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.