Markov properties of the magnetic field in the quiet solar photosphere

The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we study the temporal stochasticity of the magnetic field on the solar surface without relying on either the concept of magnetic feature or on the subjective assumptions about their identification and interaction. The analysis is applied to observations of the magnetic field of the quiet solar photosphere carried out with the Imaging Magnetograph eXperiment (IMaX) instrument on board the stratospheric balloon, Sunrise. We show that the joint probability distribution functions of the longitudinal ($B_{\parallel }$) and transverse ($B_{\perp }$) components of the magnetic field, as well as of the magnetic pressure ($B^2=B_{\perp }^2+B_{\parallel }^2$), verify the necessary and sufficient condition for the Markov chains. Therefore, we establish that the magnetic field as seen by IMaX with a resolution of 0.″15–0.″18 and 33 s cadence, which can be considered as a memoryless temporal fluctuating quantity.