| Abstract
| - Three-dimensional numerical simulations with CO $^\mathsf{5}$BOLD , a new radiation hydrodynamics code, result in a dynamic, thermally bifurcated model of the non-magnetic chromosphere of the quiet Sun. The 3D model includes the middle and low chromosphere, the photosphere, and the top of the convection zone, where acoustic waves are excited by convective motions. While the waves propagate upwards, they steepen into shocks, dissipate, and deposit their mechanical energy as heat in the chromosphere. Our numerical simulations show for the first time a complex 3D structure of the chromospheric layers, formed by the interaction of shock waves. Horizontal temperature cross-sections of the model chromosphere exhibit a network of hot filaments and enclosed cool regions. The horizontal pattern evolves on short time-scales of the order of typically 20-25 s, and has spatial scales comparable to those of the underlying granulation. The resulting thermal bifurcation, i.e., the co-existence of cold and hot regions, provides temperatures high enough to produce the observed chromospheric UV emission and - at the same time - temperatures cold enough to allow the formation of molecules (e.g., carbon monoxide). Our 3D model corroborates the finding by [CITE] that the chromospheric temperature rise of semi-empirical models does not necessarily imply an increase in the average gas temperature but can be explained by the presence of substantial spatial and temporal temperature inhomogeneities.
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