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Astron. Astrophys. 318, 700-720 (1997)

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1. Introduction

M 51 (NGC 5194) is the first external spiral galaxy from which linearly polarized radio emission was detected (at [FORMULA] cm by Mathewson et al. 1972, and at [FORMULA] and 21.2 cm by Segalovitz et al. 1976), and for which the global structure of the regular magnetic field highlighted by these observations was investigated (Tosa & Fujimoto 1978). It is also the first galaxy for which the discovery of the so-called bisymmetric magnetic structure was claimed (Tosa & Fujimoto 1978), a configuration of magnetic field which was later suspected for some other nearby spiral galaxies (see Krause 1990, Beck 1993 and Beck et al. 1996 for a review). The explanation of the origin of the bisymmetric magnetic fields has become one of the major challenges to the theory of galactic magnetic fields of the last decade.

Later observations of M 51 with better sensitivity and resolution (Neininger 1992a; Horellou et al. 1992; Neininger et al. 1993a; Neininger & Horellou 1996), and also a more careful analysis of the observational data, revealed a magnetic pattern which is considerably more complicated than a simple bisymmetric structure. This is true also for some other galaxies, e.g. M83 (Neininger et al. 1991, 1993b).

One of the goals of the present paper is to introduce and test a general way to represent the complicated magnetic patterns observed in galaxies in terms of a tractably small number of parameters. Hopefully, this will facilitate a fruitful confrontation of theory with observations. Such a parametrization can be conveniently performed in terms of the Fourier expansion of the magnetic field in azimuthal angle. The lowest Fourier harmonic corresponds to the axisymmetric magnetic field, the next higher one to the bisymmetric mode, etc. However, we emphasize that the Fourier harmonics thus derived are not necessarily connected with the dynamo modes (see Sect. 4.1) and their physical meaning should be established using models of the magnetic field generation and evolution in a given galaxy.

We attempted to build a coherent, self-consistent picture of the global magnetic structure based not only on the Faraday rotation analysis, but also on other available information coming from, e.g., intrinsic polarization angles, depolarization data, total synchrotron emission, thermal radio emission, the morphology of the galaxy, etc.

On pursuing our goals we used recent multifrequency observations of M 51, which allowed us to distinguish two magneto-ionic layers along the line of sight (the disk and halo) with significantly different magnetic fields.

We adopted the following parameters of M 51: centre coordinates [FORMULA] (Ford et al. 1985), a position angle of the major axis of [FORMULA] measured counterclockwise from north, an inclination angle [FORMULA] ([FORMULA] is face-on - see also Appendix A) (Tully 1974), and a distance to M 51 of 9.7 Mpc (Sandage & Tammann 1974).

The structure of the paper is as follows. In Sect. 2 we briefly discuss the observational data used. In Sect. 3 the number density, scale height and filling factor of the thermal electrons, as well as the scale height of the synchrotron disk and the equipartition strength of the regular and turbulent magnetic fields are estimated for M 51. We also clarify the importance of depolarization effects and estimate the depth within the galaxy visible in polarized radio emission. Section 3 is concluded by an analysis of Faraday rotation measure produced in a partially transparent layer. In Sect. 4 we propose a method of interpretation of multi-frequency polarization observations of spiral galaxies aimed at the determination of the three-dimensional structure of the galactic magnetic field. In this section we also present the results of our fits to the observed polarization angles in M 51. We estimate the global properties of the magnetic fields in Sect. 5 and discuss our results in Sect. 6. Conclusions are briefly summarized in Sect. 7. The statistical tests employed and the method for estimating uncertainties in our fitted parameters are discussed in Appendix B. For the reader's convenience the basic notation is compiled in Appendix C.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998