The Star Formation History of a Post-Starburst Galaxy Determined From
  Its Cluster Population
  The recent star formation histories (SFHs) of post-starburst galaxies have
been determined almost exclusively from detailed modeling of their composite
star light. This has provided important but limited information on the number,
strength, and duration of bursts of star formation. In this work, we present a
direct and independent measure of the recent SFH of S12 (plate-mjd-fiber for
SDSS 623-52051-207; designated EAS12 in Smercina et al. 2018) from its star
cluster population. We detect clusters from high resolution, $UBR$ optical
observations from HST, and compare their luminosities and colors with stellar
population models to estimate the ages and masses of the clusters. No clusters
younger than $\sim$70 Myr are found, indicating star formation shut off at this
time. Clusters formed $\sim$120 Myr ago reach masses up to $\sim
\mbox{few}\times10^7~M_{\odot}$, several times higher than similar age
counterparts formed in actively merging galaxies like the Antennae and NGC
3256. We develop a new calibration based on known properties for 8 nearby
galaxies to estimate the star formation rate (SFR) of a galaxy from the mass of
the most massive cluster, $M_{\rm max}$. The cluster population indicates that
S12 experienced an extremely intense but short-lived burst $\sim$120 Myr ago,
with an estimated peak of $500^{+500}_{-250}~M_{\odot}~\mbox{yr}^{-1}$ and
duration of $50\pm25$ Myr, one of the highest SFRs estimated for any galaxy in
the nearby universe. Prior to the recent, intense burst, S12 was forming stars
at a moderate rate of $\sim 3{-}5~M_{\odot}~\mbox{yr}^{-1}$, typical of spiral
galaxies. However, the system also experienced an earlier burst approximately
$1{-}3$ Gyr ago. While fairly uncertain, we estimate that the SFR during this
earlier burst was $\sim20{-}30~M_{\odot}~\mbox{yr}^{-1}$, similar to the
current SFR in the Antennae and NGC 3256.
