Índice de atividade magnética baseado na mecânica estatística não-extensiva de Tsallis para estrelas do tipo M - Rios, Luiz Daniel Alves (2019)
Stellar activity is strongly related to magnetic fields that evolve according to their rate of rotation. The period of the magnetic cycle and the period of rotation are correlated in such a way that the slow rotators have larger magnetic cycles. In addition, the overall level of magnetic activity changes over time after cycles, and local levels change according to fluctuations, ranging from time scales from a few seconds to several hours, days, or weeks. As mentioned by Mathur et al. (MATHUR et al., 2014), faster rotating stars show shorter activity cycles, while slower rotating stars generally have similar or longer Sun cycle times. As the magnetic activity that emerges from the surface of the stars is a physical mechanism produced by the stellar dynamo, the long-term variations due to the rotational period play an important role in understanding the level of activity on the star surface. The magnetic activity is measured by the behavior of the photon flux obtained by the time series. For this work, we use the time series of stars observed by the Kepler mission, in a total of 34 stars of the spectral type M. We believe that the fluctuations of this flux at different scales do not obey the Boltzmann-Gibbs canonical distribution and therefore the appearance of heavy tails in the distributions can give us an idea about the physical source that operates the stellar magnetic activity at different time scales . To this end, we will investigate the behavior of these distributions in light of the non-extensive statistical mechanics of C. Tsallis. More specifically, we use the entropic index q of Tsallis as a measure of the tail extension of the distribution which, in turn, is correlated to the level of stellar magnetic activity. We also defined a new magnetic index hSqi related to generalized standard deviation sq and based on non-extensive statistical mechanics. Thus we can find an index similar to that obtained by Mathur but with a more appropriate physical explanation, that is, taking into account the effects of long tail distribution. Finally, our work may open a new field of research in time series astrophysics within the context of non-extensiveness.