SDSS IV MaNGA -- Metallicity and ionisation parameter in local
  star-forming galaxies from Bayesian fitting to photoionisation models
  We measured gas-phase metallicity, ionisation parameter and dust extinction
for 1795 representative local star-forming galaxies using integral field
spectroscopy from the SDSS-IV MaNGA survey. We self-consistently derive these
quantities by comparing observed line fluxes with photoionisation models using
a Bayesian framework. We also present the first comprehensive study of the
[SIII]$\lambda\lambda$9069,9532 nebular lines, which have long been predicted
to be ideal tracers of the ionisation parameter. Unfortunately, we find that
current photoionisation models substantially over-predict [SIII] lines
intensity, while broadly reproducing other observed optical line ratios. We
discuss how to nonetheless make use of the information provided by [SIII] lines
by setting a prior on the ionisation parameter. Following this approach, we
derive spatially-resolved maps and radial profiles of metallicity and
ionisation parameter. The metallicity radial profiles are comparable with
previous works, with metallicity declining toward the outer parts and a
flattening in the central regions, in agreement with infall models of galaxy
formation, that predict that spiral discs build up through accretion of
material, which leads to an inside-out growth. On the other hand, ionisation
parameter radial profiles are flat for low-mass galaxies, while their slope
becomes positive as galaxy mass increases. However, the ionisation parameter
maps we obtain are clumpy, especially for low-mass galaxies. Ionisation
parameter is tightly correlated with the H$\alpha$ equivalent width
[EW(H$\alpha$)], following a nearly universal relation, which we attribute to
the change of the spectral shape of ionising sources due to ageing of HII
regions. We derive a positive correlation between ionisation parameter and
metallicity at fixed EW(H$\alpha$), in disagreement with previous theoretical
works expecting an anti-correlation.
