Following our study on the incidence, morphology and kinematics of the ionised gas in early-type galaxies we now address the question of what is powering the observed nebular emission. To constrain the likely sources of gas excitation, we resort to a variety of ancillary data, draw from complementary information on the gas kinematics, stellar populations and galactic potential from the SAURON data, and use the SAURON-specific diagnostic diagram juxtaposing the [OIII]/Hb and [NI]/Hb line ratios. We find a tight correlation between the stellar surface brightness and the flux of the Hb recombination line across our sample, which points to a diffuse and old stellar source as the main contributor of ionising photons in early-type galaxies, with post-asymptotic giant branch (pAGB) stars being still the best candidate based on ionising-balance arguments. Other ionising sources such as a central AGN, OB-stars, shocks or the interaction between the hot and warm phases of the interestellar medium are found to play only a limited or localised role in powering the diffuse nebular emission observed in our sample galaxies. These results lead us to investigate the relative importance of stellar and AGN photoionisation in explaining the ionised-gas emission observed in early-type galaxies by the Sloan Digital Sky Survey (SDSS). By simulating how our sample galaxies would appear if placed at further distance and targeted by the SDSS, we conclude that only in very few, if any, of the SDSS early-type galaxies that display modest values for the equivalent width of the [OIII] line (less than ~2.4AA) and LINER-like [OIII]/Hb values, the nebular emission is truly powered by an AGN.
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