LARGE-SCALE NONLINEAR LIMITING OF GALACTIC ALPHA-2 OMEGA-DYNAMOS

We perform axisymmetric MHD simulations for galactic (thin disc alpha2omega-dynamos with field-independent alpha-functions, in order to reveal the mechanism of the nonlinear back-reaction of large-scale dynamics on to the induction equation. The amplitudes of the magnetic field and the velocity field, after exponential growth with time, attain steady values with non-negligible oscillations. As was predicted in our earlier paper, the - B(phi)partial derivative V(z)/partial derivative z term in the equation for partial derivative B/partial derivative t is the cause of the non-linear limiting. Estimates for the steady amplitudes are given in an appendix, and they are in rough agreement with the simulation results. The steady amplitude of the velocity field is proportional to the linear growth rate multiplied by the disc thickness. The steady amplitude of the magnetic field satisfies the relation B2/8pi approximately rho0 C2 x a numerical factor x a numerical factor. The first numerical factor is a function of the linear growth rate and the period of the oscillation, while the second comes from the large-scale buoyancy effect. The steady amplitudes take various values, according to the parameters of the system. Consequently, if strict equality between the magnetic energy density and kinetic energy density of small-scale chaotic motions holds for all galactic discs, small-scale non-linear limiting must be operating. A few simulations with a field-dependent alpha-function of the Vainshtein type exhibit different spatial structure of the steady state and different temporal behaviour from the field-independent alpha-function cases, and these may be important from the observational point of view.