Hardness of ionizing radiation fields in MaNGA star-forming galaxies
  We investigate radiation hardness within a representative sample of 67 nearby
(0.02 $\lesssim $z$ \lesssim$0.06) star-forming (SF) galaxies using the
integral field spectroscopic data from the MaNGA survey. The softness parameter
$\eta$ = $\frac{O^{+}/O^{2+}}{S^{+}/S^{2+}}$ is sensitive to the spectral
energy distribution of the ionizing radiation. We study $\eta$ via the
observable quantity $\eta\prime$ (=$\frac{[OII]/[OIII]}{[SII][SIII]}$) We
analyse the relation between radiation hardness (traced by $\eta$ and
$\eta\prime$) and diagnostics sensitive to gas-phase metallicity, electron
temperature, density, ionization parameter, effective temperature and age of
ionizing populations. It is evident that low metallicity is accompanied by low
log $\eta\prime$, i.e. hard radiation field. No direct relation is found
between radiation hardness and other nebular parameters though such relations
can not be ruled out. We provide empirical relations between log $\rm\eta$ and
strong emission line ratios N$_2$, O$_3$N$_2$ and Ar$_3$O$_3$ which will allow
future studies of radiation hardness in SF galaxies where weak auroral lines
are undetected. We compare the variation of [O III]/[O II] and [S III]/[S II]
for MaNGA data with SF galaxies and H II regions within spiral galaxies from
literature, and find that the similarity and differences between different data
set is mainly due to the metallicity. We find that predictions from
photoionizaion models considering young and evolved stellar populations as
ionizing sources in good agreement with the MaNGA data. This comparison also
suggests that hard radiation fields from hot and old low-mass stars within or
around SF regions might significantly contribute to the observed $\eta$ values.
