Context . Ly α emitters (LAEs) are galaxies with strong Ly α emission, tracing early star formation and ionizing radiation. Their connection to active galactic nuclei (AGNs) is key to understanding the mechanisms behind (extended) Ly α emission. Aims . For this study, we measured the fraction of LAEs identified as radio-emitting AGNs ( f _AGN,radio ) and the fraction of radio sources that exhibit Ly α emission ( f _{Ly
α} ) to investigate the connection of radio AGN activity to Ly α emission at 1.88 < z < 3.52. Methods . We identified 928 sources that were detected in both the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) and the LOw Frequency ARray (LOFAR) surveys. These matches were drawn from 55 109 spectroscopically confirmed LAEs and 27 625 radio sources. Results . After applying completeness corrections, we obtain f _AGN,radio = 1.77 ± 0.04% and f _{Ly
α} = 18.15 ± 0.14% (for Ly α fluxes above 3×10 ⁻¹⁷ erg s ⁻¹ cm ⁻² and radio flux densities above 0.1 mJy at 144 MHz). The fraction f _AGN,radio increases from 0.4 ± 0.1% at log ₁₀ L _{Lyα,ergs
⁻¹} ≈ 42.6 to 9.7 ± 1.3% at log ₁₀ L _{Lyα,ergs
⁻¹} ≈ 44.5. The fraction f _Lyα rises from 0.7 ± 0.1% at log ₁₀ L _{150,WHz
⁻¹} ≈ 24.6 to 55.8 ± 14.5% for log ₁₀ L _{150,WHz
⁻¹} ≈ 28.3. ‘LAEs with radio AGNs’ and ‘optical AGNs with Ly α emission’ exhibit similar radio luminosity distributions above the AGN threshold ( L _150MHz > 10 ^23.9 W Hz ⁻¹ ), though optical AGNs show systematically higher Ly α luminosities. We find no statistically significant correlations of Ly α luminosity with both radio luminosity and a low-frequency spectral index, suggesting that Ly α emission is regulated by gas properties rather than jet power alone. We also find a positive correlation between the full width at half maximum (FWHM) and luminosity of the Ly α line, suggesting that more luminous sources have broader lines, potentially due to enhanced outflows or velocity dispersions. However, we find no correlation between FWHM and radio size, indicating minimal direct jet-gas interaction in these systems. Conclusions . Our results show that most Ly α emission at 1.88 < z < 3.52 is powered by star formation, with radio AGN activity confined to a small luminous subset (1.77 ± 0.04%). While luminous systems preferentially host radio AGNs, the lack of correlation between Ly α and radio luminosities in individual sources indicates that Ly α emission is governed primarily by host galaxy gas properties rather than direct AGN jet coupling.

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