THE DRAO PLANCK DEEP FIELDS: THE POLARIZATION PROPERTIES OF RADIO GALAXIES AT 1.4 GHz

The DRAO ST (Landecker et al. 2000) was used to produce a deep polarization mosaic at 1.4 GHz centered on the ELAIS N1 field, expanding upon pilot observations reported by Taylor et al. (2007) in both solid angle and sensitivity. The DRAO ST simultaneously observed the H i 21 cm line and 408 MHz continuum along with 1.4 GHz continuum. The seven dish east–west interferometer observed in full polarimetry continuum mode using the four available bands of 1406.65, 1414.15, 1426.65, and 1434.15 MHz, each with a bandwidth of 7.5 MHz. A full synthesis of each individual field requires 144 hr to complete by moving three antennas in increments of 4.3 m to provide complete sampling of the UV plane. The shortest baseline is 12.86 m while the longest baseline is 617.18 m. The primary beam has a FWHM of 1072 at 1.4 GHz and places the first grating lobe outside of the primary beam. The synthesized beam has the first sidelobe at the 3% level, while the rest of the sidelobes are less than 0.5% of the peak of the main lobe. The angular resolution of the DRAO ST at 1.4 GHz is ∼60'' and the effective beam can be fit by a two-dimensional Gaussian. However, the angular resolution of a mosaic is b_α × b_δ = 49'' × 49''cosecδ, which varies over the mosaic. A more detailed description of the DRAO ST can be found in Landecker et al. (2000).

The observations of the DRAO ELAIS N1 deep field began in 2004 August and the final deep field observation was completed in 2008 July. Since this project began, many improvements to the interferometer have been completed. These improvements include the installation of new low noise amplifiers and shielding fences to block ground radiation. In 2000, the Stokes I noise at the center of the individual fields was 280 μJy beam⁻¹ (Landecker et al. 2000). For the Taylor et al. (2007) study, the noise was improved to 210 μJy beam⁻¹. For the additional fields in our study, the rms noise level is 189 μJy beam⁻¹.

Individual fields are mosaicked together to achieve higher sensitivity and a wider field of view. Data from each individual field are included out to a radius of 93' for Stokes I and 75' for Stokes Q and U. The smaller radius cutoff for polarization results from the fact that the instrumental leakages outside 75' are expected to be large and require long integration times to measure accurately (Reid et al. 2008). The data from overlapping fields are averaged together with weights (Taylor et al. 2003)

$$\begin{equation} w_m = \left[\frac{A(\rho _m)}{\sigma _m}\right]^2\,, \end{equation} \tag{ 1 }$$

where A(ρ_m) is the primary beam attenuation at pixel distance ρ_m from the field center, and σ_m is the individual field rms noise level. The resulting rms noise level in the mosaic is then a function of location in the mosaic and is given by Taylor et al. (2003)

$$\begin{equation} \sigma = \left[\sum ^N_{m=1}w_m\right]^{-1/2}\,. \end{equation} \tag{ 2 }$$

The DRAO ELAIS N1 deep field mosaic is comprised of 40 individual fields. The first 30 fields were placed in a triangular pattern and separated by 22' to provide an rms noise level of 56 μJy beam⁻¹ per polarization. The additional ten fields were placed in the inner region of the 30 fields in order to achieve a sensitivity of 45 μJy beam⁻¹ in Stokes Q and U. Figure 1 shows the DRAO ELAIS N1 deep field pointings, for comparison the area covered by the SWIRE survey is also shown.

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The DRAO ST is equipped to receive both left- and right-handed circularly polarized radiation. The polarimetric imaging methods described in the Canadian Galactic Plane Survey (Taylor et al. 2003; Landecker et al. 2010), with the uv-plane based polarization leakage correction described by Reid et al. (2008) and Ransom et al. (2008), were used to create the deep polarization mosaic of the ELAIS N1 field. The instrumental polarization correction is less than 0.5% in the central area of the mosaic and can be as large as 1% at the edges of the mosaic (Taylor et al. 2003). The polarized sources presented in this paper are contained in the area of the mosaic where the instrumental polarization is less than 0.5%. The polarization calibrators used for the observations were 3C147 and 3C295 which are both unpolarized and unresolved. These two calibrators were observed between each 12 hr observation. Additionally, the polarization angle calibrator, 3C286, was observed once every 4 days.

The Sun also produces polarized interference, as the antenna sidelobes are highly polarized. The solar interference was removed by creating images of the Sun during the observations and removing the response from the visibility data. Terrestrial radio frequency interference is also polarized since these signals arise from stationary sources that appear as a source at the North celestial pole (NCP), because the relative position of these interfering sources relative to the telescopes remains always constant. By imaging the NCP, much of the interference can be removed from the visibility data. For some subsets of the data, there was more complex interference in which case the visibility data were flagged. The CLEANing process (Clark 1980) and modcal, a direction-dependent self-calibration (Willis 1999), were implemented to remove the majority of the artifacts from the mosaics. There are a few artifacts left and the sensitivity is limited by thermal noise levels, see Figure 2.

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The DRAO ELAIS N1 deep field mosaics were produced in Stokes I, Q, and U, centered on α₂₀₀₀ = 16^h14^m and δ₂₀₀₀ = 54°56', and have an angular resolution which varies over the mosaic according to b_α × b_δ = 49'' × 49''cosecδ. The center of the mosaic has a measured angular resolution of 49'' × 62''. The total intensity image covers 19.68 deg² while the polarization mosaics covers 15.16 deg² as there is a difference in the primary beam cutoff (see Section 2.1). The mosaicking process produces the lowest noise in the central region of the mosaic where the sum of the weights are the largest. By removing the weight distribution from the mosaic according to Equation (2), the mosaic is made to have an rms noise value for each pixel equal to the rms noise level for the maximum sum of weights. This uniform noise mosaic is used for subsequent analysis.

The rms noise level was determined by fitting a Gaussian to the distribution of flux densities in the uniform noise mosaic (Figure 2). The distribution of the pixel flux densities for Stokes I is different from the distribution of Stokes Q and U. The negative and positive skewness in Stokes I indicates a non-Gaussianity of the noise from confusion and detected sources. The Stokes Q and U mosaics are well fitted by a Gaussian to flux densities of 150 μJy (∼3σ). The non-Gaussian wings above the fit arise from real sources in the image and possibly also residual artifacts from cleaning the individual fields before mosaicking. The central area of the mosaic has an rms noise level of 55 μJy beam⁻¹ for Stokes I and 45 μJy beam⁻¹ for both Stokes Q and U. The Stokes I and polarized intensity ($P = \sqrt{Q^2 + U^2}$) mosaics from the DRAO ELAIS N1 deep field can be seen in Figure 3.

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The mosaics were searched for sources using an automated program that fits a two-dimensional Gaussian plus a constant level to each perspective source. We ran Monte Carlo simulations to (1) estimate and correct for any systematic fitting error, (2) estimate the probability of false detections, and (3) estimate the source detection probability (completeness correction) as a function of flux density. A thousand simulations were run for each of total intensity and polarized intensity. The simulated images had the same noise properties as the actual mosaics, since the source-subtracted mosaics were used as input noise mosaics for the simulations. The source-subtracted mosaics were created by running the two-dimensional Gaussian fitting program on each of the total intensity and polarized intensity mosaics and removing the found sources with a fitted peak flux density greater than 4σ from the mosaic. For each of the 1000 simulations, sources were seeded into the Stokes I image with a flux density distribution following the fit of the 1.4 GHz source counts by Windhorst et al. (1990). The sources were input in random locations with an angular size equal to the beam making every input sources unresolved. Since ∼10% of Stokes I sources were detected in polarization in the actual mosaics, 10% of the simulated Stokes I sources were selected as our input polarized sources. Each source was then given a random Π between 1% and 70% and random polarization angle between −90° and 90°. The polarized sources were then input into the Stokes Q and U images at the same location as their Stokes I counterpart.

The statistical distribution of the noise in the polarized intensity image is non-Gaussian and has a non-zero mean. The probability distribution of P for sources with intrinsic polarized flux density of P₀ follows the Rice distribution (Rice 1945; Vinokur 1965; Simmons & Stewart 1985),

$$\begin{equation} f(P|P_{\rm 0}) = \frac{P}{\sigma }{\rm exp}\left[-\frac{\big(P^2 + P_{\rm 0}^2\big)}{2\sigma ^2}\right]I_{\rm 0}\left(\frac{PP_{\rm 0}}{\sigma ^2}\right), \end{equation} \tag{ 3 }$$

where I₀ is the modified Bessel function of the first kind. If P₀ = 0 then the distribution reduces to the Rayleigh distribution,

$$\begin{equation} f(P|0) = \frac{P}{\sigma }{\rm exp}\left(-\frac{P^2}{2\sigma ^2}\right), \end{equation} \tag{ 4 }$$

which is the probability distribution of pixel amplitudes in the polarized intensity image in the absence of polarized emission. The measured polarized flux density is corrected for the polarization noise bias following the approximation of Simmons & Stewart (1985). The estimate of $P_{\rm 0} = \sqrt{P^2 - \sigma ^2}$ is a good approximation if the signal-to-noise ratio (S/N) is larger than 4.

The results for the detected sources in the 1000 simulated images show that there are systematic biases in fitting both the peak flux density and angular size of the sources. For the total intensity simulations, the peak flux density was over-estimated at an S/N of 15 at 1%–3% at an S/N of 8. The fitted angular size was over-estimated at an S/N of 15 at 1%–6% at an S/N of 8. For polarized intensity simulations, the peak flux density and angular sizes both show under-estimates of the input values. The peak flux density was under-estimated at an S/N of 300 at 1%–15% at an S/N of 5. The fitted angular size has the same value of under-estimates as the polarized peak flux density. These were corrected for prior to any analysis. The false detection rate from the 1000 simulated Stokes I and polarized intensity images is shown in Figure 4. The false detection rate reaches the 1% level at an S/N of 5.8 in polarization and 12.0 in total intensity. The high S/N of false detections in total intensity is the result of confusion. Since we require a polarized source to have a Stokes I counterpart, the Stokes I source list is cut at the 3% level (S/N of 8) in order to not remove real polarized sources from our analysis. The polarized source list is then cut at an S/N of 5.8. From the Taylor et al. (2007) polarized source list, six are not considered to be polarized sources in the new catalog. These six sources have an S/N below 5.8 confirming that a more conservative threshold for source detection was required. Cutting the new source catalog at an S/N of 8 in Stokes I and 5.8 in polarization, we have allowed for accurate calculation of the completeness correction for the radio source counts and statistical analysis of the observed radio sources (see Section 4.1).

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The sources in the actual mosaics were detected using the same procedure as in the simulations. For sources that are located in both the total intensity and polarized intensity observational areas, there are 958 sources detected in the Stokes I image down to S/N ⩾ 8. Of those, 136 have detectable polarization and the smallest fractional polarization detected of 0.73% ± 0.12%.

The polarized sources are listed in Table 1. The table gives the name, peak flux density S, Simmons & Stewart (1985) bias-corrected peak flux density P₀, percentage polarization Π₀, polarization angle, P.A. =0.5 arctan(U/Q) measured in the J2000 coordinate system, spectral index α_1420−325 calculated between our flux density averaged over all four frequency bands and the WENSS source catalog (see Section 3.4), and FIRST classification (see Section 3.3).

FIRST is a 1.4 GHz northern sky survey completed with the VLA in total intensity (1σ = 0.15 mJy) at an angular resolution of 5'' (White et al. 1997). The survey covers over 9000 deg², including our DRAO ELAIS N1 deep field. Of the 958 DRAO ELAIS N1 deep field sources, 795 have a DRAO flux density greater than 1.0 mJy, the flux density limit used for the FIRST source counts. Of these, 697 have a match in the FIRST catalog. In some cases there are multiple FIRST sources within 1' corresponding to one DRAO source. These multiple FIRST sources are generally a single multi-component radio source, where the two lobes and central component are each clearly identified. When this occurs, the DRAO source position is matched to the position of the central component, and classified as a resolved FIRST radio source. A DRAO source is classified as a compact FIRST source in cases where there is only one compact FIRST source corresponding to one DRAO source. See Figure 5 for examples of both classifications. Another source matching situation occurs when a FIRST source is larger than 1' and resolved by the DRAO ST into two apparently independent sources, i.e., two radio lobes separated by >1'. In this case, 40 DRAO sources were found to correspond to 20 FIRST sources larger than 1'. In total, taking the multiple sources into account, there are 677 radio sources with S ⩾ 1.0 mJy in the DRAO ELAIS N1 deep field that are detected in FIRST. Figure 6 shows a plot of DRAO flux density compared to FIRST flux density for sources classified as a compact FIRST radio source. The position of each compact FIRST source was compared to the DRAO position (Figure 7). The fitted DRAO position agrees with the FIRST position to within 10'', half a pixel in the DRAO mosaic. There is a systematic shift of the FIRST position compared to the DRAO position of Δα = 05 ± 02 and Δδ = 04 ± 02. There are also 98 DRAO sources with flux densities between 1.0 < S < 12.8  mJy with no FIRST counterpart, well above the incompleteness cutoff of the FIRST survey. These sources may be resolved out in FIRST but not with the DRAO ST.

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The NVSS is a 1.4 GHz survey completed with the VLA in both total intensity and polarized intensity at an angular resolution of 45'' (Condon et al. 1998). The rms noise levels for the NVSS are 0.45 mJy beam⁻¹ in Stokes I and 0.29 mJy beam⁻¹ in Stokes Q and U. There are ∼2 × 10⁶ sources in the NVSS catalog with S ⩾ 2.0 mJy. NVSS counterparts were found for 597 out of a possible 613 sources with DRAO flux density S ⩾ 2.0 mJy. The resolution of the NVSS is comparable to the resolution of DRAO and it is not surprising that in all cases there were single matches between the DRAO sources and the NVSS sources. All of the 16 DRAO sources with no NVSS counterpart have flux densities ⩽4.1 mJy, and may point to the incompleteness of the NVSS in the 2–4 mJy flux density range or these sources are variable.

Figure 8 shows the fraction of DRAO sources matched in NVSS and FIRST as a function of DRAO flux density. The DRAO sources are 100% matched to a counterpart in both NVSS and FIRST down to S_DRAO = 12.8 mJy, at which point the fraction of sources with FIRST counterparts declines slowly to 50% at the FIRST flux limit (1 mJy). The matching between DRAO and NVSS, on the other hand, remains at 100% down to just above the NVSS flux density limit and then decreases rapidly to zero. The DRAO sources that were found to have no corresponding FIRST object down to just above the NVSS flux density limit, have a positively detected NVSS source. This difference of the NVSS and FIRST catalogs at S ⩽ 12 mJy was also noted by de Vries et al. (2002), who matched sources for both surveys in the Bootes Deep Field. The fact that there are sources not detected in FIRST (resolution of 5''), but detected in both the DRAO ELAIS N1 deep field (60'' resolution) and the NVSS (45'' resolution), indicates that this is a resolution effect; i.e., diffuse emission is missed in FIRST. Care must therefore be taken in statistical comparison of source data taken from observations with different angular resolutions.

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WENSS is a northern sky survey at observed at 325 MHz and completed with the Westerbork synthesis telescope (Rengelink et al. 1997). WENSS has an angular resolution of 54'' × 54''cosecδ and a limiting flux density level of 18 mJy (5σ). 343 DRAO sources have counterparts in the WENSS catalog, including 103 of the 131 polarized sources. The resolutions of the two surveys are comparable resulting in only single source matches between DRAO and WENSS sources. The spectral index (S ∼ ν^α) distribution of the 343 DRAO ELAIS N1 deep field sources is shown in Figure 9, for both polarized sources and sources with no detectable polarization. The 103 polarized sources found in WENSS have a weighted mean of α_1420−325 = −0.77 ± 0.01 and the 240 sources with no detectable polarization found in WENSS have a weighted mean of α_1420−325 = −0.87 ± 0.01.

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De Breuck et al. (2000) determined spectral indices for 143, 000 radio sources between NVSS and WENSS and showed that this radio source population consists of a steep-spectrum galaxy and flat-spectrum quasar part separated by a spectral index of about −0.3. Following this distinction between steep- and flat-spectrum sources, we have 95 steep-spectrum polarized sources and eight flat-spectrum polarized sources. For sources with no detectable polarization we have 228 steep-spectrum sources and 12 flat-spectrum sources. The fraction of steep-spectrum to flat-spectrum sources shows little difference between polarized and unpolarized sources. The hypothesis that the distribution of polarized sources and the sources with no detectable polarization in Figure 9 was drawn from the same spectral index distribution was rejected by the Kolmogorov–Smirnov test at only the 94% confidence level.

Figure 10 shows a plot of the spectral index as a function of the degree of polarization for the 103 polarized DRAO sources with a WENSS counterpart. The horizontal line indicates the mean spectral index for polarized sources. Calculating the weighted average in bins of percentage polarization shows that the spectral index remains almost constant around the mean spectral index of −0.77 for polarized radio sources with Π₀ < 11%. Gardner & Whiteoak (1969) noted that for radio galaxies with 20 cm flux densities above 2.5 Jy there is a weak trend of an increase in fractional polarization with a decrease in spectral index. However, they found no trend with objects observed at 11 cm. On the other hand, Kronberg & Conway (1970) note that there is an opposite correlation between fractional polarization and spectral index for bright sources observed at 49 cm.

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The Euclidian-normalized differential source counts of the DRAO ELAIS N1 deep field are shown in Figure 11 for both total intensity and polarized intensity. The Stokes I source counts are plotted down to a flux density of 500 μJy and the polarized source counts (Table 2) are plotted down to 400 μJy. The polarized source counts do not include the faintest eight polarized sources as the error on the count does not provide an accurate representation of the polarized source counts below 400 μJy. The total intensity source counts follow the Wilman et al. (2008) semi-empirical simulation of the total intensity sky (a solid curve in Figure 11). Our polarized source counts can be compared to those of Taylor et al. (2007) as well as those derived by Beck & Gaensler (2004) and O'Sullivan et al. (2009), each of which is plotted in Figure 11. We confirm the Taylor et al. (2007) result that sources with P₀ < 3 mJy are found in significantly greater number than what is predicted from the bright source population. The drop in the polarized source counts around polarized flux density range of 3–10 mJy is the result of total intensity sources in the total intensity flux range of 50–100 mJy, which is shown to drop as well. The local surface density non-uniformity of sources in these flux density ranges is most likely the cause for the observed drop in the radio source counts. We can also compare our polarized radio source counts with the O'Sullivan et al. (2009) model, which is based on the total intensity sky of Wilman et al. (2008) and a polarization distribution derived from a luminosity dependence for the polarization of FRI and FRII radio galaxies. Again, our results lie above the predictions indicating potentially a strong dominant dependence on fractional polarization.

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Information of the nature of polarized radio sources can be determined from the fractional polarization Π₀. A comparison of I and P₀ for the polarized sources in the DRAO ELAIS N1 deep field can be seen in Figure 12. The solid lines indicate the loci of sources with Π₀ = 100%, 10%, and 1%. There is a clear increase in the number of sources with higher fractional polarization with a decrease in total flux density.

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The change in the distribution of Π with flux density is illustrated in Figure 13. Two different polarized flux density ranges are shown: 0.6 < P₀ < 2.0 and 2.0 < P₀ < 100 mJy. Selecting flux density bins in P₀ instead of S allows us to be complete in our polarized source sample, and the high S/N of the bins allows us to be sure that the sources are not effected by noise bias. Selecting flux density bins in P₀ instead of S allows us to be complete in our polarized source sample, and the high S/N of the bins allows us to be sure that the sources are not effected by noise bias. For a complete sample of sources, the distribution in Π₀ should be the same in both P₀ flux bins if the distribution of Π₀ does not change. The same selection is imposed on the data in both bins, leaving only the fact that the upper bin contains fewer sources. There is a higher fraction of polarized sources in the lower polarized flux density bin with Π₀>10 %, than in the higher polarized flux density bin. The hypothesis that the two polarized flux density distributions were drawn from the same distribution was rejected by the Kolmogorov–Smirnov test at the 99% confidence level.

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Unfortunately, the DRAO polarization observations are not yet sensitive enough to detect the polarization emission from starburst and normal galaxies. Since there is no polarized emission from these galaxies and the polarized source counts lie slightly above the O'Sullivan et al. (2009) model, we conclude that the polarized radio sources with P₀ < 3 mJy are more highly polarized then the strong source population. There must be a dependence on flux density, fractional polarization, and luminosity that plays a stronger role at the fainter levels of the polarized source counts. Future observations will hopefully allow us to complete source counts for the intrinsically faintest population of galaxies.

The structure of polarized radio emission can provide information on the intrinsic properties of the source. The mean spectral index of the DRAO polarized sources indicates that the majority of these polarized objects are steep-spectrum objects, which contain both diffuse and compact emission components. However, the resolution of the DRAO ELAIS N1 deep field data does not provide enough information to determine if the polarized emission is originating from the diffuse or compact components. The faintest Stokes I flux density of a DRAO source with a WENSS counterpart is 1.19 mJy. There are 751 DRAO sources down to a DRAO flux density of 1.19 mJy, 131 of which are polarized. 343 of the 751 sources are matched with a WENSS counterpart corresponding to 46% ± 3% of our sample. Table 3 shows that 79% ± 8% polarized sources are matched in WENSS while just 39% ± 3% of sources with no detectable polarization are matched.

A comparison of the 677 FIRST sources in our deep field shows that there are 374 FIRST objects (55% ± 3% of our sample) with no visible structure making them compact radio sources. The other 303 FIRST objects (45% ± 3% of our sample) were resolved. 115 of the 677 DRAO sources with FIRST counterparts have detectable polarization. As outlined in Table 4, 23% ± 5% of the polarized sources with a FIRST counterpart are classified as unresolved or compact objects whereas 77% ± 8% are considered to be resolved. For the sources with no detectable polarization the statistics are almost reversed, 62% ± 3% are compact or unresolved and 38% ± 3% are classified as resolved objects. This indicates that polarized sources tend to have structure at arcsecond scales and that the polarized emission is most likely not beamed. This confirms that the polarized radio sources tend to be lobe-dominated radio galaxies.

Figure 14 shows a histogram of the DRAO–FIRST matched polarized sources classified as either resolved or compact as a function of total intensity and polarized intensity. There is a larger number of resolved sources compared to compact sources at fainter polarized intensity levels. This increase in the number of resolved polarized sources occurs for P₀ < 3 mJy and S < 60 mJy. Resolved polarized sources are likely responsible for the increase in the polarized source counts at P₀ < 3 mJy, as seen in Figure 11. The median fractional polarization of the sources classified as resolved is 6.8% ± 0.7% whereas the median fractional polarization of the compact sources is 4.4% ± 1.1%. The DRAO ELAIS N1 deep field polarized sources classified as resolved in FIRST are more polarized than the compact sources. Hogbom & Carlsson (1974) observed 79 sources with S>1.0 Jy in polarization with the Westerbork synthesis radio telescope at 1.4 GHz and noticed that extended well-resolved diffuse areas have a higher degree of polarization than the compact source components. Our results confirm that this trend continues for polarized sources down to P₀ ⩾ 270 μJy. This indicates that the higher degree of polarization may be originating in the lobe-dominated structure. However, further high-resolution polarimetric observations will be able to determine the magnetic field structure of these highly polarized resolved radio sources.

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