Magnetic Helicity Conservation and Astrophysical Dynamos
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abstract
We construct a magnetic helicity conserving dynamo theory which 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 $\alpha-\Omega$ 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
$\partial_r\Omega< \partial_\theta v_z\omega_\theta>>0$. 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
$-\partial_r\Omega$, 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.
