Revisiting Rotation Measures from the Canadian Galactic Plane Survey: the Magnetic Field in the Disk of the Outer Galaxy

The details of the CGPS 1.4 GHz observations and subsequent processing through to the final images are reported in full detail by Landecker et al. (2010); we highlight a few key parameters in Table 1. For our analysis, we have used the data from the DRAO-ST only, without the single-dish data from the DRAO 26 m John Galt telescope and Effelsberg 100 m telescope. The data for the SLE region were processed in the same way as the CGPS data. The data were supplied in the form of mosaic images, each 51 square, with a single channel-averaged Stokes I image and Stokes Q and U images for each channel. The SLE region was combined into a single 10° square mosaic.

The identification of polarized sources and determination of their RMs followed the method of Brown et al. (2003), with some improvements. For completeness, the method is described in full below, and a flowchart of the method is shown in Figure 1.

Zoom In Zoom Out Reset image size

The first step was the identification of polarized source candidates. We began with a Stokes I source list, and searched each source location for statistically significant polarized intensity. Within the main CGPS region, we used the CGPS Stokes I source catalog from Taylor et al. (2017) as the input source list; for the SLE region we used the AEGEAN source-finder (Hancock et al. 2012, 2018) with the default parameters to generate an input source list.

Each Stokes I source in the input lists was assessed for statistically significant polarized emission at the source location. This was made difficult by the combination of two related challenges: the presence of diffuse polarized emission in many regions, as well as the position-dependent noise level across the survey. To account for these factors, we determined the local noise and foreground around each source. The local off-source region around each source was defined as an ellipse with the shape of the synthesized beam (calculated at the source location, because the beam shape changes significantly with decl.) and size equal to four times the FWHM of the beam in each dimension (producing a beam-shaped region with an area of 16 beams). Pixels within this region with Stokes I levels above 1.2 mJy beam⁻¹ (approximately 5σ across most of the survey) were classified as "source pixels" and those below this threshold as "off-source/foreground pixels"; this prevented any polarization from the target source or neighboring sources from being included in the foreground calculations. Before calculating the noise and foreground in the off-source pixels, we required that there be at least five beam-areas' worth of pixels in the off-source region; if there were insufficient pixels we increased the size of the local-region ellipse by one beam FWHM in each dimension until sufficient off-source pixels were present, or until the ellipse passed 10 FWHM in each dimension, in which case the source was discarded as being part of an extended Stokes I object.

Within the off-source pixels, the outlier-resistant ⁹ mean and standard deviation were calculated for each channel's Stokes Q and U. The means were taken as the foreground polarization around the source (Q_fg, U_fg), and the rms of the standard deviations (averaging over channels and Stokes Q and U) was taken as the local value for the noise combined with the uncertainty in the foreground estimate.

Within the on-source pixels, the noise (σ_QU ) was calculated pixel-wise as the quadrature sum of the local noise determined from the off-source pixels and an instrumental leakage term, which was set equal to 0.3% of the Stokes I map (Brown 2002):

$$\begin{eqnarray*}&&{\sigma }_{{QU}}=\sqrt{{\sigma }_{\mathrm{noise}}^{2}+{(0.003I)}^{2}}.\end{eqnarray*}$$

The foreground-subtracted and debiased polarized intensity was calculated per channel, using a modified form of the equation of Wardle & Kronberg (1974), as

$$\begin{eqnarray*}&&P=\sqrt{{(Q-{Q}_{{\rm{fg}}})}^{2}+{(U-{U}_{{\rm{fg}}})}^{2}-{\sigma }_{{QU}}^{2}}.\end{eqnarray*}$$

This value was averaged over the four channels and then divided by ${\sigma }_{{QU}}/\sqrt{4}$ (where the factor of $\sqrt{4}$ accounts for the decreased noise in the channel-averaged map) to produce a map of polarized intensity signal-to-noise ratio (S/N). If any of the on-source pixels were found to have a polarized signal-to-noise ratio greater than 5, the source was classified as a candidate polarized source, and was processed through the RM determination and additional testing described in the next section.

This procedure produced a large number of false positives. In many cases, polarized pixels belonging to other neighboring sources would be included as on-source pixels, causing sources with polarized neighbors to be labeled as candidates. Another common cause was sources associated with extended Stokes I emission, which would cause many pixels to be above the threshold and thus count as on-source, increasing the odds of encountering a high-polarization outlier in the noise distribution. Since polarized intensity does not follow Gaussian statistics, especially if interferometric image artifacts are present, the threshold S/N > 5 is not as restrictive as might ordinarily be expected (George et al. 2012). We considered this high number of false positives as tolerable, since subsequent quality control tests done after RM determination were effective in rejecting these candidates.

Candidate polarized sources were processed very similarly to the method of Brown et al. (2003). To accurately constrain the on-source pixels, a 2D Gaussian was fit to the location of the source in the map of foreground-subtracted and debiased polarized intensity calculated in the previous step. For a small number of candidates (∼10%) the Gaussian fitter failed to converge; these were visually inspected and found to be cases where the foreground subtraction was ineffective and had left significant diffuse polarization; these sources were immediately rejected. A few sources (<1%) were identified as resolved with multiple spatially separated polarized components; in these cases we fitted each component independently.

Since the Gaussian fitting routine was allowed to freely vary the centroid of the fit, it would occasionally lock onto a neighboring polarized source or additional polarized component within the same source, if it was stronger than the source that was the intended target of the fit. In cases where this occurred, the neighboring polarized emission was blanked out (by setting the polarized intensity to zero in the relevant pixels) and the fitting procedure repeated; this was iterated until the fit locked onto the correct source.

For the purposes of RM determination, pixels within the FWHM region of the fitted Gaussian, and having a polarized intensity signal-to-noise ratio greater than 5, were used. For each of these pixels, the foreground Stokes Q and U parameters were subtracted and the polarization angles of the remaining on-source polarization were calculated. These angles were subject to the "nπ" ambiguity that occurs for Faraday-rotated polarization angles, where a change in the measured polarization angle by 180° would "wrap" back into the [0°, 180°) range. Given our channel spacing, a change in polarization angle of ±90° (half a wrap) would require an RM of ±1840 rad m⁻², which is much larger than we expect in this region of the Galactic disk. We assumed that the change in polarization angle between adjacent channels will always be less than 90°, and applied corrections of ±180° as appropriate to the polarization angles to satisfy this condition.

Using the unwrapped polarization angles, a linear fit to polarization angle as a function of λ² was performed, giving per pixel the fitted RM, error in RM, and probability-of-fit. The pixel-wise RM was averaged over the on-source pixels, weighted by the inverse square of the error in RM, to give the source RM. To assess the consistency of the RM across all the source pixels, a reduced χ² value was calculated from the pixel-wise differences from the mean. The maximum (foreground-subtracted, debiased) polarized intensity and Stokes I from the on-source pixels were also determined, as well as the pixel-averaged fractional polarization.

After all of these values were computed, a series of quality control tests was applied to check for problems with the source. First, sources with fewer than five on-source pixels were rejected, where on-source was defined as being within the fitted FWHM and having polarized intensity signal-to-noise ratio greater than 5. Sources for which the fractional polarization was greater than 100%, which could happen when the Gaussian fit locked onto a diffuse polarization feature near an unpolarized Stokes I source, were rejected. Sources with fractional polarization below 2% were likewise rejected, to avoid any residual instrumental polarization leakage from being identified as a polarized source.

We observed that there was a population of partially resolved sources with strong RM gradients, for which a single value could not be assigned; the χ² value calculated from the pixel RM averaging procedure was used to confirm that the source had a single well-defined RM and did not have any significant RM gradients across the on-source pixels. We defined a threshold for each source (dependent on the number of pixels, and thus the number of free parameters) corresponding to a 95% confidence level in the χ² distribution, meaning that a source with a single RM would fall below that threshold in 95% of cases. Sources with χ² values above this threshold were considered to have too much RM variation across the pixels and were rejected.

To test for Faraday complexity, we evaluated the linearity of the relationship between polarization angle and λ² using the probability-of-fit metric returned by the linear fitting routine. The probability-of-fit was averaged over the on-source pixels, and if the average probability was below 10% the source was rejected for not having clear one-component Faraday-thin behavior.

An additional test for Faraday complexity was performed using the fractional polarization, which is expected not to vary with frequency for a Faraday-simple source (Le Roux 1961). We determined the channel-averaged fractional polarization, then performed a χ² test on the residuals (sum of the squares of the channel-wise differences from the mean). We rejected sources with χ² values above the 95% confidence level as being possibly Faraday-complex.

Sources that passed all of these criteria were then subjected to a manual inspection. This inspection verified a few conditions that were difficult to test in an automated way. First, it was confirmed that the fitted FWHM region of the Gaussian fit was inside the boundaries of the Stokes I source; sources for which a significant portion of the polarization was outside the Stokes I counterpart were rejected. Second, it was manually verified that the source's polarized intensity was statistically significant, by confirming that the polarized intensity of the source stood out from the surrounding off-source pixels; sources where the on-source polarized intensity was indistinguishable from the surroundings were rejected.

The initial processing concluded with this step, but inspection of the resulting catalog showed that sources at the edges of the mosaics were less reliable, i.e., considerably more likely to have an RM significantly different from neighboring sources. To maximize the reliability of our catalog, we removed the sources at the edges of the mosaics where the primary beam sensitivity was low, even if they passed all other tests. We used a threshold of 20% of peak sensitivity, as given by the mosaic weight maps; sources below this threshold were discarded from the catalog.

At this stage all sources that were not rejected for one or more reasons were considered as valid polarized sources with well-defined RMs. These sources went through a second manual inspection step, in which their polarized and Stokes I morphologies were inspected and recorded for source classification purposes. We identified each source as either resolved or unresolved in polarized intensity and Stokes I, as well as whether the source had any neighboring sources within approximately 1', and whether those neighboring sources were also polarized. For resolved sources, we evaluated whether the polarized intensity morphology matched the Stokes I morphology. For unresolved sources, we also noted whether there was an offset of at least 1 pixel (03) between the polarized intensity peak and the Stokes I peak, because this was seen in several sources. The source classifications were included in the final catalog.

To assess the quality of our catalog, we compared the RMs against a new master catalog of previously published RMs. ¹¹ The previously published CGPS RMs (Brown et al. 2003) were deliberately excluded and will be considered separately. Using a cross-matching radius of 30'', 601 matches were found: 564 from the catalog of Taylor et al. (2009, TSS09 in Figure 3), 16 from Van Eck et al. (2011, VE11 in Figure 3), 14 from Mao et al. (2012, Mao12 in Figure 3), 4 from Costa & Spangler (2018, CS18 in Figure 3), 2 from Tabara & Inoue (1980, TI80 in Figure 3), and 1 from Law et al. (2011, Law11 in Figure 3). The comparison of their RM values to ours is shown in the top panel of Figure 3. No sources were found that had counterparts within two or more previous catalogs.

Zoom In Zoom Out Reset image size

In general there is qualitative agreement between the new RMs and previous measurements. There is a small population of sources from Taylor et al. (2009) that are offset by approximately ±650 rad m⁻² because of a known problem with the angle unwrapping ambiguity in their algorithm. These sources appear near the two dotted lines in the top panel of Figure 3.

A few sources show conspicuously large deviations between new and old RM measurements. Both of the sources that were also present in the catalog of Tabara & Inoue (1980) have very different RMs (>100 rad m⁻² difference), as do two of the sources from Costa & Spangler (2018). However, all four of these sources show signs of Faraday complexity in the older measurements: significant changes in polarized fraction at different frequencies for the RMs of Tabara & Inoue (1980), and large linear fit residuals for those of Costa & Spangler (2018). This can explain how different RMs can be observed over different frequency ranges. We interpret this as further evidence that individual source RMs should be interpreted carefully whenever the presence of Faraday complexity cannot be reliably ruled out. In addition to these sources, one of the RMs of Mao et al. (2012) is also significantly different from ours, but no reason for this difference can be easily identified.

We further investigated the differences between our catalog and the matching sources in the catalog of Taylor et al. (2009) to search for possible systematic effects. When testing for correlations between the absolute value of the RM difference (between the two catalogs) and source properties, we found a significant anticorrelation with the signal-to-noise ratio (Spearman ρ = −0.36, p ≈ 10⁻¹⁹), as well as with related quantities such as polarized intensity. However, this correlation was no longer present (ρ = −0.027, p = 0.51) after the differences were normalized by the uncertainty in the difference (the quadrature sum of the uncertainties in the individual RMs). We interpret this to indicate that the RM uncertainties in both catalogs have the correct dependence on signal-to-noise ratio. We find no significant correlations with the uncertainty-normalized RM differences.

In addition to comparing against other observations, we also compared this new CGPS catalog against the initial CGPS catalog (Brown et al. 2003) to determine how significantly the change in processing affected the resulting RMs. Of the 380 sources in the 2003 catalog, all were present in the catalog of Taylor et al. (2017), and all but four were identified as polarized source candidates. Those four were found to be located in regions of strong, position-dependent diffuse polarized emission. This caused our foreground subtraction algorithm to assign them high uncertainties. Thus, even though clear on-source polarization could be seen by a visual inspection, our algorithm classified them as below the signal-to-noise threshold and they were discarded.

Of the remaining 376 sources, 95 did not pass the quality control tests of the new pipeline. Four were found to fail Gaussian fitting in polarized intensity (probably as a result of the improved foreground subtraction), 15 were found to not have enough pixels above the signal-to-noise threshold (as a result of the new noise calculations), 11 failed the pixel-averaging χ² test, and 15 failed the linearity probability-of-fit test (for both tests, as a result of the new noise and error estimates). These sources, and their reported results from both the new and original pipelines, were inspected, and we found that nearly all of these were close to the pass/fail thresholds in the original pipeline and were pushed across one or more of these thresholds by the changes to the noise and foreground calculations. The χ² test for constant fractional polarization was not used in the previous catalog; this test caused 43 previous sources to fail. Seven sources were found to be outside the 20% sensitivity threshold we used to remove edge sources with lower reliability.

The remaining 281 passed all tests in the improved pipeline and are included in the new catalog with updated RMs; a comparison of the updated RMs to those of the original appears in the lower panel of Figure 3. We strongly caution users of this catalog that these RMs were derived from the same observations as the 2003 catalog; they are not independent measurements and should not be combined with the previous catalog for statistical analyses. We recommend that our catalog completely replace the original CGPS catalog for all future analyses.

In Figure 4 we show the statistical properties of the rotation measures as a function of longitude. The mean RM ($\overline{\mathrm{RM}}$, top panel) generally shows smooth trends with longitude: the outer Galaxy region 130° < ℓ < 180° has a smooth and steady trend in RM from negative toward zero with increasing longitude. This indicates that the large-scale magnetic field is embedded in a ubiquitous phase of the ISM. This was confirmed by Foster et al. (2013), who used a preliminary version of this catalog and found a strong relation between RMs of extragalactic sources and the optically thin hydrogen column density in the same direction, indicating that the warm neutral medium is the main carrier of the large-scale magnetic field in the Galaxy. RMs cross zero near the anticenter, indicating that the magnetic field is nearly azimuthal in the outer Galaxy (Van Eck et al. 2011). This is supported by the study of the supernova remnant G182.4+4.3, close to the anticenter, in which the ambient field is almost perpendicular to the line of sight (Kothes & Brown 2009). In the inner Galaxy the magnetic field closely follows the spiral arms, and, starting near ℓ < 70°, the RMs show a strong swing from negative to positive with decreasing longitude. This is the reversal of the field between the local and Sagittarius arms (Van Eck et al. 2011).

Zoom In Zoom Out Reset image size

The third panel of Figure 4 shows the longitude dependence of the ratio between the standard deviation (σ_RM) and the absolute value of the mean of the RMs within the 2° bins we used to compute the statistics. We note that over a substantial range of longitude, from l ≈ 100° to l ≈ 150°, the ratio ${\sigma }_{\mathrm{RM}}/| \overline{\mathrm{RM}}|$ is well constrained, with a correlation coefficient of 0.57 (p = 0.003) between σ_RM and $| \overline{\mathrm{RM}}|$. This is consistent with the similar result presented in Brown & Taylor (2001) using RM data from the first phase of the CGPS (Taylor et al. 2003). This correlation was interpreted by Brown & Taylor (2001) to indicate a preferential alignment between the small- and large-scale magnetic field components, a precursor to the concept of an ordered–random GMF component (e.g., Jaffe et al. 2010). At longitudes where the RMs approach zero (near the anticenter and the large-scale reversal region), the ratios ${\sigma }_{\mathrm{RM}}/| \overline{\mathrm{RM}}|$ increase significantly as a consequence of dividing by very small values of $| \overline{\mathrm{RM}}|$. Enhanced variability in the Cygnus X region (see Section 4.2) also contributes deviations from the near-constant ratio seen in the mid-longitude range. The mid-longitude range of the CGPS, where the magnetic field has a sufficient line-of-sight component to yield substantial RM values, is an ideal testbed for statistical studies of the connection between small- and large-scale GMF components.

The variation of RM with Galactic latitude is shown in Figure 5 for the two latitude extensions. The absolute value of RM falls significantly away from the mid-plane, and drops almost to zero at high latitudes, as expected. However, RM variation is not symmetric around the mid-plane. This asymmetry appears to be caused by the anomaly known as Region A (Simard-Normandin & Kronberg 1980), which is primarily affecting RMs south of the Galactic disk. A more thorough analysis of the latitude extensions, using an earlier version of the catalog, was done by Cooper (2014).

Zoom In Zoom Out Reset image size

Several regions or individual points that deviate from the large-scale trends are also visible, and are usually reflected by larger variations in the RM within each bin (as shown by the second panel of Figure 4). Most of these deviations are caused by smaller-scale structures in the ISM, such as H ii regions. Several examples can be easily identified: the enhanced RM in the highest longitude bin (1915–1935) is due to a cluster of sources behind an H ii enhancement at l ≈ 1915, b ≈ +28 with much larger positive RMs than the surrounding sources; the anomalously low mean RM, large scatter, and lower source density around l = 172° are associated with a large H ii region complex centered on Sh 2-230; the similar anomaly around l = 135° is due to the W3/4/5 complex. Figure 6 shows the smoothed distribution of RMs with these regions highlighted.

Zoom In Zoom Out Reset image size

Figure 4 reveals a large scatter in RMs toward an area 15° wide centered on ℓ = 80°. This is the Cygnus X region where we are looking along our own spiral arm, the Orion spur. In Cygnus X we are looking through several layers of star-forming regions and H ii regions (Gottschalk et al. 2012), and the heavy concentrations of ionized material explain the scatter in RM. RM source density is low in this area (see Figure 4) because of the very strong extended emission, and the area is left blank in Figure 6. Pulsar RMs toward Cygnus X are almost all positive above latitude −4°, at least in the range 75° < ℓ < 82° (Figure 9 of Kothes et al. 2020). The region of positive RMs around ℓ = 75°, b = +4° may be associated with the low-longitude side of Cygnus X or may be associated with the positive RMs found at lower longitudes. A study of compact source RMs and a comparison with the RM of extended emission (as in Ordog et al. 2019) would contribute to understanding this region.

Other departures from the overall trend can be seen in Figures 2 and 6, but are less obvious in Figure 4. We can identify these features with H ii regions or supernova remnants through comparison with CGPS images of the total intensity along the Galactic plane; we use the 408 MHz maps of Tung et al. (2017), especially their Figures 6–12.

• 1.  
  A region of strong negative RM near ℓ = 143°, 0° < b < 2° is associated with the W3/4/5 H ii region complex.
• 2.  
  A region of strong negative RM near ℓ = 172°, b = −3° is associated with the H ii complex Sh 2-230. This complex spans almost the whole latitude range of the survey, accounting for a low density of RMs in this area.
• 3.  
  At ℓ = 93°, b = 0° we see an area of positive RM where the surrounding RMs are negative. This feature was reported by Clegg et al. (1992) and was noted in the 2003 CGPS RM catalog (Brown et al. 2003). This anomaly is related to the supernova remnant CTB 104A and/or its environment (Uyaniker et al. 2002).

There is also an area with very low RM magnitudes embedded within large RMs slightly below the mid-plane at approximately 62° < ℓ < 70° (see Figure 2). The reason for this is unclear. This region is largely empty in Stokes I, from the edge of Cygnus X to approximately where the Sagittarius arm begins, with no obvious Stokes I counterpart to these low RMs.

One weakness in a latitude-averaged analysis like Figure 4 is that transitions that are not parallel to the Galactic plane can be lost or misrepresented. Ordog et al. (2017) used an earlier version of this catalog to identify that the transition in the sign of RM around l = 60° is in fact not aligned with the Galactic plane but is clearly along a diagonal line (their Figure 2, reproduced in Figure 6). They also found that this transition was reflected in the diffuse polarized emission present in the CGPS data.

Ordog et al. (2019) used a pre-final version of this RM catalog (which was made without the 20% sensitivity threshold and tests for fractional polarization variation) to compare with rotation measures derived from the diffuse polarized emission that is also present in the CGPS data. They found a strong correspondence between the diffuse emission RMs and the extragalactic source RMs, except in a few regions (most of the regions that are discussed in Sections. 4.1 and 4.2) where smaller local features strongly influence the RMs. They found that along most of the lines of sight the extragalactic RMs (which probe the full line of sight through the Milky Way) were approximately twice as large as the RMs of the diffuse emission (which is distributed through the Milky Way in a complex way). The details of this result and their interpretation are not repeated here and can be found in their paper.

Stutz et al. (2014) performed a power spectrum analysis of the CGPS diffuse polarized emission at a resolution of 267. In the high-latitude extension, they found a sharp transition to a steeper power-law index at a latitude of about +9°, which indicates a transition from small-scale to large-scale structures. This is interpreted as the disk–halo interface and agrees with the location where the RMs reduce to approximately zero (Figure 5).