Markov properties of solar granulation

Aims. We estimate the minimum length on which solar granulation can be considered to be a Markovian process. Methods. We measure the variation in the bright difference between two pixels in images of the solar granulation for different distances between the pixels. This scale-dependent data is empirically analyzed to find the minimum scale on which the process can be considered Markovian. Results. The results suggest that the solar granulation can be considered to be a Markovian process on scales longer than r(M) = 300-500 km. On longer length scales, solar images can be considered to be a Markovian stochastic process that consists of structures of size rM. Smaller structures exhibit correlations on many scales simultaneously yet cannot be described by a hierarchical cascade in scales. An analysis of the longitudinal magnetic-flux density indicates that it cannot be a Markov process on any scale. Conclusions. The results presented in this paper constitute a stringent test for the realism of numerical magneto-hydrodynamical simulations of solar magneto-convection. In future exhaustive analyse, the non-Markovian properties of the magnetic flux density on all analyzed scales might help us to understand the physical mechanism generating the field that we detect in the solar surface.