Effective temperature of ionizing stars of extragalactic HII regions -- II: nebular parameter relations based on CALIFA data

We calculate the effective temperature ($T_{\rm eff}$) of ionizing star(s), oxygen abundance of the gas phase $(\rm O/H)$, and the ionization parameter $U$ for a sample of H\,{\sc ii} regions located in the disks of 59 spiral galaxies in the 0.005 < z < 0.03 redshift range. We use spectroscopic data taken from the CALIFA data release 3 (DR3) and theoretical (for $T_{\rm eff}$ and $U$) and empirical (for O/H) calibrations based on strong emission-lines. We consider spatial distribution and radial gradients of those parameters in each galactic disk for the objects in our sample. Most of the galaxies in our sample ($\sim70$ \%) shows positive $T_{\rm eff}$ radial gradients even though some them exhibit negative or flat ones. The median value of the $T_{\rm eff}$ radial gradient is 0.762 kK/$R_{25}$. We find that radial gradients of both $\log U$ and $T_{\rm eff}$ depend on the oxygen abundance gradient, in the sense that the gradient of $\log U$ increases as $\log(\rm O/H)$ gradient increases while there is an anti-correlation between the gradient of $T_{\rm eff}$ and the oxygen abundance gradient. Moreover, galaxies with flat oxygen abundance gradients tend to have flat $\log U$ and $T_{\rm eff}$ gradients as well. Although our results are in agreement with the idea of the existence of positive $T_{\rm eff}$ gradients along the disk of the majority of spiral galaxies, this seems not to be an universal property for these objects.