A model for the emission line galaxy luminosity function and flux ratios at high-redshifts

We present $[OIII]/H_{\rm \beta}$ emision line flux ratio predictions for galaxies at $z \sim 7-9$ using the MAPPINGS V v5.2.0 photoionization modelling code combined with an analytic galaxy formation model. Properties such as pressure and ionization parameter that determine emission line properties are thought to evolve towards high redshift. In order to determine the range of expected interstellar conditions we extend previous modelling of the Star Formation Rate Density (SFRD) function to calculate the metallicity and ionization parameter, and incorporate the potential impact of turbulence on the density of the ISM. To validate our emission line predictions we calculate the [OIII] line luminosity and its dependence on UV luminosity, as well as the flux ratio $[OIII]/H_{\rm \beta}$ and its variation with the line luminosity, finding that both reproduce recent JWST observations from the FRESCO survey. We also use our model to predict the number counts of emission line galaxies across a range of redshift as well as the dependence of $[OIII]/H_{\rm \beta}$ on ionization parameter and metallicity. Finally, we show that the dependence of flux ratio on luminosity may provide a diagnostic of turbulent motion in galactic discs.