Statistical Properties of the Galactic Magnetic Field in the Dynamo Model with Fluctuations of the Alpha Effect and Turbulent Diffusion

Magnetic fields in galaxies are usually originated through the action of a dynamo, which is based on the helicity of turbulent flows (alpha effect) and nonrigid rotation of a galaxy (differential rotation). They are opposed by dissipation, which tends to destroy the regular structures of the field. As a rule, dynamo equations contain averaged turbulence parameters. This approach presents difficulties in the case of galaxies with a highly inhomogeneous interstellar medium, associated, for example, with star formation. One way to solve the problem is to use random coefficients in the field equations. In this case, solutions require separate statistical analysis. This paper examines various statistical moments for the galactic magnetic field within the framework of a model assuming fluctuations of the alpha effect and turbulent diffusion.