The IMACS Cluster Building Survey. V. further evidence for starburst recycling from quantitative galaxy morphologies

Using J- and K_s-band imaging obtained as part of the IMACS Cluster Building Survey (ICBS), we measure Sérsic indices for 2160 field and cluster galaxies at 0.31 < z < 0.54. Using both mass- and magnitude-limited samples, we compare the distributions for spectroscopically determined passive, continuously star-forming, starburst, and post-starburst systems and show that previously established spatial and statistical connections between these types extend to their gross morphologies. Outside of cluster cores, we find close structural ties between starburst and continuously star-forming, as well as post-starburst and passive types, but not between starbursts and post-starbursts. These results independently support two conclusions presented in Paper II of this series: (1) most starbursts are the product of a non-disruptive triggering mechanism that is insensitive to global environment, such as minor mergers; (2) starbursts and post-starbursts generally represent transient phases in the lives of "normal" star-forming and quiescent galaxies, respectively, originating from and returning to these systems in closed "recycling" loops. In this picture, spectroscopically identified post-starbursts constitute a minority of all recently terminated starbursts, largely ruling out the typical starburst as a quenching event in all but the densest environments.