VLT/X-shooter observations of blue compact galaxies Haro 11 and ESO
  338-IG 004
  (abridged) Strongly star-forming galaxies of subsolar metallicities are
typical of the high-redshift universe. Here we therefore provide accurate data
for two low-z analogs, the well-known low-metallicity emission-line galaxies
Haro 11 and ESO 338-IG 004. On the basis of Very Large Telescope/X-shooter
spectroscopic observations in the wavelength range 3000-24000\AA, we use
standard direct methods to derive physical conditions and element abundances.
Furthermore, we use X-shooter data together with Spitzer observations in the
mid-infrared range to attempt to find hidden star formation. We derive
interstellar oxygen abundances of 12 + log O/H = 8.33+/-0.01, 8.10+/-0.04, and
7.89+/-0.01 in the two HII regions B and C of Haro 11 and in ESO 338-IG 004,
respectively. The observed fluxes of the hydrogen lines correspond to the
theoretical recombination values after correction for extinction with a single
value of the extinction coefficient C(Hbeta) across the entire wavelength range
from the near-ultraviolet to the NIR and mid-infrared for each of the studied
HII regions. Therefore there are no emission-line regions contributing to the
line emission in the NIR range, which are hidden in the optical range. The
agreement between the extinction-corrected and CLOUDY-predicted fluxes implies
that a HII region model including only stellar photoionisation is able to
account for the observed fluxes, in both the optical and NIR ranges. All
observed spectral energy distributions (SEDs) can be reproduced quite well
across the whole wavelength range by model SEDs except for Haro 11B, where
there is a continuum flux excess at wavelengths >1.6mum. It is possible that
one or more red supergiant stars are responsible for the NIR flux excess in
Haro 11B. We find evidence of a luminous blue variable (LBV) star in Haro 11C.
