Fractality of Magnetic Helicity Distribution in the Solar Corona

We find a universal power-law scaling of magnetic helicity distribution in the solar corona. Magnetic helicity is a dynamical invariant for ideal magnetohydrodynamics (MHD) and characterizes complex magnetic field structure by measuring the degree of knottiness of its field lines. We treat turbulent solar magnetic field as a superposition of random waves and develop a statistical topology method regarding the randomly tangled field lines. Based on the statistical behavior of the field lines, we consider their topology-specified structure and theoretically derive power laws for the distribution of magnetic flux and helicity. We find a power law of −7/4 to the magnetic helicity distribution when the field line topology is equivalent to handle and −5/4 when the field line topology is local open curve. We verify the universality of this new magnetic helicity fractality by observation to a number of 185 sunspots in newly emerging active regions during the 23rd and 24th solar cycle. This new distribution law reveals the fractal structure of the solar magnetic field.