Numerical simulations of surface convection in a late M-dwarf

Based on detailed 2D and 3D numerical radiation-hydrodynamics (RHD) simulations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of a prototypical late-type M-dwarf (Teff ≈ 2800K, log g = 5.0, solar chemical composition). The RHD models predict stellar granulation qualitatively similar to the familiar solar pattern. Quantitatively, the granular cells show a convective turn-over time scale of ≈ 100 s, and a horizontal scale of 80 km; the relative intensity contrast of the granular pattern amounts to 1.1%, and root-mean-square vertical velocities reach 240m/s at maximum. Deviations from radiative equilibrium in the higher, formally convectively stable atmospheric layers are found to be insignificant allowing a reliable modeling of the atmosphere with 1D standard model atmospheres. A mixinglength parameter of αMLT=2.1 provides the best representation of the average thermal structure of the RHD model atmosphere while alternative values are found when fitting the asymptotic entropy encountered in deeper layers of the stellar envelope (αMLT=1.5), or when matching the vertical velocity field (αMLT=3.5). The close correspondence between RHD and standard model atmospheres implies that presently existing discrepancies between observed and predicted stellar colors in the M-dwarf regime cannot be traced back to an inadequate treatment of convection in the 1D standard models. The RHD models predict a modest extension of the convectively mixed region beyond the formal Schwarzschild stability boundary which provides hints for the distribution of dust grains in cooler (brown dwarf) atmospheres.