Astron. Astrophys. 333, 27-30 (1998)

4. Results

We compare dynamo models for different correlation times of interstellar turbulence , which we take as a free parameter without discussing the physical origin of the turbulence.

In all our simulations we used a small seed field being a combination of a and mode and also being a mixture of a symmetric and an antisymmetric field component with respect to the galactic mid-plane. Using the symmetry parameter and the parity parameter with E total energy of the field, energy of its axisymmetric part, and energy of the even and odd field components respectively, the seed field has the values and at time .

4.1. ASS type fields between spiral arms

Models based on relative small correlation times lead to steady S0 solutions (Fig. 2, Fig. 5). The dynamo growth times are about 1.5 to 2 Gyr.

Fig. 2a-c. Magnetic field geometry for LEFT: = 30 Myr (after 3.3 Gyr), MIDDLE: = 50 Myr (after 3.3 Gyr), RIGHT: = 100 Myr (after 2.0 Gyr). The optical spiral arms are shown in light grey.

In case of = 30 Myr, which is the common standard value, we achieve magnetic pitch-angles varying between in the interarm region to in the spirals (Fig. 3). The field strength shows concentration in the interarm region (Fig. 4).

Fig. 3a and b. Magnetic pitch angles in the mid-plane at r = /2 for LEFT: = 30 Myr, RIGHT: = 50 Myr. (Both after 3.3 Gyr.)

Fig. 4a and b. Normalized field strength (solid) compared with density profile (dotted) for LEFT: = 30 Myr, RIGHT: = 50 Myr. (Position and time as in Fig. 3.)

For larger correlation times (50 Myr) we receive solutions with a more complicated geometry: The magnetic field in the very inner part of the galaxy has bisymmetric structure and rotates with a period of about 4 Gyr. In the outer parts a steady field is excited that is dominated by a S0 mode. The magnetic pitch angles vary between in the spirals and between the spirals (Fig. 3). The field concentration between the spiral arms is weakly enlarged in comparison to the model with smaller correlation time (Fig. 4). The magnetic field strength variation reaches a value of almost 30%. Having in mind that the intensity of synchrotron radiation goes roughly with (equilibrium with cosmic rays assumed), already 20% variation in B would explain the magnetic arms in e.g. NGC 6946 (cf. Beck & Hoernes 1996).

In the models with relative small correlation times the field generation seems rather based on the differential rotation that affects the dynamo induced field all over the galactic plane, whereas the diffusivity weakens the field more intensively in the spiral arms.

4.2. BSS type fields within spiral arms

In case of a large correlation time (100 Myr) the type of the dynamo changes significantly. This model leads to a S1 dynamo solution (Fig. 2, Fig. 5). Its magnetic field is clearly concentrated within the spiral arms (Fig. 6). The solution is oscillating and therefore the magnetic pitch angle varies in time.

Fig. 5. Symmetry parameter M for = 100 Myr (solid) compared with the ASS type solutions for = 50 Myr (dashed) and = 30 Myr (dotted).

Fig. 6. Normalized field strength (solid) compared with density profile (dotted) in the mid-plane at r = /2 for = 100 Myr (after 2 Gyr).

The dynamo growth time for this model is very short being about 0.1 Gyr.

We interpret this behaviour as being due to the strong -effect that works mostly in the spiral arms where the turbulent velocity is assumed as large.

Taking into account the estimation that should not exceed the turbulent velocity (cf. Beck et al. 1996), we should note that such a model is in this sense very artificial.

4.3. The role of nonaxisymmetric contributions

It can be seen from the dynamo equation that the influence of the spiral galactic profile onto the induced magnetic field is essentially based on the spiral contribution of the turbulence. The density profile contributes only via magnetic feedback, which is based on the field strength including the equipartition field , and via magnetic buoyancy. Considering an artificial model with = 50 Myr having an axisymmetric turbulence ( = const., cf. Eq.  15) but nonaxisymmetric density profile we indeed achieve a steady S0 solution with a weak field concentration and dilution respectively where the density varies most strongly (Fig. 7).

Fig. 7a and b. A model with axisymmetric turbulence contribution ( = const., cf. Eq.  15): LEFT: Normalized field strength (solid) compared with density profile (dotted), RIGHT: Magnetic pitch angles . = 50 Myr. Located in the mid-plane at r = /2, after 3.42 Gyr.

Neglecting the radial-azimuthal density profile ( = const., cf. Eq.  15) however does not show a significant effect since the field generation seems to be dominated by the turbulence contribution.

© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998
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