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We explore mechanisms to produce extremely high Ly-alpha/HeII flux ratios, orto enhance the observed number of Ly-alpha photons per incident ionizingphoton, in extended AGN-photoionized nebulae at high-redshift. Usingphotoionization models, we explore the impact of ionization parameter, gasmetallicity, ionizing spectrum, electron energy distribution, and cloud viewingangle on the relative fluxes of Ly-alpha, HeII and other lines, and on theobserved number of Ly-alpha photons per incident ionizing photon. We find thatlow ionization parameter, a relatively soft or filtered ionizing spectrum, lowgas metallicity, kappa-distributed electron energies, or reflection of Ly-alphaphotons by HI can all result in significantly enhanced Ly-alpha relative toother lines (>10%), with log Ly-alpha/HeII reaching values up to 4.6. In thecases of low gas metallicity, reflection by HI, or a hard or filtered ionizingspectrum, the observed number of Ly-alpha photons per incident ionizing photonis itself significantly enhanced above the nominal Case B value of 0.66 due tocollisional excitation, reaching values up to 5.3 in our 'extreme case' model.At low gas metallicity (e.g. 0.1 x Solar), the production of Ly-alpha ispredominantly via collisional excitation rather than recombination. Inaddition, we find that collisional excitation of Ly-alpha becomes moreefficient if the ionizing continuum is pre-filtered through an optically thinscreen of gas closer to the AGN. We also show that Ly-alpha / HeII ratios ofthe z~3.5 quasars studied by Borisova et al. (2016) are consistent withAGN-photoionization of gas with moderate to low metallicity and/or lowionization parameter, without requiring exotic ionization/excitation mechanismssuch as strong line-transfer effects. We also present UV-optical diagnosticdiagrams to distinguish between photoionization by Pop III stars and AGNphotoionization.

Photoionization models for extreme Ly$\alpha$ $\lambda$1216 and HeII $\lambda$1640 ratios in quasar halos, and PopIII vs AGN diagnostics