A methodology to select galaxies just after the quenching of star formation

We propose a new methodology aimed at finding star-forming galaxies in the phase which immediately follows the star-formation (SF) quenching, based on the use of high- to low-ionization emission line ratios. These ratios rapidly disappear after the SF halt, due to the softening of the UV ionizing radiation. We focus on [O III] $lambda$5007/H$alpha$ and [Ne III] $lambda$3869/[O II] $lambda$3727, studying them with simulations obtained with the CLOUDY photoionization code. If a sharp quenching is assumed, we find that the two ratios are very sensitive tracers as they drop by a factor $sim$ 10 within $sim$ 10 Myr from the interruption of the SF; instead, if a smoother and slower SF decline is assumed (i.e. an exponentially declining star-formation history with $e$-folding time $ au=$ 200 Myr), they decrease by a factor $sim$ 2 within $sim$ 80 Myr. We mitigate the ionization -- metallicity degeneracy affecting our methodology using pairs of emission line ratios separately related to metallicity and ionization, adopting the [N II] $lambda$6584/[O II] $lambda$3727 ratio as metallicity diagnostic. Using a Sloan Digital Sky Survey galaxy sample, we identify 10 examples among the most extreme quenching candidates within the [O III] $lambda$5007/H$alpha$ vs. [N II] $lambda$6584/[O II] $lambda$3727 plane, characterized by low [O III] $lambda$5007/H$alpha$, faint [Ne III] $lambda$3869, and by blue dust-corrected spectra and $(u-r)$ colours, as expected if the SF quenching has occurred in the very recent past. Our results also suggest that the observed fractions of quenching candidates can be used to constrain the quenching mechanism at work and its time-scales.