LOW-FREQUENCY OBSERVATIONS OF LINEARLY POLARIZED STRUCTURES IN THE INTERSTELLAR MEDIUM NEAR THE SOUTH GALACTIC POLE

The visibility data in each snapshot was flagged for radio frequency interference (RFI) using aoflagger (Offringa et al. 2012). A benefit of the radio quiet environment within the MRO is that less than 1% of data is typically flagged as a result of RFI (Offringa et al. 2015).

Calibration was carried out using the real-time calibration and imaging system, referred to as the rts (Mitchell et al. 2008; Ord et al. 2010), but utilized in an off-line mode to perform an additional polarimetric analysis. For all observations, a pointed scan of 3C444 was used to calibrate the bandpass and to set the absolute flux scale. The flux density of 3C444 at 154 MHz is 81 Jy with a spectral index²⁸ of α = −0.88 (Slee 1977, 1995), tied to the Baars et al. (1977) flux scale. The uncertainty on the absolute calibration is estimated to be better than 10% (Hurley-Walker et al. 2016, in preparation).

For each observing epoch and frequency band, targeted observations of 3C444 were used to measure the direction independent bandpass gains with the rts, and a polynomial fit was determined for each of the 24 coarse channels. After the bandpass was applied, complex Jones matrices were fitted and the overall solution derived was applied to all visibility data associated with the same observing session, using the calibration scheme described in Section 2.1 of Bernardi et al. (2013). Independent solutions were obtained for each observing session and frequency band. Previous experience has shown that bandpass solutions are stable over an entire night of observing, and so it was assumed that the solutions were not time variable (Bernardi et al. 2013; Hurley-Walker et al. 2014). The relative phase between the instrumental polarizations, i.e., the XY-phase, was not constrained during calibration due to the lack of a bright polarized calibrator in the field. This will result in an excess of leakage from Stokes U into V (Sault et al. 1996); however, based on observations with a 32-tile prototype of the MWA (Bernardi et al. 2013), we estimate that this will result in no more than 20%–30% leakage.

The rts uses a simple short-dipole analytic model to determine the tile beam used for calibration and imaging. While this is an over-simplification of the true tile beam over the entire frequency range and field of view available to the MWA, it has been shown (Bernardi et al. 2013) that this is sufficient for polarimetric observations below 200 MHz and restricted to fields passing close to or through zenith. To minimize polarization leakage as a result of deviations of the primary beam model from the true beam, only near-zenith observations of the EoR-0 field have been included in this study. Similarly, our investigations primarily use data from the EoR low-band (154 MHz), where the model and true beam match well (Sutinjo et al. 2015). Based on observational tests (Sutinjo et al. 2015), we estimate polarization leakage (primarily Stokes I into Stokes Q) of approximately 1% near zenith and a few percent toward the edge of a typical 25° × 25° field.

Using all available baselines to generate a naturally weighted image results in a point-spread function (PSF) with a narrow 6' full width at half maximum (FWHM) Gaussian-like peak associated with the longest baselines and a broad ∼50' FWHM Gaussian-like component associated with the dense inner core of the MWA. Figure 1 shows a cut of the naturally weighted MWA beam profile and its decomposition into narrow and broad Gaussian-like components. The rts does not perform image deconvolution on extended emission during the imaging process and the structured naturally weighted PSF complicates flux scale measurements of diffuse features. To ensure a near-Gaussian beam and to improve imaging of large-scale features, (u, v) visibilities were tapered with an 82 λ Gaussian taper and baselines above 300λ were excluded. The effect of the tapering can be seen in Figure 1; the resulting naturally weighted PSF is now a single-component near-Gaussian beam with 54' × 47' FWHM at a position angle of −18. This corresponds to a conversion factor of 1 Jy beam⁻¹ = 5.6 K at 154 MHz (Wrobel & Walker 1999).

Zoom In Zoom Out Reset image size

For a 112 s snapshot image using the (u, v)-tapered visibilities, the PSF response in the image plane exhibits two weak (3% level) negative point-like sidelobes ∼4° from the peak and a two slightly stronger (10% level) positive point-like sidelobes ∼8° from the PSF peak. The sidelobe levels reduce with longer integration times. By avoiding deconvolution, we can minimize processing requirements while only incurring image flux density errors, as a result of non-Gaussian PSF structure, of the order of a few percent. To verify the fidelity of the diffuse structure in the dirty maps, a single EoR snapshot was calibrated and deconvolved using miriad (Sault et al. 1995). The deconvolution process did not greatly affect the diffuse structures in the image and the resulting image was found to be consistent, to within a few percent, with the dirty images generated by the rts in the zenith region. It should be noted that miriad does not have the capability to calibrate nor correct MWA data for wide-field polarimetric effects and so the results are only valid near zenith. To validate the wider field polarimetric results from the rts a second independent processing pipeline based on wsclean (Offringa et al. 2014) was used to compare results against. This pipeline also has internal knowledge of the MWA beam and can apply the appropriate corrections for wide-field polarimetry. The output dirty maps from the wsclean pipeline were found to be consistent with the rts maps over the available field of view and for all four Stokes parameters. Subtle edge differences were noted, at a level less than 1%, owing to slightly different implementations of the MWA beam model.

Using the rts, calibrated 25° wide full Stokes (I, Q, U, and V) dirty image cubes were generated for each snapshot, with 160 kHz frequency channels across the 30.72 MHz band. The images are corrected for dipole projection effects and wide-field effects across the entire field of view during the resampling stage (Ord et al. 2010). A sampling of 3 pixels across the naturally weighted synthesized beam is used in the final imaging. Assuming a receiver temperature of 50 K and a sky temperature of 350 K (Tingay et al. 2013) and taking into consideration the flagging, weighting, and baselines used for imaging, we estimate a theoretical sensitivity of 35 mJy beam⁻¹ (1σ) per snapshot over the entire 30.72 MHz band at 154 MHz. When combined with all 44 snapshots in our deepest field (epoch 1), this results in a theoretical sensitivity of 5.3 mJy beam⁻¹. Using the continuum Stokes V image of the deepest field as a guide, we measure an actual image rms of 5.9 mJy beam⁻¹. Table 2 summarizes the measured continuum image noise and the synthesized beam parameters for all epochs processed in "diffuse" imaging mode. For total intensity, image rms is dominated by classical confusion and sidelobe confusion (Franzen et al. 2015; Wayth et al. 2015); this is also true for the point-source and pulsar imaging presented below. Similarly, for linear polarization, image rms is limited by diffuse polarized structure within the observed field.

Full Stokes dirty image cubes of the inner 400 square degree region of the field were also produced using uniformly weighted images (the restricted field of view was due to memory limitations encountered when processing a field at increased resolution). The image cubes are considered "dirty" because no deconvolution was performed. All baselines shorter than 50 λ were excluded and no (u, v)-tapering was applied. The resulting cubes were better suited for searches of polarized point sources because large-scale emission was effectively filtered out. Table 2 summarizes the measured continuum image noise and the synthesized beam parameters for the two epochs processed in this imaging mode (designated as the "point" mode).

Additional targeted imaging was performed in an attempt to detect a known field pulsar, PSR J2330–2005 (PSR B2327–20), to aid in localizing linearly polarized features. While not ideal, owing to increased sidelobe confusion and PSF structure, natural weighting was used to improve sensitivity. All available baselines were utilized except those below 100λ; these were excluded to limit confusion and contamination from diffuse emission. Full Stokes dirty image cubes of a 16 square degree region centered on the pulsar (α = 23^h30^m26885, δ = −20°05'2963) were produced for epochs 1 and 3. Table 2 summarizes the measured continuum image noise and the synthesized beam parameters for the two epochs processed in this imaging mode (designated as "pulsar" mode).

The band-averaged epoch 1 total intensity (Stokes I) images optimized for diffuse emission and for point-source analysis are shown in Figure 2. While neither of these images has been deconvolved for the PSF, the beam has been shown to be near-Gaussian and does not significantly degrade the images. To demonstrate that these dirty maps accurately recover diffuse structures, reprocessed 408 MHz Haslam et al. (1982; Remazeilles et al. 2015) and 1.4 GHz HIPASS (Calabretta et al. 2014) images of the same region have been included in Figure 2 for comparison. The low level diffuse emission observed in the MWA diffuse map correlates well with diffuse emission seen in the Haslam et al. (1982) 408 MHz data and, while these features are weaker at 1.4 GHz, they are also present in the HIPASS 1.4 GHz data.

Zoom In Zoom Out Reset image size

The resulting band-averaged total intensity (Stokes I) and linear polarization (Stokes Q and U) dirty images for the epoch 1 and 3 observations of the EoR-0 field are shown in Figure 3. Because no point-source subtraction or peeling (point-source subtraction with direction-dependent calibration) was performed, the Stokes I images are confusion limited and dominated by point sources within the field. Despite the presence of sources with peak brightnesses exceeding 25 Jy beam⁻¹ in total intensity, the linear polarization maps contain mostly smooth features and these are uncorrelated with features in Stokes I. A few of the brightest sources are just perceptible in the polarization maps at about the 1% level but do not affect the overall structure of the diffuse emission seen in those maps. The Q and U maps are mostly dominated by smooth extended structures ranging from 1° to 8° in extent and filament-like features, a number of which are approximately aligned in a northwest direction. Note that while the Stokes I maps are virtually identical in epochs 1 and 3, the Stokes Q and U maps are quite different. In particular, the epoch 3 U image appears to exhibit features found in the epoch 1 Q image and the epoch 3 Q image appears to have inverted features from the epoch 1 U image. The changes observed between the epochs appear consistent with a rotation in the Q–U plane. As will be shown in Section 3.4, these changes are a result of ionospheric Faraday rotation.

Zoom In Zoom Out Reset image size

For comparison and diagnostic purposes, the band-averaged circular polarization (Stokes V) images and polarized intensity (P) images (formed from the band-averaged Q and U images such that $P=\sqrt{{Q}^{2}+{U}^{2}}$) are shown for epochs 1 and 3 in Figure 4. The circular polarization maps clearly exhibit leakage from Stokes U into Stokes V at the ∼10% level in epoch 1 and the ∼20% level in epoch 3; due to a combination of frequency-dependent XY phase errors that have not been accounted for and uncertainties in the beam model. We note that this is relatively high but even if corrected for, the improvement in Stokes U would only be at a level that is already dominated by existing errors associated with the PSF and sidelobe confusion. We also note that the leakage from Stokes U to Stokes V is not prominent in the uniformly weighted image used for point-source analysis; because the point sources are significantly weaker in Stokes U compared to the diffuse emission and so any leakage would be below the Stokes V noise level.

Zoom In Zoom Out Reset image size

Comparing the polarized intensity images between epoch 1 and 3, one would expect that the images should remain constant between epochs. However, there are clear differences between the two. The epoch 1 image has significantly brighter structures whereas the epoch 3 image does not. These differences are caused by significantly different ionospheric conditions between the two epochs resulting in different levels of depolarization in the band-averaged Q and U images used to form the polarized intensity images. The polarized intensity image from epoch 1 is dominated by a large (∼4° × 7°) and bright feature (peaking at ∼1.8 Jy beam⁻¹) centered around α = 23^h50^mand δ = −31°. Depolarization canals, unresolved regions with little or no emission in linear polarization, are further clearly visible; many of them laying preferentially in a northwest orientation. The most prominent depolarization canals appear to be associated with the bright extended feature. In particular, one curves around the lower extent of the feature (starting around α = 0^h, δ = −35°) and then extends linearly toward the northwest edge of the field (through α = 23^h30^m, δ = −25°).

When propagating through a magnetized plasma, a linearly polarized signal undergoes Faraday rotation. The effect is particularly pronounced at long wavelengths as the magnitude of rotation is proportional to the wavelength squared:

$$\begin{eqnarray}&&\chi ({\lambda }^{2})={\chi }_{0}+\phi {\lambda }^{2},\end{eqnarray} \tag{ 1 }$$

where χ(λ²) is the measured linear polarization angle (rad) at wavelength λ (m), χ₀ is the intrinsic polarization angle (rad), and the overall strength of the effect is characterized by the Faraday depth ϕ (rad m⁻²). The Faraday depth along the sightline to a source is defined as (Burn 1966)

$$\begin{eqnarray}&&\phi (d)=0.81{\int }_{d}^{0}{n}_{e}{B}_{\parallel }\cdot {dl},\end{eqnarray} \tag{ 2 }$$

where n_e is the electron density (cm⁻³) and B_∥ is the magnetic field component parallel to the line of sight (μG). The integral is performed along the line of sight (of which dl is the differential element) from the observer to a distance d (pc). If Faraday rotation is not taken into consideration at long wavelengths, sources at any appreciable Faraday depth will depolarize over the available observing band, an effect known as bandwidth depolarization.

RM synthesis (Brentjens & de Bruyn 2005) is a technique that takes advantage of the Fourier relationship between the complex polarized intensity as a function of wavelength squared, $P({\lambda }^{2})=Q({\lambda }^{2})+{iU}({\lambda }^{2})$, and the Faraday dispersion function (FDF) F(ϕ), which is the polarized intensity as a function of Faraday depth (Burn 1966), i.e.,

$$\begin{eqnarray}&&P({\lambda }^{2})=W({\lambda }^{2}){\int }_{-\infty }^{+\infty }F(\phi ){e}^{2i\phi {\lambda }^{2}}d\phi ,\end{eqnarray} \tag{ 3 }$$

where W(λ²) is a weighting function and ϕ is the Faraday depth. RM synthesis reconstructs the FDF F(ϕ) from an irregularly sampled P(λ²). The rotation measure spread function (RMSF), which is the Faraday depth equivalent of the PSF, is the Fourier transform of the weighting function and depends on bandwidth, channel weighting, and wavelength.

In general, frequency channels may be weighted by W(λ²) to account for varying sensitivity across the band. However, measuring the Q and U image noise in the presence of large-scale structures, which vary dramatically as a function of frequency, is problematic. To simplify processing, we have weighted all frequency channels in the image cubes equally, i.e., W(λ²) = 1. We anticipate only a slight loss in overall sensitivity resulting from this choice of weighting scheme because the observed sensitivity across the band is relatively smooth when measured in uniformly weighted images. Using definitions from Brentjens & de Bruyn (2005), for the 154 MHz band with 160 kHz channels, the resulting RMSF provides a resolution of δϕ = 2.3 rad m⁻², maximum-scale-size sensitivity of 1.0 rad m⁻² and Faraday depth range of $| {\phi }_{\max }| =160$ rad m⁻². Because the maximum-scale size is smaller than the resolution δϕ, these observations cannot resolve Faraday-thick structures.

The incomplete sampling available in λ² results in sidelobes at about the 10% level in the RMSF. These have been accounted for by using the RM clean algorithm, as described by Heald (2009). In summary, the RM clean algorithm deconvolves peaks in Faraday space with the RMSF to determine the location and amplitude of clean components. The resulting clean components are then convolved with a Gaussian restoring function that has an FWHM equivalent to the RMSF resolution (i.e., δϕ = 2.3 rad m⁻²).

Figure 5 highlights features observed in Faraday space at three different Faraday depths (+1.0 rad m⁻², +3.0 rad m⁻², and +7.1 rad m⁻²) in the epoch 1 data. The vast majority of the diffuse structure appears at low Faraday depths (∼1 rad m⁻²) and is dominated by a bright extended feature (labelled "Low RM"), which was noted in the epoch 1 polarized intensity map (see Figure 4). Depolarization canals also dominate the entire field-of-view at this Faraday depth with several of the more significant canals oriented in an approximately SE–NW alignment. At a Faraday depth of +3.0 rad m⁻², the bulk of the features seen at +1.0 rad m⁻² are gone and are replaced by a number of ∼2°–4° wide structures in the SE corner of the EoR-0 field (the brightest of which is labelled "Mid RM"). At +7.1 rad m⁻², a small, barely resolved, feature is seen to the east (labelled as "High RM"). Just SE of this source is a slightly more extended component that peaks at approximately +9 rad m⁻². The mid-to-high RM features may be associated with the increased level of diffuse polarized emission observed by Bernardi et al. (2013) toward the SGP at similar Faraday depths. Figure 6 shows the Faraday depth at peak emission in the Faraday depth cube for each line of sight in the field. The figures show that the majority of the EoR-0 field is dominated by features at low Faraday depths and that these features vary quite smoothly across the field. Apart from the small number of sources already described at higher Faraday depths, there are a number of weak features at negative Faraday depths near the edge of the field; these are not likely to be associated with real features and are caused by a combination of decreased sensitivity at the edge of the field and sidelobe structures contaminating the field at a low signal to noise.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The deconvolved FDFs for the samples taken in the low and high RM regions are shown in Figure 7. The residual rms is 16 mJy beam⁻¹ RMSF⁻¹, 42 mJy beam⁻¹ RMSF⁻¹, and 29 mJy beam⁻¹ RMSF⁻¹ for the low, mid, and high RM sources, respectively. The high RM FDF appears to contain more than one peak: a main peak at ϕ = +7.2 rad m⁻², an intermediate 530 mJy beam⁻¹ RMSF⁻¹ peak at ϕ = +3.5 rad m⁻² and a 230 mJy beam⁻¹ RMSF⁻¹ peak at ϕ = +0.7 rad m⁻². The additional minor peaks in the high RM FDF fluctuate between epoch 1 and 3 and are due to sidelobe contamination, which introduces frequency-dependent structure into the Faraday spectra that is also time dependent.

Zoom In Zoom Out Reset image size

The ionosphere affects observations through positional shifts of background sources and through Faraday rotation of linearly polarized signals. A gradient in total electron content (TEC) of the ionosphere across the field of view will result in positional shifts of sources; this has been observed previously with the MWA and studied in detail (Loi et al. 2015a, 2015b, 2015c). For diffuse polarization, the effect is an order of magnitude smaller than the size of the features being studied and can safely be ignored.

The absolute TEC, in combination with the magnetic field in the direction being observed, can measurably contribute to the observed RM of a background source. The TEC at a given time, from a given location on the Earth, observed toward a particular line of sight, can be estimated based on Global Positioning System models (Arora et al. 2015). Using the TEC estimated by these models in combination with terrestrial magnetic field models, the predicted ionospheric component of Faraday rotation may be determined. An implementation of these models can be found in the albus (Willis et al. 2016) package. We used albus to determine the mean Faraday rotation introduced as a result of the ionosphere during the course of the epoch 1 observation and estimated it to be −0.7 ± 0.2 rad m⁻². When corrected for ionospheric Faraday rotation, the distribution of RM in the EoR-0 field peaks at 1.0 rad m⁻² with a standard deviation of σ_ϕ = 0.34 rad m⁻²; see Figure 8. A few further sub-peaks are seen within this distribution but the vast majority of features are contained within −2 < ϕ < +10 rad m⁻².

Zoom In Zoom Out Reset image size

When images are compared across the three epochs at 154 MHz, the total intensity maps remain unchanged. However, there are clear differences in the linear polarization maps, particularly between epoch 1 and the two subsequent epochs. Using RM synthesis and searching for peak emission in Faraday depth for each line of sight revealed that all of the observed structures were consistent between the epochs but that they had been shifted in Faraday space. This is shown in Figure 9 for the epoch 1 and epoch 3 data; here the peak intensity maps are consistent, but the peak emission occurs at +0.3 rad m⁻² in epoch 1 and at ϕ = −1.2 rad m⁻² in epoch 3. Both albus (Willis et al. 2016) and ionfr (Sotomayor-Beltran et al. 2013) predict a shift in the ionospheric component of approximately −1.5 rad m⁻² in Faraday rotation from epoch 1 to epoch 3 (ionospheric RM of −0.7 rad m⁻² for epoch 1 and −2.2 rad m⁻² for epoch 3). When these shifts are applied to the Faraday depth cubes, the peak emission for both epochs occurs at ∼1.0 rad m⁻², verifying that the shift is associated with the ionosphere and not caused by variability or the instrument. The significantly higher Faraday rotation induced by the ionosphere in epoch 3, most likely as a result of a known Coronal Mass Ejection event (Kaplan et al. 2015), also explains the structural differences observed between the two epochs in the band-averaged Q and U images shown in Figure 3. This highlights the need for a correction to mitigate the effects of ionospheric Faraday rotation. However, it also demonstrates that the ionosphere is quite stable as a function of time and direction over the MWA field of view and that, to first order, a single shift in Faraday depth (as opposed to a grid of multiple direction dependent shifts) is sufficient to correct for these ionospheric effects.

Zoom In Zoom Out Reset image size

An interesting possibility with the MWA, given the high sensitivity to diffuse structures that the instrument provides, is to use the diffuse polarized background to track and measure the influence of ionospheric and heliospheric Faraday rotation. An estimate of the ionosphere-corrected Faraday rotation toward a source of bright diffuse emission (ϕ_src) can be determined by performing a least-squares fit that minimizes ${\phi }_{\mathrm{src}}-({\phi }_{\mathrm{obs}}-{\phi }_{\mathrm{ALBUS}})$ over multiple observing snapshots and/or epochs, where ϕ_obs is the observed Faraday rotation toward the source and ϕ_ALBUS is the estimated ionospheric Faraday rotation at the time of the observation. By observing over multiple epochs, to overcome the relatively large errors associated with individual predictions of ϕ_ALBUS, the overall error in ϕ_src can be minimized. Once an estimate of the ionosphere-corrected Faraday rotation is established, it can be used to estimate the ionospheric component of Faraday rotation at that source location at any epoch. Using this approach for all available snapshots in each of the three epochs, the fit to ϕ_src of the high RM source (see Figure 5) was determined to be ϕ_src = 7.20 ± 0.01 rad m⁻². Figure 10 plots the ionospheric component (${\phi }_{\mathrm{obs}}-{\phi }_{\mathrm{src}}$) at the high RM source location for each snapshot and epoch. The measured component tracks both predictive models quite well from epoch to epoch and even from snapshot to snapshot. This demonstrates that observations of diffuse polarization may allow the effects of the ionosphere to effectively be calibrated in fields where the RM structure has been previously determined, without the need to resort to predictive models. The technique also has the potential to aid ionospheric studies by mapping ionospheric changes both temporally and spatially over a wide field of view. In combination with predictive models, this technique may also provide a means to detect and track the propagation of space weather events, as caused by coronal mass ejections or solar flares, by observing the shift they impart on the RM signature of the diffuse polarized background (Oberoi & Kasper 2004).

Zoom In Zoom Out Reset image size

To examine filamentary magnetized structures believed to result from turbulence in the local ISM Burkhart et al. (2012), polarization gradient maps of the Stokes vector (Q and U) were formed using the method described by Gaensler et al. (2011). The polarization gradient function is defined as

$$\begin{eqnarray}&&| {\boldsymbol{\nabla }}{\boldsymbol{P}}| =\sqrt{{\left(\displaystyle \frac{\partial Q}{\partial x}\right)}^{2}+{\left(\displaystyle \frac{\partial U}{\partial x}\right)}^{2}+{\left(\displaystyle \frac{\partial Q}{\partial y}\right)}^{2}+{\left(\displaystyle \frac{\partial U}{\partial y}\right)}^{2}}.\end{eqnarray} \tag{ 4 }$$

Time-dependent effects were examined by comparing changes in the gradient map from snapshot to snapshot and against the time-averaged data set. Figure 11 shows gradient maps from the epoch 1 observation using a single 112 s snapshot compared against a gradient map using all of the available data from that epoch. When corrected for ionospheric effects, the structures seen in these gradient maps are centered at a Faraday depth of +1.0 rad m⁻² as this is where the bulk of the polarized emission exists (see Figure 8).

Zoom In Zoom Out Reset image size

The most prominent features in Figure 11 remain stable as a function of time. Minor changes can be seen in the fainter structures and these are primarily due to a combination of image noise, sidelobe confusion, and errors associated with incomplete (u, v) sampling. We note that the first few snapshots of epoch 1 are detrimentally affected by the presence of the Galactic plane within a far sidelobe because this epoch included low elevation beam-former pointings that were not used in the epoch 2 or epoch 3 data. The projected baselines of the MWA are severely foreshortened for sources at low elevation and the array is particularly sensitive to bright and extended sources in those locations (Thyagarajan et al. 2015). Nonetheless, when integrating data over a wide range of hour angles, the source sidelobe effects are diluted and the exclusion of the affected snapshots has a minimal impact on the final integrated gradient map. Gradient maps were also produced for the remaining epochs at 154 MHz, but no significant changes were observed once the maps were corrected for ionospheric Faraday rotation.

To examine the evolution of gradient map features as a function of observing frequency, gradient maps were created for the three GLEAM bands, i.e., epochs 2(a), 2(b), and 2(c). The EoR-0 field was only fully visible in the first snapshot of the epoch 2 data because the Sun was in the process of setting just as the field was passing through zenith. As such, the sensitivity is limited to that of a single snapshot in these data. Figure 12 shows the resulting gradient maps for each band of epoch 2 data, with channels across each 30.72 MHz band averaged to increase the signal to noise. The point-like sources that begin to appear in epoch 2(b) and dominate in epoch 2(c), result from apparent polarization leakage from bright Stokes I sources. The level of leakage increases with frequency and angular distance from zenith. For the most part, this leakage is due to errors in the primary beam model and will be reduced once improved beam models are implemented into the imaging pipeline (Sutinjo et al. 2015). The leakage in epoch 2(a) is minimal because this is where the beam model and instrument were designed to perform optimally; thus, its behavior is well-defined. Increased noise levels are also evident at the edge of the field in the higher frequency bands as a result of the decreased field of view available in those bands.

Zoom In Zoom Out Reset image size

Comparing the gradient maps in the three different bands, the dominant features are stationary with respect to spatial coordinates in the epoch 2(a) and 2(b) images. Some features, such as the linear feature that runs from NW to SE near the western edge, remain persistent over all three of the bands. The weaker structures are more difficult to trace, particularly in epoch 2(c), as a result of the poor sensitivity available in a single snapshot and systematic issues associated with the beam, noise, and available field of view.

An alternative view of the frequency-dependent behavior of the polarized gradients in the field can be obtained from the deep epoch 1 EoR-0 observations, albeit over the limited range of frequencies available in that observation (138.88–169.60 MHz). The epoch 1 data provide sufficient sensitivity, as a result of the longer tracking observation available, to study the polarization gradient evolution on a per-160 kHz channel basis. Figure 13 presents an animation of the gradient map as a function of frequency across the 30.72 MHz band of the 154 MHz epoch 1 observations; in this animation, subsets of 6 × 160 kHz channels have been frequency-averaged to form a smaller number of 1.28 MHz channels. The polarized gradients are now more prominent in each of the frequency channels and can be seen to vary smoothly in intensity as a function of frequency but show no significant spatial movement. In general, once features appear at lower frequencies, they continue to persist up to the higher frequency gradient maps. For example, the gradient around the bright polarized feature labelled "Low RM" in Figure 5 persists over the entire band. However, SE to NW gradients appear toward the east and west only in the upper portion of the band. Similarly, features in the northern part of the image, some forming loop-like structures, also only appear in the upper end of the band.

The uniformly weighted polarization image cubes generated using all of the longest MWA baselines are well suited for the detection of polarized point sources. An initial inspection of the RM cube, created using the uniformly weighted Stokes Q and U cubes, reveals a clear detection of the extragalactic source PKS J0021–1910 (PKS B0018–194). A cut-out image for the source and its associated FDF are shown in Figures 14 and 15, respectively. In the uncorrected epoch 3 data, the source has an RM of +5.6 rad m⁻² and is detected with a signal to noise of 10 in each snapshot. When corrected for ionospheric effects using albus predictions of the ionospheric Faraday rotation, a fit of ϕ = +7.8 ± 0.1 rad m⁻² is obtained for this source. With a total intensity of 4.7 Jy beam⁻¹ and a polarized intensity of 140 mJy beam⁻¹, the source is 3.0% polarized. The polarimetric characteristics of the source are consistent with a measurement made at 1.4 GHz, RM = 3.6 ± 5.2 rad m⁻² and 3.67% polarization (Taylor et al. 2009).

Zoom In Zoom Out Reset image size

A subsequent search was performed concentrating on the locations of known polarized sources, using the Taylor et al. (2009) catalog as a reference. The catalog contains 399 polarized sources within the 400 sq. degree region imaged around the EoR-0 field. We use a conservative 14σ cut-off in the time-averaged data cube to ensure that spurious detections are not made as a result of polarization leakage from bright Stokes I sources and the associated sidelobe structure this leakage introduces into the Faraday spectra. Any sources with $| \mathrm{RM}| \lt 1$ rad m⁻² were also filtered out because these would most likely trigger false-positives as a result of polarization leakage. In all, two sources were detected: PKS 0002–2153 (PKS B2359–221) and PKS J0021–1910 (PKS B0018–194). The FDFs for these sources are shown in Figure 15.

Zoom In Zoom Out Reset image size

Since deep observations were made at two epochs, a further test of the sources was made by checking whether their RMs were shifted in Faraday space by an amount that was consistent with the expected shift caused by the different ionospheric conditions between the two epochs. The advantage of this method is that it can identify real sources that were confused with instrumental leakage, because in at least one of the epochs, such a source would be shifted sufficiently away from RM = 0.0 rad m⁻² to allow a positive identification. All of the previously detected sources were verified using this method and two additional sources were also identified: PKS J2337–1752 (PKS B2335–181) and PKS J0020–2014 (PKS B0017–205). Figures 16(a) and (c) show the RM synthesis components detected in epochs 1 and 3. In epoch 1 the instrumental component and the source components are confused near RM = 0.0 rad m⁻² for both PKS J0020–2014 and PKS J2337–1752. In epoch 3, the ionosphere clearly shifts the source RM away from the instrumental component, thus enabling a positive identification. The FDFs for these two sources are shown in Figure 16.

Zoom In Zoom Out Reset image size

The parameters associated with all detected point sources are summarized in Table 3. All but PKS J2337–1752 have RMs consistent with those measured by Taylor et al. (2009). Not all of the sources appear to have been significantly depolarized at MWA wavelengths compared to observations at 1.4 GHz, which suggests that there is not a systematic reason to explain the overall small number of detections. The two most highly polarized extragalactic sources, PKS J0020–2014 and PKS J0021–1910, are also the two largest sources in spatial extent among our detected sources. PKS J0020–2014 is a giant radio galaxy with a redshift of z = 0.197 (Ishwara-Chandra & Saikia 1999) and an extent of 1.22 Mpc, while PKS J0021–1910 is a known double radio source with a redshift of z = 0.0952 and an extent of 270 kpc (Reid et al. 1999).²⁹ The remaining sources are all relatively compact.

The pulsar PSR J2330–2005 does not appear in the Taylor et al. (2009) catalog and is not detected in the uniformly weighted MWA data. It is, however, detected in both circular and linear polarization and in both epochs in the targeted search, using naturally weighted data with short baselines removed (to avoid confusion from the diffuse structures). The parameters associated with the pulsar are summarized in Table 3 and the FDF is shown in Figure 17. The secondary peaks in the FDF for the pulsar are unlikely to be real—most likely they are due to a combination of thermal noise and sidelobe noise as a result of the complicated PSF beam shape that results from natural weighting. In circular polarization, we measure a total flux density for the pulsar at 154 MHz of 8.9 ± 1.1 mJy in epoch 1 and 9.6 ± 1.0 mJy in epoch 3. We estimate a fractional circular polarization of ∼7% based on the total intensity of 140 mJy measured at the pulsar position; however, the field is highly confused in total intensity at this level. As such, the total intensity is most likely over-estimated and the fractional polarization is thus a lower limit. This would be consistent with the 22% circular polarization observed in the integrated pulse profile of the pulsar at 648 MHz (McCulloch et al. 1978).

Zoom In Zoom Out Reset image size

Offringa et al. (2016) performed a deep point-source survey of the EoR-0 field using 45 hr of MWA data and achieved a sensitivity of 0.6 mJy beam⁻¹ in polarization. Using a novel peeling algorithm, spectra for the 586 brightest sources in the field were presented. Unfortunately, PKS J0020–0014 is a resolved source and so was discarded from the catalog and PSR J2330–2005 fell outside of the restricted field of view of the survey. PKS J0021–1910 appears in the catalog but is not detected in polarization. The Offringa et al. (2016) survey did not consider Faraday rotation of the source and so linearly polarized sources with non-zero RM are depolarized. In addition, when combining results from multiple epochs, ionospheric Faraday rotation was also not considered; this too would lead to depolarization of linearly polarized sources (a similar issue was encountered by Moore et al. 2016 in PAPER observations). It is thus not surprising that linearly polarized sources were not detected by Offringa et al. (2016), but circularly polarized sources should not be as greatly affected when combining data from multiple epochs. Indeed, on closer inspection, PSR J2330–2005 is detected in the Offringa et al. (2016) data at the 6.3% level with a circularly polarized flux density of 6.5 mJy (A.R. Offringa 2016, private communication).

The linearly polarized features seen in Figure 3 are highly prominent even in single 112 s snapshot images. LOFAR observes similar features at 160 MHz in long (∼6 hr), high resolution (∼3'–4'), and sensitive (∼70–300 μJy PSF⁻¹) observations (Jelić et al. 2014) of the ELAIS-N1 field (l = 84°, b = +45°) and Jelić et al. (2015) observations of the 3C196 field (l = 171°, b = +33°) but at significantly lower signal to noise. The LOFAR observations differ from the MWA observations in that they incorporate longer baselines, are at lower Galactic latitudes, and their imaging utilizes a robust image weighting of zero, which results in higher resolution (∼3'–4') images compared to the ∼50' naturally weighted and (u, v)-tapered images of the MWA presented here. Factoring in the beam size, the Jelić et al. (2014) LOFAR observations have a sensitivity of ∼650 mK at the ∼4' scale, whereas the MWA epoch 1 observations have a sensitivity of ∼33 mK at the ∼50' scale.

The unique baseline distribution and radio quiet location of the MRO (Offringa et al. 2015) give excellent sensitivity to structures of 1°–10° in extent and sample a region not accessible to other low-frequency instruments such as LOFAR (van Haarlem et al. 2013), for example. While the 128 tiles of the MWA provide a total of 8128 baselines out to almost 3 km, the peak sensitivity of the array is derived from its dense inner core, which was specifically designed for EoR science. Figure 18 shows the fraction of baselines as a function of baseline length. Approximately 8.5% of the available baselines (689) are shorter than 60 m and nearly 15% (1183) are shorter than 120 m. The combination of sensitivity to large-scale structure and the relatively large (u, v)-tapered naturally weighted beam explain why the observed polarized features are so much brighter in the MWA images. In addition to providing increased sensitivity, the large number of short baselines also provide excellent snapshot imaging capabilities. This enables variations in ionospheric Faraday rotation to be monitored and calibrated for on short timescales. Although not utilized here, it is possible that observations of the linearly polarized emission may also be used to constrain XY-phase during the calibration phase; thus reducing the effect of leakage from Stokes U into Stokes V.

Zoom In Zoom Out Reset image size

Ultimately, the Amsterdam-ASTRON Radio Transients Facility and Analysis Center (Prasad et al. 2014) should provide LOFAR with short baseline imaging capability. Similarly, the LWA (Long Wavelength Array, Ellingson et al. 2009) has a compact baseline configuration; however, it operates at longer wavelengths compared to the MWA and will be more greatly affected by the ionosphere.

The single-dish observations of Vinyaikin & Paseka (2015) at low frequencies (151.5–290 MHz) over a number of selected regions of the sky also detected the presence of 5°–10° features in linear polarization. They suggested that these features would be undetectable by interferometric observations because of the lack of short-spacings. However, despite being an interferometer, the MWA provides sensitivity to these scale sizes and thus bridges the gap between traditional single-dish and interferometric observations.

A feature of the observed linear polarization is the lack of correlation with the Stokes I map at 154 MHz (see Figure 3). The stark difference between features in linear polarization and total intensity has been noted at other wavelengths, e.g., Wieringa et al. (1993) at 325 MHz; Haverkorn et al. (2003b) at 350 MHz; Bernardi et al. (2013) at 189 MHz; Gray et al. (1998) and Gaensler et al. (2011) at 1.4 GHz; and Sun et al. (2014) at 2.3 and 4.8 GHz. The prevailing interpretation is that the ionized foreground gas modulates small-scale RM structures onto an intrinsically highly polarized smooth synchrotron background via Faraday rotation.

The observed linearly polarized emission at 154 MHz is restricted to low Faraday depths ranging from ϕ = −2 to 9 rad m⁻² (see Figure 8), with no other significant emission seen out to $| {\phi }_{\max }| =160$ rad m⁻². The distribution in RM is similar to that observed with the 32-tile MWA prototype (Bernardi et al. 2013) at 189 MHz in a larger region that includes the EoR-0 field, and to LOFAR observations at 150 MHz in the ELAIS-N1 (Jelić et al. 2014) and 3C196 fields (Jelić et al. 2015).

The mean brightness temperature of the linearly polarized emission observed with the MWA at 154 MHz is ∼1.8 K in the east (toward the SGP) for the band-averaged data, but increases toward the center of the EoR-0 field to a mean brightness temperature of ∼4 K and a peak of 11 K. Increased levels of polarized emission were observed in this region by Bernardi et al. (2013) at 189 MHz with 156 resolution using the 32-tile prototype of the MWA, with peaks up to 13 K. Similarly, observations by Mathewson & Milne (1965) at 408 MHz with 48' resolution and Wolleben et al. (2006) at 1.4 GHz with 30' resolution also suggest higher than ambient levels of polarized emission in this region. The emission appears to be coincident with part of a polarized structure identified by Wolleben (2007), which may be associated with the southern extension of the North Polar Spur. However, as noted by Bernardi et al. (2013), there is little correspondence in detailed structure of the linearly polarized maps seen at MWA wavelengths and those at either 408 MHz and 1.4 GHz.

Diffuse emission in total intensity is weak in the EoR-0 field and difficult to separate from bright confusing sources that are within the field; a significant fraction of the diffuse emission may exist at spatial scales to which the MWA is not sensitive. However, an estimate of fractional polarization can be obtained by extrapolating total intensity measurements from higher frequency observations. At 408 MHz (Mathewson & Milne 1965), the total intensity flux is 19.5 ± 2 K, the measured polarized flux is ∼3–4 K (15%–21% polarized), and the temperature spectral index³⁰ for the total intensity emission around the SGP (Guzmán et al. 2011) is β = 2.55 (α = −0.55). Extrapolating to 154 MHz, the total intensity is estimated to be ∼246 K. We observe ∼4 K polarization at 154 MHz, which corresponds to 1.6% fractional polarization and a peak of 11 K (∼4.5% fractional polarization). This is significantly lower than the fractional polarization at 408 MHz, but is in line with the 1.5% fractional polarization seen with LOFAR at 150 MHz in the ELAIS-N1 field (Jelić et al. 2014).

An estimate of the distance to the polarized emission can be determined by comparing the RM of the emission against the overall contribution to RM of the Galaxy in the direction of the field. In the direction of the brightest features in the polarized intensity map, we measure a typical ionosphere-corrected RM of +1.0 ± 0.3 rad m⁻² (see Figure 8). Estimates of the full Galactic contribution to RM in this same region, based on measurements of extragalactic Faraday rotation (Oppermann et al. 2015), result in an RM of +9.0 ± 1.6 rad m⁻². If the thermal electron density in the Milky Way is assumed to be an exponential disk with a mid-plane free electron density ${n}_{e,0}$ (cm⁻³) with a scale height H and a uniform vertical magnetic field B_z (μG), then the expected RM (rad m⁻²) out to a distance z (pc) is (Mao et al. 2010)

$$\begin{eqnarray}&&\mathrm{RM}=0.812{B}_{z}{n}_{e,0}H(1-{e}^{-z/H}).\end{eqnarray} \tag{ 5 }$$

Using the measured RM at extragalactic distances, +9.0 ± 1.6 rad m⁻², we can estimate the conditions of the magnetized plasma in the direction of the EoR-0 field as a function of the scale height H. Solving for z, using the measured RM of the observed diffuse emission (+1.0 ± 0.3 rad m⁻²), we estimate the distance to this emission is $z\sim (0.12\pm 0.04)H$. Estimates of the scale height toward the SGP, which is effectively the thick-disk component of the Milky Way, range between 930 pc (Berkhuijsen et al. 2006) and 1830 pc (Gaensler et al. 2008); this corresponds to a distance of ∼110–220 pc to the polarized features. There are a significant number of assumptions and uncertainties associated with this estimate, but it is sufficient to determine that the source of the polarized emission is in the local region of the Galaxy. The structures may even be constrained to lie within the local bubble, which extends out to 50–200 pc from the Sun but is elongated toward high southern Galactic latitudes (Lallement et al. 2003).

A more significant effect that may be used to localize the features with improved precision is that of depolarization. There are three prominent effects that can cause depolarization at long wavelengths: bandwidth, beam, and depth depolarization. Bandwidth depolarization occurs when there is a significant rotation of the polarization angle across a single spectral channel. Beam depolarization is caused by fluctuations in polarization angle across the synthesized beam. Depth depolarization is caused by fluctuations in polarization angle along the line of sight. For the MWA, bandwidth depolarization is negligible for Faraday depths out to $| {\phi }_{\max }| =160$ rad m⁻² (see Section 3.3). The combined effects of depth depolarization and beam depolarization limit our ability to detect polarized emission beyond a certain distance, known as the polarization horizon (Landecker et al. 2002). The polarization horizon depends on frequency, synthesized beam width, and physical properties of the medium in the observing direction (due to variations in the magnetic field and length-scale density along different lines of sight).

At 1.4 GHz, the polarization horizon is typically of the order of thousands of parsecs, e.g., Gaensler et al. (2001), whereas at 408 MHz this reduces to ∼150 pc (Mathewson & Milne 1965). At 154 MHz with the MWA, beam depolarization is a major concern owing to the large PSF of the observations presented here. However, LOFAR observations at significantly higher resolution observe levels of fractional polarization (Jelić et al. 2014) similar to that seen with the MWA. Depth depolarization is also a significant effect that will limit our long wavelength observations to structures that are relatively local compared to higher frequency observations because more distant structures are significantly depolarized by the foreground ISM. Assuming depth depolarization is the dominant factor and assuming uniform synchrotron emissivity, electron density, and magnetic field in a volume of ISM, the path length L at which integrated emission is totally depolarized is defined as (Uyanıker et al. 2003)

$$\begin{eqnarray}&&L\sim \displaystyle \frac{\pi }{(0.81{\lambda }^{2}{n}_{e}{B}_{\parallel })}.\end{eqnarray} \tag{ 6 }$$

Here n_e is the electron density (cm⁻³), λ is the wavelength (m), and B_∥ is the magnetic field parallel to the line of sight (μG). We assume an electron density of n_e = 0.015 cm⁻³, which is consistent with most estimates of the volume-average electron density in the thick-disk component of the warm ionized medium (Gaensler et al. 2008). We can estimate B_∥ using the local horizontal field of ∼2.0 μG (Beck et al. 1996) projected for the direction of the observation; this gives B_∥ = 0.6 μG. At the center of the MWA band, total depolarization occurs at a distance of L ∼ 125 pc and so most polarized features observed can be assumed to be at ≲125 pc. This estimate contains uncertainties with respect to the value of n_e and B_∥ used in the direction of the the EoR field. We also note that at path-lengths beyond the polarization horizon, the radiation is partially repolarized again (Burn 1966; Sokoloff et al. 1998) and so some fraction of emission will exist from beyond the horizon. An even greater uncertainty exists with respect to beam depolarization, which will be significant at MWA wavelengths. However, as the observed polarized structures are larger in extent than the MWA beam and exhibit smooth features in Faraday space (see Figure 6) this effect may not be as great in this instance.

A third estimate of the distance to the emission can be derived from known pulsars within the field. This approach is similar to the first approach, which used the RM contribution of the Galaxy, but relies on the RM toward a nearby pulsar to reduce the uncertainty associated with current models of the Galaxy. Using this approach, the distance L to the polarized emission can be estimated as

$$\begin{eqnarray}&&L=\displaystyle \frac{{d}_{\mathrm{pulsar}}\times \mathrm{RM}}{{\mathrm{RM}}_{\mathrm{pulsar}}}.\end{eqnarray} \tag{ 7 }$$

Here d_pulsar is the distance to the pulsar, RM is the measured RM from the polarized emission and RM_pulsar is the RM of the pulsar.

The diffuse polarized emission in the EoR-0 field has an RM distribution that peaks at +1.0 ± 0.3 rad m⁻². A search through the ATNF Pulsar Catalog³¹ v1.54 (Manchester et al. 2005) revealed a single known pulsar within the EoR-0 field, PSR J2330–2005 (see Figure 5). The pulsar has a dispersion measure (DM) of 8.456 ± 0.002 pc cm⁻³ (Stovall et al. 2015), an estimated DM-based distance of 490 ± 100 pc (Taylor & Cordes 1993) and an RM of +16 ± 3 rad m⁻² (Hamilton & Lyne 1987). Based on these parameters, this would place the polarization emission at a distance of 31 ± 12 pc.

In our targeted search of the pulsar field, we detect PSR J2330–2005 in both linear and circular polarization. In linear polarization, we consistently find a weak 19 mJy beam⁻¹ peak (14% fractional polarization) and measure an RM of +9.6 ± 0.1 rad m⁻² in both epochs 1 and 3. The measured RM is lower than that reported in the ATNF Pulsar Catalog. However, Hamilton & Lyne (1987) report an RM of +9.5 ± 0.2 rad m⁻² from unpublished observations and Johnston et al. (2007) measure an RM of +9.5 ± 0.6 rad m⁻², both of which are highly consistent with our measurement. If we take our measured RM instead of the RM from the ATNF Pulsar Catalog, we place the distance to the polarized emission at 51 ± 20 pc. Based on the measured RM to the pulsar, we estimate the average electron density on the line of sight of this pulsar to be 0.0183 ± 0.002 cm⁻² and the magnetic field B_∥ = 1.31 ± 0.01 μG; these are consistent with those expected in the solar neighborhood.

We recognize that the estimate of the distance toward the polarized emission of ∼110–220 pc, based on the estimated contribution of Galactic RM toward extragalactic sources, and the L ≲ 125 pc distance based on depth depolarization contain significant uncertainties. The estimate based on a relatively nearby pulsar within the observed field, however, is only limited by uncertainties in the measured distance of the pulsar and any inhomogeneities that may exist in the magnetic field and electron density toward the pulsar. As such, we adopt 51 ± 20 pc as our estimate of the distance toward the observed polarized emission.

Based on Taylor et al. (2009) observations at 1.4 GHz, there are 399 known polarized sources within the 400 sq. degree region of the EoR-0 field. The 154 MHz flux density of these sources, in total intensity, cannot be accurately determined from the high-resolution MWA maps shown in Figure 2 because the field suffers greatly from sidelobe confusion. Instead, the spectral slope of each source can be determined by comparing the 1.4 GHz Taylor et al. (2009) observations with 158 MHz GLEAM observations of the field (Hurley-Walker et al. 2016, in preparation). Based on the measured spectral slopes and assuming no depolarization, one would expect ∼191 of the Taylor et al. (2009) 1.4 GHz sources to be detected in polarization at 154 MHz. In all, only four of these sources were detected at 154 MHz with the MWA.

It is useful to consider the depolarization ratio for the sources within the MWA field. We determine the depolarization ratio (DP) between 1.4 GHz and 154 MHz using (Beck 2007):

$$\begin{eqnarray}&&\mathrm{DP}{(1400,154)=({P}_{154}/{P}_{1400})(1400/154)}^{\alpha }\end{eqnarray} \tag{ 8 }$$

where α is the measured spectral index of the source. DP(1400, 154) = 1 when there is no change in fractional linear polarization from 1.4 GHz to 154 MHz, i.e., no depolarization. DP(1400, 154) = 0.5 when the fractional linear polarization at 154 MHz is half that at 1.4 GHz. In order to depolarize all remaining 187 Taylor et al. (2009) sources at 154 MHz to below the sensitivity limits of the MWA observations, a DP(1400, 154) upper limit of <0.08 would be required.

Mulcahy et al. (2014) searched for polarized sources in a deep 8 hr 151 MHz LOFAR observation around M51 with significantly higher resolution (20'') and sensitivity (100 μJy beam⁻¹), albeit over a much smaller field-of-view (17 square degrees). In all, a total of six polarized sources were detected. Three of the sources have Taylor et al. (2009) counterparts and have a measured DP(1400, 151) of 0.196, 0.038, and 0.029. These depolarization ratios would be consistent with those required to depolarize all known 1.4 GHz polarized sources in our MWA field-of-view even without taking into consideration the additional beam depolarization that would be expected with the larger MWA beam.

While it is beyond the scope of this paper to analyze further, it is interesting to note that the four extragalactic sources detected with the MWA are not significantly more depolarized at 154 MHz compared to 1.4 GHz, i.e., DP(1400, 154) ranges between 0.26 and 0.91 (see Table 3). As such, they are characteristically different to the sources detected by Mulcahy et al. (2014) with LOFAR and the MWA field sources that have clearly depolarized below our detection threshold. This could hint at a very small population of sources (one per 100 sq. deg) that do not show significant changes in depolarization with wavelength. The population is small enough that LOFAR may not yet have observed such sources with the limited number of fields observed in full polarization with its smaller field of view. We do note, however, that two of the least depolarized sources detected with the MWA are associated with unresolved polarized hot spots of relatively large radio galaxies (0.27 and 1.22 Mpc in extent). If these hot spots lie outside the local environment of the host galaxy, they may not suffer as greatly from the effects of depolarization as ones that are embedded within a magnetized plasma.

The structures seen in polarization gradient maps are generally caused by differential Faraday rotation (Shukurov & Berkhuijsen 2003; Fletcher & Shukurov 2007), a foreground Faraday screen (Haverkorn & Heitsch 2004; Fletcher & Shukurov 2007; Gaensler et al. 2011), or intrinsic emission (Sokoloff et al. 1998; Sun et al. 2014).

Differential Faraday rotation causes depolarization contours that may manifest themselves as polarization gradients. They arise where synchrotron emission and Faraday rotation occur in the same region. For a given wavelength (λ), depolarization occurs at position x in the plane of the sky under the condition where $2|$RM$(x)| {\lambda }^{2}=\pi n$ (Shukurov & Berkhuijsen 2003) and n = 1, 2, 3,... The resulting depolarization contours are infinitely thin, i.e., unresolved by the beam, and will shift as a function of frequency. As such, the contours in this interpretation are not directly related to any real structures in the ISM—hence the alternate name of "Faraday ghosts."

A second interpretation of depolarization canals is that they are caused by gradients in a foreground Faraday screen (Fletcher & Shukurov 2007). In this interpretation, features in the radio polarization gradient map are physically associated with specific structures in the ISM. These structures are caused by a sudden increases or decreases of the electron density or magnetic field. As such, these features remain spatially fixed but appear and disappear as a function of frequency as different depths are probed. Features exhibiting such behavior have been observed at centimeter wavelengths, see Gaensler et al. (2011), but the evolution of these features has not yet been explored over large fractional bandwidths.

A third interpretation is that the features are intrinsically polarized and caused by random anisotropic magnetic fields (Shukurov & Berkhuijsen 2003). This results in smooth synchrotron emission in total intensity, which is not observable since it is spatially filtered by the instrument, but with intrinsically polarized structures on smaller scales that are observable. In general, the structures will not shift or evolve as a function of frequency; however, more distant features will only be seen at shorter wavelengths as a result of the polarization horizon (see Section 4.3). As such, there will be an increase in the number of observed features as a function of increasing frequency.

The three different interpretations can be easily distinguished with a multi-frequency analysis of the gradient maps. We have shown that significant features are observed in the EoR gradient maps when full-band 154 MHz data are utilized (Figure 11). These features are of the order of 1° in extent and are consistent with the beam size, i.e., unresolved. Assuming a distance of 51 ± 20 pc, they have a spatial extent of 0.9 ± 0.3 pc, which is consistent with the ∼0.5 pc spatial extent observed in similar unresolved features in the Galactic plane at 1.4 GHz (Gaensler et al. 2011). These gradient map features are also present in multi-band GLEAM snapshot data (Figure 12), but the maps are limited by poor sensitivity and instrumental leakage, which affect the higher frequency end of the band.

The deep epoch 1 observations, however, provide sufficient sensitivity on a per-160 kHz channel basis to examine the frequency-dependent behavior of the gradient function, see Figure 13. If we consider the polarization horizon, as described in Equation (6), the gradient function cube explores a square frustum centered on the EoR-0 field. In this instance, the back of the frustum (upper end of the observing band) probes more deeply (polarization horizon of 150 pc) and the front of the frustum (lower end of the observing band) probes nearby features (polarization horizon of 100 pc).

When the gradient function cube is explored, the gradient features vary smoothly as a function of frequency but show no significant spatial movement. The lack of spatial translation of the features rules out the differential Faraday rotation interpretation. Furthermore, most features that peak at the lower end of the band tend to persist toward the higher end of the band, with an accumulation of features with increasing frequency. This observation tends to support an intrinsic polarization interpretation but does not completely rule out a foreground Faraday screen (which generally results in features that do not vary as a function of wavelength).

A limitation of the polarization gradient method is that it is only sensitive to structures that have a scale-size similar to that of the synthesized beam of the instrument (Robitaille & Scaife 2015). Gradient features larger than the beam size are resolved spatially in the plane of the sky. The same is not true for features that extend spatially in a direction perpendicular to the plane of the sky since the gradient function is only performed over the two spatial dimensions and not in the frequency direction (which, as described in the previous paragraph, can act as a proxy for depth). This may result in features appearing larger in depth than in spatial extent and confuse the distinction between features caused by interpretations 2 and 3 above.

To distinguish between interpretations 2 and 3, we can determine whether the observed RM gradient in the field is sufficiently large enough to result in the polarization gradients we observe. If an RM gradient results in a polarization gradient then this is evidence of a foreground Faraday screen (interpretation 2). However, if a polarization gradient appears where there is no clear RM gradient, then this is evidence of intrinsic polarization (interpretation 3). To test this, we consider a uniform linearly polarized background:

$$\begin{eqnarray}&&{\boldsymbol{P}}={P}_{0}{e}^{2i(\psi +\phi {\lambda }^{2})}\end{eqnarray} \tag{ 9 }$$

where ψ is the intrinsic polarization angle, ϕ is the Faraday depth, and P₀ is magnitude of the polarized intensity. From this equation, assuming P₀ is constant, the relationship between the polarization gradient $(| {\boldsymbol{\nabla }}{\boldsymbol{P}}|$) and RM gradient ($| {\rm{\nabla }}\phi |$) for Faraday-thin polarized emission can be derived as (Burkhart et al. 2012)

$$\begin{eqnarray}&&| {\boldsymbol{\nabla }}{\boldsymbol{P}}| =2{\lambda }^{2}{P}_{0}| {\rm{\nabla }}\phi | .\end{eqnarray} \tag{ 10 }$$

The intrinsic polarized intensity, P₀, cannot be obtained from our MWA observations directly because of depolarization. Instead, we can estimate it based on the intensity of synchrotron emission out to our adopted distance of the polarized emission. Nord et al. (2006) estimate a local emissivity of ₇₄ = 0.36 ± 0.17 K pc⁻¹ at 74 MHz. Taking a distance of 51 ± 20 pc, the estimated total intensity is 500 ± 300 mJy beam⁻¹ assuming a temperature spectral index of β = −2.55 (see Section 4.2). If we assume approximately 30% intrinsic polarization (Sun et al. 2008) this equates to P₀ = 150 ± 90 mJy beam⁻¹ at 154 MHz. Similarly, Peterson & Webber (2002) estimate ₁₀ = 3.0 ± 0.7 × 10⁻⁴⁰ W m⁻³ Hz⁻¹ sr⁻¹ at 10 MHz. Using the same assumptions as above, this results in P₀ = 530 ± 230 mJy beam⁻¹. At 154 MHz, these estimates suggest that a 0.01 rad m⁻² beam^−0.5 RM gradient would result in a 0.011 ± 0.007 Jy beam^−1.5 gradient in polarization for the Nord et al. (2006) estimate and 0.040 ± 0.017 Jy beam^−1.5 gradient for the Peterson & Webber (2002) estimate.

We can compare this with our observed gradients. Figure 19 shows the RM, RM gradient, and polarization gradient in a region of the EoR-0 field, where significant gradients are observed in polarization. There is one clear RM gradient feature, the S-shaped feature on the left of the RM gradient map running from top to bottom, that is associated with one of the filaments observed in the polarization gradient map. The feature peaks at ∼0.02 rad m⁻² beam^−0.5 in the RM gradient map and at ∼0.024 Jy beam^−1.5 in the polarization map. This particular feature seems consistent with a polarization gradient resulting from a Faraday screen in which P₀ = 160 mJy beam⁻¹, a value that is within the Nord et al. (2006) and Peterson & Webber (2002) estimates. The structure is reminiscent of the Burkhart et al. (2012) "Case 2" scenario associated with supersonic- and subsonic-type turbulence. In this scenario, there is a jump in RM spatially as a result of strong turbulent fluctuations in the magnetic field or electron density along the line of sight, weak shocks, or edges of a foreground cloud.

Zoom In Zoom Out Reset image size

The brightest polarization gradient feature, just west of the S-shaped feature in Figure 19, has no obvious counterpart in the RM gradient map. It is likely that this, and similar features throughout the wider field, are polarization gradients resulting from intrinsically polarized structures and are not caused by foreground Faraday screens. The presence of polarization gradients with RM gradient counterparts and also those without counterparts hint that the observed polarized structure results from a combination of both instrinsically polarized structures and a foreground Faraday screen.

In Section 4.5, we investigated possible causes for the structures seen in the polarization gradient maps and concluded that they could result from a combination of both instrinsically polarized structures and a foreground Faraday screen. An alternate method of distinguishing between these two causes is through a structure function analysis (Sun et al. 2014). The structure function of complex polarization (P = Q + iU) and that of polarized intensity $(p=| P| )$ are defined respectively as

$$\begin{eqnarray}&&{\mathrm{SF}}_{P}(\delta \theta )\equiv \langle | P(\theta )-P(\theta +\delta \theta ){| }^{2}\rangle \end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{\mathrm{SF}}_{p}(\delta \theta )\equiv \langle {[p(\theta )-p(\theta +\delta \theta )]}^{2}\rangle \end{eqnarray} \tag{ 12 }$$

Here δθ is the angular separation between two lines of sight. A comparison of the two structure functions can indicate whether the observed polarized structures are intrinsic or caused by Faraday screens (Sun et al. 2014). For intrinsic polarization, there will be no correlation between polarized intensity and polarization angle, so the slope of SF_p will be similar to that of SF_P. Alternatively, if the polarized structures are caused by Faraday screens with beam depolarization, then the slope of SF_P will be flatter than SF_p since much of the intrinsic structure will be smeared out by Faraday screens.

The resulting structure functions for SF_p and SF_P are shown in Figure 20 for epoch 1 observations of the EoR-0 field. At angular separations less than about 90', the slope of the structure function effectively represents the smoothing effect of the MWA PSF (54'). At very large angular separations, the structure function is less constrained because of limited sensitivity of the MWA to structures ≳10° and the available field of view (25° × 25°). For this analysis, we focus on the region between 120' < δθ < 270' to avoid data affected by instrumental constraints. We note that there is observed curvature in the structure function for SF_P in the fitting region, possibly associated with a contaminating sidelobe structure. While this results in a poorer fit for SF_P compared to that of SF_p, the slope of SF_P is consistent to, or at most steeper, than that of SF_p. If the slope of SF_P were flatter than that of SF_p this would be suggestive of polarization caused by Faraday screens (Sun et al. 2014). However, the similarity in slope of SF_p and SF_P, within 3σ fitting errors, suggests that the structures are dominated by intrinsic polarization.

Zoom In Zoom Out Reset image size

In observations of the Galactic plane at 4.8 GHz, Sun et al. (2014) also find evidence of intrinsic polarization whereas at 2.3 GHz a structure function analysis suggests the presence of a Faraday screen. The reasoning for the different behavior is that higher frequency observations (4.8 GHz) probe more deeply because they are less affected by the presence of a Faraday screen. One would expect that MWA observations would be particularly sensitive to the effects of a Faraday screen because they are observed at long wavelengths. However, the structure function analysis suggests that the observed diffuse polarization is intrinsic in nature and must therefore be associated with structures that are very local.

The structure function analysis performed here suggests that intrinsic polarization is dominating in this field. This is consistent with the multi-frequency polarization gradient analysis performed in Section 4.5, which found evidence of both intrinsic and Faraday screen causes for the observed polarization gradients. Currently, the structure function analysis is limited by the effective range of angular separations that could be used. Deconvolution and imaging of even larger fields would aid in widening this range and improving the structure function analysis; however, this will be left for future work.

As described in Section 3.3, the 154 MHz MWA observations provide a narrow RMSF of δϕ = 2.3 rad m⁻². Combined with the maximum-scale size sensitivity of 1.0 rad m⁻² the MWA observations are only able to detect simple components even in the presence of Faraday complex structure. The presence of a Faraday-thick structure would be entirely resolved by the MWA RMSF, resulting in a two-peak FDF (see Figure 3, Li et al. 2011). A Faraday-thin structure, however, would result in a simple FDF with a single component; see Appendix B of Brentjens & de Bruyn (2005).

A mix of structures has been observed in Faraday spectra observed in the Galactic anti-center with the WSRT at 324–387 MHz with ∼3' resolution (Schnitzeler et al. 2007, 2009). The vast majority of lines of sight observed in a 9° × 9° field have Faraday spectra that are reasonably well fit by a simple model dominated by a single bright peak. Only a small fraction of lines of sight exhibit Faraday complexity.

Looking at the Faraday spectra from the 154 MHz MWA EoR-0 observations, the vast majority of Faraday structure is simple and dominated by peaks at low RM; see Figures 7 and 8. This indicates that the extent of the polarized emission in Faraday depth is less than the MWA RMSF. The Faraday spectra are similar to those observed in diffuse polarization at similar wavelengths with LOFAR in the ELAIS-N1 (Jelić et al. 2014) and 3C196 fields (Jelić et al. 2015) with a narrower RMSF (0.9 rad m⁻²). It is unlikely that these are unresolved Faraday-thick structures because of the excellent resolution available in Faraday space with the MWA and LOFAR. Without introducing a more involved scenario, in which a secondary peak in Faraday space is weakened to a level below our detection threshold, a simple explanation of the peak is that the polarized emission is Faraday-thin, meaning the polarized structure is intrinsic. This would be consistent with findings of the polarization gradient function analysis and the structure function analysis discussed in Sections 4.5 and 4.6.