Astron. Astrophys. 329, 911-919 (1998)

1. Introduction

The interpretation of radio-polarization data of spiral galaxies reveals the existence of large-scale magnetic fields with very special properties. Their explanation is of high interest because galaxies are the only astrophysical configurations with observable internal flow systems - in basic contrast to stars and planets whose magnetism therefore needs a more speculative theory for explanation. In all cases very similar versions of the theory of turbulent dynamos have been developed but the results are not without difficulties. In particular, there is little success to understand the relation between the considered flow field and the associated -effect. The observed butterfly diagram of the solar activity seems to indicate a very small in the solar convection zone but the application of the widely accepted mixing-length theory does not comply. On the other hand, the observed grand design of most of the known galactic magnetic fields requires a very small inducing role of the galactic differential rotation, or - with other words - a relatively large -effect.

In the present paper, therefore, we present computations of the induction equation without dynamo terms, i.e. without alpha-effect. The fields are thus considered as generally decaying but with an unknown decay rate. While the galactic differential rotation always amplifies the magnetic fields, the interstellar turbulence will destroy them. The latter, however, is nonlinearly quenched by the magnetic field itself and its electromotive force (EMF) possesses a complex tensorial structure. It is thus not trivial to compute the resulting fields in order to compare them with the observations. The computations are performed in order to gain some insight into the field amplification caused by differential rotation, the lifetime of the magnetic field in the considered nonaxisymmetric geometry and also the existence of periods with the observed large values of both the magnetic amplitude and the pitch angles.

The key properties of the galactic large-scale magnetic field pattern are:

• [1.] Field amplitude is several G but not exceeding 10 G.
• 2. Field lines have pitch angles up to 35 .
• 3. Fields often exhibit a clear azimuthal modulation.

In the following these topics are discussed in more detail, in particular in relation to the theoretical concepts strengthened or weakened by them.

1.1. Field strength

The observed magnetic field energy is of order of the energy of the interstellar turbulence. The equipartition field strength

with density of order g/cm³ and turbulence velocity of about 10 km/s becomes 3.5 G. As the observed values are exactly of this order (Wielebinski 1993) a turbulent background of the nonlinear fixing of the induced fields is suggested. The theory here meets the discussion about the so-called -quenching. It is based on the philosophy that the magnetic feedback on the turbulence completely quenches any diffusion even with field strengths much below its equipartition value (Parker 1992; Vainshtein & Cattaneo 1992). However, the coincidence between observed fields and their theoretical equipartition value strongly favors the canonical eddy diffusivity concept with quenching in a way as described by Kitchatinov et al. (1994), Brandenburg & Donner (1997) or Ziegler (1996) for various turbulence models.

1.2. Pitch angles

The pitch angles reflect the ratio of the radial and the toroidal magnetic field strengths. Dynamos of -type are characterized by very small pitch angles, e.g. 0.001 for the sun. For galaxies pitch angles of 10-35 deg are reported. They are always decreasing outwards (Beck 1993). Such observed values indicate that the differential rotation in galaxies (basically ) does not play a dominant role in the induction equation. Frozen-in fields as a consequence of a very small magnetic diffusivity are wound up by any differential rotation up to very small pitch angles. Only for relatively large diffusivities one can thus expect to explain the observed large pitch angles. In NGC 4414 pitch angles up to 45 have been found (see below, Urbanik 1997).

1.3. Nonaxisymmetry

For at least one case (M81) there is a clear bisymmetric azimuthal structure so that in one magnetic arm the field spirals into the center and the other one magnetically spirals outwards. It is not trivial to explain such asymmetry of type BSS (i.e. m odd) by means of a dynamo theory (Elstner et al. 1992). In Rüdiger et al. (1993) models are presented with anisotropic -effect and large rigid-rotation core (compared to the vertical thickness of the galaxy) which should produce the desired BSS models. So far there is still no nonlinear confirmation of this result due to the complexity of working 3D dynamo codes (Moss et al. 1991; Panesar & Nelson 1992; Moss & Brandenburg 1995). In the present paper we are therefore testing the hypothesis that the BSS structures are produced by the modification of an initially uniform magnetic field by the flow field in spiral galaxies - without dynamo effect.

Of special interest is the case of NGC 6946 possessing pitch angles between 20 and 30 . As Beck & Hoernes (1996) report, the large-scale magnetic fields are concentrated between the optical spiral arms, but the asymmetry is of the ASS type. The turbulent part of the magnetic field in the spiral arm reaches 15 G while a regular field of 10 G is located in the interarm region.

It is a nonaxisymmetry without reversal of the magnetic polarity (ASS, m even). Almost no azimuthal dependence exists for the flocculent galaxy NGC 4414. It is hard to imagine this grand design magnetism as a result of the inducing action of the galactic differential rotation starting with an external uniform magnetic field. An external uniform magnetic field subject the differential rotation will always produce a BSS-type field (cf. Otmianowska-Mazur & Chiba 1995). A wound-up ASS-type field can only be produced from an initially odd-m field with radial components in the equatorial plane, e.g. quadrupoles of type S0. The existence of such a rather artificial starting field, however, is unlikely, so that flocculent galaxies such as NGC 4414 seem to require the action of a galactic dynamo (cf. Beck 1996).

© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
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