ROTATION MEASURE SYNTHESIS OF GALACTIC POLARIZED EMISSION WITH THE DRAO 26-m TELESCOPE

The axisymmetric reflector, of diameter 25.6 m, is equatorially mounted. The mesh surface has an accuracy of ∼0.5 cm rms. The receiver is mounted at the prime focus on a fiberglass tripod. The telescope can observe the sky between −30° and +90° in an almost fully automated fashion.

The feed is scaled from the design of Wohlleben et al. (1972), which was developed for the Effelsberg 100 m Telescope. The DRAO 26 m Telescope has the same ratio of focal length to diameter, f/d = 0.3, and the feed provides excellent performance at its design frequency, 1420 MHz, where the aperture efficiency achieved is ∼0.53 and the beam is circular with half-power width of 36'.

Feed performance has been computed across the operating band (Smegal 2005). Feed radiation patterns are highly circular (with equal half-power widths in the E- and H-planes) at 1400 MHz. At lower frequencies, the H-plane pattern is wider than the E, and conversely for frequencies above 1400 MHz. This leads to increased instrumental polarization at frequencies away from 1400 MHz. Figure 1 shows the beamwidth of the telescope across the entire frequency band. The small variations in beamwidth are real (they are highly repeatable), but their cause is unknown.

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The receiving system is designed to accept all the power from an incoming signal and to produce outputs that describe its polarization state. Two antennas of orthogonal polarization, whether linearly or circularly polarized, will together collect all the incoming power. Given the a priori knowledge that the linearly polarized component of synchrotron emission dominates any circularly polarized content (Pacholczyk 1970), we designed the receiving system to measure small linearly polarized components in largely unpolarized signals. The two channels of the receiver accept right-hand circular polarization (R) and left-hand circular polarization (L). Stokes parameters Q and U that describe linear polarization can then be derived by correlation techniques.

Consider the incoming signals as the sum of two circularly polarized field components

$$\begin{equation} {E_r} = {{E_{\rm R}}\,e^{i{\omega }t}}, \quad {\rm {and}} \end{equation} \tag{ 2 }$$

$$\begin{equation} {E_l} = {{E_{\rm L}}{\thinspace }\quad e^{{\thinspace }i{\omega }t + {\delta }}}. \end{equation} \tag{ 3 }$$

In terms of these components, the desired outputs from the polarimeter are

$$\begin{equation} {I} = \case{1}{2}\big(E_{\rm L}^2 + E_{\rm R}^2\big), \end{equation} \tag{ 4 }$$

$$\begin{equation} {Q} = {{E_{\rm L}}{E_{\rm R}} {\rm {cos}}{\delta }}, {\thinspace }{\thinspace }{\rm {and}} \end{equation} \tag{ 5 }$$

$$\begin{equation} {U} = {{E_{\rm L}}{E_{\rm R}} {\rm {sin}}{\delta }}. \end{equation} \tag{ 6 }$$

${V} = {{\frac{1}{2}}(E_{\rm L}^2 - E_{\rm R}^2)}$ is small and we will ignore it.

The alternative scheme, receiving two linear polarizations, leads to the derivation of Q as the (small) difference between two large quantities, and is therefore quite susceptible to instrumental effects such as gain variations between receiver channels.

The operation of the feed as a collector of circularly polarized signals can be more easily understood by considering it as a transmitter and showing that it radiates circularly polarized signals. An orthomode transducer combines two monochromatic signals A and B of equal amplitude from coaxial inputs, launches them as separate signals in rectangular waveguide and then combines them in a single square waveguide where they travel in orthogonal (non-interacting) TE₁₀ and TE₀₁ modes. A power splitter in square waveguide converts A and B into $\frac{1}{2}(A+B)$ and $\frac{1}{2}(A-B)$. A differential phase shifter, also built in square waveguide, provides a 90° relative phase shift between these signals and so generates outputs $\frac{1}{2}(A+iB)$ and $\frac{1}{2}(B-iA)$, which are circularly polarized components. A smooth transition from square to circular waveguide transfers these two outputs to the feed, from which they will emerge as circularly polarized signals in free space.

By reciprocity, this device will collect the two circularly polarized components E_l and E_r described in Equations (2) and (3) from an incoming wave and will deliver them to the coaxial inputs of the two receiver channels. In the following, we denote E_l simply as L and E_r as R, and recognize that they are broadband signals. Powers will be denoted as RR = E_r E*_r, LL = E_l E*_l, RL = Re(E_r E*_l), and LR = Im(E_r E*_l).

The return loss of the polarizer at the receiver inputs is 20 dB: only 1% of the power in a signal injected into the polarizer at either port returns to that port. The isolation between the two ports is better than 30 dB (0.1% of signal power). The dissipative loss is less than 2% (0.1 dB) and the axial ratio of the device (measured by transmitting from it and analyzing the radiated signal) is of the order of ±10%.

2.2.1. Phase Shifter, Power Splitter, and Orthomode Transducer

The phase shifter is built in square waveguide (12.7 × 12.7 cm); its overall length is ∼60 cm. Dielectric slabs line all four walls, their dimensions chosen to give a difference in insertion phase as close as possible to 90° between orthogonal TE₁₀ and TE₀₁ modes in the waveguide. The design (developed with electromagnetic simulation software) gives a phase difference of 90° ± 2° and in practice a performance of 90° ± 5° is achieved. This design is based on the device developed by Srikanth (1997) using corrugations in the waveguide walls to provide the differential phase shifts across the band 18.9–26.5 GHz. The fractional bandwidth of the two devices is similar (essentially an entire waveguide band) and the performance is similar. In our case, use of corrugations would have resulted in lower loss but the overall length would have been about three times larger. The dielectric that we used was Teflon (dielectric constant ≈ 2.3). We explored designs using materials with higher dielectric constant in the hope of reducing the length of the device, but were unable to make an improvement, either in size or performance, over the design using Teflon.

Dissipative loss of the phase shifter is slightly unequal in the two orthogonal modes because more dielectric is used in one plane than in the other. The losses are about 0.05 and 0.1 dB.

The input and output of the power splitter are both in square waveguide, but the orientations differ by 45°. The device is fabricated from eight flat triangular plates bolted together. Its length is 20.6 cm.

The orthomode transducer is a commercially available device, originally developed for the Very Large Array by Atlantic Microwave (their model number OM6500). It has a square waveguide input and two outputs in rectangular WR650 waveguide. Fabricated from cast aluminum, it is a low-loss device (loss is probably less than 0.05 dB or 1%).

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The receiver is mounted at the prime focus in an insulated, temperature-controlled box. The air temperature inside the focus box is kept at 25.0 ± 0.1 °C. The two-channel receiver and the signal-processing system are depicted schematically in Figure 2. Directional couplers permit injection of noise calibration signals. Circulators (unidirectional devices which allow the low-noise amplifiers to receive signals from the antenna ports but isolate the amplifiers from reflections from the polarizer and feed) preceding the first amplifiers prevent backscattering and thus reduce cross-coupling between the two hands of polarization, which would lead to instrumental polarization. The low-noise amplifiers (LNAs) are commercial uncooled HEMT amplifiers with noise temperature ∼35 K, but elements preceding them add about 30 K to their noise temperature. The receiver follows a conventional design, with a single-stage down-conversion taking the radio frequency (RF) band of 1277–1762 MHz to baseband. The 3 dB bandwidth of the system is 485 MHz. The overall system temperature, including receiver noise, ground and atmospheric emission is estimated to be ∼140 K.

A set of scans along the meridian, 12 arcmin spaced, was defined which would provide sampling slightly surpassing the Nyquist criterion of the entire sky from −30° to 87° declination at the highest frequency. Long scans extend from the horizon limit at −30° declination to 87°, close to the north celestial pole, and short scans from −30° to 60°. To avoid oversampling around the pole, every second scan is a short scan. A quasi-random sequence of scans was devised, aiming to avoid systematic effects while making optimal use of the observing time. With a scanning speed of 52.5 arcmin min⁻¹, short scans take 1.7 hr and long scans 2.2 hr. Scans are made exclusively at night to avoid contributions from solar emission through the sidelobes, but calibration sources are observed during the hour before sunset and after sunrise. For the final survey, each scan will be observed twice, as an up and a down scan, resulting in double coverage of every pixel. The region presented in this paper was observed in 2008 April and is non-uniformly covered.

Resolution was reduced to 1° by smoothing in the image plane to approximate full Nyquist sampling. The rms noise in one channel (237 kHz width) was found to be ∼80 mK in total power and ∼40 mK in polarization. This is about 1.6 times higher than the theoretical value of 25 mK, calculated based on our system temperature, bandwidth, and integration time. The reasons for the higher rms noise are (1) the deactivation of one of the four FFT lanes on each FPGA due to temperature problems,⁸ which resulted in a loss of 25% of digitized samples and thus increased the rms noise by a factor of 1.15; and (2) weighting of the digitized samples using a Blackman–Harris windows function, which, in effect, made use of only 50% of the input signal and thus increased rms noise by a factor of 1.41.

We now discuss the most important post-processing and calibration steps. These are (1) correction of instrumental effects (including corrections for bandpass, relative phase shift across the band, and cross-talk introduced in the receiving system by a left polarized signal entering the right channel and vice versa), (2) subtraction of ground radiation, and (3) removal of scanning effects. A correction of the cross-polar response of the telescope beam, which requires a deconvolution of the final maps with the beam pattern, was not attempted. While bandpass and phase corrections were averaged over a few channels, all other corrections were performed on each channel individually.

In addition to the electronic gain calibration, which is part of the real-time processing chain (Section 4), daily flux calibrations are derived from observations of two of our four flux calibrators (see Figure 6). We used Cyg-A, Tau-A, and Vir-A as our primary calibrators. Cas-A was used as secondary calibrator whenever none of the primary calibrators was visible. The flux of the secondary calibrator was derived from the primary calibrators. A calibration observation consisted of 11 declination scans spaced by 12 arcmin, yielding a map of the source. A two-dimensional Gaussian was fitted to the calibration observations and the amplitude of the fitted Gaussian was used as the calibration value. Table 2 summarizes the flux values and spectral indices (α) used for the primary calibrator and derived for the secondary calibrators. We found that flux values slightly different from the published values gave the best overall consistency across the four calibrators. The final data are tentatively calibrated in main-beam brightness temperature by assuming an aperture efficiency of 53% over the entire band, a value originally determined for 1.4 GHz by Higgs & Tapping (2000). In the future, when survey data over a much larger period need to be calibrated, it is planned to take intrinsic variability of Cas-A into account.

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The relative phase between the two polarization channels (R and L) was unknown and was determined through observations of 3C286 and 3C270. Both sources are at high Galactic latitudes and have well-known RMs of ≈0. At 1.4 GHz, the percentage polarization and polarization angles of 3C286 and 3C270 are 9.3% and 32°, and 8.0% and 123°, respectively (Tabara & Inoue 1980). This measurement revealed a phase gradient of about 30° across the band (Figure 6). A phase calibration is not done on a regular basis since this gradient will be stable until changes to the receiver are made that affect the path length or delay of the signal paths.

Cross-coupling of one hand of polarization into the other results in instrumental polarization. In the final polarization maps, this effect leads to a conversion of Stokes I into U and Q, leading to the additional signals $\mathrm{\mbox{\it U}}_{\mathrm{inst}} = f_\mathrm{{\it U}}\,\mathrm{{\it I}}$ and $\mathrm{\mbox{\it Q}}_{\mathrm{inst}} = f_\mathrm{{\it Q}}\,\mathrm{{\it I}}$. This type of instrumental polarization is the result of imperfections in the feed and mismatches in the receiver. The coefficients f_U and f_Q were determined daily from the flux calibration. The integrated polarization from the primary calibrators is very close to zero and they were considered to be unpolarized. Any polarization detected is then of instrumental origin. As it is evident in the final maps, the removal of cross-talk is not sufficient for a complete correction for instrumental polarization. The images still show spurious polarization features around bright sources produced by the cross-polar response of the telescope. The correction of cross-polar response will require a cleaning (deconvolution) of the final polarization data, which is planned for the complete survey and requires fully Nyquist-sampled maps in all Stokes parameters.

Ground radiation is received through the side- and spillover lobes of a telescope. It can contribute a signal an order of magnitude stronger than the sky, especially at low elevations. As a temporary approach for the data presented in this paper, ground radiation profiles were determined by plotting the observed Stokes I, U, and Q intensities versus elevation. Only scans made between 13^h and 17^h R.A. were used, avoiding the bright emission from the Galactic plane. Ground contribution was then retrieved from these scatter plots by taking the lower envelope in Stokes I, and a median value for Stokes U and Q.

Scanning effects (stripes) in the final maps were removed by a technique known as "basket weaving." This technique removes baseline effects by comparing the overlaps of scans made in different directions and times with the assumption that the baselines vary and the sky brightness remains constant (Sieber et al. 1979). The stripes are most likely caused by variations of the electromagnetic properties of the ground surrounding the telescope affecting the ground pick-up, time-variability of the noise figure of the LNAs, or small errors in the flux calibration. Basket weaving was applied on each channel individually. To cope with the high data volume, the basket weaving algorithm ran on a cluster consisting of 40 CPUs. A problem with the basket weaving technique is the floating baseline level which can introduce large-scale distortions in the maps. The Stokes I map is more affected by these distortions then the Stokes U and Q maps. The maps presented here (Figure 7) show the R.A. range mostly free of distortions (a gradient is still present in the total intensity map at R.A. > 20^h).

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RM-Synthesis consists of two separate steps: (1) de-rotation of Stokes U and Q, and (2) cleaning of the RM-Spectra. In the first step, the final data cube is de-rotated for a range of RM values. Here, we used RMs from −1250 to 1250 rad m⁻² in steps of 10 rad m⁻². For each RM value, the Stokes U and Q values in each pixel and channel are de-rotated by the angle RM λ². The de-rotated cube is then collapsed (averaged) into a two-dimensional map of polarized intensities, which forms a slice of the RM-Synthesis cube. RM-Spectra are constructed for each pixel from the series of two-dimensional maps at different RMs.

The second part of RM-Synthesis is cleaning. Cleaning is necessary because the observed spectra are "contaminated" with spurious line features caused by sidelobes in the rotation measure spread function (RMSF). The RMSF is the response function (the instrumental response) with which the spectrum is convolved and is the result of incomplete frequency coverage. Figure 8 shows an RMSF for our observations, which is a typical RMSF for data in our frequency range, coverage, and flagging. Using an analogy to synthesis imaging, the RMSF can be understood as the "dirty beam." The observed spectra ("dirty images") need to be deconvolved (with an appropriate clean algorithm) to obtain the "cleaned images." The clean model consists of a series of delta peaks. To obtain cleaned RM-spectra, the RM-model is convolved with a Gaussian (the "restoring beam") with a width corresponding to the expected resolution in RM-Synthesis, which, in our case, was slightly less than 132 rad m⁻². Figure 8 shows a cleaned and an uncleaned RM-Spectrum. Spurious components at the ∼5% level are still present and are visible at ±850 rad m⁻² in the spectrum shown.

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Our frequency range and spectral resolution determine: (1) the resolution of the RM-Spectra (the resolution in Faraday depth), (2) the largest scale in Faraday depth we are sensitive to, and (3) the maximum observable Faraday depth. These values are summarized in Table 3. In our case, the largest scale in Faraday depth we can measure is smaller than the resolution. This is an important constraint to keep in mind: two peaks in our RM-spectrum do not necessarily indicate two different Faraday rotation layers, but may also arise from a continuous distribution of RMs in Faraday depth, a few RMTFs wide, of which only the two edges are resolved.

Figure 9 shows two slices of the RM-Synthesis cube. The rms sensitivity of these images is ∼3 mK, the rms noise expected from the entire 470 MHz bandwidth. This high sensitivity is one of the great benefits of RM-Synthesis. Furthermore, the abundant frequency coverage permits quite aggressive flagging of RFI, leading to good signal-to-noise ratio even outside the protected radio astronomy bands. Finally, we note that RM-Synthesis eliminates the problem of bandwidth depolarization: it provides an adaptive filter that can be tuned to the characteristics of the emission.

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The strength of RM-Synthesis, however, is in revealing three-dimensional structures in Faraday space. This requires a λ²-coverage matched to the expected Faraday rotation. Our resolution in Faraday depth is probably sufficient to map the general trend of RMs, but will only allow us to resolve out multiple RM components for highly Faraday-rotated parts of the ISM. Our frequency range (λ²-coverage), however, will allow us to detect highly Faraday-rotated structures even if the fractional polarization of these regions is extremely low. Without RM-Synthesis, the data would be "confusion limited" in the sense that faint but highly Faraday-rotated emission could not be separated from the usually stronger, unrotated "foreground." RM-Synthesis helps by separating differently Faraday-rotated structures.

The data presented here are preliminary products in the sense that they are not yet absolutely calibrated: ground radiation profiles were determined in an area of the sky containing large-scale Galactic emission in Stokes I, U, and Q, which makes the separation of ground and sky emission difficult. An independent, absolute temperature scale has not been established for the telescope. Instrumental polarization is visible in the maps caused by the cross-polar response of the telescope, which is most obvious along the Galactic plane. Smaller problems are remaining scanning effects. Despite the preliminary state of these data, the final Stokes U and Q maps at 1.4 GHz compare very well with the DRAO Low-Resolution Polarization Survey at 1.4 GHz (Wolleben et al. 2006), which convinces us that our proof-of-concept study will provide valuable input for future RM-Synthesis observations with single-antenna telescopes.

A few large-scale structures in the 0 rad m⁻² RM-Synthesis slice (Figure 9, top panel) are immediately obvious. Polarized emission from the North-Polar Spur is clearly visible as an arc-like filament in the center of the map, going in R.A. from 14^h to 17^h30^m, and in decl. from −5° to 20°. South of the Galactic plane, at R.A. from about 19^h to 21^h30^m and decl. from −25° to 0°, a patch of polarized emission is visible, which has been interpreted as part of the Loop I structure (Wolleben 2007). At R.A. = 18^h30^m and decl. = 60° another polarized filament is visible, most likely associated with Loop III. Polarized emission within a narrow strip along the Galactic plane can be assumed to be instrumental polarization.

The RM-Synthesis slice at 60 rad m⁻² (Figure 9, bottom panel) is chosen as an example for polarized emission at high positive RMs. Most features in this slice actually peak at slightly different RMs. The most obvious structure is centered on R.A. = 17^h30^m and decl. =20°, about 20° in size. Other structures along the Galactic plane and structures close to the edges of the map may be spurious.

Previous polarization surveys could detect polarized emission from the North-Polar Spur only at Galactic latitudes above ∼25°, while in total intensity the spur can clearly be traced down to lower latitudes. The two filaments found at high positive RMs run from the southern tip of the polarized emission of the North-Polar Spur to the Galactic plane. The two filaments may therefore be associated with the North-Polar Spur, perhaps representing highly Faraday-rotated low-latitude emission of the spur. We postpone further analysis and interpretation until sampling and angular resolution are improved.

In summary, the two filaments at 60 rad m⁻² are good examples of structures that are only visible in polarization and which can be revealed only by RM-Synthesis. Such high RM require a strong magnetic field parallel to the line-of-sight. The filaments are most likely structures in the magnetic field, perhaps produced by supernovae or stellar winds in the ISM, compressing the ambient magnetic field.

Our RM-Synthesis data reveal faint, Faraday-rotated structures at RM ≲−25 rad m⁻². Some of these structures are filamentary in shape and seem to be associated with the North-Polar Spur, although not with its southern tip but other parts of its shell at higher Galactic latitudes. Thus, it is possible that our RM-Synthesis data reveal, in fact, the three-dimensional structure of the magnetic field of the North-Polar Spur, but more complete coverage of this region is required to confirm this interpretation.

Wide-band polarimetric data present a challenge for calibration in that the receiver characteristics and performance can vary significantly over the band. Furthermore, the orientation and magnitude of sidelobes and spillover lobes depends on frequency, resulting in highly frequency-dependent ground radiation profiles. In our data, we find channels that are virtually free of instrumental polarization while other channels are almost free of ground radiation.

These effects can be very useful for calibration. For example, channels free of ground radiation can be used as "anchor points" for an absolute calibration, making the removal of ground radiation more robust in the presence of large-scale emission structures in the data. Similarly, channels free (or nearly so) of cross-talk can be very useful for the determination of the cross-polar component of the instrumental polarization.

An important observation is that we find unexpectedly high RM values for the diffuse emission. Diffuse emission is subject to various depolarization effects along the line-of-sight, which has led to the argument that most of the diffuse polarized emission at ≲2 GHz must be of local origin within a few kpc. We find RMs as high as 100 rad m⁻² for some of the diffuse emission, which may either indicate that the emission comes from a larger distance, or that the local magnetic field is stronger than previously believed.

Previous RM surveys of the diffuse Galactic emission revealed only moderate RMs of less than a few tens of rad m⁻² (Brouw & Spoelstra 1976). We conclude that Faraday rotation should be measured using wide-band spectro-polarimetric observations. The relation between polarization angle and λ² is not always linear for the diffuse Galactic emission, rendering the traditional techniques of determining RM by least-square fitting inadequate for diffuse emission.