We have measured line-strength gradients in Mg2, [Fe] and Hbeta for 13 galaxies, using two instruments on the KPNO 4-m telescope. The metal-line strengths are consistent with an average abundance gradient of DELTA[Fe/H]/DELTA log r= - 0.2 +/- 0.1, or a reduction in mean metallicity of the stellar population of 40 per cent over a factor of 10 in radius. Although line-strength gradients cannot be simply transformed to metallicity gradients, these values are the same as those inferred from colour gradients. These shallow gradients present a significant challenge to current theories of galaxy formation. The dissipative models of Larson & Carlberg produce gradients that are steeper than those measured in giant ellipticals. On the other hand, models of the formation of ellipticals that rely only on stellar interactions, such as dissipationless hierarchical merging, have no mechanism for the generation of metallicity gradients. White has shown that an existing gradient would be diluted by about a factor of 2 over three merger events. Together, these considerations support the hypothesis that giant ellipticals form by stellar mergers, and that the fine-strength gradients originate in their lower mass progenitors which formed predominantly by dissipational collapse. We find no correlations between the size of the gradient and any other global parameter of the galaxies, such as luminosity or flattening. Our sample, however, spans only about a factor of 10 in luminosity. We find that the contours of constant fine strength have the same shape as the isophotes. The correlations between local colours and local line strengths indicate that dust does not play a significant role in the generation of colour gradients in elliptical galaxies. We confirm the findings of previous workers that the slope of the [Fe] versus Mg2 relation within ellipticals is steeper than the equivalent relation for the nuclei of ellipticals. This can be interpreted as evidence for an enrichment of Mg over Fe compared to the solar values used in the models. Age differences or a younger population cannot be invoked to account for the difference. Mg could be enhanced with respect to Fe over the solar value in the giant ellipticals either by enhanced early star formation or by skewing of the initial mass function to produce more massive stars. Alternatively, a deficiency of [Fe] could be produced if the binary fraction in elliptical galaxies were lower than the local value. We find that Hbeta absorption is constant or increases with increasing radius in almost all of the galaxies we observe. We suggest that this is due to the dilution of the Hbeta absorption feature by emission in the centres of these galaxies, an effect which decreases with increasing radius. Our results are consistent with no gradient in the age of the stellar population. We find that the galaxies with the bluest 1550 - V colours have the strongest Hbeta emission. We speculate that the inverse relationship between Mg2 and 15 50 - V might be due to the presence of an otherwise undetected blue ionizing nucleus in galaxies with high values of Mg2, and that both the activity and the high metallicity might result from the star formation associated with the formation of a core. We investigate the relationship between metallicity and escape velocity proposed by Franx & Illingworth. Their suggestion that metallicity is a function of the local escape velocity is confirmed by using a more direct indicator of metallicity and a separate calculation of V(esc) for each galaxy. While this result supports the view that abundance gradients and the colour-magnitude relation for ellipticals arise from a common physical cause, the decoupling of Mg2 and [Fe] gradients indicates that other effects, depending on the details of the star formation history, are at work. NGC 4472 and 7626 have anomalous core kinematics and enhanced Mg2 within their cores. This suggests that the formation of the cores was accompanied by significant star formation activity that generated a high-metallicity population. This high metallicity does not support models in which the anomalous core is the remnant of a captured low-mass galaxy, as even the most metal-rich low-mass galaxies have lower central line strengths than those found in the centres of NGC 4472 and 7626.
