A similarity solution to the kinematic α²ω dynamo equation with time-dependent coefficients

The indication of an association between the galactic magnetic field strength and the current star formation rate in some nearby galaxies, and the possible time variation of star formation activities in a galaxy, stimulates studies on a dynamo with time-dependent parameters. A simplified kinematic α²ω dynamo equation is set up, and a similarity solution to this equation is presented. The temporal variation of the field lies solely in the temporal variation of a length scale of the dynamo. When the solution is applied to a simple slab model, it is found that only even modes exist. An example shows that the time dependence of the field can be very different from a constant parameter kinematic dynamo.