## 5. DiscussionWe have demonstrated that the nonlinear evolution of the helicity following from Eq. (4) gives a basically different type of galactic magnetic field evolution to that following from Eq. (5). Eq. (4), being based on local helicity conservation, results in magnetic field decay, after a stage of kinematic growth. If the molecular diffusivity of the magnetic field is taken into account, this decay is followed by a stabilization at a very low magnetic field strength, corresponding to the estimate of Vainshtein and Cattaneo (1992). The scenario of magnetic field and helicity dynamics can then be described as follows. Large-scale dynamo action produces large-scale magnetic helicity. Due to the local conservation of helicity, suppression of field generation results. An equilibrium is possible if molecular diffusivity is present, so the equilibrium magnetic field strength is very low. Eq. (5) allows for the transport of helicity, so the local
value of the helicity changes during magnetic field evolution. The
scenario of magnetic field and helicity dynamics can be presented as
follows. As usual, magnetic helicity of the large-scale magnetic field
is produced, however the total magnetic helicity is not now conserved
locally, but the magnetic helicity of the small-scale magnetic field
is redistributed by a helicity flux. The equilibrium state is given by
a balance between helicity production and transport. The helicity
conservation law now expresses the conservation of an integral of the
helicity over the galactic disc. However this conservation law is
trivial, because the integral vanishes identically as helicity is an
odd function with respect to © European Southern Observatory (ESO) 2000 Online publication: September 5, 2000 |