2.1.4. Gradients in metallicity and mass-to-light ratio
Metallicity gradients have been found in ellipticals which go roughly as
(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,
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) / r2 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 r1/4 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 re. 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 ( 1/2re) of elliptical galaxies. Typically one finds M/L 14h.