Hydrodynamic simulations of cool stellar atmospheres with MANCHA

Abstract

Context. Three-dimensional time-dependent simulations of stellar atmospheres are essential to study the surface of stars other than the Sun. These simulations require the opacity binning method to reduce the computational cost of solving the radiative transfer equation down to viable limits. The method depends on a series of free parameters, among which the location and number of bins are key to set the accuracy of the resulting opacity. Aims. Our aim is to test how different binning strategies previously studied in one-dimensional models perform in three-dimensional radiative hydrodynamic simulations of stellar atmospheres. Methods. Realistic box-in-a-star simulations of the near-surface convection and photosphere of three spectral types (G2V, K0V, and M2V) were run with the MANCHA code with grey opacity. After reaching the stationary state, one snapshot of each of the three stellar simulations was used to compute the radiative energy exchange rate with grey opacity, opacity binned in four τ-bins, and opacity binned in 18 {τ, λ}-bins. These rates were compared with the ones computed with opacity distribution functions. Then, stellar simulations were run with grey, four-bin, and 18-bin opacities to see the impact of the opacity setup on the mean stratification of the temperature and its gradient after time evolution. Results. The simulations of main sequence cool stars with the MANCHA code are consistent with those in the literature. For the three stars, the radiative energy exchange rates computed with 18 bins are remarkably close to the ones computed with the opacity distribution functions. The rates computed with four bins are similar to the rates computed with 18 bins, and present a significant improvement with respect to the rates computed with the Rosseland opacity, especially above the stellar surface. The Rosseland mean can reproduce the proper rates in sub-surface layers, but produces large errors for the atmospheric layers of the G2V and K0V stars. In the case of the M2V star, the Rosseland mean fails even in sub-surface layers, owing to the importance of the contribution from molecular lines in the opacity, underestimated by the harmonic mean. Similar conclusions are reached studying the mean stratification of the temperature and its gradient after time evolution.