Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere

Three-dimensional numerical simulations with CO5BOLD, a new radiation hydrodynamics code, result in a dynamic, thermally bifurcated model of the non-magnetic chromosphere of the quiet Sun. The 3-D 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 3-D 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 seconds, 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 3-D model corroborates the finding by Carlsson & Stein (1994) 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.