6.1. The magnetic field in the halo
The available polarization measurements performed at the two pairs of widely separated wavelengths allowed us to determine the magnetic field structure in two regions along the line of sight. In the text above we called these regions the disk and the halo. This usage was justified in Sect. 4.3.
Our results represent the first indication of a magneto-ionic halo in a galaxy seen nearly face-on. The detection of a radio halo in an edge-on galaxy is a difficult observational problem, even more so the determination of the magnetic field structure. In the galaxies seen nearly face-on some of the difficulties are alleviated. First, the halo and its magnetic field are illuminated by a strong background source of polarized emission, the disk. Second, the polarization measurements over the entire disk can be used to reveal the global azimuthal structure of the field in the halo as it was done in the present paper. It is important to note that the magnetic field in M 51 has different structures in the disk and the halo. If the field structures were similar to each other, the detection of the magneto-ionic halo might be difficult.
According to our fits we estimate the halo radius to be about 10 kpc. This estimate agrees with the data on X-ray emission from M 51 which also indicate a halo radius of about 10 kpc (Ehle et al. 1995).
With the values of and Z from Table 2, the estimated strength of the regular magnetic field in the halo decreases from about 3µG at the radial distance of 3-6 to about 1µG at -9 kpc. The field is basically axisymmetric. The upper limits on the mode in the halo are estimated from our fits as and for -6 and 6-9 kpc, respectively.
It is interesting to compare the values of the regular magnetic field in the halo with the upper limit on the total magnetic field strength estimated from the equilibrium between thermal and magnetic energy densities in the X-ray emitting gas (Ehle et al. 1995). With and a volume filling factor of 0.8, their results yield . Our results are consistent with this limit. If the true total field strength is close to the above upper limit, the turbulent field in the halo has a strength of about 6µG exceeding that of the regular magnetic field.
The global field directions are in general opposite in the disk and the halo of M 51. This implies that the regular magnetic field in the halo cannot be simply advected from the disk. Such reversals appear in the dynamo theory for galactic halos (Ruzmaikin et al. 1988, Sect. VIII.1; Sokoloff & Shukurov 1990; Brandenburg et al. 1992) and could be due to the topological pumping of magnetic field by a galactic fountain flow (Brandenburg et al. 1995). Moreover, the dominance of the axisymmetric field in the halo is also consistent with the mean-field dynamo theory which predicts that non-axisymmetric magnetic modes can be maintained only in a thin galactic disk and most likely decay in a quasi-spherical halo (see Ruzmaikin et al. 1988). We cannot say anything about the parity of the halo field with respect to the midplane because the galaxy is not transparent at in the rings where the halo is present and, in addition, the synchrotron emission from the halo is negligible.
6.2. The azimuthal structure of the field
The azimuthal distributions of polarization angle in M 51 seen over the radial range -15 kpc are successfully represented by a superposition of only two azimuthal modes of the large-scale magnetic field, and in the disk.
Even though we restrain ourselves from identifying these magnetic harmonics with dynamo-generated axisymmetric and bisymmetric modes before a more careful theoretical analysis has been made, we mention that dynamo theory also predicts that the two leading azimuthal modes and typically dominate in spiral galaxies. Furthermore, it follows from the dynamo theory that non-axisymmetric magnetic structures should be more often a superposition of the two azimuthal modes than a purely bisymmetric mode (Ruzmaikin et al. 1988, p. 231; Beck et al. 1996). A similar superposition of modes, but with a dominance of the bisymmetric mode, was found earlier in M81 by Sokoloff et al. (1992) (see also Krause et al. 1989b). In M31 the axisymmetric magnetic mode is dominant (Ruzmaikin et al. 1990), and for NGC 6946 a superposition of and magnetic modes was suggested by Beck & Hoernes (1996).
Of course our results do not imply that higher azimuthal magnetic modes are not present in M 51, but only that the accuracy of the available observations is insufficient to reveal them. One can expect that the amplitudes of the harmonics with are considerably smaller than those of the modes and 1.
Since the theory of the galactic mean field dynamo predicts an efficient generation of the bisymmetric mode in M 51 with the maximum of the eigenmode at (Baryshnikova et al. 1987; Krasheninnikova et al. 1989), we are tempted to identify the mode revealed for with a bisymmetric field generated by the dynamo. This suggestion is confirmed by the closeness of the pitch angles and of the and 1 modes to each other in the two innermost rings: this is typical of the dynamo-generated fields in a thin disk (Ruzmaikin et al. 1988). This conclusion is also plausible for -12 kpc. We also note that a nonlinear dynamo model of Bykov et al. (1996) predicts a mixture of magnetic modes, which is roughly similar to that detected here, to be found in some vicinity of the corotation radius, i.e. just near 6 kpc in M 51.
The azimuthal modes inferred for the outermost ring can be hardly identified directly with the dynamo modes because the pitch angles of individual modes are positive. These modes rather arise due to distortions imposed by non-axisymmetric density and velocity distributions possibly caused by the encounter with the companion galaxy NGC 5195 (Howard & Byrd 1990). Concerning the total horizontal regular magnetic field, its pitch angle is negative for and positive in the rest of the sectors. Inspection of polarization maps in Fig. 1 confirms that the pattern of polarization angles at these radii in the northern part is strongly distorted on a rather large scale.
6.3. Inner and outer spiral structure
Inspection of Table 4 shows that for the disk most of the fitted parameters of the inner rings ( kpc) differ systematically from those of the outer rings. The phase angle varies by about between the rings at 3-6 kpc and 6-9 kpc, and also between 9-12 kpc and 12-15 kpc, but not between 6-9 and 9-12 kpc. The inner pattern is more coherent and has stronger magnetic field than the outer pattern. Thus it seems that the magnetic field structure in the outer rings is not a smooth continuation of the structure in the inner rings, but that rather two distinctly different magnetic field structures are present in M 51.
This result is very interesting as Elmegreen et al. (1989) showed, using optical plates, that M 51 contains an inner and an outer spiral structure which are overlapping between kpc and kpc. The inner Lindblad resonance, corotation radius and outer Lindblad resonance of the inner structure are kpc, kpc, and kpc, respectively. The outer spiral structure is dynamically coupled to the inner structure as with kpc. Elmegreen et al. also found a phase jump in the spiral mode at kpc, the boundary between the two spiral structures This is consistent with the inner and outer spirals being two separate features with different pattern speeds, which are and , respectively. The outer spiral arms are thought to be material arms driven by the companion, whereas the inner spiral arms are due to density waves caused by the outer arms.
A discontinuity in the magnetic field pattern indicates that different physical effects contribute to the field structure at and . The discontinuity occurs at the radius where the inner spiral structure ends and the outer spiral structure becomes dominant. Therefore, the two magnetic field structures can be physically connected with the inner and outer spiral patterns proposed by Elmegreen et al. (1989).
The relatively strong magnetic field and its regular pattern in the inner region are compatible with the idea of a dynamo acting under more or less steady conditions. In the outer regions, where the spiral arms are produced by a recent encounter with NGC 5195 about years ago (Howard & Byrd 1990), the magnetic field may be the remnant of an older one disrupted by the velocity perturbation. Therefore it is understandable that the pitch angles are irregular and the values of and are small.
We note that at kpc the maxima in polarized intensity are not located on the spiral arms but in between the arms (see Fig. 1a) as is also the case in M81, IC 342, NGC 1566 and NGC 6946 (Krause et al. 1989a, b, Ehle et al. 1996, Beck & Hoernes 1996). This suggests that the interaction between the density-wave spiral arms and the magnetic fields is more complicated than simple compression by shock waves. As the inner and outer spiral structures are different in physical nature, it is interesting to know whether or not the polarized intensity is enhanced in the interarm regions of the outer structure as well. A close inspection of Figs. 1a and 1b yields that at kpc in the sectors to the polarized emission is at maximum in between the arms, whereas in the southwest in the sectors to there are maxima on as well as in between the arms. The tongue in polarized emission at 2.8 cm running south along seems to be located on the arm. However, higher resolution is required to confirm this coincidence.
We conclude that the magnetic field pattern in the disk of M 51 appears to be not one global structure, but consists of an inner pattern associated with the inner spiral structure of density wave arms and an outer pattern related to the outer spiral structure of material arms. The interaction between magnetic fields and the spiral patterns is not yet understood.
6.4. Pitch angles of the magnetic field and of the spiral arms
The pitch angle of the fitted regular magnetic field is given by
The pitch angle is constant with azimuth only when the field is represented by a single mode (that is, either or vanishes) or when the two modes have equal pitch angles, . The former is the case for the halo, where . However, the field in the disk has a varying pitch angle because and slightly differ from each other at -12 kpc (if the median values are considered) and exhibit a stronger difference in the outermost ring.
A comparison of the pitch angles of the magnetic field and the spiral arms may provide important clues to their interaction, whose physical nature still remains unclear.
We compared the pitch angles of the magnetic field in the disk derived from Eq. (10) with the pitch angles of the dust lanes running along the inside of the optical spiral arms as tabulated by Howard & Byrd (1990). In each ring the optical pitch angles were averaged in the same sectors as were used for the model fits (see Fig. 8). The comparison was possible only for the inner two rings, as at larger radii the measured optical pitch angles and the magnetic model pitch angles have too few sectors in common.
Comparing the corresponding sectors we found general agreement between optical and magnetic model pitch angles. For the ring 3-6 kpc the mean of the optical pitch angles is and that of the magnetic pitch angles is , whereas for the ring 6-9 kpc these values are and , respectively. The errors are one standard deviation from the mean value and are due to intrinsic variation in pitch angle in each ring. Although the agreement is quite good, we note that the optical pitch angles show larger variations than those of the fitted magnetic field.
Altogether, we conclude that on average the magnetic field inferred from our fits is well aligned with the spiral arms, although local misalignments may be considerable (see Fig. 8).
6.5. The origin of the vertical field
Remarkably enough our analysis has revealed a vertical magnetic field only for -15 kpc even though the model has been tailored to detect this component.
For the upper limit of the vertical magnetic field can be obtained from fits with . For the sake of simplicity we used a one-component model of the magnetic field for this purpose. The resulting upper limit for a line-of-sight averaged vertical magnetic field is , or, taking for the total contribution of the disk and halo we have assuming that is uniformly directed at all positions along the line of sight. As all other results of this paper, this limit applies to the field averaged over the beam area of about .
The vertical magnetic field detected in the outer ring can be
either due to the flaring of the galactic disk with the regular
magnetic field remaining parallel to the disk surface or simply
represent a part of a general distorted magnetic pattern. In the
former case the ratios and
(vertical to radial fields for each mode) must
be close to the tangent of the angle between the disk surface and the
midplane, i.e., about 0.2 for -15 kpc (see
Table 2). However, from Table 5 we obtain
and for the mean
values. Moreover, and
must be equal to each other. This is not the case either. Therefore,
we believe that the vertical magnetic field detected at
-15 kpc is a result of strong
three-dimensional distortions in the regular magnetic field in this
ring. Such distortions seem to be natural, e.g. due to tidal effects
since this ring is far from the galactic center and closest to the
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998