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Astron. Astrophys. 329, 895-905 (1998)

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6. Three dimensional calculations

In this section we discuss only results obtained using the Model I velocities. We attempted to compare the results described in Sect. 5.1, obtained by using the 2D code, with those from a comparable calculation, for the same velocity data, using the 3D code. After some experimentation we adopted parameter values [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] cm2 s-1, [FORMULA] kpc for the simulations described below. Thus the value of [FORMULA] in [FORMULA] is [FORMULA] cm2 s-1. It is plausible that the halo values of [FORMULA] may be rather larger than [FORMULA] cm2 s-1, but we chose the above value for computational convenience (smaller values of [FORMULA] require a finer z -mesh). However our results are not very sensitive to the precise values of these parameters. We set [FORMULA], close to, but a little reduced from, the nominal value, of 3.75 and [FORMULA] corresponds to a maximum value of [FORMULA] of 1.5 km s-1 at [FORMULA]. The integration grid had NI  = NJ  = 101, NK  = 41.

The code was run for approximately 2 Gyr using the Method 1 reduction of the raw velocity data. For these calculations we used the velocity field mentioned in Sect. 5.1in connection with Fig. 3, that is a slightly modified form of that used for the majority of the calculations using the 2D dynamo code. The evolution of the global energies in the azimuthal modes is shown in Fig. 6, (the normalization cannot be directly compared with that of the two dimensional calculations), and Fig. 7 gives projections of the magnetic field vectors onto planes [FORMULA] for several heights above the disc plane at time 1.2 Gyr. (Note that the length of the arrows representing the magnetic field vectors have been normalized to the maximum field strength present in each plot, and so the figures cannot be used directly to compare field strengths at different values of z.) A 2D calculation with broadly similar parameters ([FORMULA] kpc), except that [FORMULA] cm2 s-1, can be used for comparison. The evolution of the modal energies is shown in Fig. 4, and can be compared with those shown in Fig. 6, and the field structure for this run at 1.2 Gyr, given in Fig. 8, can be compared with the various panels of Fig. 7. Although clearly the field structure in the 3D case does depend on z, and the diffusion is larger in that case, the plots in Figs. 4 and 6, and those in Figs. 7 and 8 possess sufficient similarities to suggest that little additional information on the [FORMULA] structure of the fields is being revealed by the 3D simulation. Thus we did not pursue these 3D calculations further.

[FIGURE] Fig. 6. Variation of energies in modes [FORMULA] for 3D calculation described in Sect. 6. The unit of time is 28 Gyr.

[FIGURE] Fig. 7. Snapshots of field structure projected on to plane [FORMULA] for 3D calculation of Fig. 6 with [FORMULA] kpc at t=1.2 Gyr, for [FORMULA] pc.

[FIGURE] Fig. 8. Snapshot of field structure for 2D run with parameters approximating those of Fig. 7, at t=1.2 Gyr.

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997