Molecular hydrogen (H) is the fundamental component of the molecular gas reservoir that fuels star formation and black hole growth. While prominent hot H emission ( K) has been explored in nearby galaxies, its excitation mechanisms at higher redshifts remain poorly constrained. We present a systematic study of hot molecular gas traced via ro-vibrational H emitters at z~0.2-1.5 using JWST slitless spectroscopy. Exploiting JWST’s great sensitivity to near-infrared H ro-vibrational transitions such as H 1-0 S(1), we build a sample of 144 H-luminous galaxies and characterize their multi-wavelength properties. About 96.5% and 80% of these galaxies are detected in the radio and far-infrared (FIR) bands, respectively, and their hot H emission strongly correlates with the radio and FIR radiation. Based on radio excess, X-ray emission, and optical diagnostics, 62 sources (43%) exhibit significant AGN activity. The H line luminosities of the sample show a sublinear dependence on radio luminosity, while the relation between the H luminosities and total infrared luminosities is approximately linear after excluding the radio-excess sources. These scaling relations suggest that star formation provides a baseline contribution to hot H excitation, while radio-excess sources require an additional contribution from AGN-related processes such as jet- or wind-driven shocks. These results reveal a multi-channel excitation scenario and shed new light on the interplay between star formation, AGN activity, and the interstellar medium during galaxy evolution.

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