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We provide one of the most comprehensive metallicity studies at z $\sim$ 4 byanalyzing the UV/optical HST photometry, and rest-frame VLT-FORS2 ultravioletand VLT-XSHOOTER optical spectra of J0332-3557, a gravitationally lensed galaxymagnified by a factor of 20. With a 5$\sigma$ detection of the auroral OIII]1666 line, we are able to derive a direct gas metallicity estimate for ourtarget. We find Z_gas = 12 + log(O/H) = 8.26 $\pm$ 0.06, which is compatiblewith an increasing of both the gas fraction and the outflow metal loadingfactor from z $\sim$ 0 to z $\sim$ 4. J0332-3557 is the most metal-richindividual galaxy at z $\sim$ 4 for which the C/O ratio has been measured. Wederive a low log(C/O) = - 1.02 $\pm$ 0.2, which suggests that J0332-3557 is inthe early stages of ISM carbon enrichment driven mostly by massive stars. Thelow C/O abundance also indicates that J0332-3557 is characterized by a low starformation efficiency, higher yields of oxygen, and longer burst duration. Wefind that EW(C III])1906,9 is as low as $\sim$ 3 \AA. The main drivers of thelow EW(C III])1906,9 are the higher gas metallicity and the low C/O abundance.J0332-3557 is characterized by one diffuse and two more compact regions $\sim$1 kpc in size. We find that the carbon emission mostly originates in thecompact knots. Our study on J0332-3557 serves as an anchor for studiesinvestigating the evolution of metallicity and C/O abundance across differentredshifts.

A comprehensive metallicity analysis of J0332-3557: establishing a z ~ 4 anchor for direct gas metallicity and C/O abundance investigations