The MOSDEF Survey: Stellar Continuum Spectra and Star Formation
  Histories of Active, Transitional, and Quiescent Galaxies at
  1.4$<$\lowercase{z}$<$2.6
  Using the MOSDEF rest-frame optical spectroscopic survey, we investigate the
star-formation histories (SFHs) of different galaxy types, ranging from
actively star forming to quiescent at $1.4\leq~z\leq2.6$. SFHs are constrained
utilizing stellar continuum spectroscopy, specifically through a combination of
Balmer absorption lines, the 4000$\AA$ break, and the equivalent width of the
H$\alpha$ emission line. To attain a sufficiently high signal-to-noise ratio
(S/N) to conduct these measurements we stack spectra of galaxies with similar
spectral types, as determined from their rest-frame $U-V$ and $V-J$ colors. We
bin the MOSDEF sample into five spectral types, subdividing the quiescent and
star-forming bins to better explore galaxies transitioning between the two. We
constrain the average SFHs for each type, finding that quiescent and
transitional galaxies in the MOSDEF sample are dominated by an SFH with an
average star-formation timescale of $\tau\sim0.1-0.2$~Gyr. These findings
contrast with measurements from the low-redshift Universe where, on average,
galaxies form their stars over a more extended time period ($\tau>1$~Gyr).
Furthermore, our spectral index measurements correlate with mass surface
density for all spectral types. Finally, we compare the average properties of
the galaxies in our transitional bins to investigate possible paths to
quiescence, and speculate on the viability of a dusty post-starburst phase.
