Studying the ISM at ~10 pc scale in NGC 7793 with MUSE -- I. Data
  description and properties of the ionised gas
  Using MUSE AO data, we probe the ISM in the local spiral galaxy NGC 7793 at a
spatial resolution of $\sim$ 10 pc. We identify HII regions and compile a
catalogue of supernova remnants (SNRs), planetary nebulae (PNe) and Wolf Rayet
stars (WR). We compute electron densities and temperatures from the
[SII]6716/6731 and [SIII]6312/9069 line ratios. We study the properties of the
ionised gas through BPT diagrams combined with gas velocity dispersion. We
spectroscopically confirm 2 previously detected WR stars and a SNR and report
the discovery of 7 WR, 1 SNR, and 2 PNe. The diffuse ionized gas (DIG) fraction
is between $\sim$ 27 and 42% depending on the method used to define the HII
region boundaries. In agreement with previous studies, we find that the DIG
exhibits enhanced [SII]/H$\alpha$ and [NII]/H$\alpha$ ratios and a median
temperature that is $\sim$ 3000 K higher than in HII regions. We also observe
an apparent inverse correlation between temperature and H$\alpha$ surface
brightness. Overall, the observed [SII]6716/6731 ratio is consistent within
1$\sigma$ with $n_e$ < 30 cm$^{-3}$, with an almost identical distribution for
the DIG and HII regions. The velocity dispersion of the ionised gas indicates
that the DIG has a higher degree of turbulence than the HII regions. Comparison
with photoionisation and shock models reveals that the diffuse component can
only partially be explained via shocks and that it is most likely consistent
with photons leaking from density bounded HII regions or with radiation from
evolved field stars. [abridged]
