The MOSDEF Survey: Stellar Continuum Spectra and Star Formation Histories of Active, Transitional, and Quiescent Galaxies at 1.4 < z < 2.6

&#169; 2018. The American Astronomical Society. All rights reserved. Using the MOSFIRE Deep Evolution Field (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 ≤ z ≤ 2.6. SFHs are constrained utilizing stellar continuum spectroscopy, specifically through a combination of Balmer absorption lines, the 4000 &#197; break, and the equivalent width of the Hα 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 τ ∼ 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 (τ &gt; 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.