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Thermal and radiative AGN feedback have a limited impact on star formation in high-redshift galaxies

The effects of Active Galactic Nuclei (AGNs) on their host-galaxies depend on the coupling between the injected energy and the interstellar medium (ISM). Here, we model and quantify the impact of long-range AGN ionizing radiation -- in addition to the often considered small-scale energy deposition -- on the physical state of the multi-phase ISM of the host-galaxy, and on its total Star Formation Rate (SFR). We formulate an AGN Spectral Energy Distribution matched with observations, which we use with the radiative transfer (RT) code Cloudy to compute AGN ionization in a simulated high-redshift disk galaxy. We use a high-resolution ($\sim6$ pc) simulation including standard thermal AGN feedback and calculate RT in post-processing. Surprisingly, while these models produce significant AGN-driven outflows, we find that AGN ionizing radiation and heating reduce the SFR by a few percent at most for a quasar luminosity ($L_{bol}=10^{46.5}$ erg s$^{-1}$). Although the circum-galactic gaseous halo can be kept almost entirely ionized by the AGN, most star-forming clouds ($n\gtrsim10^{2-3}$ cm$^{-3}$) and even the reservoirs of cool atomic gas ($n\sim0.3-10$ cm$^{-3}$) -- which are the sites of future star formation (100 - 200 Myrs), are generally too dense to be significantly affected. Our analysis ignores any absorption from a putative torus, making our results upper limits on the effects of ionizing radiation. Therefore, while the AGN-driven outflows can remove substantial amounts of gas in the long term, the impact of AGN feedback on the star formation efficiency in the interstellar gas in high-redshift galaxies is marginal, even when long-range radiative effects are accounted for.