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We study the 3.4 − 4.4 μm fundamental rovibrational band of H₃⁺, a key tracer of the ionization of the molecular interstellar medium (ISM), in a sample of 12 local (d < 400 Mpc) (ultra)luminous infrared galaxies ((U)LIRGs) observed with JWST/NIRSpec. TheP,Q, andRbranches of the band are detected in 13 out of 20 analyzed regions within these (U)LIRGs, which increases the number of extragalactic H₃⁺detections by a factor of 6. For the first time in the ISM, the H₃⁺band is observed in emission; we detect this emission in three regions. In the remaining ten regions, the band is seen in absorption. The absorptions are produced toward the 3.4 − 4.4 μm hot dust continuum rather than toward the stellar continuum, indicating that they likely originate in clouds associated with the dust continuum source. The H₃⁺band is undetected in Seyfert-like (U)LIRGs where the mildly obscured X-ray radiation from the active galactic nuclei might limit the abundance of this molecule. For the detections, the H₃⁺abundances,N(H₃⁺)/N_H = (0.5 − 5.5)×10⁻⁷, imply relatively high ionization rates,ζ_H2, of between 3 × 10⁻¹⁶and > 4 × 10⁻¹⁵s⁻¹, which are likely associated with high-energy cosmic rays. In half of the targets, the absorptions are blueshifted by 50–180 km s⁻¹, which is lower than the molecular outflow velocities measured using other tracers such as OH 119 μm or rotational CO lines. This suggests that H₃⁺traces gas close to the outflow-launching sites before it has been fully accelerated. We used nonlocal thermodynamic equilibrium models to investigate the physical conditions of these clouds. In seven out of ten objects, the H₃⁺excitation is consistent with inelastic collisions with H₂in warm translucent molecular clouds (T_kin ∼ 250–500 K andn(H₂) ∼10^2 − 3cm⁻³). In three objects, dominant infrared pumping excitation is required to explain the absorptions from the (3,0) and (2,1) levels of H₃⁺detected for the first time in the ISM. 

We present ten novel [OIII]λ4363 auroral line detections up toz ∼ 9.5 measured from ultra-deep JWST/NIRSpec MSA spectroscopy from the JWST Advanced Deep Extragalactic Survey (JADES). We leverage the deepest spectroscopic observations taken thus far with NIRSpec to determine electron temperatures and oxygen abundances using the directT_emethod. We directly compare these results against a suite of locally calibrated strong-line diagnostics and recent high-zcalibrations. We find the calibrations fail to simultaneously match our JADES sample, thus warranting a self-consistent revision of these calibrations for the high-zUniverse. We find a weak dependence between R2 and O3O2 with metallicity, thus suggesting these line ratios are inefficient in the high-zUniverse as metallicity diagnostics and degeneracy breakers. We find R3 and R23 are still correlated with metallicity, but we find a tentative flattening of these diagnostics, thus suggesting future difficulties when applying these strong line ratios as metallicity indicators in the high-zUniverse. We also propose and test an alternative diagnostic based on a different combination of R3 and R2 with a higher dynamic range. We find a reasonably good agreement (median offset of 0.002 dex, median absolute offset of 0.13 dex) with the JWST sample at low metallicity, but future investigations are required on larger samples to probe past the turnover point. At a given metallicity, our sample demonstrates higher ionization and excitation ratios than local galaxies with rest-frame EWs(Hβ) ≈200 − 300 Å. However, we find the median rest-frame EWs(Hβ) of our sample to be ∼2× less than the galaxies used for the local calibrations. This EW discrepancy combined with the high ionization of our galaxies does not offer a clear description of [OIII]λ4363 production in the high-zUniverse, thus warranting a much deeper examination into the factors influencing these processes.