The MOSDEF Survey: Significant Evolution in the Rest-Frame Optical
  Emission Line Equivalent Widths of Star-Forming Galaxies at z=1.4-3.8
  We use extensive spectroscopy from the MOSFIRE Deep Evolution Field (MOSDEF)
survey to investigate the relationships between rest-frame optical emission
line equivalent widths ($W$) and a number of galaxy and ISM characteristics for
a sample of $1134$ star-forming galaxies at redshifts $1.4\lesssim z\lesssim
3.8$. We examine how the equivalent widths of [OII]$\lambda\lambda 3727, 3730$,
H$\beta$, [OIII]$\lambda\lambda 4960, 5008$, [OIII]$+$H$\beta$, H$\alpha$, and
H$\alpha$+[NII]$\lambda\lambda 6550, 6585$, depend on stellar mass, UV slope,
age, star-formation rate (SFR) and specific SFR (sSFR), ionization parameter
and excitation conditions (O32 and [OIII]/H$\beta$), gas-phase metallicity, and
ionizing photon production efficiency ($\xi_{\rm ion}$). The trend of
increasing $W$ with decreasing stellar mass is strongest for [OIII] (and
[OIII]+H$\beta$). More generally, the equivalent widths of all the lines
increase with redshift at a fixed stellar mass or fixed gas-phase metallicity,
suggesting that high equivalent width galaxies are common at high redshift.
This redshift evolution in equivalent widths can be explained by the increase
in SFR and decrease in metallicity with redshift at a fixed stellar mass.
Consequently, the dependence of $W$ on sSFR is largely invariant with redshift,
particularly when examined for galaxies of a given metallicity. Our results
show that high equivalent width galaxies, specifically those with high $W({\rm
[OIII]})$, have low stellar masses, blue UV slopes, young ages, high sSFRs, ISM
line ratios indicative of high ionization parameters, high $\xi_{\rm ion}$, and
low metallicities. As these characteristics are often attributed to galaxies
with high ionizing escape fractions, galaxies with high $W$ are likely
candidates for the population that dominates cosmic reionization.
