Application of the Markov Chain Model to Sunspots and Solar Plages for the Period 1910 to 1937 Using Data fromEbro Catalogues

Abstract

In this article, we analyzed the morphological evolution of the sunspot and solar calcium plage groups recorded at the Ebro Observatory in the period 1910–1937 to make predictions about several properties of these solar structures by using Markov chain models. For this purpose, we first checked the applicability of first and second order models to all the data series by carrying out dependency tests, which ensure that the current morphological type presented by the structures has a dependence with the morphology presented in previous observations. Next, as a first approximation, we applied the first order Markov chain model to the total number of transitions between the different morphological types of sunspots and solar plage groups to estimate the probability of occurrence associated with each transition, the prevalence time that these structures spend within each morphological type, the extinction-occultation forecast, the expectation of these structures converting into a determined morphological type, and the occurrence daily rate associated to each type after a certain number of transitions. In addition, we also analyzed the observed morphology of the structures at the time of their appearance and extinction. Our main results show that both sunspots and solar plage groups become morphologically stable after their transition to a new type. Nevertheless, this stability seems to decrease once the decay phase starts and their morphology changes to the observed type during the last stage of their evolution sequence. Finally, we also studied the temporal and spatial homogeneity of the data, concluding that the two solar structures evolve with similar patterns in the northern and southern hemispheres, but both Solar Cycles 15 and 16 as well as each solar cycle phase, i.e. solar minimum, ascending phase, solar maximum and descending phase, present small deviations in all the analyzed properties. These deviations may affect some aspects of the morphological evolution of both sunspots and solar plage groups.