The effect of local magnetic fields in quiet regions of stellar atmospheres simulated with MANCHA

Our aim is to characterize the effects of the local magnetic fields in quiet regions of stellar atmospheres. We compute magneto-hydrodynamic and purely hydrodynamic simulations of G2V, K0V and M2V star. The magnetic simulations are started from the hydrodynamical ones, adding the Biermann battery term in the induction equation to produce a magnetic seed, that is enhanced by the action of the small-scale dynamo. Once the magnetic field is saturated, we compare the simulations with and without magnetic fields and characterize the differences in statistics of velocities, appearance of granulation, and the mean stratification of a number of relevant parameters. These differences are also compared with the deviations produced by different treatments of the opacity in the simulations. The saturation values of the magnetic fields are $\sim 100$ G for the three stars in their surface, consistent with the recent results for cool stars, and other results for the Sun in the literature. The local magnetic fields have a negligible effect on the velocities of the plasma or the mean stratifications of the simulated stars. In contrast, they produce changes in the bolometric intensity of the intergranular lanes and the power spectrum at small scales of the temperature and vertical velocity of downflows. Significant differences between the hydrodynamic and magneto-hydrodynamic simulations are also found for the kinetic energy. This difference in energy can be explained by the transformation of kinetic into magnetic energy, which is consistent with the action of the small-scale dynamo.