Carbon monoxide in the solar atmosphere II.: Radiative cooling by CO lines

Aims. The role of carbon monoxide as a cooling agent for the thermal structure of the mid-photospheric to low-chromospheric layers of the solar atmosphere in internetwork regions is investigated. Methods. The treatment of radiative cooling via spectral lines of carbon monoxide ( CO) has been added to the radiation chemo-hydrodynamics code CO5BOLD. The radiation transport has now been solved in a continuum band with Rosseland mean opacity and an additional band with CO opacity. The latter is calculated as a Planck mean over the CO band between 4.4 and 6.2 mu m. The time-dependent CO number density is derived from the solution of a chemical reaction network. Results. The CO opacity indeed causes additional cooling at the fronts of propagating shock waves in the chromosphere. There, the time-dependent approach results in a higher CO number density compared to the equilibrium case and hence in a larger net radiative cooling rate. The average gas temperature stratification of the model atmosphere, however, is only reduced by roughly 100 K. Also the temperature fluctuations and the CO number density are only affected to small extent. A numerical experiment without dynamics shows that the CO cooling process works in principle and drives the atmosphere to a cool radiative equilibrium state. At chromospheric heights, the radiative relaxation of the atmosphere to a cool state takes several 1000 s. The CO cooling process thus would seem to be too slow compared to atmospheric dynamics to be responsible for the very cool temperature regions observed in the solar atmosphere. Conclusions. The hydrodynamical timescales in our solar atmosphere model are much too short to allow for the radiative relaxation to a cool state, thus suppressing the potential thermal instability due to carbon monoxide as a cooling agent. Apparently, the thermal structure and dynamics of the outer model atmosphere are instead determined primarily by shock waves.