  Numerical models of gas inflow towards a supermassive black hole (SMBH) show
that star formation may occur in such an environment through the growth of a
gravitationally unstable gas disc. We consider the effect of nuclear activity
on such a scenario. We present the first three-dimensional grid-based radiative
hydrodynamic simulations of direct collisions between infalling gas streams and
a $4 \times 10^6~\text{M}_\odot$ SMBH, using ray-tracing to incorporate
radiation consistent with an active galactic nucleus (AGN). We assume inflow
masses of $ \approx 10^5~\text{M}_\odot$ and explore radiation fields of 10%
and 100% of the Eddington luminosity ($L_\text{edd}$). We follow our models to
the point of central gas disc formation preceding star formation and use the
Toomre Q parameter ($Q_T$) to test for gravitational instability. We find that
radiation pressure from UV photons inhibits inflow. Yet, for weak radiation
fields, a central disc forms on timescales similar to that of models without
feedback. Average densities of $> 10^{8}~\text{cm}^{-3}$ limit photo-heating to
the disc surface allowing for $Q_T\approx1$. For strong radiation fields, the
disc forms more gradually resulting in lower surface densities and larger $Q_T$
values. Mass accretion rates in our models are consistent with 1%--60% of the
Eddington limit, thus we conclude that it is unlikely that radiative feedback
from AGN activity would inhibit circumnuclear star formation arising from a
massive inflow event.
