  We derive central values and logarithmic gradients for the Hbeta, Mg and Fe
indices of 35 early-type galaxies in the Coma cluster. We find that pure
elliptical galaxies have on average slightly higher velocity dispersions, lower
Hbeta, and higher metallic line-strengths than galaxies with disks (S0). The
gradients strongly correlate with the gradients of sigma, but only weakly with
the central index values and galaxy velocity dispersion. Using stellar
population models with variable element abundance ratios from Thomas, Maraston
& Bender (2003a) we derive average ages, metallicities and [alpha/Fe] ratios in
the center and at the effective radius. We find that the [alpha/Fe] ratio
correlates with velocity dispersion and drives 30% of the Mg-sigma relation,
the remaining 70% being caused by metallicity variations. We derive negative
metallicity gradients (-0.16 dex per decade) that are significantly flatter
than what is expected from gaseous monolithic collapse models, pointing to the
importance of mergers in the galaxy formation history. The gradients in age are
negligible, implying that no significant residual star formation has occurred
either in the center or in the outer parts of the galaxies, and that the
stellar populations at different radii must have formed at a common epoch. For
the first time we derive the gradients of the [alpha/Fe] ratio and find them
very small on the mean. Hence, [alpha/Fe] enhancement is not restricted to
galaxy centers but it is a global phenomenon. Our results imply that the
Mg-sigma local relation inside a galaxy, unlike the global Mg-sigma relation,
must be primarily driven by metallicity variations alone.
