Stars and gas in the most metal-poor galaxies I: COS and MUSE observations of SBS 0335-052E

Among the nearest most metal-poor starburst-dwarf galaxies known, SBS 0335-052E is the most luminous in integrated nebular He II {\lambda}4686 emission. This makes it a unique target to test spectral synthesis models and spectral interpretation tools of the kind that will be used to interpret future rest-frame UV observations of primeval galaxies. Previous attempts to reproduce its He II {\lambda}4686 emission luminosity found that X-ray sources, shocks, and single Wolf-Rayet stars are not main contributors to the He II-ionizing budget; and that only metal-free single rotating stars or binary stars with a top-heavy IMF and an unphysically-low metallicity can reproduce it. We present new UV (COS) and optical (MUSE) spectra which integrate the light of four super star clusters in SBS 0335-052E. Nebular He II, [C III], C III], C IV, and O III] UV emission lines with equivalent widths between 1.7 and 5 A, and a C IV {\lambda}{\lambda}1548, 1551 P-Cygni like profile are detected. Recent extremely-metal poor shock + precursor models and binary models fail to reproduce the observed optical emission-line ratios. We use different sets of UV and optical observables to test models of constant star formation with single non-rotating stars which account for very massive stars, as blueshifted O V {\lambda}1371 absorption is present. Simultaneously fitting the fluxes of all high-ionization UV lines requires an unphysically-low metallicity. Fitting the P-Cygni like + nebular components of C IV {\lambda}{\lambda}1548, 1551 does not constrain the stellar metallicity and time since the beginning of star formation. We obtain 12+log(O/H)=7.45\pm0.04 and log(C/O)=-0.45(+0.03)(-0.04) for the galaxy. Model-testing would benefit from higher spatial resolution UV and optical spectroscopy of the galaxy.