Advances in mean-field dynamo theory and applications to astrophysical turbulence

Abstract

Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies, and the early Universe are discussed. We focus particularly on aspects of spatio-temporal nonlocality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and timescales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modeling this regime may be related to shortcomings in modelling solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking. † Email address for correspondence: brandenb@nordita.org † In the following, we continue using the lowercase symbols u and b instead of U ′ and B ′ to denote fluctuations of U and B.

On the Origin of Solar Torsional Oscillations and Extended Solar Cycle

“…Our model describes the dynamo processes distributed in the convection zone. Previously, it was argued that such type of distributed dynamo models provides satisfactory agreement with solar and stellar observations (Pipin 2015;Brandenburg 2018;Viviani et al 2018). Previous models of the torsional oscillations were constructed by coupling the dynamo equations with equations of the angular momentum transport (e.g.…”

Dynamo theories

“…Other interesting essays on small-scale dynamo theory include the work of Vincenzi (2002) on the Kazantsev model, a chapter by Tobias et al (2011a) on MHD dynamos in the collective book The Nature of Turbulence, and a few sections of Davidson's (2013) book reviewing the current state of research on Turbulence in Rotating, Stratified and Electrically Conducting Fluids. Accessible reviews of large-scale dynamo theory, including diverse perspectives on nonlinear effects and interactions between large-and small-scale dynamos, can be found in Hughes & Tobias (2010), Brandenburg (2018) and Hughes (2018). The seemingly inextricable problem of nonlinear saturation of large-scale dynamos is specifically discussed in two reviews by Proctor (2003) and Diamond et al (2005).…”

Chiral magnetohydrodynamic turbulence in core-collapse supernovae

“…When dividing the variables of the induction equation into the ensemble-averaged values and fluctuating components, the α effect appears in the turbulent electromotive force as an induction term. It is a consequence of the forced symmetry breaking in rotating astrophysical bodies, such as the Sun, stars, and accretion disks, and has been widely studied as an origin of the largescale magnetic field commonly observed in these objects [57][58][59][60]. On the other hand, the CME is a pure quantum effect that originates from the explicit parity symmetry breaking by the chirality of fermions.…”