## 5. Two dimensional calculations
Most of these simulations were performed with a grid defined by
, but some were repeated at higher resolution
to verify that these values were large enough. We adopted standard
galactic parameters of kpc (4 exponential
scale lengths), pc (equal to the gravity
softening parameter in the dynamical calculations), so the disc aspect
ratio is . Thus with canonical values of
cm ## 5.1. The main calculations
We used as standard velocity data that from the first calculation
described in Sect. 3(Model I), reduced by Method 1, including
azimuthal Fourier components . We did verify
that the results were not radically changed by taking We attempted firstly to complete a simulation over 10 Gyrs with
cm We now discuss in more detail a simulation with
cm
Fig. 3 shows plots of the energies in azimuthal modes against time. In these plots, the mode is clearly dominant. This might appear a little surprising given the nature of the field plots in Fig. 2. However, there are large parts of the disc where the field is predominantly axisymmetric, and the rather more striking nonaxisymmetric features are quite localized. This is more clearly seen in a short trial run with kpc, with a slightly different velocity field to that used for the calculations described above. This excludes much of the region where the field is approximately axisymmetric, and accordingly gives larger relative energies in modes - see Fig. 4. (Note that here the scale for the energies differs from that of Fig. 2.) In general, the global magnetic energy in the mode is rather less than in , and that these contributions fluctuate quite strongly, see Fig. 3.
For comparison, in Fig. 5 we show field configurations at time
1.2 Gyr for simulations with parameters ,
cm
It is clear that the larger value of adopted for Fig. 5b tends to give rather broader magnetic features and increasing the value of for fixed has the opposite effect. Note that, although in the case illustrated in Fig. 5b we have increased in keeping , this has little effect on the field geometry. ## 5.2. Test with Method 3 velocitiesWe performed a limited comparison between results obtained using velocity data obtained by use of procedures 1 and 3. For this we took a time independent velocity field, corresponding to an early epoch of the simulation, and followed the evolution of the magnetic field for about 2 Gyr. The magnetic structures obtained showed strong similarities, but for the same parameter values those obtained with the Method 3 velocities were spatially narrower and generally (and not unexpectedly) exhibited rather more shearing. ## 5.3. Results using data from the Model II dynamical simulationWe also investigated magnetic field evolution, using data from the second simulation described in Sect. 3. We used the same procedure as for the two dimensional calculation described in Sect. 5.1. Clearly, the detailed results were different. However we found that the same general features of magnetic field morphology appeared, namely ring-like and short armed structures, with vectors of magnetic field and non-circular velocities well aligned. © European Southern Observatory (ESO) 1998 Online publication: December 16, 1997 |