M^3D: Mosaicking M33 with MUSE datacubes I. Unveiling the diversity of HII regions in M33 with MUSE
We present new VLT/MUSE observations of a 3 $\times$ 8 arcmin$^2$ mosaic along the southern major axis of the Local Group galaxy M33. These data provide an unprecedented view of the galaxy's interstellar medium (ISM) and allow us to resolve ionised nebulae at a spatial scale of $\approx$5 pc. We identified and catalogued 131 HII regions, down to Hαluminosities of $\approx 5\times$10$^{35}$ erg s$^{-1}$, one order of magnitude fainter than previous surveys on nearby galaxies beyond the Local Group, and we compared these regions with the spatial distribution of ionising stars and embedded star clusters. For each region, we extracted the corresponding integrated optical spectra and measured the intensity of key optical emission lines (Hβ, [OIII], [NII], Hα, [SII], [SIII]), other weaker optical lines when detectable, and Paschen lines to characterise the physical properties of the ioinised gas, such as density, dust attenuation, and metallicity. Our spatially resolved line ratio and flux maps reveal a remarkable diversity in ionisation properties, from dust-obscured regions hosting young stellar objects to highly ionised bubbles exhibiting high [OIII]/Hβratios. Our data reveal a diversity of ionisation fronts, ranging from well-defined to partial to absent. The radial profiles we obtained indicate the presence of both optically thin (density-bounded) HII regions permitting the escape of ionising photons and fully ionised, optically thick (ionisation-bounded) HII regions. The richness of this MUSE mosaic offers an unprecedented view of the ionised ISM at $\approx$5 pc resolution, providing direct insight into how stellar feedback shapes its environment.