Magnetic Helicity Conservation and Astrophysical Dynamos

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Abstract
We construct a magnetic helicity conserving dynamo theory that incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large-scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the "twist and fold" dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large-scale fields in equipartition with the turbulent energy density. The prospects for driving a fast dynamo under these circumstances are uncertain, but if it is possible, then the field must be largely force-free. On the other hand, there is an efficient analog to the α-Ω dynamo. Systems whose turbulence is driven by some anisotropic local instability in a shearing flow, like real stars and accretion disks, and some computer simulations may successfully drive the generation of strong large-scale magnetic fields, provided that ∂rΩ∂θvzωθ > 0. We show that this criterion is usually satisfied. Such dynamos will include a persistent, spatially coherent vertical magnetic helicity current with the same sign as -∂rΩ, that is, positive for an accretion disk and negative for the Sun. We comment on the role of random magnetic helicity currents in storing turbulent energy in a disordered magnetic field, which will generate an equipartition, disordered field in a turbulent medium, and also a declining long-wavelength tail to the power spectrum. As a result, calculations of the Galactic "seed" field are largely irrelevant.