Deciphering stellar metallicities in the early Universe: Case study of a
  young galaxy at z = 4.77 in the MUSE eXtremely Deep Field
  Directly characterising the first generations of stars in distant galaxies is
a key quest of observational cosmology. We present a case study of ID53 at
z=4.77, the UV-brightest (but L*) star-forming galaxy at z>3 in the MUSE
eXtremely Deep Field with a mass of $10^9$ M$_{\odot}$. In addition to very
strong Lyman-$\alpha$ (Ly$\alpha$) emission, we clearly detect the (stellar)
continuum and an NV P-Cygni feature, interstellar absorption, fine-structure
emission and nebular CIV emission lines in the 140 hr spectrum. Continuum
emission from two spatially resolved components in Hubble Space Telescope data
are blended in the MUSE data, but we show that the nebular CIV emission
originates from a subcomponent of the galaxy. The UV spectrum can be fit with
recent BPASS stellar population models combined with single-burst or continuous
star formation histories (SFHs), a standard initial mass function, and an
attenuation law. Models with a young age and low metallicity
(log10(age/yr)=6.5-7.6 and [Z/H]=-2.15 to -1.15) are preferred. The intrinsic
H$\alpha$ luminosity of the best-fit models is an order of magnitude higher
than the H$\alpha$ luminosity inferred from Spitzer/IRAC data, which either
suggests a high escape fraction of ionising photons, a high relative
attenuation of nebular to stellar dust, or a complex SFH. The metallicity
appears lower than the metallicity in more massive galaxies at z=3-5,
consistent with the scenario according to which younger galaxies have lower
metallicities. This chemical immaturity likely facilitates Ly$\alpha$ escape,
explaining why the Ly$\alpha$ equivalent width is anti-correlated with stellar
metallicity. Finally, we stress that uncertainties in SFHs impose a challenge
for future inferences of the stellar metallicity of young galaxies. This
highlights the need for joint (spatially resolved) analyses of stellar spectra
and photo-ionisation models.
