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

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5. Global structure of the regular magnetic field

In this section we derive the strength and the direction of the regular magnetic field, and we discuss the global properties of these parameters.

Results of the fits presented in Table 4 can be converted into the amplitudes of the regular magnetic field (see Eq. (7)) using the estimates of [FORMULA] and [FORMULA] given in Table 2. The results are compiled in Table 5 (of course, the pitch angles and phases of individual modes remain the same as given in Table 4). A note of caution is appropriate here: the resulting amplitudes [FORMULA] were obtained assuming that [FORMULA] is independent of azimuthal angle. For each ring we also give the strength of the regular magnetic field averaged over the azimuth, [FORMULA], where [FORMULA] with [FORMULA] for the disk and [FORMULA] for the halo. Uncertainties were calculated with allowance for errors in both [FORMULA] and [FORMULA]. The large errors, especially at 12-15 kpc, are mainly due to the errors in [FORMULA].


Table 5. Amplitudes of magnetic modes and the regular magnetic field averaged along azimuth in [FORMULA]

In Fig. 7 we show the radial variation of [FORMULA] and that of the total and regular magnetic field strengths, B and [FORMULA], obtained from the total nonthermal emission and the observed degree of polarization as described in Sect. 3.1 and given in Table 1. We note that for each ring there is a close agreement between the two values of the regular magnetic field which were obtained from completely independent physical parameters and methods. Between [FORMULA] and 15 kpc the exponential radial scale length of the regular magnetic field obtained from the synchrotron emission is [FORMULA].

[FIGURE] Fig. 7. The radial variation of the strength of the regular magnetic field obtained from our fits and averaged in the rings (circles with error bars), the total magnetic field obtained from the total intensity of the nonthermal emission assuming energy equipartition between cosmic-ray particles and magnetic field (dashed) and its regular component obtained using the observed degree of polarization (solid).

Apart from the comparison of the ring averages in Fig. 7 one could also compare the azimuthal variation of the transverse magnetic field as given by the fits with the azimuthal distribution of the polarized intensity in each ring. However, as this would require the knowledge of [FORMULA] and [FORMULA] as functions of azimuthal angle, we postpone this to a later paper.

As can be seen from Table 4 the magnetic fields in the halo and in the disk inside [FORMULA] kpc are horizontal. In the halo we have [FORMULA], [FORMULA] and [FORMULA], which means that the radial component of the regular magnetic field is directed inwards, with the azimuthal component directed counterclockwise; that is, [FORMULA] and [FORMULA] - see Eq. (8). Meanwhile, in the disk we have [FORMULA] and both are negative together with the pitch angles. Therefore, for [FORMULA] -9 kpc the radial field in the disk is directed outwards, with [FORMULA] directed clockwise at almost all [FORMULA]. We conclude that the regular magnetic fields in the disk and the halo have almost opposite directions everywhere within [FORMULA] kpc except in the northwestern part of the ring at [FORMULA] -6 kpc.

In Fig. 8 the direction of [FORMULA] in each sector is shown for the disk and the halo separately. The length of the vectors is proportional to [FORMULA] with scaling factors specified in the caption.

[FIGURE] Fig. 8a and b. Directions of the horizontal regular magnetic field in the disk (a, left) and halo (b, right) of M 51 according to the fits presented in Table 4. For clarity we scaled the vectors as follows: they are proportional to [FORMULA] in the inner two rings in the disk, to [FORMULA] in the two outer rings in the disk, to [FORMULA] for 3-6 kpc in the halo, and to [FORMULA] for 6-9 kpc in the halo. The vertical component at [FORMULA] -15 kpc was not included. The vectors are shown superimposed onto an optical picture of M 51. The sectors and rings used are indicated.

In the outer ring, 12-15 kpc, the magnetic field structure is distorted. The values of [FORMULA] and [FORMULA] differ considerably from those for [FORMULA] and are even positive. Inspection of the polarization map in Fig. 1a confirms that in the northern part the magnetic pattern at these radii is plagued by strong distortions still having a rather large spatial scale.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998