We present evidence for stochastic star formation histories in low-mass (M* < 10^10 Msun) galaxies from observations within the Galaxy And Mass Assembly (GAMA) survey. For ~73,000 galaxies between 0.05<z<0.32, we calculate star formation rates (SFR) and specific star formation rates (SSFR = SFR/M*) from spectroscopic Halpha measurements and apply dust corrections derived from Balmer decrements. We find a dependence of SSFR on stellar mass, such that SSFRs decrease with increasing stellar mass for star-forming galaxies, and for the full sample, SSFRs decrease as a stronger function of stellar mass. We use simple parametrizations of exponentially declining star formation histories to investigate the dependence on stellar mass of the star formation timescale and the formation redshift. We find that parametrizations previously fit to samples of z~1 galaxies cannot recover the distributions of SSFRs and stellar masses observed in the GAMA sample between 0.05<z<0.32. In particular, a large number of low-mass (M* < 10^10 Msun) galaxies are observed to have much higher SSFRs than can be explained by these simple models over the redshift range of 0.05<z<0.32, even when invoking mass-dependent staged evolution. For such a large number of galaxies to maintain low stellar masses, yet harbour such high SSFRs, requires the late onset of a weak underlying exponentially declining SFH with stochastic bursts of star formation superimposed.
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