The turbulence in galaxies is assumed to be driven by a sample of stochastically occurring supernova explosions. For simplicity, we replace the complicated real flow by the velocity field of the explosions themselves. The resulting turbulence model can be used to determine the turbulent electromotive force, < u′ × B′ >, a basic quantity in the dynamo theory.
If the distribution function of the SN explosion rate is known, it is sufficient to compute the α-effect for a single explosion in a rotating, density stratified galaxy. We use an axisymmetric simulation code to determine the helical velocity field of the explosion, and consider only explosions located on the rotation axis. The (homogeneous) magnetic field is assumed to be purely vertical. Therefore, only the α
-component of the α-tensor can be obtained with this method.
The induced magnetic field fluctuations must be correlated with the velocity field in order to get the turbulent electromagnetic force. The resulting α-effect for a sample of explosions starting in the galactic midplane possesses a z-profile with an amplitude of about 60m/s. It is always negative in the northern hemisphere and positive in the southern hermisphere. The scale of the α-profile is about 60pc. The influence of the density distribution proved to be small. We consider the extreme case of uniform explosion rate and find α-values of only few meters per second for a density scale height of 100pc.