Magnetic Helicity Conservation and Astrophysical Dynamos

We construct a magnetic helicity conserving dynamo theory which incorporatesa calculated magnetic helicity current. In this model the fluid helicity playsa small role in large scale magnetic field generation. Instead, the dynamoprocess is dominated by a new quantity, derived from asymmetries in the secondderivative of the velocity correlation function, closely related to the `twistand fold' dynamo model. The turbulent damping term is, as expected, almostunchanged. Numerical simulations with a spatially constant fluid helicity andvanishing resistivity are not expected to generate large scale fields inequipartition with the turbulent energy density. The prospects for driving afast 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 anefficient analog to the $\alpha-\Omega$ dynamo. Systems whose turbulence isdriven by some anisotropic local instability in a shearing flow, like realstars and accretion disks, and some computer simulations, may successfullydrive the generation of strong large scale magnetic fields, provided that$\partial_r\Omega< \partial_\theta v_z\omega_\theta>>0$. We show that thiscriterion 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 forthe Sun. We comment on the role of random magnetic helicity currents in storingturbulent energy in a disordered magnetic field, which will generate anequipartition, disordered field in a turbulent medium, and also a declininglong wavelength tail to the power spectrum. As a result, calculations of thegalactic `seed' field are largely irrelevant.Comment: 28 pages, accepted by The Astrophysical Journa