  The electromagnetic energy flux in the lower atmosphere of the Sun is a key
tool to describe the energy balance of the solar atmosphere. Current
investigations on energy flux in the solar atmosphere focus primarily on the
vertical electromagnetic flux through the photosphere, ignoring the Poynting
flux in other directions and its possible contributions to local heating. Based
on a realistic Bifrost simulation of a quiet-Sun (coronal hole) atmosphere, we
find that the total electromagnetic energy flux in the photosphere occurs
mainly parallel to the photosphere, concentrating in small regions along
intergranular lanes. Thereby, it was possible to define a proxy for this energy
flux based on only variables that can be promptly retrieved from observations,
namely, horizontal velocities of the small-scale magnetic elements and their
longitudinal magnetic flux. Our proxy accurately describes the actual Poynting
flux distribution in the simulations, with the electromagnetic energy flux
reaching $10^{10}$ erg\,cm$^{-2}$\,s$^{-1}$. To validate our findings, we
extended the analysis to SUNRISE/IMaX data. First, we show that Bifrost
realistically describes photospheric quiet-Sun regions, as the simulation
presents similar distributions for line-of-sight magnetic flux and horizontal
velocity field. Second, we found very similar horizontal Poynting flux proxy
distributions for the simulated photosphere and observational data. Our results
also indicate that the horizontal Poynting flux in the observations is
considerably larger than the vertical electromagnetic flux from previous
observational estimates. Therefore, our analysis confirms that the
electromagnetic energy flux in the photosphere is mainly horizontal and is most
intense in localized regions along intergranular lanes.
