Emission line galaxies provide a crucial tool for the study of galaxy formation and evolution, providing a means to trace a galaxys star formation history or metal enrichment, and to identify galaxies at a range of stellar masses. In this paper we present a study of emission line galaxies in the SHARDS Frontier Fields medium-band survey. Through detailed flux calibrations we combine the first results of the SHARDS-FF survey with existing Hubble Frontier Field data to select 1,098 candidate emission line galaxies from the Hubble Frontier Filed clusters Abell 370 and MACS J1149.5+2223. Furthermore, we implement this deep medium-band imaging to update photometric redshift estimates and stellar population parameters and discover 38 predominantly low-mass H{alpha} emitters at redshifts 0.24 < z < 0.46. Overall, 27 of these sources have corresponding UV data from the Hubble Space Telescope which allows us to distinguish these sources and investigate the burstiness of their star formation histories. We find that more than 50% of our sample show an enhancement in H{alpha} over UV, suggesting recent bursts in star formation on time scales of a few, to tens of megayears. We investigate these sources and find that they are typically low-mass disky galaxies with normal sizes. Their structures and star formation suggest that they are not undergoing mergers but are bursting due to alternative causes, such as gas accretion.
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