Stability and reconnection of magnetic fields play a fundamental role in natural and manmade plasma. In these applications the field's topology determines the stability of the magnetic field. Here I will describe the importance of one topology quantifier, the magnetic helicity, which impedes any free decay of the magnetic energy. Further constraints come from the fixed point index which hinders the field to relax into the Taylor state.

KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.

Brandenburg, Axel

KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.

Kinetic helicity needed to drive large-scale dynamos2013In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 87, no 4, p. 043104-Article in journal (Refereed)

Abstract [en]

Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called a effect when the turbulence is helical and if the domain is large enough for the a effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos.

Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity.

Kepler data from G-, K-, and M-type stars are used to study conditions that lead to superflares with energies above 10(34) erg. From the 117,661 stars included, 380 show superflares with a total of 1690 such events. We study whether parameters, like effective temperature or rotation rate, have any effect on the superflare occurrence rate or energy. With increasing effective temperature we observe a decrease in the superflare rate, which is analogous to the previous findings of a decrease in dynamo activity with increasing effective temperature. For slowly rotating stars, we find a quadratic increase of the mean occurrence rate with the rotation rate up to a critical point, after which the rate decreases linearly. Motivated by standard dynamo theory, we study the behavior of the relative starspot coverage, approximated as the relative brightness variation. For faster rotating stars, an increased fraction of stars shows higher spot coverage, which leads to higher superflare rates. A turbulent dynamo is used to study the dependence of the Ohmic dissipation as a proxy of the flare energy on the differential rotation or shear rate. The resulting statistics of the dissipation energy as a function of dynamo number is similar to the observed flare statistics as a function of the inverse Rossby number and shows similarly strong fluctuations. This supports the idea that superflares might well be possible for solar-type G stars.