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]