**2.1.4. Gradients in metallicity and mass-to-light ratio**

Metallicity gradients have been found in ellipticals which go roughly as

(2.10) |

(Faber, 1977). This result is extremely important in theories of galaxy formation and will be discussed further in Section 8.

There is some evidence
(Bond, 1981;
Terlevich, 1982)
which suggests
that the shape of the stellar mass function may depend on metallicity.
If this were generally true, the observed metallicity gradients may be
coupled with radial variations in *M*/*L*. In principle, the mass
distribution in ellipticals may be found by applying the equations of
stellar hydrodynamics. For a spherical galaxy, one obtains,

(2.11) |

Here is the
luminosity density of the stars with radial velocity
dispersion _{r}
and tangential dispersion
_{t}.
is
the gravitational potential and by Poisson's equation
*d* / *dr* =
*GM*(*r*) / *r*^{2} where
*M*(*r*) is the
total mass enclosed within *r*. A simple application of Eq. (2.11) in
the case of isotropic dispersions
(_{r} =
_{t}), constant
*M*/*L* and
given
by the *r*^{1/4} profile shows that the velocity dispersion
should fall quite steeply with increasing radius (e.g.,
Bailey and Macdonald,
1981).
The measurement of velocity dispersion at large radii is still
a difficult observational task, hence no general conclusions may yet
be drawn. There is some evidence that the velocity dispersions fall at
large radii
(Davies, 1981;
Efstathiou, Ellis and
Carter, 1982).
However, in the case of NGC 4473
(Young et al., 1978)
the dispersion profile stays constant out to
*r*_{e}. If the measurements are
correct, then one explanation would be that this galaxy has a gradient
in *M*/*L*. From Eq. (2.11) we see that a flat velocity
dispersion profile is obtained if
*M*(*r*)
*r*. The two cD galaxies that have been studied so
far (Dressler, 1979;
Carter et al., 1981)
both show evidence for a
rise in *sigma* with increasing radius, indicating a rise in
*M*/*L*. Equation
(2.11) has been used by several authors to determine the mass-to-light
ratios in the central regions
(
1/2*r*_{e}) of elliptical
galaxies. Typically one finds
*M*/*L*
14*h*.