The surface luminosity profile of elliptical galaxies follows the
so called 
law (de Vaucouleurs 1948):
where R is the distance from the center, 
is the
half-luminosity ratio of the galaxy (see Section 2.4), 
the
surface luminosity at
. The 
law is a straight line when the surface
brightness
is plotted against the 1/4 power of the distance
from the center (see Fig. 6).
In contrast, the surface luminosity profile of a disk galaxy follows an exponential:
where 
is the central surface luminosity and h the exponential
scale length of the disk. Eq. 15 is a straight line when the surface
brightness is plotted against the distance from the
center (see Fig. 7).
Note how the 
law appears in Fig. 7 and how the exponential
law appears in Fig. 6.
The surface luminosity distribution of spiral galaxies with a bulge and S0 galaxies can be described as the sum of the Eq. (14) and (15). The example in Fig. 6 and 7 shows the surface brightness profile of a Bulge+Disk system, where Bulge and Disk have the same total luminosity (see Section 2.4) and half-luminosity radii.
In reality, one does not expect Eq. 14 and 15 to fit
the measured luminosity profiles of galaxies in all of the radial
range. It is well known that the profiles of point sources (for
example stars) appear broadened by the earth atmospheric
turbulence. This effect, called ``seeing'' in the astronomical jargon,
spreads light from the inner to the outer regions of galaxies,
smearing the cusp of the 
law. In the outer parts, errors in
sky subtraction can distort the measured profile.
