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We measured gas-phase metallicity, ionisation parameter and dust extinctionfor 1795 representative local star-forming galaxies using integral fieldspectroscopy from the SDSS-IV MaNGA survey. We self-consistently derive thesequantities by comparing observed line fluxes with photoionisation models usinga Bayesian framework. We also present the first comprehensive study of the[SIII]$\lambda\lambda$9069,9532 nebular lines, which have long been predictedto be ideal tracers of the ionisation parameter. Unfortunately, we find thatcurrent photoionisation models substantially over-predict [SIII] linesintensity, while broadly reproducing other observed optical line ratios. Wediscuss how to nonetheless make use of the information provided by [SIII] linesby setting a prior on the ionisation parameter. Following this approach, wederive spatially-resolved maps and radial profiles of metallicity andionisation parameter. The metallicity radial profiles are comparable withprevious works, with metallicity declining toward the outer parts and aflattening in the central regions, in agreement with infall models of galaxyformation, that predict that spiral discs build up through accretion ofmaterial, which leads to an inside-out growth. On the other hand, ionisationparameter radial profiles are flat for low-mass galaxies, while their slopebecomes positive as galaxy mass increases. However, the ionisation parametermaps we obtain are clumpy, especially for low-mass galaxies. Ionisationparameter is tightly correlated with the H$\alpha$ equivalent width[EW(H$\alpha$)], following a nearly universal relation, which we attribute tothe change of the spectral shape of ionising sources due to ageing of HIIregions. We derive a positive correlation between ionisation parameter andmetallicity at fixed EW(H$\alpha$), in disagreement with previous theoreticalworks expecting an anti-correlation.

SDSS IV MaNGA -- Metallicity and ionisation parameter in local star-forming galaxies from Bayesian fitting to photoionisation models