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2.1. Global field structure from RM's

The likely global structure of the magnetic field in our Galaxy can be gleaned from two examples, shown below, Messier 51 (NGC 5194) seen face-on, and NGC 891, an edge-on example. Both were imaged at more than one radio frequency, so that the local projected plane of polarization is corrected for Faraday rotation (propto lambada2) to its intrinsic orientation. Figure 1 shows a large scale ordered magnetic field component that is approximately parallel to the spiral arms. The edge-on image of NGC 891 in Figure 2 gives a projected view of the above-plane magnetic structure, which has a characteristic X-shape. The magnetic field lines are directed vertically outward above the nuclear zone, and gradually become more parallel to the disk at larger galactocentric radii.

Figure 1

Figure 1. NGC 891 imaged with the Effelsberg radio telescope, with Faraday RM-corrected, projected magnetic field orientations [1]. By permission of R. Beck.

Figure 2

Figure 2. Face-on galaxy M51, showing an overlay of the optical image, radio contours, and the RM-corrected magnetic field orientations as in Fig. 1. [2]. Reproduced from Sterne und Weltraum by permission of R. Beck.

To calculate the HECR propagation paths to us, especially below ~ 1018 eV, we need to know the 3-D magnetic structure of the Milky Way, and any superimposed magnetic turbulence. The 2-D images in Figs 1 and 2 give important clues on the Milky Way's projected global field pattern. Galactic dynamo calculations have predicted either a dipole or quadrupole field structure, and these have been so far been difficult to verify observationally in any nearby galaxy, including the Milky Way. There is some evidence to show that neither a pure dipole or quadrupole give an ideal fit to the data, but one or the other seems to give a good approximation in some restricted investigations. The 3-D off-plane structure of the Milky halo has been difficult to discern observationally because there is relatively little Faraday rotation at high Galactic latitudes (b), hence at high z-heights above the plane. Models for our Galaxy's magnetic structure are best based on an all-sky distribution of the RM's of extragalactic radio sources, and/or of (mostly Galactic) pulsars. Pulsar RM's to date have been smaller in number than their e.g.r.s. counterparts, and their RM pathlengths through the ISM cover only part of the extragalactic source pathlength. An advantage of pulsar magnetic probes is that the pulsar dispersion measures (DM) can be used, via an ISM model of ne, to model the RM path length through the Milky Way disk. Future larger numbers of RM and DM for the pulsars may lead to the most definitive 3-D Galactic disk field models for propagation paths and deflections of HE charged particles.

Meanwhile, recent progress has been made with ever larger numbers of extragalactic source RM's, as is illustrated in a recent all-sky plot of ca. 2250 rotation measures from a recent compilation made in 2009 [3]. A 3-panel plot in Figure 4 shows the clearest demonstration yet for an underlying magnetic field in our region of the Milky Way disk. This brings us to the most immediately relevant zone for calculating corrected UHECR arrival directions from outside the Galaxy.

The smoothed RM plot in Figure 4 is derived from 1500 newly determined RM's, plus ca. 750 additional RM's published in the literature. The 1500 set are an extension of the 555 RM set of Simard-Normandin, Kronberg & Button and were determined by the same 7-step procedure described in that paper [5]. They were then smoothed using a procedure developed by Simard-Normandin & Kronberg [4], which iteratively tests for, and rejects RM outliers, and/or unreliable RM values. These include genuinely anomalous RM's that deviate from the "RM consensus" in a given (l, b) direction.

Using this new compilation, Kronberg & Newton-McGee [3] produced plots, shown in Figure 5, of similarly smoothed RM's for different subsets of only low Galactic latitude RM's - in this plot only for RM's at latitudes |b| leq 15°. The smoothing full width was close to 20°, and this is near to ideal for "filtering out" an underlying coherent component of the Galactic disk field. These results, together with the higher latitude RM's in Figure 3 are being used with other input to construct propagation models to match with UHECR observations.

Figure 3

Figure 3. A smoothed representation of 2257 Faraday rotation measures in Galactic coordinates with the Galactic centre at (0,0). (Kronberg & Newton-McGee, [3]). Blue and red circles represent positive and negative RM's respectively, and the circle size is proportional to RM strength.

Figure 4

Figure 4. (a) Variation of RM's over the Galactic plane, when smoothed with a resolution roughly comparable with the width and (height) of a spiral arm. Black and orange identify RM's on either side of l = 0°. (b) The orange points are folded about l = 0°, and their RM sign is reversed (i.e. fold, reverse). (c) The difference between the curves in (a),(b) at |l| leq 90° for a range of shift angles was minimized to obtain a least squares minimized, optimum relative shift of 11° ± 2° (fold, reverse, shift).

2.2. |Bt| vs. galactocentric radius

Another all-sky investigation has used the 408 MHz all sky continuum synchrotron radiation survey of Haslam et al [6] and a more recent 1.4 GHz survey by Reich & Reich [7]. Breuermann et al [8] and more recently Berkhuijsen [9] have combined these data with various modeling assumptions to estimate the variation of total magnetic field strength, |Bt|, with Galactocentric radius in the disk plane. This is shown in Figure 5. It shows an approximately exponential decay form

Equation 1 (1)

where R0B = 11 ± 0.4 kpc. We note from Fig. 5 that |Bt| remains a surprisingly strong 4 µG at R = 17 kpc. The results in Fig. 5 give good overall agreement with similar results from Broadbent et al. [10] and more recent study by Strong et al. [11]. The latter are based on gamma-ray emission and, notably, they are independent of the CR/magnetic energy equipartition assumptions needed in the radio sky analyses.

These results lead us into the less determined metagalaxy zone, or interface to the magnetic structure of the IGM in the local Universe (Zone (5))

Figure 5

Figure 5. The variation of modeled interstellar magnetic field strength, |Bt|, as a function of Galacto-centric radius out to 17 kpc from Berkhuijsen [9]. See text for further details. Reproduced with permission from Elly Berkhuijsen.

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