On the resilience of helical magnetic fields to turbulent diffusion and the astrophysical implications
Abstract
The extent to which large-scale magnetic fields are susceptible to turbulent diffusion is important for interpreting the need for in situ large-scale dynamos in astrophysics and for observationally inferring field strengths compared to kinetic energy. By solving coupled evolution equations for magnetic energy and magnetic helicity in a system initialized with isotropic turbulence and an arbitrarily helical large-scale field, we quantify the decay rate of the latter for a bounded or periodic system. The magnetic energy associated with the non-helical large-scale field decays at least as fast as the kinematically estimated turbulent diffusion rate, but the decay rate of the helical part depends on whether the ratio of its magnetic energy to the turbulent kinetic energy exceeds a critical value given by M1, c = (k1/k2)2, where k1 and k2 are the wavenumbers of the large and forcing scales. Turbulently diffusing helical fields to small scales while conserving magnetic helicity requires a rapid increase in total magnetic energy. As such, only when the helical field is subcritical can it so diffuse. When supercritical, it decays slowly, at a rate determined by microphysical dissipation even in the presence of macroscopic turbulence. In effect, turbulent diffusion of such a large-scale helical field produces small-scale helicity whose amplification abates further turbulent diffusion. Two curious implications are that (1) standard arguments supporting the need for in situ large-scale dynamos based on the otherwise rapid turbulent diffusion of large-scale fields require re-thinking since only the large-scale non-helical field is so diffused in a closed system. Boundary terms could however provide potential pathways for rapid change of the large-scale helical field. (2) Since M1, c ≪ 1 for k1 ≪ k2, the presence of long-lived ordered large-scale helical fields as in extragalactic jets do not guarantee that the magnetic field dominates the kinetic energy.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- February 2013
- DOI:
- 10.1093/mnras/sts433
- arXiv:
- arXiv:1209.2230
- Bibcode:
- 2013MNRAS.429.1398B
- Keywords:
-
- accretion;
- accretion discs;
- dynamo;
- magnetic fields;
- stars: magnetic field;
- galaxies: jets;
- cosmology: miscellaneous;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- Astrophysics - Astrophysics of Galaxies;
- Astrophysics - Solar and Stellar Astrophysics;
- Physics - Plasma Physics
- E-Print:
- published in MNRAS (in this replacement, the missing .bbl file has been added)