2025MNRAS.543.1322H

In this work, we test the validity of $T_{\rm e}$-$T_{\rm e}$ relations in resolved (10-200 pc) measurements of four nearby, low-metallicity (7.25 $\le$ 12 + log(O/H) $\le$ 8.33), low-mass (10$^{6.78}$ $\le$ $M_*$/M$_\odot$ $\le$ 10$^{8.7}$), starburst (10$^{-4.5}$ $\le$ sSFR $\le$ 10$^{-0.3}$) galaxies. We obtain Very Large Telescope/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 mid-plane into extraplanar gas likely belonging to galactic winds. We measure electron temperatures from five different auroral lines: [N II] $\lambda$5755, [O II] $\lambda \lambda$7319, 7330, [S II] $\lambda \lambda$4069, 4076, [S III] $\lambda$6312, and [O III] $\lambda$4363. We compare the resulting $T_{\rm e}$-$T_{\rm e}$ relations with previous studies of H II regions in nearby spiral galaxies. Our results show that $T_{\rm e}$-$T_{\rm e}$ relations in low-metallicity starburst galaxies do not significantly deviate from $T_{\rm e}$-$T_{\rm e}$ relations in H II 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.