2 The alignment of magnetic and velocity fields

As noted by Beck et al. (1999), the regular magnetic field in the bar region of NGC 1097 seems to be aligned with the velocity field of A92, especially in regions with stronger velocity shear. This can be seen from a comparison of Fig. 1, where we present the polarization map of NGC 1097, with the magnetic field orientation indicated with dashes, and Fig. 2 where a velocity field from A92 is shown. Such an alignment is not typical of normal spiral galaxies where magnetic field lines are inclined to the streamlines by $10^\circ{-}30^\circ$, presumably due to the dynamo action (e.g., Beck et al. 1996; Beck 2000; Shukurov 2000). In the presence of a strongly sheared velocity, the local structure of the magnetic field will be controlled by the local velocity shear. In barred galaxies, the shear of the noncircular velocity field is strong enough to make the form of their magnetic fields markedly different from those found in normal spiral galaxies.

Ignoring the effects of dynamo action, the large-scale field will be frozen into the flow in regions with , where $u\simeq 100\,{\rm km\,s^{-1}}$ is the regular shearing velocity, $L\simeq 3\,\,{\rm kpc}$is its scale in the bar region, and $R_{\rm m}$ is the magnetic Reynolds number based on the turbulent magnetic diffusivity $\eta$. Thus, the field will be aligned with the flow if .

Figure 2: The velocity and gas density (grey scale, lighter shades correspond to higher values) fields in the frame corotating with the bar, from Model 001 of A92. The sense of rotation is clockwise. The bar major axis is at an angle of $45^\circ$ to the vertical, the frame radius is $8\,{\rm kpc}$ and the corotation radius is $r_{\rm c}\approx 6\,{\rm kpc}$.

However, the alignment of magnetic field and the flow can be affected by dynamo action even at large values of $R_{\rm m}$. Dynamo action is needed to maintain the global magnetic field against the effects of winding by differential rotation and tangling by turbulence, which would lead eventually to enhanced Ohmic decay. Therefore, we also require that the dynamo is unable to misalign the field and the streamlines: the local growth rate of the magnetic field $\gamma$ must be smaller than the shear rate, i.e. with $\gamma\simeq D^{1/2}\eta/h^2$, where $D=\alpha uh^3/(L\eta^2)$ is the local dynamo number, h is the disc semi-thickness, and $\alpha$ is the alpha-coefficient. This yields , or , where $v_{\rm t}$is the turbulent velocity and $\alpha\leq v_{\rm t}$ (since $\alpha$ cannot exceed the turbulent speed - see, e.g., Sect. V.4 in Ruzmaikin et al. 1988). In normal galaxies where u is dominated by the streaming velocity produced by the spiral pattern and so $L/h\simeq2{-}3$ and $v_{\rm t}/u\simeq 1$, this inequality is not satisfied and we can not expect strong alignment between the streamlines and magnetic lines. Indeed, the magnetic pitch angle (i.e. the angle between the regular magnetic field and the streamlines) is about 1/3 radian, plausibly consistent with this estimate. On the other hand, the shear rate u/L is significantly larger in barred galaxies and we can expect a much closer alignment in the regions where and , where the above inequality is satisfied. In other words, we expect that barred galaxies contain large regions where dynamo action is overwhelmed by the local velocity shear resulting in a tight alignment of the magnetic field with the shearing velocity (more precisely, with the principal axis of the rate of strain tensor). On the other hand, there may be regions of enhanced diffusivity and/or reduced shear where the alignment is reduced (see Fig. 7).

The velocity field, but not the magnetic field, looks different in the inertial and corotating frames. We can expect a rather close general alignment between $\vec B$ and $\vec u$ in the reference frame corotating with the bar for the following reason. Nonaxisymmetric magnetic field patterns must rotate rigidly to avoid winding up by differential rotation (and it is the dynamo which can maintain such fields). With a nonaxisymmetric perturbation from the bar (or spiral arms), the magnetic modes that are corotating with the perturbation will be preferentially excited (e.g. Mestel & Subramanian 1991; Moss 1996, 1998; Rohde et al. 1999). Thus, the regular magnetic field will corotate (or nearly corotate) with the bar, and this is a physically distinguished reference frame. (All magnetic field configurations discussed in this paper, except those in Sect. 4.5, do exactly corotate with the bar.) So, an approximate alignment between $\vec B$ and $\vec u$ is expected in the corotating, but not in the inertial, frame.