(Abridged) We present a stellar population analysis of the absorption line strength maps for 48 early-type galaxies from the SAURON sample. Using the line strength index maps of Hbeta, Fe5015, and Mgb, measured in the Lick/IDS system and spatially binned to a constant signal-to-noise, together with predictions from up-to-date stellar population models, we estimate the simple stellar population-equivalent (SSP-equivalent) age, metallicity and abundance ratio [alpha/Fe] over a two-dimensional field extending up to approximately one effective radius. We find a large range of SSP-equivalent ages in our sample, of which ~40% of the galaxies show signs of a contribution from a young stellar population. The most extreme cases of post-starburst galaxies, with SSP-equivalent ages of <=3 Gyr observed over the full field-of-view, and sometimes even showing signs of residual star-formation, are restricted to low mass systems(sigma_e <= 100 k/ms or ~2x10^10 M_sol). Spatially restricted cases of young stellar populations in circumnuclear regions can almost exclusively be linked to the presence of star-formation in a thin, dusty disk/ring, also seen in the near-UV or mid-IR. The flattened components with disk-like kinematics previously identified in all fast rotators (Krajnovic et al.) are shown to be connected to regions of distinct stellar populations. These range from the young, still star-forming circumnuclear disks and rings with increased metallicity preferentially found in intermediate-mass fast rotators, to apparently old structures with extended disk-like kinematics, which are observed to have an increased metallicity and mildly depressed [alpha/Fe] ratio compared to the main body of the galaxy. The slow rotators generally show no stellar population signatures over and above the well known metallicity gradients and are largely consistent with old (>=10 Gyr) stellar populations.
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