Context. Sulphur-bearing species are detected in various environments within Galactic star-forming regions and are particularly abundant in the gas phase of outflow and shocked regions in addition to photo-dissociation regions. Thanks to the powerful capabilities of millimetre interferometers, studying sulphur-bearing species and their region of emission in various extreme extra-galactic environments (e.g. starburst and active galactic nuclei) and at a high-angular resolution and sensitivity is now possible. Aims. In this work, we aim to investigate the nature of the emission from the most common sulphur-bearing species observable at millimetre wavelengths towards the nuclear starburst of the nearby galaxy NGC 253. We intend to understand which type of regions are probed by sulphur-bearing species and which process(es) dominate(s) the release of sulphur into the gas phase. Methods. We used the high-angular resolution (1.6″ or ∼27 pc) observations from the ALCHEMI ALMA Large Program to image several sulphur-bearing species towards the central molecular zone (CMZ) of NGC 253. We performed local thermodynamic equilibrium (LTE) and non-LTE large velocity gradient (LVG) analyses to derive the physical conditions of the gas where the sulphur-bearing species are emitted, and their abundance ratios across the CMZ. Finally, we compared our results with previous ALCHEMI studies and a few selected Galactic environments. Results. To reproduce the observations, we modelled two gas components for most of the sulphur-bearing species investigated in this work. We found that not all sulphur-bearing species trace the same type of gas: strong evidence indicates that H2S and part of the emission of OCS, H2CS, and SO are tracing shocks, whilst part of SO and CS emission rather traces the dense molecular gas. For some species, such as CCS and SO2, we could not firmly conclude on their origin of emission. Conclusions. The present analysis indicates that the emission from most sulphur-bearing species throughout the CMZ is likely dominated by shocks associated with ongoing star formation. In the inner part of the CMZ where the presence of super star clusters was previously indicated, we could not distinguish between shocks or thermal evaporation as the main process releasing the S-bearing species.
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