We investigate the bursty star formation histories (SFHs) of dwarf galaxies using the distribution of log($L_{Halpha}/L_{UV}$) of 185 local galaxies. We expand on the work of Weisz et al. 2012 to consider a wider range of SFHs and stellar metallicities, and show that there are large degeneracies in a periodic, top-hat burst model. We argue that all galaxies of a given mass have similar SFHs and we can therefore include the $L_{Halpha}$ distributions (subtracting the median trend with stellar mass, referred to as $Delta text{log}(L_{Halpha})$) in our analyses. $Delta text{log}(L_{Halpha})$ traces the amplitude of the bursts, and log($L_{Halpha}/L_{UV}$) is a function of timescale, amplitude, and shape of the bursts. We examine the 2-dimensional distribution of these two indicators constrain the SFHs. We use exponentially rising/falling bursts to determine timescales ($e$-folding time, $tau$). We find that galaxies below $10^{7.5}$ M$_{odot}$ undergo large (amplitudes of $sim 100$) and rapid ($tau < 30$ Myr) bursts, while galaxies above $10^{8.5}$ M$_{odot}$ experience smaller (maximum amplitudes $sim 10$), slower ($tau gtrsim 300$ Myr) bursts. We compare to the FIRE-2 hydrodynamical simulations and find that the burst amplitudes agree with observations, but they are too rapid in more massive galaxies ($M_* > 10^8$ M$_{odot}$). Finally, we confirm that stochastic sampling of the stellar mass function can not reproduce the observed distributions unless the standard assumptions of cluster and stellar mass functions are changed. With the next generation of telescopes, measurements of $L_{UV}$ and $L_{Halpha}$ will become available for dwarf galaxies at high-redshift, enabling similar analyses of galaxies in the early universe.
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