Type Ia supernovae and the formation history of early-type galaxies

Using the standard prescription for the rates of supernovae Type II and Type Ia, we compare the predictions of a simple model of star formation in galaxies with the observed radial gradients of abundance ratios in a sample of early-type galaxies to infer the relative contribution of each type of supernova. The data suggest a correlation between the fractional contribution of Type Ia to the chemical enrichment of the stellar populations (1-xi) and central velocity dispersion of order 1 - xi similar to -0.16 log sigma(0) + 0.40, so that the Type Ia contribution in stars ranges from a negligible amount in massive (sigma(0) similar to 300 km s(-1)) galaxies up to 10 per cent in low-mass (similar to100 km s(-1)) elliptical galaxies. Our model is parametrized by a star-formation time-scale (t(SF)) that controls the duration of the starburst. A correlation with galaxy radius as a power law (t(SF) proportional to r(beta)) translates into a radial gradient of the abundance ratios. The data imply a wide range of formation scenarios for a simple model that fixes the luminosity profile, ranging from inside out (beta = 2), to outside in formation (beta = -1), as is consistent with numerical simulations of elliptical galaxy formation. An alternative scenario that links tSF to the dynamical time-scale favours inside-out formation over a smaller range 0 4 < β < 0.6. In both cases, massive galaxies are predicted to have undergone a more extended period of star formation in the outer regions with respect to their low-mass counterparts.