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Draft version October 19, 2009
A Preprint typ eset using L TEX style emulateap j v. 08/22/09

FARADAY ROTATION STRUCTURE ON KILOPARSEC SCALES IN THE RADIO LOBES OF CENTAURUS A
I. J. Feain1 , R. D. Ekers1 , T. Murphy2,3 , B. M. Gaensler2 , J-P Macquart4 , R. P. Norris1 , T. J. Cornwell1 , M. Johnston-Hollitt5 , J. Ott6 , and E. Middelberg7

arXiv:0910.3458v1 [astro-ph.CO] 19 Oct 2009

1. CSIRO Australia Telescope National Facility, PO Box 76, Epping NSW 1710, Australia; ilana.feain@csiro.au 2. Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006, Australia 3. School of Information Technologies, The University of Sydney, NSW 2006, Australia 4. Curtin Institute of Radio Astronomy, Curtin University of Technology, GPO Box U1987, WA 6845, Australia 5. School of Chemical and Physical Sciences, Victoria University of Wellington, PO Box 600, Wellington, New Zealand 6. National Radio Astronomical Observatory, Charlottesville, P.O. Box O, 1003 Lopezville Road, Socorro, NM 87801-0387 , USA and 7. Astronomisches Institut der Universitat Bochum, Universitatsstr. 150, 44801 Bochum, Germany Ё Ё Draft version October 19, 2009

ABSTRACT We present the results of an Australia Telescope Compact Array 1.4 GHz spectropolarimetric aperture synthesis survey of 34 square degrees centred on Centaurus A--NGC 5128. A catalogue of 1005 extragalactic compact radio sources in the field to a continuum flux density of 3 mJy beam-1 is provided along with a table of Faraday rotation measures (RMs) and linear polarised intensities for the 28% of sources with high signal-to-noise in linear polarisation. We use the ensemble of 281 background polarised sources as line-of-sight probes of the structure of the giant radio lobes of Centaurus A. This is the first time such a method has been applied to radio galaxy lobes and we explain how it differs from the conventional methods that are often complicated by depth and beam depolarisation effects. Assuming a magnetic field strength in the lobes of 1.3 B1 µG, where B1 = 1 is implied by equipartition between magnetic fields and relativistic particles, the upper limit we derive on the maximum possible difference between the average RM of 121 sources behind Centaurus A and the average RM of the 160 sources along sightlines outside Centaurus A implies an upper limit on the volume-averaged thermal - plasma density in the giant radio lobes of ne < 5 в 10-5 B1 1 cm-3 . We use an RM structure function analysis and report the detection of a turbulent RM signal, with rms RM = 17 rad m-2 and scale size 0.3 , associated with the southern giant lobe. We cannot verify whether this signal arises from turbulent structure throughout the lobe or only in a thin skin (or sheath) around the edge, although we favour the latter. The RM signal is modelled as possibly arising from a thin skin with a thermal plasma density equivalent to the Centaurus intragroup medium density and a coherent magnetic field that reverses its sign on a spatial scale of 20 kpc. For a thermal density of n1 10-3 cm-3 , the skin magnetic field strength is 0.8 n-1 µG. 1 Subject headings: galaxies: individual (Centaurus A, NGC 5128) -- techniques: interferometric, polarimetric
1. INTRODUCTION

The lobes of radio galaxies are magnetised, quasifreely expanding rarified cavities inflated by relativistic jets propagating outwards through the intergalactic medium from a central supermassive black hole (e.g. Begelman et al. 1984). As such, radio lobes could be excellent sites for high-energy particle acceleration and even the production of ultra-high-energy cosmic rays (Benford & Protheroe 2008; Fraschetti & Melia 2008; Hardcastle et al. 2009). Knowledge of the physical conditions in radio lobes, including both the lobe magnetic field strength and thermal plasma density, are important to explore any high-energy acceleration mechanisms in full (Kronberg et al. 2004). Understanding the magnetic and thermal properties of radio lobes in detail is also fundamental to our understanding of galaxy formation in terms of feedback processes between the AGN and the interstellar/intergalactic medium (Croton et al. 2006; Croft et al. 2006; Elbaz et al. 2009). Linearly polarised electromagnetic radiation passing through a magnetised thermal plasma causes rotation in
Electronic address: ilana.feain@csiro.au

the angle of polarisation of the radiation at a rate given by, = 0.81 ne B l 2 = RM 2 (1)

where (in radians) is the position angle of the radiation at wavelength (in meters), ne is the thermal electron density (in cm-3 ), B is the line of sight component of the magnetic field (in µG), l is the path length through the rotating material (in pc) and RM is the Faraday rotation measure (in units of rad m-2 ). If radio galaxy lobes contain magnetised, thermal plasma they will have an associated intrinsic Faraday depth. Observations of RMs in radio sources have shown that internal Faraday rotation in radio lobes is quite small (Kronberg et al. 1986, 2004; Schoenmakers et al. 1998; Palma et al. 2000) with estimates of the thermal electron densities of ne < 10-6 cm-3 , assuming a thermal plasma is distributed uniformly across the lobes. Such low inferred thermal matter densities are orders of magnitude lower than the upper limits on hot


2

Feain et al. plasma. In this scenario, all the polarised signal from any element of the background source is rotated by the entire line of sight through the screen. The screen can cause spatial depolarisation due to variations in RM in the screen across the angular size of the source. This probes scale sizes in the screen on scale sizes smaller than the background source size. No depth depolarisation occurs. This technique is often used to investigate the magnetic structure of the Milky Way (Brown et al. 2003, 2007; Mao et al. 2008), nearby galaxies (Han et al. 1998; Gaensler et al. 2005) and galaxy clusters (Kim et al. 1991; Hennessy et al. 1989). Note that scenarios 2 and 3 above are not affected by back-versus-front differences such as the LaingGarrington effect (Laing 1988; Garrington et al. 1988). The typical angular size subtended by radio galaxy lobes is too small to include a statistically significant number of compact polarised background sources, at least for the source densities reached with current sensitivity (typically mJy beam-1 ). Hence, up until now, all studies of the Faraday rotation in radio galaxy lobes have been restricted to using emission from the lobes themselves, as in scenario 1 above (recent examples include Kharb et al. 2009; Laing et al. 2008). The outer lobes of the nearest radio galaxy, Centaurus A, subtend a large enough angular size ( 45 deg2 ) that hundreds of polarised sources are detected along sightlines behind them. For the first time, we can investigate the magnetised plasma in radio lobes -- using scenario 3 -- without the complexities added by depth and beam depolarisation effects. This is the basis for the analysis presented in this paper. We have recently completed a large spectropolarimetric imaging campaign at 1.4 GHz with the Australia Telescope Compact Array (ATCA) and the Parkes 64 m radio telescope, to image in full the polarised structure of the nearest radio galaxy, Centaurus A. The full spectropolarimetric images of Centaurus A from ATCA and Parkes data combined will be reported in a subsequent paper (Feain et al. 2010, in preparation). An additional result of the ATCA component of the observations, we have also observed in full polarisation 1005 compact radio sources in the background of Centaurus A: some along lines of sight through the lobes and some along lines of sight beyond (outside) the boundaries of the radio lobes. In this paper we present a catalogue of these 1005 compact radio sources. RMs and polarised flux densities are presented for a subset (281) of the sources. We investigate the spatial correspondence between the radio lobes of Centaurus A and the both the distributions of RMs and fractional polarisation of the background sources. This paper is divided into sections in the following way: §2 describes the ATCA radio continuum observations and §3 outlines the calibration and data processing procedures. In §4, we define the procedure used for source finding, give the format for the source catalogue and provide the URL where the entire catalogue can be accessed. §5 describes the Rotation Measure Synthesis technique with which we derived reliable RMs and

(keV) gas obtained from measurements of X-ray cavities around radio lobes (Blanton et al. 2001; Fabian et al. 2000; Nulsen et al. 2005). Whereas only upper limits exist on the uniform thermal matter density inside radio lobes, there is conflicting evidence regarding the presence of a Faraday rotating thin skin (or sheath) around the lobes caused by entrainment of intergalactic plasma. For example, in the case of Cygnus A, Dreher et al. (1987) attribute observed RM variations of thousands of rad m-2 wholly to the foreground intracluster medium that Cygnus A is embedded within. Bicknell et al. (1990), however, use the same data to show that this RM structure could arise from a thin skin around the radio lobes where Kevin-Helmholtz instabilities have caused a mixing of the lobe plasma with the intergalactic medium. More recently, a similar debate has arisen as to the origin (intracluster medium versus thin skin) of RMs (and RM variations) in excess of ±1000 rad m-2 across the radio galaxy PKS 1246-410 in the centre of the Centaurus cluster1 (Taylor et al. 2002; Rudnick & Blundell 2003; Ensslin et al. 2003; Taylor et al. 2007). There are three distinct scenarios we consider (but see Burn 1966) when using Faraday rotation to probe the properties of a magnetised, thermal plasma: 1. The diffuse polarised synchrotron emission from the lobes is mixed with the magnetised, thermal (Faraday rotating) plasma. In this case, the emission from the back of the source will have been rotated more than the emission from the front of the source and so `depth depolarisation' can occur along any line of sight. In addition, `beam depolarisation' can occur due to variations in RM on scales smaller than the observing beam. In the former situation (i.e. not applicable to beam depolarisation) the concept of Faraday depth is introduced. Accurate determination of Faraday depth is complex, but necessary to extract information on the magnetic field and thermal density within the source (Cioffi & Jones 1980). Radio galaxy lobes embedded in clusters or groups are often used to probe the cluster/group medium (Dreher et al. 1987; Clarke et al. 2001; Eilek & Owen 2002; Taylor et al. 2002; Laing et al. 2008). Here one must first show that the rotating plasma arises purely from the foreground medium itself rather than the lobes or skin of the radio source (Rudnick & Blundell 2003). 2. The polarised emission is diffuse and located behind the Faraday rotating plasma. This is similar to the above scenario in terms of beam depolarisation, however no depth depolarisation occurs because there is no mixing of the emitting and rotating regions. For example, extended radio galaxies could be used to directly probe Galactic magnetic fields. 3. The polarised emission is unresolved and located behind the magnetised, thermal (Faraday rotating)
1 The Centaurus cluster at z = 0.01 is lo cated b ehind the Centaurus group at z = 0.0018 that contains the radio galaxy Centaurus A.


Faraday rotation structure in the lobes of Centaurus A polarised flux densities for 281 out of the 1005 sources catalogued. In §6 we show the RM distribution and briefly compare the total and polarised intensity source counts from our data with total and polarised intensity source counts from the literature. We also compute a lower limit on the very small scale RM fluctuations from the lobes of Centaurus A. §7 presents a detailed investigation into the spatial variations in the ensemble of 281 Faraday rotation measures. We fit and subtract out the Milky Way foreground RM component leaving a residual excess RM dispersion on angular scales 0.3 . We model this excess as possibly arising from a thin skin around the southern giant radio lobe. Finally, our concluding remarks are given §8. We adopt a distance to Centaurus A of 3.8 Mpc from Rejkuba (2004). At 3.8 Mpc, 1 corresponds to 66 kpc.
2. OBSERVATIONS

3

The data used in this paper were obtained as part of a larger (45 deg2 ) radio synthesis imaging survey of Centaurus A (NGC 5128), the nearest active galaxy in the Universe. The ATCA was used in mosaic mode over four epochs between 2006 December and 2008 March to observe a total field of view covering 5 в 9 (in 406 pointings) and centred on RA(J2000) 13h 25m 27.6s , DEC(J2000) -43 01 09 . The standard continuum correlator configuration was employed for the observations at all epochs. This correlator configuration (full 128 2) was chosen because it allows dualfrequency observations using 2в128 MHz bandwidth observing windows split into 32 channels (the spectral resolution is 1.77 channels) per window. We centred the two frequency windows on 1344 and 1432 MHz; used in this way, the two windows overlap by 40 MHz and the total useable bandwith is 192 MHz. Observations were carried out with four complementary array configurations, each with a maximum baseline of 750 m. The ATCA's linearly polarised feeds measure crosspolarisation data which allowed us to derive the four relevant Stokes parameters (I , Q, U, V ). The temporal variations in the atmospheric phase were tracked with a two minute observation of PKS B1316-46 about once an hour. In addition, the parallactic angle coverage of PKS B1316-46 was sufficient to enable us to solve for the polarisation leakages in each 12 hr observing block. PKS B1934-638 was observed once a day and used both to correct for the instrumental bandpass and derive the absolute flux density scale. On average, each of the 406 pointings in the mosaic received 100-120 minutes integration.
3. DATA CALIBRATION AND POST-PROCESSING

residual RFI was evident, manually flagged. miriad was used in the standard way to derive and apply the instrumental bandpass, gain, phase and absolute flux density calibration. The typical level of polarisation leakage in an individual pointing was 0.1% at the phase centre, 0.5% at the half-power point and 1.7% at 0.1-power. The off-axis polarisation leakage of the ATCA is reduced substantially by the combination of mosaicing and tracking a source over a wide range of paralactic angles; we measured the leakage across the calibrated final mosaic to be 0.1%. After calibration and disregarding the edge channels, there were 24в 8 MHz channels between 1296 and 1480 MHz. Faraday rotation measures were derived across the full 24-channel band. The ionospheric variations in RM above the ATCA over the course of the observations are typically 1 rad m-2 (MacMillan & Maus 2005; Bilitza & Reinisch 2008). The variations in the ionospheric RM between observations will cause a slight amount of depolarisation, leading to a few percent decrease in the measured polarisation of the sources. In this paper, we concentrate on the polarisation properties of the compact extragalactic radio sources in the background to Centaurus A. For the purposes of analysing these background radio sources, the foreground large scale emission from the giant lobes of Centaurus A was considered to be contamination. We therefore filtered out this large scale emission from our data by disregarding all visibilities from baselines shorter than 300 metres (1.4 k). The final angular resolution for this data (after filtering) is 60 в33 , 3 (as given in Table 1). For this work, each of the 406 ATCA pointings were considered, calibrated, deconvolved and restored individually (using the same size beam for all pointings) and then stitched together with linear mosaicing. For each individual pointing, a Stokes I , Q, U and V image was produced (the latter to measure the noise properties in each channel) for every one of the 24 independent (8 MHz wide) frequency channels and, for Stokes I only, a continuum image was also created using multi-frequency synthesis (Sault & Wieringa 1994). For the latter Stokes I image alone, a single iteration of phase-only self-calibration was applied; no self-calibration was necessary for the Stokes Q or U images. A mask was applied to the spatially filtered dataset in order to create an image with a roughly uniform sensitivity; the point source sensitivities for the final continuum image as well as the individual 8 MHz Stokes Q and U images are given in Table 1. Figure 1 shows the mask that was applied to the spatially filtered image: the large blanked region in the centre of the mosaic is due to high residual sidelobes around the very bright (Speak 7.5 Jy beam-1 at 1.4 GHz) central region of Centaurus A. The two smaller blanked regions south of the Centaurus A core are associated with the residual sidelobes of two bright background sources (pks 1320-446 and pmn j1318-4620). The edge of the mosaic was also masked to remove elevated noise levels (> 0.3 mJy beam-1 ) where primary beam correction was significant. Figures 2 and 3 show the

The data were inspected for radio frequency intereference (RFI) and flagged accordingly using Root Mean Square (RMS)-Based flagging in the automated RFI detection algorithm pieflag (Middelberg 2006). Approximately 5% and 30% of our visibilities at 1384 and 1432 MHz, respectively, were flagged. Each baseline and channel was then visually inspected and, where


4
TABLE 1 Observational Parameters Parameter Continuum Bandwidth (MHz) 192 (mJy beam-1 ) 0.15 m a j в m i n 63 в33 Position Angle 3 Position angle is defined with nor Stokes (Q, U ) 8 per channel 0.5 per channel 63 в33 3 and east +90 . th 0

Feain et al. Columns (8,9,10): Fitted ma jor and minor axis and position angle from imfit Columns (11,12,13): Deconvolved ma jor and minor axis and position angle from imfit

5. POLARISATION AND FARADAY ROTATION MEASURE

continuum intensity and corresponding linear polarised intensity (not corrected for Ricean bias) for a representative portion of the surveyed area. Figure 1 has a roughly uniform sensitivity that is given in Table 1. The total survey area, after masking, is 33.93 deg2 .
4. SOURCE FINDING

The polarised fluxes and Faraday rotation measures (RMs) were derived for 281 of the 1005 catalogued sources listed in Table 2 as follows. At each source position in Table 2, we extracted the Stokes Q and U values and their expected RMS error (based on the sensitivity of the map at that position) in each of the 24 independent spectral channels in our data-set. Converting from frequency to 2 , where is the observing wavelength of each channel, we then have a dependence of the complex Stokes vector (Q, U ) as a function of 2 at the peak position of each source. For pure Faraday rotation, this vector should have a phase that varies linearly with 2 at a rate equal to the source's RM. We extracted this RM from each data-set via rotation measure synthesis (Brentjens & de Bruyn 2005; Heald et al. 2009), in which we compute the Fourier transform of the complex Stokes vector to yield the amplitude of the polarized flux, P , as a function of Faraday depth, . For a source with a single valued RM, the RM synthesis spectrum will have a single peak whose height is equal to the polarized flux, and width (RM resolution) determined by the wavelength coverage of the observation. The polarisation position angle is given by the Q and U values at the peak polarised emission. This method achieves signal-to-noise corresponding to the full bandwidth of the observation, but with bandwidth smearing effecting only the individual channel width. Any deviations from 2 behaviour resulting from complex Faraday rotation structure over the background source are seen as structure in the rotation measure synthesis spectrum. This analysis was applied to all 1005 sources in Table 2, with the individual (Q, U ) measurements weighted by the inverse square of the sensitivity for each spectral channel. The total bandwidth and spectral resolution of our data mean that the FWHM in Faraday depth for a single RM component is 280 rad m-2 , and that we are sensitive to RMs with magnitudes less than 3500 rad m-2 . The resulting Faraday depth functions exhibit spectral sidelobes because of incomplete wavelength coverage (in the same way that an aperture synthesis image shows sidelobes because of incomplete u - v coverage). Since we can compute the RM transfer function for each source (i.e., the Faraday depth spectrum of a source of unit polarized intensity and zero RM), we can deconvolve our data-set using the same iterative clean approach routinely applied to radio interferometric images (Hogbom 1974). SpecifiЁ cally, we have implemented rmclean, as described by Heald et al. (2009). When the above prescription is applied to all sources, we now have 1005 deconvolved spectra of P (in units of

Source detection was performed using the miriad routine sfind (Hopkins et al. 2002) on the total intensity image in Figure 1. We ran sfind in its original mode, which uses a `Search and Destory' algorithm much the same as the AIPS task VSAD, to find all sources in the image and fit them with a gaussian. This extracted an initial list of candidate sources with a peak flux density greater than 3 mJy beam-1 (20 ). To obtain more accurate fits than those produced by sfind we then ran the miriad task imfit to do a constrained gaussian fit (restricting the fit to a small region around the ob ject) for each source detected in the initial candidate list. We ran this iteratively, subtracting each fitted source from the image, to produce a residual map. We identified poor fits by comparing the rms noise in a small region around the source in the original image and in the residual map. Cases in which the rms noise increased after the fitted source was subtracted from the image were investigated further. Sources with poor fits and sources with multiple components are identified as such in the catalogue. The final catalogue consists of 1005 compact sources to a detection threshold of 3 mJy beam-1 . The associated error in the peak flux density for each source has been estimated by the quadrature sum of the rms noise in the image and the uncertainty in transfering the flux scale of the ATCA primary calibrator pks b1934-638 (1-2%2 ). The error in the integrated flux density, I , for each source was estimated, using Equation 16 in Condon (1997) to be, I , (2) A where A is the peak flux density. The format of the catalogue in Table 2 is: I = A в Column (1): Source Name. Columns (2,3): Right Ascension and Declination in J2000 coordinates. Columns (4,5): Peak flux density averaged over the full bandwidth in units of mJy and its associated error. Columns (6,7): Integrated flux density averaged over the full bandwidth in units of mJy and its associated er r o r .
2

see ATNF Technical Memo AT/39.3/040.


Faraday rotation structure in the lobes of Centaurus A

5

Fig. 1.-- The masked, spatially filtered total intensity radio continuum image of the Centuarus A field used to find and catalogue the compact radio sources given in Table 2. The grey shading shows the regions of our field that we used for source finding. In these regions, many of the compact radio sources can be seen. Masked regions, shown in white, correspond to areas where the sensitivity of the image is poorer, in the vicinity of very bright sources (both the core of Centaurus A as well as two foreground sources with flux densities > 2Jy in the southern lobe) or near the edge of the mosaic where primary beam correction was significant. The contours correspond to a Parkes 1.4 GHz image at 14 resolution (courtesy Mark Calabretta) with levels 1.5, 2, 2.5, 3, 4, 5, 6, 10, 100 Jy beam-1 . The horizontal-striped region beyond the edge of the mask that does not contain point sources is beyond the observed mosaic. The image is shown pro jected in a sin coordinate system.


6

Feain et al.

TABLE 2 Catalogue of the compact continuum radio sources brighter than 3 mJy beam-1 in the field shown in Figure 1. The table below shows the format of the catalogue and gives the results for the brightest 20 sources; the full catalogue of 1005 radio sources is available electronically.

Source 131452- 132554- 132340- 133130- 131921- 132748- 132148- 131708- 132301- 133118- 132104- 131710- 132031- 133520- 132551- 131749- 131739- 132936- 131713- 133357- 401056 464302 410125 464508 443649 391158 383251 385451 384925 411956 411451 430400 410338 391148 400425 414536 452221 442312 410934 464138

RA (J2000) hh:mm:ss.ss 13:14:52.67 13:25:54.85 13:23:40.83 13:31:30.39 13:19:21.77 13:27:48.95 13:21:48.82 13:17:08.88 13:23:01.68 13:31:18.68 13:21:04.51 13:17:10.90 13:20:31.43 13:35:20.53 13:25:51.63 13:17:49.75 13:17:39.58 13:29:36.61 13:17:13.41 13:33:57.33

Dec(J2000) ddd:mm:ss.s -40:10:56.4 -46:43:02.3 -41:01:25.9 -46:45:08.9 -44:36:49.5 -39:11:58.1 -38:32:51.1 -38:54:51.4 -38:49:25.2 -41:19:56.7 -41:14:51.3 -43:04:00.5 -41:03:38.5 -39:11:48.4 -40:04:25.7 -41:45:36.1 -45:22:21.5 -44:23:12.1 -41:09:34.5 -46:41:38.0

Sp eak mJy bm- 708.7 456.3 441.5 430.0 387.1 355.3 308.1 302.0 299.2 278.6 274.4 267.5 267.4 253.9 233.0 226.4 216.0 206.7 197.3 192.9

1

Sp eak mJy bm- 7.2 4.6 4.5 4.3 3.9 3.6 3.1 3.1 3.6 4.4 2.8 2.7 12.9 2.6 2.4 2.3 2.2 2.1 2.0 2.3

1

Sint mJy 761.0 545.2 479.1 514.0 453.3 378.1 328.2 319.0 321.7 444.5 317.1 302.5 326.4 271.7 250.9 249.9 249.1 237.6 223.6 328.0

Sint mJy 7.7 5.5 4.9 5.2 4.6 3.8 3.3 3.2 3.9 7.1 3.3 3.1 15.7 2.8 2.5 2.5 2.6 2.4 2.3 3.9

B

f it maj

B

f it min

B

f it pa

B

decon maj

B

decon min

B

decon pa

63. 63. 63. 63. 64. 63. 63. 63. 63. 65. 66. 63. 61. 63. 63. 63. 63. 63. 63. 88.

8 4 6 6 1 9 8 8 8 1 0 9 8 9 7 8 0 6 3 9

35. 39. 35. 39. 38. 34. 34. 34. 35. 50. 36. 36. 41. 34. 35. 36. 38. 37. 37. 39.

0 2 5 0 0 6 7 4 0 9 4 8 1 8 1 0 1 6 2 8

3.1 4.1 3.4 4.0 4.1 2.9 3.0 3.0 2.0 -7.3 0.1 3.0 8.3 3.0 3.3 3.5 4.1 3.9 3.6 10.8

11.7 21.3 13.1 21.0 19.2 10.9 10.7 10.0 13.1 40.2 22.0 16.2 --­ 11.1 12.2 14.5 --­ 18.2 17.4 63.4

9.9 6.4 8.5 8.6 11.2 10.3 10.4 9.8 8.4 12.7 12.0 10.9 --­ 10.7 9.4 9.8 --­ 8.2 5.6 19.9

84.8 86.3 82.8 85.8 80.2 -17.1 84.5 -12.0 -52.4 -75.3 -29.8 -88.0 --­ -80.1 77.4 80.7 --­ 83.8 86.7 17.1


Faraday rotation structure in the lobes of Centaurus A

7

as a minimum criterion for a reliable RM determination (see, e.g., Figure 9 of Brentjens & de Bruyn 2005). For sources with polarized fluxes above this threshold, we computed the uncertainty in RM as the FWHM of the RM transfer function divided by twice the SNR. Of the 1005 catalogued continuum radio sources, 281 (28%) polarised sources were robustly detected according to the detection criteria described above and are listed in Table 3. The format of Table 3 is: Column (1): Source Name. Columns (2,3): Right Ascension and Declination in J2000 coordinates. Columns (4,5): Peak polarised flux density (after correction for the Ricean bias) in units of mJy bm-1 and its associated signal to noise ratio (SNR). Columns (6,7): Measured Faraday rotation measure and its associated uncertainty derived using RM synthesis and RM clean in units of rad m-2 . Columns (8): Column 6 after correcting for the Galactic contribution (see §7) in units of rad m-2 . Figure 5 shows the distribution in the total intensity to polarised intensity plane of the 281 sources in our sample whose debiased polarised intensities have a SNR7. The dashed, diagonal lines represent lines of constant fractional polarisation.
5.1. Which sources are behind the lobes?

Fig. 2.-- A representative portion of the total intensity image shown in Figure 1. The rms level is 0.18 mJy beam-1 .

Fig. 3.-- As Figure 2 but shown in linear polarised intensity, before bias corrrection. The rms level is 0.07 mJy beam-1

mJy beam-1 )3 as a function of (in units of rad m-2 ). Some examples are shown at varying signal-to-noise in Figure 4. For each source, we identified the peak value of P as a function of , and then applied a parabolic fit around this peak to yield the best-fit estimate of the polarized flux and RM. We then debiased the polarized flux by estimating the observed RMS noise, QU , in the real and imaginary parts of tHe spectrum far from the peak, and subtracting QU in quadrature from the peak value of P (see Simmons & Stewart 1985). The ratio of the debiased polarized flux to the noise then yields the signal-to-noise ratio (SNR) of the detection of Faraday rotation. We adopted a threshold SNR 7
3 Strictly sp eaking, P is in units of surface brightness p er unit , i.e., mJy beam-1 rad -1 m2 , and the polarized flux is determined by integrating P as a function of . However, for sources of unresolved Faraday depth the peak surface brightness is equal to the total flux, in the same way that the peak surface brightness of a point source in an image of intensity is equal to its integrated flux.

For much of the rest of this paper, we wish to analyse separately the polarised sources located behind the lobes of Centaurus A from polarised sources whose sightlines pass outside of the lobes. The latter are used as a control sample and to model and subtract the RM component from the Milky Way. We define what constitutes behind the radio lobes to correspond to an `edge' where, at 1.4 GHz and 14 resolution, the surface brightness of the lobes drops below 1.5 Jy beam-1 ; this is the last contour in Figures 1 and 7. At approximately this value, the surface brightness of the lobes decreases sharply (but there is clearly still diffuse emission from the lobes present, probably out to the edges of our mosaic). Using a 1.5 Jy beam-1 threshold, 121 out of the total 281 RMs are behind the radio lobes with the remaining 160 RMs along sightlines outside the lobes. We have tested the sensitivity of our results to the exact value of the boundary chosen for inside versus outside the lobes. We are co