Remarkable Symmetries in the Milky Way Disc's Magnetic Field

Keywords: magnetic fields — methods: observational — Galaxy: disc — Galaxy: structure — radio continuum: ISM

Early extragalactic radio source (EGRS) Faraday rotation measure (RM) probes of the Milky Way magnetic field by Gardner & Davies (1966), and the first pulsar RM analyses by Manchester (1972, 1974) revealed a prevailing magnetic field in the local spiral arm that is clockwise as viewed from the north Galactic pole. Further study with a 555-source extragalactic RM dataset produced the discovery of a large-scale field reversal in the direction of the Sagittarius — Carina arm (Simard-Normandin & Kronberg 1979). Subsequent numerical analyses by Simard-Normandin & Kronberg (1980) found a prevailing local field pointing to l ~75°, a more complex pattern in the north Galactic hemisphere, an anomalously high off-plane, high-RM zone (‘Region A’), a ~30° angular autocorrelation scale of RMs off the plane, and a Galactic magneto-ionic scale height of ~1.8 kpc.

Confirmation of a large-scale Sagittarius — Carina field reversal has since come from several EGRS and pulsar RM studies (Rand & Lyne 1994; Han et al. 1999; Frick et al. 2001; Weisberg et al. 2004). Variants of this model have been proposed by Han et al. (2006) — a bisymmetric model with field reversals at each arm/interarm interface; Vallée (2008) — a concentric ring model having one field reversal; and Sun et al. (2008) — who concluded that a combined axisymmetric and toroidal model best describes the Galactic magnetic field. Men et al. (2008), using pulsar RMs, concluded that neither a concentric ring model nor a bisymmetric or axisymmetric field model alone suffices when attempting to describe the Galactic magnetic field.

The high density of EGRS RMs in the |b| < 4° Canadian Galactic Plane Survey (CGPS) (Brown, Taylor & Jackel 2003), and in the |b| < 1.5° Southern Galactic Plane Survey (SGPS) (Brown et al. 2007) were used to probe both small-scale (Haverkorn et al. 2006), and larger-scale field structures (Brown et al. 2007). The best-fit model of the latter has a clockwise field everywhere except for two reversals, one in the Scutum — Crux arm and the other in the molecular ring at a smaller galactocentric radius of ≈3.7 kpc. Since this work was completed, Van Eck et al. (2011) extended the previous results of Brown et al. (2003, 2007) above after closing observational gaps in the ‘mid-plane’ (|b|  3° sources. Also since this work was completed, Taylor et al. (2009) published a very large RM compilation using two closely spaced L-band wavelengths in the NVSS survey. However, the NVSS catalogue's zone of avoidance in the southern celestial sphere gives it limited applicability for this investigation since it removes approximately one-third of the 0° < |b| < 15° ‘near-plane’ zone RMs which are the focus this paper.

Conflicting conclusions among some of the above publications illustrate the difficulties in unravelling the magnetic structure of the Galaxy. This paper presents an all-sky plot of the Milky Way's smoothed RM pattern, but focuses solely on the global magnetic structure in the near-plane zone up to |b| ~15°. It uses an improved and expanded set of extragalactic source Faraday RMs of unprecedented average accuracy, most of which were derived from linear polarization measurements over a wide range of wavelengths, from λ ~2 cm to λ ~23 cm.

The smoothing ‘beam’ of ~21° is comparable to a spiral arm (and inter-arm) width dimension, thereby providing a resolution comparable to some current magnetic field images of nearby external galaxies such as M51. In the ‘above-disk’ RM sky, the smoothed RM patterns are quite different from those near the disk. Interpretation of the |b|  12° RM sky requires a three-dimensional modeling analysis, and this will be the subject of a following paper (Pshirkov et al. 2011).

We use a new 2257-RM compilation of ≃1500 revised and more accurate EGRS RMs of our own (Newton-McGee & Kronberg, in prep.), combined with the published CGPS/SGPS RMs, and smaller published lists from Klein et al. (2003), and from Mao et al. (2008). These RM surveys also enable us to explore the match between the ‘in-plane’ RMs, mostly the CGPS/SPGS data, and the ‘near-plane’ RMs from our own new data, both above and below the Galactic plane.

Figure 1 shows an equal area, all-sky projection of the smoothed RMs. The RM smoothing method is described in Simard-Normandin & Kronberg (1980), in which an iterative calculation of the mean RM was performed at each source location, RM (l _i , b _i ), using all neighbour source RMs within a 15° radius. At each iteration for a given source, RM values >1.3σ from the mean were eliminated as ‘outliers’, and a minimum of 4 RMs was required to define a smoothed RM value at that (l, b). We retested their outlier rejection criterion of ~1.3σ, using both higher and lower σ trial rejection levels, and confirm that it is optimal. The criterion was to minimize the distribution width in ∣RM∣ of Galaxy-corrected RMs using only sources at high |b| where the Galactic contribution to RM is smallest compared to the source-to-source RM scatter.

Figure 1 An all-sky equal-area projection RM plot of the smoothed RMs from our 2257-source compilation of extragalactic source RMs. The smoothing method is described in the text.

In the southern Galactic plane from l ≈ 270° to l ≈355°, one major RM sign change occurs at our smoothing resolution, at l ≈ 310° (Figure 2(a)). We note that changes of RM sign on smaller scales have been found in the ‘mid-plane’ zone by Brown et al. (2007), and Van Eck et al. (2011). Our smaller number of sign changes is purely an effect of our smoothing half-width, ≈21°, which averages over some (real) smaller-scale RM sign changes. This also applies to other l-zones near b = 0°, and at some higher latitudes that we do not discuss in this paper. Our method effectively isolates larger-scale RM features in the vicinity of the Milky Way disc, as they would be seen by an extragalactic observer.

Figure 2 Panel (a): Plot of all smoothed RMs having |b|  <10° versus l. Panel (b): Smoothed RMs with reversed sign and ‘flipped’ about l = 0°. Panel (c): As in (b) except ‘flipped’ about l = 349° (–11°).

The analysis that follows focuses on |b|  15°. It imposes cuts of the RM data variously, and as discussed below, at |b| = 2°, 5°, 10°, 12°, — and finally 20° to explore the outer |b| limits of the disc-associated field (Section 3.3). Putting these angles in the context of disc z-heights, an RM sightline at |b| = 10° corresponds to a 1.4 kpc z-height in the Milky Way disk at 8 kpc from the Sun. This reference value of 1.4 kpc is similar to several estimates of the disc magneto-ionic scale height (e.g., Simard-Normandin & Kronberg 1980 and more recent analyses). It is also comparable to the galaxy's synchrotron radiation thick disc height of ~1.2–1.9 kpc (Beuermann et al. 1985), and to the ionized gas z-height estimate (Gaensler et al. 2008).The following analysis indicates clear large-scale patterns and symmetries on our side of the Milky Way disc that were either not previously apparent, or as clear.

The smoothed RMs for |b| < 10° are shown in Figure 2(a). The second Galactic l-semicircle is then folded, at l = 0°, onto the first. When we then reverse the RM signs in this folded semi-circle (Figure 2(b)) a clear symmetrical and anti-symmetrical pattern emerges in the smoothed RMs. Specifically, the forms of the smoothed or averaged RMs are strikingly similar, but they have opposite signs on opposite sides of the Galactic center.

Figure 2(b) also shows clearly that the Galactic centre direction, l = 0°, is not the correct symmetry axis. An 11° relative shift of the folded datasets needs to be applied — i.e., fold, invert sign, and shift, in that order. This same order is followed throughout the paper. For optimum determination of this shift, we examined RMs between 44° to 76° of the post-shift folding centre, and applied a least squares minimization of the residual as a function of shift angle. Figure 2(c) shows the remarkably good overlap that results. This shift corresponds to a pointing of the prevailing local B-field to l = 84.5 ′ 1°, i.e. inward from the l = 90° tangential by 5.5 ′ 1°.

Independently, when we examine the all-sky RM map in Figure 1 at higher latitudes near l = 180°, a similar change from negative to positive RMs is evident near the anti-centre direction nearly all the way to the South Galactic Pole. Above the plane, a similar negative-to-positive RM ‘border’ can be traced as far as b ≃ +45°, where it then follows a different sign boundary near to the b = 45° line. We do not attempt to interpret this latter northern high-latitude wandering here, except to note that Frick et al. (2001) attribute the north — south pattern asymmetry at higher |b| to either a stronger field in the southern Galactic hemisphere or to the Sun being located close to the top of a magnetic loop.

The l = 84.5 ′ 1° magnetic direction is very close to the value of l = 82.8 ′ 4.1° for local field lines derived from starlight polarizations by Heiles (1996), after correcting for larger-scale spiral arm curvature. In general, any magnetic pitch angle determination will slightly depend on precisely what distance range from the Sun is defined as local. Since our Galactic disk RMs represent typical pathlengths up to several kpc through the disc (see Section 2), this remarkably close agreement between the present analysis and the Galactic curvature-corrected starlight polarization results may be partly coincidental. The agreement with completely independent starlight polarization results is nonetheless worth noting.

The patterns seen in Figure 2 indicate that an extragalactic observer would see at least our side of the Milky Way disc with a very patterned and organized magnetic spiral structure, with a local pitch angle of 5.5° near the location of the Sun. This, combined with the symmetrical and antisymmetrical RM patterns seen in Figure 2, strongly indicates that the Milky Way disc is laid out like other ‘magnetically organized’ spiral galaxies.

We now repeat the procedures in Figure 2, using sources having |b| < 10°, but omit the RMs at the very low latitudes (|b| < 2°), i.e., close to the Galactic mid-plane. We also exclude any CGPS RMs that are found up to |b| = 4°. This leaves 210 RMs from our compilation at 2° < |b| < 10°, and these are spread around the entire l circle. As mentioned above, all the (l, b) subset exclusions were done before re-smoothing.

Figure 3 shows patterns that are virtually identical with Figure 2(a), including the crossover points. Application of our fold–reverse–shift–optimize technique in Figure 2(b) and (c) yields the same best-fit spiral pitch angle, l ₀ = 84.5° ′ 1°, as when the |b| < 2° RMs are included. The same result (not shown) is also obtained for the ‘|b| < 2° only’ subset of RMs. This result is notable for two reasons. (1) The close agreement occurs between two key non-overlapping datasets — our source sample above |b| = 2°, and the CGPS/SGPS RMs at the lowest |b|s. This also provides a convincing posterior check on the reliability of both RM data sets. (2) Astrophysically, it demonstrates a close coupling between the magnetic field structure in the ISM of the in-plane zone, and at ∣z∣-heights up to ~1 kpc away from the mid-plane.

In the above we did not distinguish RM data above and below the plane. We next test for magnetic sign asymmetries and antisymmetries across the Galactic plane. As in Figure 3, we omit all RMs at |b| < 2°. To have adequate statistics for this purpose, we slightly extend the upper boundaries in |b| to ′12°. Then we re-apply the fold–reverse–shift–optimize technique separately for RMs at –12° < b < –2° and +12° > b > +2°.

Figure 3 Plot of the smoothed RMs around the Galactic plane as in Figure 2(a), but excluding all the CGPS and SGPS sources, and all other sources at the lowest Galactic latitudes below |b| = 2°.

The same best fit procedure for the prevailing Galactic B-field direction gives l ₀ = 84.5 ′ 2° in the negative b range, and l ₀ = 86.5 ′ 2° in the positive b range. The magnetic field patterns in l are therefore the same within the error limits, above and below the plane, 84.5° (or 11° relative shift after folding). They also agree with the ‘full-plane’ results in Figure 2.

The respective plots are combined in Figure 4. Here we see that, at our ~21° smoothing resolution, the sign of the prevailing disc magnetic field pattern does not change through the mid-plane. More explicitly, within the longitude boundaries l ~280° to ~60° (the ‘inner’ longitude range) where the RM signs change with l, these changes replicate locally with even symmetry, i.e., RM(+b) ≃RM(–b).

Figure 4 Separate plots of the smoothed RMs around the Galactic plane, splitting by negative b (open circles) and positive b (filled circles), and extending the upper |b| limit of data selection to ∣12∣°. It demonstrates the consistency of the prevailing magnetic field sign across the Galactic disc.

It is important here to emphasise that, at these inner longitudes, the even RM sign symmetry across the mid-plane just demonstrated in Figure 4 holds only at latitudes within the |b|  15° zone of the galactic disk that that we have been discussing. At some ‘inner’ longitudes, sign changes in certain l ranges do occur beyond |b| ~15°. This can be seen in Figure 1, and partially seen in the (un-blanked portion of the) RM distribution of Taylor et al. (2009). The nearest approximation to our cross-plane sign symmetry result was obtained by Frick et al. (2001) in their wavelet analysis of the 555 RM dataset of Simard-Normandin et al. (1981). Our new combination of the CGPS and SGPS plus the |b|  15° subset of our new 1500 RMs can now more precisely clarify how, and at what off-plane latitudes, systematic changes in RM sign with b do occur. The RM sign symmetry in b qualitatively confirms the conclusion of Frick et al. (2001), but contrasts with the conclusion of Jansson et al. (2009) on RM sign antisymmetry with respect to b. However, RM antisymmetry does occur at some longitudes if all RMs at |b| < 15° are blanked out.

Outward of l ~280° (l < 280°) and of l60°, the Galactic field has the same prevailing sign above, in, and below the Galactic plane. This includes the ‘in-plane’ RM regions of the CGPS and SGPS (|b| < 4° and <1.5°, respectively). Below the plane, the RMs keep the same prevailing sign at all l ranges from l  60° to l  330° right down to the South Galactic Pole. These results confirm that the symmetry of ‘outer longitude’ RMs with respect to the mid-plane is consistent with an overall quadrupole (even) symmetry of the large scale field. This question is further investigated in a following paper that analyses the entire |b| > 10° RM data of Figure 1 (Pshirkov et al., 2011).

Note the general point of distinguishing outer l’s (i.e., toward the anticentre) from true radial distances from the Sun to the outer Galaxy.

Finally, we revisit evidence for the thickness of the magnetic field coherence zone in our vicinity of the Milky Way disc. To do this, we raise the upper |b| boundary further from the plane, recalling that |b| = 10° corresponds to a 1.4 kpc z-height at 8 kpc distance (approximately the distance to the Galactic centre). Our RM smoothing resolution at this distance is close to optimal for this purpose. To put our RM smoothing ‘beam’ in a wider scale context: at 6 kpc distance our ‘beam’ is roughly comparable to (a) the full width of the spiral arm ionized gas; (b) a spiral arm width in HI in the Galactic (x, y) plane; and (c) approximately an inter-arm separation.

As the selection boundaries of |b| increase away from |b| ~10°, the sharp features and symmetries seen in Figures 2 and 3 become progressively less distinct. Figure 5 shows all smoothed RM points having individual RMs pre-selected to 5° < |b| < 20°. While the distinctive shapes in Figures 2 and 3 can still be recognised, they are no longer as pronounced. That is, our fold–reverse–shift method no longer produces a clear merging of patterns, and the underlying spiral pattern ‘fades away’ as we proceed toward the Galactic halo. In this way we have established the approximate transition zone between the Milky Way's magnetic disk and halo, which is in the range 1–2 kpc above the Galactic mid-plane. The location of this transition agrees with the conclusion of Jansson et al. (2009), based on a combination of the WMAP 22 GHz data and a smaller set of RMs.

Figure 5 Plot of the smoothed RMs as in Figures 3 and 4, but including only RMs at a higher range of 20° > |b| > 5°. Points above the plane (diamond symbols) and below it (square symbols) are distinguished.

We have discussed new and striking underlying magnetic field patterns in the Galactic disc by suitably analysing an expanded and revised compilation of 2257 extragalactic RMs. The unprecedented clarity of our results comes from: (1) the increased numbers, and wide λ² range used for RMs immediately around the Galactic plane; and (2) our chosen smoothing scale, corresponding to z ~1 kpc at a distance of 6 kpc, preferentially detects features on a spiral arm and inter-arm scale up to ~8 kpc from the Sun. Our analysis is thus sensitive to the large-scale underlying magnetic geometry of the Galactic disc and favours longer Galactic path lengths.

The RM variations in a band from b = +10° to –10° about l = 0° around the Galactic plane show clear and sharp sign changes. There is striking mirror symmetry about a reference direction l = –5.5°. This gives a precisely determined, l = 84.5 ′ 1° (i.e., l = 90 – 5.5°), mean magnetic field direction in the vicinity of the Sun — more precisely determined than in earlier analyses. In a three-dimensional representation, this inward spiral tilt occurs over the approximate ~1.5 kpc z-height of the Milky Way disc, at least in our broad Galactic vicinity. We clearly rule out a circular magnetic field pattern near our Galactic radius. The distinct ‘softening’ of the RM(l) patterns at |b|  15° in Figure 5 indicates that these global patterns are confined to z-heights within 1–2 kpc of the Milky Way's disc, and that other magnetic patterns emerge as we proceed further from the Galactic plane into the halo.

We have shown in Section 3.2 that the prevailing magnetic field direction does not change sign across the galactic disc, i.e., that the magnetic field sense is even with respect to z = 0. This applies at all l ranges at |b| < 12°, i.e., where B changes sign with l, the same sign is locally preserved on the opposite side of the Galactic plane. It is consistent with, but does not uniquely confirm, the quadrupole symmetry predicted by dynamo theory (e.g., Vallée 1992).

The improved definition of the magnetic structure of the Galactic disc is of interest for understanding and comparing the global magnetic structure of the Milky Way and other galaxies, and their evolution (e.g., Beck et al. 1997; Shukurov et al. 2006), and for understanding the propagation of charged, very-high-energy cosmic ray nuclei through our Galaxy (e.g., Auger Collaboration 2007).