Helicity Constrained Model of a Galactic Dynamo

Abstract

Magnetic fields correlated on kiloparsec scales are seen in disc galaxies. The origin could be due to amplification of small scale seed fields by a turbulent dynamo. Helicity conservation imposes constraints on dynamo action and one can study the minimal field strength of the large scale magnetic field that could arise despite the constraint. The calculation of helicity is technically complicated because of open boundaries and the usual form for the MHD invariant needs to be modified to take this into account. A general formalism has been developed to calculate the field strength using a quasi-linear dynamo model. As a first step, a galactic disk dynamo model has been built analytically while making the usual assumptions of shear and the alpha effect. We find quadrupolar solutions that are matched to a vacuum field with D = 11. The general approach to solving the quasi-linear dynamo using the full set of relative helicity boundary conditions are described