Electron temperature relations in low metallicity, diffuse, and extraplanar gas of starburst galaxies

In this work, we test the validity of $T_e$ - $T_e$ relations in resolved (10-200~pc) measurements of four nearby, low-metallicity (7.25 $\leq$ 12+log(O/H) $\leq$ 8.33), low-mass (10$^{6.78}$ $\leq$ M$_*$/M$_\odot$ $\leq$ 10$^{8.7}$), starburst (10$^{-4.5}$ $\leq$ sSFR $\leq$ 10$^{-0.3}$) galaxies. We obtain VLT/X-Shooter spectra of NGC~5253, NGC~0625, SBS~0335-052E and IC~2828, targeting regions within these galaxies with bright point-like sources and diffuse gas. Our observations are designed to extend from the galaxy midplane into extraplanar gas likely belonging to galactic winds. We measure electron temperatures from five different auroral lines: [NII]~$\lambda$5755, [OII]~$\lambda\lambda$7319,30, [SII]~$\lambda\lambda$4069,76, [SIII]~$\lambda$6312, and [OIII]~$\lambda$4363. We compare the resulting $T_e$ - $T_e$ relations with previous studies of HII regions in nearby spiral galaxies. Our results show that $T_e$ - $T_e$ relations in low-metallicity starburst galaxies do not significantly deviate from $T_e$ - $T_e$ relations in HII regions of local spiral galaxies. We do not find significant differences in the diffuse, extraplanar gas. These results suggest that auroral lines provide a reliable metallicity diagnostic not only for high-redshift galaxies but also for the extended diffuse gas in extreme environments like outflows.