Fractal multi-scale nature of solar/stellar magnetic fields

Abramenko Valentyna, avi@bbso.njit.edu, Big Bear Solar Observatory, United States

Abstract
Continuously varying magnetic field is a main reason for the solar/stellar activity. The 11-year solar cycle is one of the most astonishing and widely known examples of the self-organized generation of the magnetic field. Although we know that there is no two absolutely similar solar cycles, yet, persistency and regularity of the solar periodicity through thousands of years remains impressive. A drastically different picture arises when one looks on the photosphere: chaos of mixed-polarity magnetic elements of all sizes until the resolution limits of modern instruments, continuously renewing during 1-2 days - the magnetic carpet. Dualism of the solar magnetism is usually explained by a simultaneous action of two dynamos: a global dynamo operating in the convective zone and responsible for the 11-year solar cycle, and local, or turbulent dynamo, which might operate inside the near-surface layer and to be responsible for generation of small-scale magnetic fields forming the magnetic carpet. The explanation seems to oversimplify the reality because resent studies of distribution of the magnetic flux accumulated in magnetic flux tubes showed the non-interrupted lower law for many decades (Parnell et al. 2009) thus supposing a common (for all scales) mechanism for the magnetic field generation. One of the promising ways to handle the problem is to consider the solar dynamo process as a non-linear dynamical system (NDS), with intrincis properties of multifractality and intermittency. Like any NDS, the solar dynamo is then capable to self-organization on large scales and display a chaotic nature on small scales. Moreover, in this case the dynamo is intrinsically multi-scale process when inter-scale exchange is on work. This paradigm offers new approaches to understand the solar and stellar magnetism. The goal of this invited talk is to show how the ideas of multifractality, self-organized criticality, percolation, multifractality and intermittency are currently elaborated for exploring the solar (and stellar) magnetism.