empirical model rather than a law of physics, it was so entrenched in astronomy during the 20th century that it was referred to as a "law".

References

External links

Eric Weisstein's World of Astronomy entry
Astrophysics Equations of astronomy {{Astrophysics-stub