## 5. Results## 5.1. `Standard' model for NGC 6946As a main result we achieve a basically axisymmetric magnetic field
(ASS) with a clear maximum of the strength of the regular field within
the interarm regions (Fig. 4, Fig. 5a). The field is strongest at
kpc radius (Fig. 6). The
magnetic field mode The magnetic pitch angle reaches values between ("magnetic arms") and ("magnetic interarm" = gaseous arms) (Fig. 5b) and thus varies by about around the pitch angle of the gaseous arms in our models (assumed to be constant). Fig. 7 shows the mean value of the magnetic pitch angle taken in the galactic mid-plane averaged over all azimuthal angles.
## 5.2. Role of the corotation radiusThe corotation radius of the spiral pattern and the interstellar
gas influences the geometry of the magnetic field. For radii smaller
than the region with maximal
magnetic field is shifted towards the spiral arm preceding in the
sense of rotation (with enhanced correlation time); outside corotation
radius the field is shifted towards the following arm (Fig. 9). Hence,
a shift of 90
This phenomenon is expected to be due to the fact that the interstellar gas rotates faster than the spiral pattern for radii smaller than . The partially frozen-in magnetic field lines are then transported by the gas from the interarm region towards the preceding arm. For radii larger than the process works in the opposite manner. This explains the observed similarity between the magnetic arms and their preceding optical arms (Frick et al. 1999) (see also Sect. 6.3). According to Elmegreen et al. (1992) the corotation radius of NGC 6946 is located at about 2.6´ ( kpc at the distance assumed in this paper). The "magnetic arms" are observed between about 5 and 12 kpc radius (see Fig. 1) so that we would expect a phase shift with respect to the preceding arm of -. From the observational data, the mean shift is only between and for the four main arms (Frick et al. 1999, see also Sect. 6.3) which fits better to a large corotation radius (Fig. 9b). More detailed data of the galaxy's velocity field are required to determine the corotation radius with higher accuracy. Note that a behaviour opposite to that in our models was found for
the ## 5.3. Role of the spiral arm pitch angleWe further performed calculations with varied pitch angle of the gaseous arms and hence the turbulence profile (Eq. (12)). The main and striking result is that the magnetic pitch angle
is
We expect that a more complicated and more realistic spiral arm profile would not lead to qualitative different results. ## 5.4. Radial decrease of mid-plane turbulence intensity?The model we discussed in Sect. 5.1 is based on a mid-plane
turbulence intensity that does not vary in radial (and azimuthal)
direction. Since there are observations suggesting an
outward-decreasing turbulence intensity profile (Boulanger &
Viallefond 1992, see Sect. 4.3) we try to understand the consequences
of such a profile by an appropriate simulation. We chose a slightly
reduced decrease where the turbulence intensity in the galactic
mid-plane varies linearly from 14 km s Two main consequences appear being different to the `standard' model presented in Sect. 5.1: -
The absolute value of the magnetic pitch angle now decreases in the outward direction, but it has also larger values at inner radii compared with the `standard' model (Fig. 7). -
The magnetic field shows a considerable asymmetry with respect to the galactic mid-plane: The magnetic field modes A0 and A2 are excited besides the S0 and S2 modes. The asymmetry is well seen in a meridional plot of the azimuthal magnetic field () in Fig. 14b. This asymmetry leads to a strong vertical magnetic field () passing through the inner galactic disk without changing its sign which should be observable via strong Faraday rotation (Fig. 15) (see Sect. 6.4). The parity of the magnetic field is shown in Fig. 13. The asymmetry mentioned above leads to a value of 0.5 (dashed curve).
The behaviour of the magnetic pitch angle can be estimated by (Beck et al. 1996). In the linear case, the approximations
and
with the characteristic scale
height give the estimation In the nonlinear case (adopted here) a quenching function must be added in order to represent the influence of -quenching. This gives The quenching function, which in a simple estimation is (Beck et al. 1996), forces the absolute value of the magnetic pitch angle to increase outwards since the magnetic field is large around and decreases outwards. This behaviour is well seen in the calculations shown in Fig. 7 (standard model) and Fig. 18. This effect is blurred in case of outward-decreasing turbulence intensity where the absolute value of the magnetic pitch angle decreases outwards (Fig. 7, dashed). Using the estimation (17) we can also explain the enlarged magnetic pitch angles within the the gaseous arms where the correlation time is assumed to be larger than in the magnetic arms. Note that, according to Eq. (17), the same radial variation of the magnetic pitch angle occurs if one assumes a radial decrease of the correlation time e.g. because the mean size and/or lifetime of molecular clouds decreases outwards. ## 5.5. Role of the rotation curveWe discuss here how the field generation is influenced by the shape
of the rotation curve. To avoid numerical problems due to the limited
resolution of our simulations at the sharp increase of the velocity
for 1 kpc, we approximate the
rotation curve by Sofue (1996) using a Brandt-type law with
= 220 Gyr The investigation of Sofue's rotation curve leads to a magnetic field with rather small absolute values of the magnetic pitch angle due to the stronger differential rotation (Fig. 7, dotted). The magnetic field is more concentrated at inner radii (Fig. 6). The contribution of higher magnetic field modes (2) and thus the influence of the spiral arms is smaller than in the `standard' model. These field properties can be seen by comparing the magnetic fields of different models in the galactic mid-plane (Fig. 16). Note that for very inner radii the approximation of the rotation curve given in Sofue (1996) is not very accurate. Therefore we expect that, for a better approximation of the sharp velocity increase, the above mentioned differences to the `standard' model would be even larger.
© European Southern Observatory (ESO) 1999 Online publication: October 4, 1999 |