Apparent motion of penumbral grains in a sunspot simulation

Context. The bright heads of penumbral filaments, penumbral grains (PGs), are manifestations of hot plasma flows rising to the surface. They are observed to move horizontally towards the sunspot umbra or away from it. Recent analyses of observations indicate that the direction of this motion is related to the inclination of the surrounding magnetic field. Aims. The penumbra of a sunspot, simulated by the radiative magnetohydrodynamic code MURaM, is analysed to obtain typical physical conditions in PGs, compare them with those in the surroundings, describe their spatial distribution, and study their evolution. Methods. We used time series of images mapping intensity, temperature, magnetic field vector, and velocity vector in horizontal slices at the visible surface, in subsurface layers, and in vertical cuts through the simulation box to track PGs and compare, both statistically and in individual cases, the physical quantities inside them with those in the surroundings. Results. The statistical analysis of the simulation results provides average values of temperature, magnetic field strength and inclination, vertical velocity, and their changes with radial distance from the spot centre. We find a subtle difference between simulated PGs with opposite directions of motion when comparing the magnetic field inclinations inside and outside the PGs. The case studies, documented by movies, show that the differences in inclinations and the direction of motion may change during the lifetime of some PGs and that the turbulence in the surface layers introduces some randomness in the apparent motions of PGs.