A comprehensive classification of galaxies in the SDSS: How to tell true
  from fake AGN?
  We use the W_Ha versus [NII]/Ha (WHAN) diagram to provide a comprehensive
emission-line classification of SDSS galaxies. This classification is able to
cope with the large population of weak line galaxies that do not appear in
traditional diagrams due to a lack of some of the diagnostic lines. A further
advantage of the WHAN diagram is to allow the differentiation between two very
distinct classes that overlap in the LINER region of traditional diagnostic
diagrams. These are galaxies hosting a weakly active nucleus (wAGN) and
"retired galaxies" (RGs), i.e. galaxies that have stopped forming stars and are
ionized by their hot evolved low-mass stars. A useful criterion to distinguish
true from fake AGN (i.e. the RGs) is the ratio (\xi) of the
extinction-corrected L_Ha with respect to the Ha luminosity expected from
photoionization by stellar populations older than 100 Myr. This ratio follows a
markedly bimodal distribution, with a \xi >> 1 population composed by systems
undergoing star-formation and/or nuclear activity, and a peak at \xi ~ 1
corresponding to the prediction of the RG model. We base our classification
scheme on the equivalent width of Ha, an excellent observational proxy for \xi.
Based on the bimodal distribution of W_Ha, we set the division between wAGN and
RGs at W_Ha = 3 A. Five classes of galaxies are identified within the WHAN
diagram: (a) Pure star forming galaxies: log [NII]/Ha < -0.4 and W_Ha > 3 A.
(b) Strong AGN (i.e., Seyferts): log [NII]/Ha > -0.4 and W_Ha > 6 A. (c) Weak
AGN: log [NII]/Ha > -0.4 and W_Ha between 3 and 6 A. (d) RGs: W_Ha < 3 A. (e)
Passive galaxies (actually, line-less galaxies): W_Ha and W_[NII] < 0.5 A. A
comparative analysis of star formation histories and of other properties in
these different classes of galaxies corroborates our proposed differentiation
between RGs and weak AGN in the LINER-like family. (Abridged)
