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 suggests 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 \sim - 0.16 \log \sigma _ { 0 } +0.40 , so that the type Ia contribution in stars ranges from a negligible amount in massive ( \sigma _ { 0 } \sim 300 km s ^ { -1 } ) galaxies up to 10 \% in low-mass ( \sim 100 km s ^ { -1 } ) elliptical galaxies .
Our model is parametrized by a star formation timescale ( t _ { SF } ) which controls the duration of the starburst .
A correlation with galaxy radius as a power law ( t _ { SF } \propto r ^ { \beta } ) translates into a radial gradient of the abundance ratios .
The data implies 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 t _ { SF } to the dynamical timescale favours inside-out formation over a smaller range 0.4 < \beta < 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 .