The impact of source and survey modelling on the connection between [O III] emitters and Ly α forest transmission at z ~ 6

James Webb Space Telescope (JWST) surveys of [O III]-emitting galaxies are offering fresh insight into the connection between galaxies and the intergalactic medium at redshift z ~ 6. Recent measurements of the cross-correlation between [O III]-emitting galaxies and Ly $\alpha$ forest transmission present an apparent challenge to numerical models. Here we improve upon previous theoretical work by constructing an empirical model that connects haloes with the observed population of [O III] emitters and incorporates the geometry and depth of the JWST surveys into mock galaxy survey catalogues. We compare these mocks to recent measurements of [O III] emitter clustering and the one and two dimensional galaxy-Ly $\alpha$ transmission cross-correlation. The large scatter in our mock survey measurements of the cross-correlation enable a statistically good match to the observational data, albeit the peak of the one dimensional correlation in our mocks occurs at a scale $\approx$10 cMpc below that observed. The large scatter implies that, at present, current galaxy-IGM observations may struggle to rule out a broad range of ionising source models. We anticipate that further progress will strongly benefit from increased observational sample sizes, as well as simulations performed in box sizes >250 cMpc that use a variety of source models.