The star formation histories of rapidly quenched galaxies at z~1

I will present measurements of the star formation histories of ~40 z~1 galaxies with strong Balmer absorption lines indicating recent and rapid quenching of star formation, alongside well defined control samples of star-forming and quiescent galaxies. High quality VLT spectra and multiwavelength photometry, combined with a comparison between both state-of-the-art Bayesian parameterised and unparameterised SFH model fitting, provide tight constraints on physical properties such as the age and strength of the starburst, and fraction of old stars. A significant fraction are consistent with being close to single-epoch burst events with peak star formation rates consistent with sub-mm galaxies. This data provides a perfect example of the science that will be possible in the upcoming MOONS GTO reference survey at 0.8<z