The MOSDEF Survey: Detection of [OIII]$\lambda$4363 and the direct-method oxygen abundance of a star-forming galaxy at z=3.08

We present measurements of the electron-temperature based oxygen abundance for a highly star-forming galaxy at z=3.08, COSMOS-1908. This is the highest redshift at which [OIII]$\lambda$4363 has been detected, and the first time that this line has been measured at z>2. We estimate an oxygen abundance of 12+log(O/H)$=8.00^{+0.13}_{-0.14}$. This galaxy is a low-mass ($10^{9.3}$ M$_{\odot}$), highly star-forming ($\sim50$ M$_{\odot}$ yr$^{-1}$) system that hosts a young stellar population ($\sim160$ Myr). We investigate the physical conditions of the ionized gas in COSMOS-1908 and find that this galaxy has a high ionization parameter, little nebular reddening ($E(B-V)_{\rm gas}<0.14$), and a high electron density ($n_e\sim500$ cm$^{-3}$). We compare the ratios of strong oxygen, neon, and hydrogen lines to the direct-method oxygen abundance for COSMOS-1908 and additional star-forming galaxies at z=0-1.8 with [OIII]$\lambda$4363 measurements, and show that galaxies at z$\sim$1-3 follow the same strong-line correlations as galaxies in the local universe. This agreement suggests that the relationship between ionization parameter and O/H is similar for z$\sim$0 and high-redshift galaxies. These results imply that metallicity calibrations based on lines of oxygen, neon, and hydrogen do not strongly evolve with redshift and can reliably estimate abundances out to z$\sim$3, paving the way for robust measurements of the evolution of the mass-metallicity relation to high redshift.