  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.
