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 \leq 2.6 .
SFHs are constrained utilizing stellar continuum spectroscopy , specifically through a combination of Balmer absorption lines , the 4000 Å 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 \sim 0.1 - 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 .