A Closer look at Bursty Star Formation with $L_{H\alpha}$ and $L_{UV}$
  Distributions
  We investigate the bursty star formation histories (SFHs) of dwarf galaxies
using the distribution of log($L_{H\alpha}/L_{UV}$) 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 $L_{H\alpha}$ distributions
(subtracting the median trend with stellar mass, referred to as $\Delta
\text{log}(L_{H\alpha})$) in our analyses. $\Delta \text{log}(L_{H\alpha})$
traces the amplitude of the bursts, and log($L_{H\alpha}/L_{UV}$) 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 $L_{H\alpha}$ will become available for dwarf
galaxies at high-redshift, enabling similar analyses of galaxies in the early
universe.
