We present a new morphological indicator designed for automated recognition of galaxies with faint asymmetric tidal features suggestive of an ongoing or past merger. We use this new indicator, together with preexisting diagnostics of galaxy structure to study the role of galaxy mergers in inducing (post-)starburst spectral signatures in local galaxies, and investigate whether (post-)starburst galaxies play a role in the build up of the `red sequence'. Our morphological and structural analysis of an evolutionary sample of 335 (post-)starburst galaxies in the SDSS DR7 with starburst ages 0<tSB<0.6 Gyr, shows that 45% of galaxies with young starbursts (tSB<0.1 Gyr) show signatures of an ongoing or past merger. This fraction declines with starburst age, and we find a good agreement between automated and visual classifications. The majority of the oldest (post-)starburst galaxies in our sample (tSB~0.6Gyr) have structural properties characteristic of early-type disks and are not as highly concentrated as the fully quenched galaxies commonly found on the `red sequence' in the present day Universe. This suggests that, if (post-)starburst galaxies are a transition phase between active star-formation and quiescence, they do not attain the structure of presently quenched galaxies within the first 0.6 Gyr after the starburst.
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