VLT/MUSE view of the highly ionized outflow cones in the nearby
  starburst ESO338-IG04
  The Ly$\alpha$ line is an important diagnostic for star formation at high
redshift, but interpreting its flux and line profile is difficult because of
the resonance nature of Ly$\alpha$. Trends between the escape of Ly$\alpha$
photons and dust and properties of the interstellar medium (ISM) have been
found, but detailed comparisons between Ly$\alpha$ emission and the properties
of the gas in local high-redshift analogs are vital for understanding the
relation between Ly$\alpha$ emission and galaxy properties. For the first time,
we can directly infer the properties of the ionized gas at the same location
and similar spatial scales of the extended Ly$\alpha$ halo around ESO 338-IG04.
We obtained VLT/MUSE integral field spectra. We used ionization parameter
mapping of the [SII]/[OIII] line ratio and the kinematics of H$\alpha$ to study
the ionization state and kinematics of the ISM of ESO338-IG04. The velocity map
reveals two outflows. The entire central area of the galaxy is highly ionized
by photons leaking from the HII regions around the youngest star clusters.
Three highly ionized cones have been identified, of which one is associated
with an outflow. We propose a scenario where the outflows are created by
mechanical feedback of the older clusters, while the highly ionized gas is
caused by the hard ionizing photons emitted by the youngest clusters. A
comparison with the Ly$\alpha$ map shows that the (approximately bipolar)
asymmetries observed in the Ly$\alpha$ emission are consistent with the base of
the outflows detected in H$\alpha$. No clear correlation with the ionization
cones is found. The mechanical and ionization feedback of star clusters
significantly changes the state of the ISM by creating ionized cones and
outflows. The comparison with Ly$\alpha$ suggests that especially the outflows
could facilitate the escape of Ly$\alpha$ photons [Abridged].
