A low frequency study of linear polarization in radio galaxies
Vijay H. Mahatma, Martin J. Hardcastle, Jeremy Harwood, Shane P. O'Sullivan, George Heald, Cathy Horellou, Daniel J. B. Smith
MMNRAS , 1– ?? (2020) Preprint 23 December 2020 Compiled using MNRAS L A TEX style file v3.0
A low frequency study of linear polarization in radio galaxies
V. H. Mahatma , ★ , M. J. Hardcastle , J. Harwood , S. P. O’Sullivan , G. Heald ,C. Horellou and D.J.B. Smith Centre for Astrophysics Research, School of Physics, Astronomy & Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK Thüringer Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany School of Physical Sciences and Centre for Astrophysics & Relativity, Dublin City University, Glasnevin, D09 W6Y4, Ireland. CSIRO Astronomy and Space Science, PO Box 1130, Bentley, WA 6102, Australia Chalmers University of Technology, Dept of Space, Earth and Environment, Onsala Space Observatory, SE-43992 Onsala, Sweden
Accepted 2020 December 22. Received 2020 December 11; in original form 2020 August 19
ABSTRACT
Radio galaxies are linearly polarized – an important property that allows us to infer the prop-erties of the magnetic field of the source and its environment. However at low frequencies,Faraday rotation substantially depolarizes the emission, meaning that comparatively few po-larized radio galaxies are known at low frequencies. Using the LOFAR Two Metre Sky Surveyat 150 MHz and at 20 arcsec resolution, we select 342 radio galaxies brighter than 50 mJyand larger than 100 arcsec in angular size, of which 67 are polarized (18 per cent detectionfraction). These are predominantly Fanaroff Riley type II (FR-II) sources. The detection frac-tion increases with total flux density, and exceeds 50 per cent for sources brighter than 1 Jy.We compare the sources in our sample detected by LOFAR to those also detected in NVSSat 1400 MHz, and find that our selection bias toward bright radio galaxies drives a tendencyfor sources depolarized between 1400 and 150 MHz to have flatter spectra over that frequencyrange than those that remain polarized at 150 MHz. By comparing observed rotation measureswith an analytic model we find that we are preferentially sensitive to sources in low massenvironments. We also infer that sources with one polarized hotspot are inclined by a smallangle to the line of sight, while sources with hotspots in both lobes lie in the plane of the sky.We conclude that low frequency polarization in radio galaxies is related to a combination ofenvironment, flux density and jet orientation.
Key words: polarization – galaxies: active – galaxies: jets – techniques: polarimetric –radiation mechanisms: non-thermal
The synchrotron radiation by which we observe the jets and lobes ofradio-loud active galactic nuclei (RLAGN) arises from relativisticelectrons gyrating in magnetic fields. As a consequence of thisprocess, the radiation is intrinsically linearly polarized. RLAGN,which can have a maximum degree of polarization of up to ∼
70 percent (Pacholczyk 1970), are strong sources of polarized radiationwhich can be observed by radio telescopes (see reviews by Saikia& Salter 1988; Wielebinski 2012). Information on the polarizedintensity from RLAGN is important to obtain for the followingreasons: • Since the position angle of the electric field vector of the ra-diation we observe is perpendicular to the projected magnetic fielddirection in the plane of the sky, polarization observations, if cal- ★ Contact e-mail: [email protected] ibrated correctly, can directly give information on the structure ofmagnetic fields in the plane of the sky. This has led to studies of themagnetic field structure in the jets, lobes and hotspots of RLAGN,and their surrounding environment, on parsec scales (e.g. Gabuzdaet al. 1992; Homan 2005) to kiloparsec scales (e.g. Laing 1980;Hardcastle et al. 1997; Laing et al. 2008; O’Sullivan & Gabuzda2009; Guidetti et al. 2011 and see review by Bridle & Perley 1984).The hotspots of RLAGN, which are thought to contain compressedand ordered magnetic fields (Laing 1980; Hughes et al. 1989), areexpected to be prime locations for polarized emission, so obser-vations of polarization may enhance our understanding of particleacceleration processes. • A lack of detectable polarization for high surface brightnessobjects gives evidence for substantial depolarization – a combina-tion of factors such as the finite telescope beam, inhomogeneousmagnetic field structures in the lobes or in their surrounding envi-ronment and Faraday rotation will reduce the observed polarization(as described below). Measurements of depolarization in the lobescan, in principle, trace their magnetoionic properties and their ther- © a r X i v : . [ a s t r o - ph . GA ] D ec V. H. Mahatma mal particle content, or that of their environment (Dreher et al.1987; O’Sullivan et al. 2017, 2019; Knuettel et al. 2019).Effects caused by Faraday rotation results in frequency-dependentdepolarization: as linearly polarized emission travels through bire-fringent magnetised media (the intergalactic medium, for example),a difference in the phase velocity occurs for the right and left circularpolarization constituents of the linear polarization. This manifestsas a wavelength-dependent rotation of the polarization angle as 𝜒 = 𝜒 + 𝑅𝑀𝜆 [rad] (1)where 𝜒 is the observed polarization angle (in radians), 𝜒 is theintrinsic polarization angle, 𝑅𝑀 is the rotation measure (in rad m − )and 𝜆 is the wavelength (in m). The 𝑅𝑀 is related to the propertiesof the line-of-sight magnetised media by 𝑅𝑀 = . ∫ telescopesource 𝑛 𝑒 (cid:174) B (cid:107) · d (cid:174) l [rad m − ] (2)where 𝑛 𝑒 is the electron density (in cm − ), (cid:174) B (cid:107) is the line of sightmagnetic field strength (in 𝜇 Gauss) and the integral is taken withrespect to the path lengths d (cid:174) l (in parsecs) through all interveningmaterial between the source and the telescope. Differential Fara-day rotation, and/or inhomogeneous magnetic field structures in thesource, lead to different polarization angles across the telescopebeam, which are then vector-averaged and lead to depolarization.Further depolarization can occur when these effects apply signif-icantly within the observing bandwidth, since Faraday rotation isfrequency-dependent.Depolarization of linearly polarized emission from RLAGNconfirms the presence of magnetic fields in thermal plasma alonglines of sight through their environments. Significant depolariza-tion is generally attributed to environments local to the source thatcause large 𝑅𝑀 s (e.g. in the interstellar or intracluster medium;Hardcastle 2003 and Carilli & Taylor 2002, respectively, or in theshocked gas surrounding radio lobes; Hardcastle et al. 2012), andhence 𝑅𝑀 s are useful in inferring properties of the environmentwhich are otherwise difficult to obtain. For RLAGN environmentswell described by hot ( 𝑇 ∼ K) plasma that radiates in X-raysdue to thermal bremsstrahlung, sensitive X-ray maps allow a mea-sure of the gas density 𝑛 𝑒 (e.g. Croston et al. 2008; Hicks et al.2013; Mahatma et al. 2020), but may be expensive to obtain forlarge samples of radio galaxies. 𝑅𝑀 maps can give valuable (butindirect) information on the surrounding environment of RLAGN,while giving constraints on the structure of magnetic fields.In general, the interpretation of observed 𝑅𝑀 s is difficult, asthey are in general a superposition of Faraday rotation from; theEarth ionosphere, the magnetized plasma in the Galaxy, the inter-galactic medium, the intracluster/intragroup medium and within thesource itself. Radio lobes in particular carry entrained thermal gasfrom their surroundings (Bicknell 1984), and source-intrinsic Fara-day rotation can also be a significant contributor to observed 𝑅𝑀 swhen the Galactic contributions have been subtracted. Precise 𝑅𝑀 information can help to disentangle effects from different line ofsight contributions if their respective 𝑅𝑀 s are found. In order toaccurately quantify the 𝑅𝑀 and polarization properties of RLAGNin general, large-sample statistics are needed. It should be noted that, except in the case of differential Faraday rotationacross the band, the magnitude of the 𝑅𝑀 and depolarization of a sourceare not strictly related, rather the latter is associated with the dispersion in 𝑅𝑀 across the telescope beam or along the line of sight. Low frequency ( ∼
100 MHz) linearly polarized source detections,particularly in a statistical study, are scarce. Due to the 𝜆 factorin Equation 1, Faraday rotation, and by extension depolarization,is much more important at low frequencies. RLAGN samples withpolarization information exist in surveys at 1.4 GHz or greater (e.g.Taylor et al. 2007; Hales et al. 2014; Rudnick & Owen 2014), wheredepolarization is less significant in general, although this is alsodue to the fact that there are many more completed large-area radiosurveys at GHz frequencies. Taylor et al. (2009) produced an 𝑅𝑀 map of the sky using the NRAO VLA Sky Survey (NVSS; Condonet al. 1998), a 1400 MHz survey, detecting 37,543 polarized radiosources at declinations > − ◦ . However at lower frequencies thetotal flux density for any steep-spectrum RLAGN ( 𝛼 (cid:54) − . 𝑆 ∝ 𝜈 𝛼 ) is much higher , which may give adequate polarized signalto noise for low surface brightness regions that are undetected athigher frequencies. Moreover, and more crucially, since the 𝑅𝑀 precision depends on the interval in 𝜆 , low frequency instrumentscan out-perform centimetre-wave instruments by a few orders ofmagnitude in 𝑅𝑀 precision. Larger source counts at these frequen-cies will test the robustness of the previously mentioned polarizationstudies, after understanding the detection statistics and possible se-lection biases of large samples at low frequencies. In sampling thisnew low-frequency parameter space, it is crucial to have radio tele-scopes with the ability to perform wide-area surveys of the skycombined with the required sensitivity to observe large samples ofRLAGN – past surveys such as 3CRR (Laing et al. 1983) are severelybiased towards the most luminous sources such as Fanaroff-Rileytype-II objects (FR-II; Fanaroff & Riley 1974). Recently, Riseleyet al. (2020) presented the POlarised GaLactic and ExtragalacticAll-Sky MWA Survey-the POlarised GLEAM Survey (POGS) inthe frequency range 169-231 MHz at a resolution of 3 arcmin (atthe highest), with 484 polarized RLAGN detected in the entiresouthern sky. However, instruments with the capability to performsub-arcmin resolution surveys are more ideal in resolving the differ-ent components of RLAGN (core and lobes) and also mitigate theeffects of beam depolarization in small angular size sources.The LOw Frequency ARray (LOFAR; van Haarlem et al. 2013)is one such instrument, giving an angular resolution of 6 arcsec at150 MHz. LOFAR is able to obtain a Faraday depth resolution(ability to resolve structures in Faraday depth space, where Fara-day depth is the more generalised form of 𝑅𝑀 in Equation 1) of ∼ − at 150 MHz, significantly better than that obtained byhigher-frequency instruments (a factor of 200 better than the up-coming VLA Sky Survey, VLASS; Lacy et al. 2019). Additionally,LOFAR’s mixture of long and short baselines and its sensitivityto large extended structures (such as the lobes of nearby FR-I andFR-II radio galaxies) enables straightforward selection of RLAGN.The LOFAR Two-Metre Sky Survey (LoTSS; Shimwell et al. 2019),an on-going survey of the northern hemisphere enables large sam-ples of RLAGN to be obtained for polarization studies. The firstdata release (DR1; Shimwell et al. 2019) covered the area of theHobby-Eberly Telescope Dark Energy eXperiment (HETDEX: Hillet al. 2008) Spring field; over 420 square degrees on the sky within161 ◦ < RA < ◦ and 45 . ◦ < DEC < ◦ , observed at 6 arcsecresolution with a median sensitivity of ∼ 𝜇 Jy beam − . With alarge low-frequency sample of polarized RLAGN, in combinationwith measurements at higher frequencies, we may start to answer Down until the self-absorption regime which affects the radio continuumat frequencies lower than ∼
100 MHz (e.g. Scheuer & Williams 1968)MNRAS , 1– ????
100 MHz (e.g. Scheuer & Williams 1968)MNRAS , 1– ???? (2020) olarization properties of radio galaxies questions about the main driver of observed wavelength-dependentdepolarization. Moreover, we may test whether polarized emissionis seen as a result of the physical effects of the ‘Faraday screen’(i.e. an external magnetoionic medium), or whether different AGNproperties drive different levels of polarized emission for a popu-lation of sources. A statistical study of the observational nature ofpolarized emission from RLAGN will also be a vital prerequisitefor upcoming radio surveys (Square Kilometre Array, VLASS), forwhich broad-band radio polarimetry is a scientific goal (Heald et al.2020).The polarization data in LoTSS have already been analysedby Van Eck et al. (2018), Van Eck et al. (2019) and O’Sullivanet al. (2018) (hereafter OS18), using the 𝑅𝑀 synthesis technique(see Section 2.2). In the former two studies, the authors searchedfor polarized point sources and diffuse sources, respectively, withinthe HETDEX region at an angular resolution of 4.3 arcmin, withthe study of Van Eck et al. (2018) producing a catalogue of 92polarized point sources. OS18 studied the sources in this cataloguein the LoTSS DR1 area ( ∼
80 per cent of which have optical iden-tifications) at a higher resolution of 20 arcsec. These sources haveradio luminosities consistent with being RLAGN, and while thesample includes a mixture of extended radio galaxies and blazars,the majority of detections came from the hotspots of large FR-IIradio galaxies. Stuardi et al. (2020) presented a polarization studyof giant radio galaxies, which are > . 𝑅𝑀 synthesis (Brentjens & de Bruyn 2005) to produce polarization and 𝑅𝑀 maps of all sources and compare the bulk observational andphysical properties between the detected and non-detected sources,with the aim of inferring the primary driver of observed polarizedemission in radio galaxies. In Section 2 we describe the selectionof our parent sample and our polarized detection criteria. In Sec-tion 3 we present our analysis and results on detectability, hostgalaxies, observed and predicted 𝑅𝑀 s using an analytic model. Wesummarise our results and conclude in Section 4.Throughout this paper we define the spectral index 𝛼 in thesense 𝑆 ∝ 𝜈 𝛼 . We use a Λ CDM cosmology in which 𝐻 = − Mpc − , Ω 𝑚 = 0.27 and Ω Λ = 0.73. LoTSS DR2 (scheduled for public release in early 2021) will havea northern sky coverage of over 5700 deg , including the DR1 areawhich covered 424 deg . While DR1 does not contain polarizationinformation, DR2 contains Stokes QU cubes (at 20 arcsec angularresolution) as data products, enabling polarization information to beextracted in this sky area. However, DR2 does not contain opticalIDs for radio sources at the time of writing. For the purposes ofour study we required a sample of radio galaxies with physical information such as radio luminosities. Hence, we use the DR2polarization products to find polarized radio galaxies in the DR1catalogue, which is publicly available and includes a value addedcatalogue with optical identifications (Shimwell et al. 2019; Duncanet al. 2019; Williams et al. 2019). This is particularly importantsince a radio galaxy catalogue from the DR1 sources has beenmade (Hardcastle et al. 2019), which we use to select sources forthis study.The DR1 radio galaxy selection details are given by Hardcas-tle et al. (2019), but we briefly describe them here. Sources wereselected as having an optical ID from either Pan-STARRs (Cham-bers et al. 2016) or the Wide Infrared Survey Explorer (WISE;Wright et al. 2010), and either a spectroscopic redshift or a photo-metric redshift with a fractional error < 10%. From this sample of71,955 sources, star-forming galaxies (SFG) were identified usingthe MPA-JHU catalogue and were removed. Objects were furtherremoved if their WISE colours were consistent with those of SFGcolours unless either; they are classed as AGN in the MPA-JHU cat-alogue, their total radio luminosity 𝐿 > W Hz − and theirhost galaxy 𝐾 𝑠 -band absolute magnitude 𝑀 𝐾 𝑠 >-25, or 𝑀 𝐾 𝑠 >-25and log ( 𝐿 ) > . − . ( + 𝐾 𝑠 ) , resulting in a sample of23,344 RLAGN. Given the nature of the selection criteria applied, itis likely that some RLAGN have been missed from the survey, par-ticularly if their hosts are strongly star-forming galaxies, unless theradio luminosity 𝐿 > W Hz − (which selects radio-loudquasars). For the purposes of our study we require extended andbright double-lobed radio galaxies and so this sample adequatelydescribes the population of radio galaxies detected in DR1.In order to create a sample with a polarization detection frac-tion high enough for a statistical study, we selected sources that areboth bright and large – this also removes compact objects such asblazars that are not of interest to this study. From the RLAGN cata-logue of Hardcastle et al. (2019), we selected sources with total fluxdensity 𝑆 (cid:62)
50 mJy (as are all sources detected in polarization inthe study by Stuardi et al. 2020) and with angular size 𝐿 (cid:62)
100 arc-sec . These criteria resulted in a total of 382 sources in the DR1 areaof 424 deg , from which we study the bulk polarization propertiesin the rest of the paper. To produce polarization and 𝑅𝑀 maps of our sample, we utilised the 𝑅𝑀 synthesis technique (Brentjens & de Bruyn 2005), using pyrm-synth , a Python script developed primarily for LOFAR Stokes Qand U cubes. The complex polarization ( 𝑃 = 𝑄 + 𝑖𝑈 ) can be writtenas 𝑃 ( 𝜆 ) = ∫ +∞−∞ 𝐹 ( 𝜙 ) 𝑒 𝑖𝜙𝜆 𝑑𝜙 (3)(Burn 1966), where 𝑃 ( 𝜆 ) is the polarized intensity as a func-tion of wavelength ( 𝜆 ) squared and 𝐹 ( 𝜙 ) is the Faraday spectrum(polarized intensity as a function of the Faraday depth 𝜙 ). 𝑅𝑀 synthesis transforms the cubes from frequency space into Faraday Various other values for these criteria were tested, with the result thatlower cut-off values resulted in a large number of undetected and unresolvedsources in polarization for the purposes of this study. https://github.com/sabourke/pyrmsynth_lite MNRAS , 1– ?? (2020) V. H. Mahatma depth space by inverting Equation 3 so that (an approximated recon-struction of) the Faraday spectrum is calculated. The reconstructedFaraday spectrum ( ¯ 𝐹 [ 𝜙 ] ) is then used to measure the peak polar-ized signal for each pixel in the image. The value of 𝜙 at whicha peak in the Faraday spectrum is found is taken as the 𝑅𝑀 ofeach pixel . This technique has already been extensively applied toLOFAR data (Van Eck et al. 2018, 2019; O’Sullivan et al. 2018,2019; Stuardi et al. 2020; O’Sullivan et al. 2020). We extracted the(unCLEANed) Stokes Q and U cubes of all sources in our sam-ple, which were spatially masked with a 3 𝜎 cut-off based on theStokes I image of the source at 20 arcsec resolution. We inputtedthe QU cubes for each source into pyrmsynth, using the rmcleantool (Heald et al. 2009) to deconvolve the Faraday spectrum usinga maximum of 1000 iterations, fitting a Gaussian to the peak of thereconstructed CLEANed Faraday spectrum, resulting in linearly po-larized intensity and 𝑅𝑀 maps. Note that this procedure implicitlyassumes only one peak in the Faraday spectrum of each source, butwe verified that multiple and equally strong peaks were not present(except in the case of leakage – see below) by inspecting the spectra.We limited the Faraday depth range to -150 (cid:54) 𝜙 (rad m − ) (cid:54) 𝛿𝜙 = . − . Though the Faraday depth magnitude can be up to 450 radm − for LOFAR, with initial analysis we found that we do not detectpeaks in the Faraday spectra outside the range stated above. Withthis spectral setup of RM synthesis we are sensitive to scales (cid:54) − in Faraday space. As no corrections were made for leakagesignal, which can dominate near Faraday depths close to zero, wefurther exclude the range − (cid:54) 𝜙 (cid:54) . − from the fittingof the peak in the Faraday spectrum. Hence, we are only Faradaydepth-complete outside this range. The linear polarization and 𝑅𝑀 maps of six sources in our sample are shown in Figure 1 and Figure2. It should be noted that the typical Galactic 𝑅𝑀 in the HETDEXregion is 0 (cid:54) 𝑅𝑀 Galactic (rad m − ) (cid:54) +
23 (Oppermann et al. 2015).To determine which sources have detections of polarized emis-sion, given the relatively low resolution of the maps and the ex-pectancy of low S/N polarization, we use a simple island-findingmethod by masking non-detected pixels . First, we remove back-ground noise pixels by masking pixels which have surface bright-nesses less than the mean pixel value in the image plus 3 𝜎 𝑏 , where 𝜎 𝑏 is the standard deviation of the pixel brightnesses in the image.For some sources that were clearly not polarized (sporadic regionsof high pixel intensity, mostly off-source) but still had unmaskedregions, particularly those with large angular size, we manuallydisallowed a detection. Detections were also manually disallowedwhich still had unmasked regions of nearby polarized sources inthe map unrelated to the source (i.e. background quasars). For somesources generally with small angular sizes and hence a low num-ber of background pixels present in the maps (as the cubes wereconstructed near the source to only contain on-source pixels), meanpixel surface brightnesses and 𝜎 𝑏 were generally overestimated asthe 3 𝜎 𝑏 threshold prevented detections of clearly polarized hotspots.We therefore implemented a procedure to iteratively mask >5 𝜎 𝑏 re-gions in the polarized intensity maps and re-calculate 𝜎 𝑏 , until thefractional difference between 𝜎 𝑏 in the current and last iteration be-came (cid:0) 𝜎 𝑏, last − 𝜎 𝑏, current (cid:1) / 𝜎 𝑏, current < × − . For some sourceimages still containing too few background pixels, where the image Note that this value for the 𝑅𝑀 applies in the case of a delta function forthe Faraday spectrum. Each map has a pixel size of 4.5 arcsec is dominated by bright emission, we reduce the masking criterionto pixels >3 𝜎 𝑏 .We then label as detections of polarized emission where groupsof unmasked pixels are in a 2 × 𝜎 QU , where 𝜎 QU is given as the mean of the detected pixels in the linearlypolarized rms map output from 𝑅𝑀 synthesis . For the 𝑅𝑀 of eachsource, we take a weighted mean pixel value from the 𝑅𝑀 map as (cid:104) 𝑅𝑀 (cid:105) = (cid:205) 𝑖 𝑤 𝑖 𝑅𝑀 𝑖 (cid:205) 𝑖 𝑤 𝑖 (4)where 𝑤 𝑖 is the normalised pixel brightness of pixel 𝑖 of all detectedpixels in the polarized intensity map. The 𝑅𝑀 error is given by 𝜎 𝑅𝑀 = RMSF FWHM2 × 𝑆 / 𝑁 (5)(Brentjens & de Bruyn 2005), where the RMSF FWHM (Full WidthHalf Maximum) is 1 .
16 rad m − for LoTSS pointings, and the sig-nal to noise ratio 𝑆 / 𝑁 is the peak pixel brightness over the rmsvalue in that pixel. An additional, more dominant error arises fromthe systematic error of the ionospheric 𝑅𝑀 correction includedin 𝑅𝑀 synthesis, and results in uncertainties of 0.1-0.3 rad m − (Sotomayor-Beltran et al. 2013). We give conservative error esti-mates by adding in quadrature the error from Equation 5 and amaximum systematic error of 0.3 rad m − for each source. We alsocorrect our polarized intensities for Ricean bias, which can be sig-nificant at low signal to noise, using Equation 5 of George et al.(2012). No corrections have been made for the dependence of thederived Faraday spectrum on spectral index, but it does not affectthe peak of the Faraday spectrum and hence the corrections areminimal (Brentjens & de Bruyn 2005).We then identified sources where we find evidence of leakagesignal being manifested as detections – the Faraday depth rangewe excluded from 𝑅𝑀 synthesis ( − (cid:54) 𝜙 (cid:54) . − ) is notprecisely centred on zero due to the ionospheric 𝑅𝑀 correction(s)shifting the leakage signals. It is possible for this exclusion rangeto not capture all sources with leakage signal and some of ourdetected sources which have 𝑅𝑀 s below -3 rad m − and above +1.5rad m − may show strong leakage, particularly at the locations of thesidelobes of the leakage signal. Since leakage signals will generallyhave low fractional polarization ( Π (cid:54) Π (cid:54)
1% that were detected at − . (cid:54) 𝜙 (cid:54) − − and 1 . (cid:54) 𝜙 (cid:54) − in their Faraday spectra. Thisresulted in the removal of seven sources. Faraday spectra of threedetected sources in our sample that were not excluded are shown inFigure A1.Applying our methods we finally obtain a reliable polarizationdetection in 67 out of 382 sources – a detection fraction of 18 per centat 150 MHz. We regard the non-detected sources as depolarized.This represents a polarized radio galaxy surface density within theHETDEX field, for sources brighter than 50 mJy and larger than100 arcsec in angular size, of 0.16 ± .
02 deg − (errors quoted here The rms is given by the average spread of the ‘wings’ of the Faradayspectrum over Stokes Q and U, limited by our Faraday depth range of -150 (cid:54) 𝜙 (rad m − ) (cid:54) , 1– ????
02 deg − (errors quoted here The rms is given by the average spread of the ‘wings’ of the Faradayspectrum over Stokes Q and U, limited by our Faraday depth range of -150 (cid:54) 𝜙 (rad m − ) (cid:54) , 1– ???? (2020) olarization properties of radio galaxies (a) ILTJ120122.67+492554.0 (b) ILTJ120122.67+492554.0(c) ILTJ121506.07+534953.2 (d) ILTJ121506.07+534953.2(e) ILTJ144218.66+504403.7 (f) ILTJ144218.66+504403.7 Figure 1.
150 MHz polarized FR-Is from our RLAGN sample. Coloured pixels represent 20 arcsec polarization detections: left panels are the polarized intensityand the right panels are the 𝑅𝑀 s, while black contours display the 6 arcsec Stokes I emission (beam sizes shown as magenta and black circles in the lower leftof each image, respectively). Red circles show the position of the catalogued host galaxy in LoTSS DR1.MNRAS , 1– ?? (2020) V. H. Mahatma (a) ILTJ110251.61+531307.1 (b) ILTJ110251.61+531307.1(c) ILTJ115531.76+545351.5 (d) ILTJ115531.76+545351.5(e) ILTJ124012.79+533438.9 (f) ILTJ124012.79+533438.9
Figure 2.
150 MHz polarized FR-IIs from our RLAGN sample. See Figure 1 for image descriptions. MNRAS , 1– ????
150 MHz polarized FR-IIs from our RLAGN sample. See Figure 1 for image descriptions. MNRAS , 1– ???? (2020) olarization properties of radio galaxies represent Poisson statistics). As a comparison with recent studiesfrom the LoTSS data in the same area, Van Eck et al. (2018) found92 point sources at a surface density of 0.16 ± .
02 deg − at 4.3arcmin resolution, while Mulcahy et al. (2014) and Neld et al. (2018)found 6 securely-detected polarized sources in a single LOFARpointing at the same resolution as ours, finding a surface densityof 0.30 ± .
12 deg − , demonstrating consistency between LOFARstudies and confirming that RLAGN are the predominant sourceof polarization at 150 MHz. Subsets of our detected sources arepresented in Figure 1 and Figure 2. The most important limitation to our analysis is the use of un-CLEANED Stokes QU cubes that are used to produce polarizedintensity (dirty) maps. We cannot reliably CLEAN the cubes priorto 𝑅𝑀 synthesis due to the low signal to noise in each channel of thecubes. The effect of this is higher noise and artefacts in the resultingpolarized intensity maps, particularly around bright point sources,than in the case of CLEANed maps. Since the aims of our study donot rely on accurate astrometry and analysis of spatial structure, thelow image fidelity due to the use of dirty QU cubes does not affectour analysis or results.We also note the issue of using 𝑅𝑀 synthesis and the asso-ciated rms map in polarized intensity to determine detection rates:imperfect imaging and calibration (as is the case here) can lead tonon-Gaussian tails in the Stokes Q and U Faraday spectra, whencethe rms is calculated. While this will overestimate errors, it mayalso cause high false detection rates in low signal to noise pixels(George et al. 2012) where relatively low detection thresholds areused (3 𝜎 QU , as used here). While George et al. (2012) propose8 𝜎 QU to serve as a detection threshold, we note that our detec-tion method involved visual inspection, and in the case of polarizedemission not associated with a core, lobe or hotspot (i.e structuresof high intensity in the Stokes I image), sources were discarded asfalse detections. A 5 𝜎 QU threshold was tested, giving the result thatlow signal to noise sources that had clearly polarized emission (e.g.in hotspots) were undetected with our method. In this section we present a statistical analysis of the polarizationproperties of our RLAGN sample. Unless otherwise stated, to dis-tinguish the characteristics of two distributions we quote the 𝑝 -valuefrom a Wilcoxon-Mann-Whitney test (Mann & Whitney 1947), us-ing a 95 per cent confidence level (i.e. a p-value < .
05 means wecan reject the null hypothesis that the two samples have identicalmedian values).
In the top panel of Figure 3 we plot the distributions in 150 MHz fluxdensity and angular size of our detected and non-detected sources.We see that, statistically, our polarized sources (hatched beige) aresignificantly brighter compared to those that are depolarized (grey),as expected. Further, the detection fraction is greater than 50 percent for sources brighter than 1 Jy. On the other hand, there arestatistically similar medians in angular size between detected andnon-detected sources, meaning that the detectability of polarizationamongst RLAGN in our sample is driven primarily by flux densityrather than, or in addition to, angular size. Similar statistics are seen with physical properties as shown in the bottom panel of Figure3, where the polarized sources are more luminous but similar inphysical size. This is consistent with the idea that brighter and moreluminous RLAGN have a preference for detectable polarization.In the left panel of Figure 4 we plot the 6 arcsec total flux den-sity against the 20 arcsec polarized flux density for our polarizedsources. We do not see any clear correlation, meaning that althoughthe polarized detection fraction increases with flux density (as seenin Figure 3), the amount of polarized emission is not entirely drivenby total flux density . Rather, a range of polarized emission is de-tected in RLAGN for a large range in total flux density at 150 MHz.This is consistent with a model in which the level of polarizedemission seen in RLAGN is strongly related to the characteristicsof the associated Faraday screen and the attributed depolarization,some components of which are unrelated to the source (e.g. theforeground IGM). We also plot the fractional polarization Π (ratioof polarized emission to total emission in the polarization-detectedpixels) against the total flux density measured in the 20 arcsec StokesI image, in the right panel of Figure 4 (the red dashed line indicatesthe approximate sensitivity to polarization by taking an average of3 𝜎 𝑄𝑈 from all sources). As expected, since the latter observableis the denominator of the former, the fractional polarization de-creases with increasing total flux density. However there is a largescatter, particularly for > 𝑝 − value < 0.05).While FR-II hotspots are the predominant source of polarization at150 MHz (O’Sullivan et al. 2018), it is important to quantify thedetection fractions between FR-Is and FR-IIs, as well as to comparetheir fractional polarization.We use the code of Mingo et al. (2019), which categorizessources into FR-I and FR-II based on whether the peak radio emis-sion is located close to our away from the centre of the source,respectively, to morphologically categorize the polarized sourcesin our sample. While visual inspection may be used to classify oursources, an automated classification based on the definition of the We note that the flux density cut in selecting sources in our sampleintroduces a selection bias, and our results do not necessarily apply forsources with 𝑆 <
50 mJy.MNRAS , 1– ?? (2020) V. H. Mahatma
150 MHz total flux (mJy) S o u r c e c o un t s p-value: 6.66e-11 DetectionsNon-detections 10 Angular size (arcsec) S o u r c e c o un t s p-value: 0.162 DetectionsNon-detections10
150 MHz luminosity (W/Hz) S o u r c e c o un t s p-value: 4.8e-08 DetectionsNon-detections 10 Physical size (kpc) S o u r c e c o un t s p-value: 0.063 DetectionsNon-detections
Figure 3.
Distributions of observational and physical radio properties of our RLAGN sample; 150 MHz flux density (top left), angular size (top right),radio luminosity (bottom left) and physical size (bottom right). Grey and hatched beige bars represent our non-detected and detected sources in polarization,respectively.
FR dichotomy (as used by Mingo et al. 2019) represents a systematicmorphological stratification of our sample without cognitive bias.The 382 objects in our sample were separated based on the code intothree categories; FR-I, FR-II and indeterminate. The latter categoryrepresents the case where the code cannot clearly determine themorphology, and this is usually the case for more compact objectsor objects with non-symmetric lobes where there may be FR-I-likelobes on one side of the jet and FR-II-like lobes on the other, whichare likely due to projection effects in many cases (Harwood et al.2020). Due to the ability of LOFAR to observe both compact andextended structures of RLAGN, we expected the code to classify alarge number of sources which can be visually identified as eitherFR-I or FR-II as indeterminate. Some of the authors (VHM, MJHand JH) visually checked the 6 arcsec total intensity maps of theindeterminate sources in our sample, and re-classified each sourceas either FR-I or FR-II where appropriate. Around ∼
10 per cent ofthe indeterminate sample were sources that could be clearly iden- tified as an FR-I or an FR-II, and were moved to those categories.We also checked the sources in the original FR-I and FR-II samples,to conservatively check for obvious contaminants from either class.Only a small number ( (cid:54)
MNRAS , 1– ????
MNRAS , 1– ???? (2020) olarization properties of radio galaxies
150 MHz total flux (mJy) -2 -1 M H z li n e a r l y p o l a r i z e d f l u x ( m J y ) Detections 10 Polarization-masked 150 MHz total flux (mJy) -4 -3 -2 -1 Π ( M H z ) Detections
Figure 4.
150 MHz linearly polarized flux density (left) and fractional polarization (right) against total flux density for our detected sources. Note that for theright panel we only plot the total flux density for the regions of the source that are polarized. Uncertainties are shown as 3 𝜎 error bars, but are not visibledue to the logarithmic scale.Dashed lines give an indicative estimate of our sensitivity to polarized emission, plotted as 3 𝜎 mean ,𝑄𝑈 , where 𝜎 mean ,𝑄𝑈 is theaverage rms error of polarized fluxes in our sample.
150 MHz total flux (mJy) -2 -1 M H z li n e a r l y p o l a r i z e d f l u x ( m J y ) FR-IFR-II 10 Polarization-masked 150 MHz total flux (mJy) -4 -3 -2 -1 Π ( M H z ) FR-IFR-II
Figure 5.
Same as Figure 4, for sources classed as FR-I (beige) and FR-II (blue) according to the criteria of Mingo et al. (2019). Note that indeterminate-morphology sources are not plotted.Sample Counts Sample detection fraction (%)RLAGN 382 17.5FR-I 122 3.4FR-II 146 10.2Indeterminate 114 3.9
Table 1.
Polarization detection fractions for our RLAGN sample, and theFR-I, FR-II and indeterminate subsets based on morphology. Counts referto the total number of sources in that sample.
We reproduce Figure 4 in Figure 5, now labelling the sourcesas FR-I (beige) and FR-II (blue). We see that in general, at a given 150 MHz total flux density, FR-II sources tend to be brighter inpolarization than FR-I sources, although with large scatter. In Figure6 we plot the distribution in fractional polarization Π for FR-Iand FR-II sources, showing a statistically higher median Π forFR-IIs, where FR-IIs solely dominate at Π > The host galaxy properties of RLAGN populations give valuableinformation on the drivers of AGN activity. It is important to deter-
MNRAS , 1– ?? (2020) V. H. Mahatma Π (150 MHz) S o u r c e c o un t s p-value: 1.44e-09 FR-IIFR-I
Figure 6.
Distribution of fractional polarization between FR-I (hashed or-ange) and FR-II (blue) radio galaxies. Dashed lines represent median values. mine if there are differences in detection fractions as a function ofhost galaxy type. In particular, we test the hypothesis that polarizedand depolarized RLAGN at 150 MHz can be driven by the sametype of host galaxy.In Figure 7 we plot the distributions of host galaxy optical 𝐾𝑠 and 𝑟 − band absolute magnitudes, available in the LoTSS DR1catalogue, for our polarized (yellow) and depolarized (grey) sources.We see that the distributions in both optical bands are similar – the 𝑝 values (quoted above both figures) from a two-sample Kolmogorov-Smirnov (KS) test are both > 0.05, indicating that we cannot rejectthe hypothesis that both polarized and depolarized subsets havesimilar distributions, at a confidence level of 95 per cent. The opticaland near-IR intrinsic brightness of the host galaxies that drive radiojets in our sample are not in general associated with a detection ofpolarized emission.In terms of polarized radio sources, Banfield et al. (2014) findthat quasar-type galaxies typically host sources with lower fractionalpolarization than quiescent galaxies. O’Sullivan et al. (2015) obtainsimilar results and find differences in the fractional polarizationbetween High Excitation Radio Galaxies (HERGs) and Low Exci-tation Radio Galaxies (LERGs), finding that LERGs can achievehigher intrinsic degrees of polarization at GHz frequencies, andO’Sullivan et al. (2017) relate this to LERGs having more intrinsi-cally ordered magnetic fields in the radio plasma. We instead testthe low frequency detectability in polarization by comparing the de-tection rates of HERGs and LERGs using the WISE colour-colourplot, given by WISE mid-infrared apparent magnitudes at 3.4, 4.6,12, and 22 𝜇 m (W1, W2, W3, W4 bands). While this does not givea direct classification of the HERG and LERG status of a particulargalaxy, the majority of LERGs tend to have lower values of W1-W2and W2-W3, while HERGs tend to have higher values of colour,with higher levels of dust-obscuration (which may arise due to thepresence of an optically thick torus surrounding the accretion sys-tem). The position of a particular object in the WISE colour-colourplot can therefore give information on the nuclear properties of agalaxy.In the top panel of Figure 8 we present the WISE colour-colour plot for our RLAGN sample. We find that the hosts of the
30 28 26 24 22 20
Rest-frame Ks -band absolute magnitude S o u r c e c o un t s p-value: 0.198 DetectionsNon-detections28 26 24 22 20 18
Rest-frame r -band absolute magnitude S o u r c e c o un t s p-value: 0.929 DetectionsNon-detections
Figure 7.
Distributions in rest frame absolute magnitudes in the opticalKs band (top) and r-band (bottom) of the host galaxies of our polarizationdetected sources (hashed beige) and our non-detected sources (grey). polarized sources in our sample have significantly higher valuesof W1-W2 and W2-W3 than depolarized sources, shown by thelarger fraction of polarized objects in the upper-right hand side ofthe plot (statistics were tested for distributions in W1-W2 and W2-W3 between polarized and depolarized sources, with 𝑝 − values <0.05). We have over-plotted the ‘AGN wedge’, defined by Mateoset al. (2012), who select luminous AGN selected in X-rays. Thisregion is typically occupied by obscured AGN and quasars (i.e.HERGs), which, at low redshift, tend to be associated with FR-IIradio galaxies (Zirbel 1997). In the bottom panel of Figure 8 weseparate our sample into FR-I and FR-II objects, and it is clearlyseen that the majority of the sources with higher values of WISEcolours are FR-II sources (while there are still a comparable amountof FR-II sources where FR-Is are situated). Further, in Figure 9, weshow the fractional polarization Π as a function of the W1-W2 colour. We see that there is a tendency for FR-IIs to have ahigher W1-W2 colour than FR-Is, for a given Π , though withlarge overlap. We therefore have insufficient evidence to suggest MNRAS , 1– ????
Distributions in rest frame absolute magnitudes in the opticalKs band (top) and r-band (bottom) of the host galaxies of our polarizationdetected sources (hashed beige) and our non-detected sources (grey). polarized sources in our sample have significantly higher valuesof W1-W2 and W2-W3 than depolarized sources, shown by thelarger fraction of polarized objects in the upper-right hand side ofthe plot (statistics were tested for distributions in W1-W2 and W2-W3 between polarized and depolarized sources, with 𝑝 − values <0.05). We have over-plotted the ‘AGN wedge’, defined by Mateoset al. (2012), who select luminous AGN selected in X-rays. Thisregion is typically occupied by obscured AGN and quasars (i.e.HERGs), which, at low redshift, tend to be associated with FR-IIradio galaxies (Zirbel 1997). In the bottom panel of Figure 8 weseparate our sample into FR-I and FR-II objects, and it is clearlyseen that the majority of the sources with higher values of WISEcolours are FR-II sources (while there are still a comparable amountof FR-II sources where FR-Is are situated). Further, in Figure 9, weshow the fractional polarization Π as a function of the W1-W2 colour. We see that there is a tendency for FR-IIs to have ahigher W1-W2 colour than FR-Is, for a given Π , though withlarge overlap. We therefore have insufficient evidence to suggest MNRAS , 1– ???? (2020) olarization properties of radio galaxies W − W W − W AGN
DetectionsNon-detections2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 W − W W − W AGN AGN
FR-INon-detectionsFR-II
Figure 8.
WISE colour-colour diagrams of host galaxies in our sample (top)and in our morphological categories (bottom). Colour coding is the sameas for previous figures. Uncertainties are of the order <1% and hence errorbars are not shown. The solid lines indicate the ‘AGN wedge’, as defined byMateos et al. (2012). that quasars with higher values of WISE colour tend to drive radiolobes with higher polarization. Rather, FR-II sources are more likelyto be detected due to their more powerful jets than FR-Is, and tendto be hosted by dust-obscured galaxies with a torus, also associatedwith radiatively efficient accretion in HERGs (Laing et al. 1994;Evans et al. 2006; van der Wolk et al. 2010; Gürkan et al. 2014).While this may present an apparent contradiction with the results ofBanfield et al. (2014),O’Sullivan et al. (2015) and O’Sullivan et al.(2017), in that we have a higher detection rate of polarization forquasar/HERG-type radio galaxies (mostly FR-IIs as seen in Figure8), we emphasise their results are based on the modelled intrinsic fractional polarization at high frequencies, while ours is based onobserved polarization at low frequencies. Further, and on a relatednote, it is very likely that LERG FR-Is which may have high intrinsicdegrees of polarization are generally depolarized in our sampledue to high Faraday dispersions in the centres of their hot gasenvironments, which are not likely to be detected with LOFAR at150 MHz (see Section 3.3). Hence, we suggest that the 150 MHz W − W Π ( M H z ) FR-IFR-II
Figure 9.
Fractional polarization against host galaxy W1-W2 colour for FR-I(yellow) and FR-II (blue) radio galaxies. polarization in radio galaxies is not driven by a particular type ofoptical brightness or nuclear emission in the host galaxy relative tothe population of radio galaxies, but an association exists betweenpolarization and WISE colour due to the association between theFR-class and WISE colour.
Any frequency dependence of the measured fractional polarizationcan give evidence for depolarization for any given source. To inves-tigate this, we compared the polarization properties of our sampleat 150 MHz with the polarization measured for the same objectswith NVSS at 1.4 GHz (Taylor et al. 2009), as was done by Van Ecket al. (2018) for their sample at 4.3 arcmin resolution. Taylor et al.(2009) present a 1.4 GHz sample of polarized sources in the sky atdeclination north of 𝛿 = − ◦ , which also covers the LoTSS area.The NVSS completeness limit of 2.5 mJy gives an ideal compari-son survey, though the restoring beam at 45 arcsec is more than afactor of two larger than that of our sample. Van Eck et al. (2018)find that their LOFAR-detected sample contains sources with mostof their polarized emission in broad Faraday-thick components (astheir sources have higher fractional polarization with NVSS thanwith LOFAR, with LOFAR only being sensitive to structures (cid:46) − in Faraday depth). We apply some similar comparisonswith our sample to investigate the line-of-sight environments ofRLAGN.We identify our sources with the Taylor et al. (2009) sample byusing a positional cross-match criterion with a separation limit of135 arcsec (three NVSS beams). Lower separation limits of one ortwo NVSS beams resulted in fewer correct cross-matches since oursources are centered on the optical ID, whereas the NVSS polarizedsources are centred on the polarized emission, such as hotspots,which can be more than two NVSS beams from the optical ID.To ensure our cross-matching criteria selected the correct NVSSsource, we convolved our LOFAR images with a 45 arcsec beam, andcompared each image to the cross-matched NVSS source in StokesI and in polarization, by downloading Stokes IQU cubes using the MNRAS , 1– ?? (2020) V. H. Mahatma
NRAO postage-stamp server . We also ensured that sources thatdid not have an NVSS counterpart were not missed by our cross-matching criteria (i.e. polarized hotspots in NVSS that are more thanthree NVSS beams from the optical ID). We found that one source(ILTJ105715.33+484108.6) was missed due to its large angular size,and included it as a correct NVSS counterpart.Using this method we find 58 NVSS counterparts to our parentRLAGN sample of 382 sources. Out of these sources, 24/58 are de-tected in polarization in our LOFAR sample, giving approximatelya 40% LOFAR detection rate. However, we note that out of the67 polarized sources in our sample, there is an absence of polar-ized NVSS counterparts in 44/67. This is surprising as we wouldnaively expect all 67 LOFAR detections to also be detected withNVSS since the fractional polarization should be higher at higherfrequencies and since our sources, being larger than 100 arcsec,are all resolved with NVSS. Beam depolarization could be moreprominent in NVSS due to its factor of two larger beam – compar-ing the polarized intensity NVSS and LOFAR images at 45 arcsec,we find only one source with significant depolarization in the NVSSimages, which we regard as insufficient to explain the lack of NVSSdetections. We instead attribute the lack of polarized NVSS coun-terparts to the fact that LOFAR is more sensitive to steep-spectrumsources relative to NVSS, so that many steep-spectrum sources thatsuffer little depolarization (so that they are detected at 150 MHz)are undetected in NVSS. As a check, we calculated the expectedFaraday dispersion 𝜎 𝑅𝑀 assuming external Faraday rotation usingour LOFAR and NVSS polarized counterparts using Π / Π = exp (− 𝜎 𝑅𝑀 𝜆 + 𝜎 𝑅𝑀 𝜆 ) (6)(Sokoloff et al. 1998). The average 𝜎 𝑅𝑀 in our sample is 0.24 radm − . For comparison, the median 𝜎 𝑅𝑀 for 20 double radio galaxiesmeasured by O’Sullivan et al. (2017) is 12.5 rad m − , implying thatthe sources detected by LOFAR have very little depolarization.Moreover, Equation 3 implies that the Faraday dispersion functionmust be narrow for less depolarization at long wavelengths.In order to confirm if the lack of polarized NVSS counter-parts is due to their steep spectra, we further cross-matched thesources in our sample with no NVSS polarized counterparts (us-ing the same criteria as above) with the NVSS source catalogue(Condon et al. 1998). In Figure 10 we display the distributions in150 MHz flux density, 1400 MHz flux density and spectral indexbetween those two frequencies (corrected for the difference in beamsizes). The top panel indicates that the polarized NVSS sourceswhich are also polarized with LOFAR (blue) are brighter at 150MHz than those that are not polarized with LOFAR (beige hatched,note the 𝑝 − value above the figure), as expected. However in themiddle panel, there is no statistical evidence for different averageflux densities at 1400 MHz, implying LOFAR is more sensitive tosteep-spectrum sources at low frequencies. In both panels, the blackdashed histogram denotes those sources polarized with LOFAR withno polarized NVSS counterpart, showing that they are fainter thanpolarized NVSS sources both at 150 MHz and 1400 MHz. In thebottom panel, affirming our earlier inferences, we see that whilethe average spectral indices of the NVSS polarized sources withLOFAR polarization are steeper than those without LOFAR polar-ization as expected, the sources polarized with LOFAR but not withNVSS are even steeper (WMU tests performed between all threedistributions have 𝑝 − values (cid:54) .
150 MHz total flux density (mJy) S o u r c e c o un t s p-value: 0.00162 NVSS pol (no LOFAR)NVSS+LOFAR polLOFAR pol (no NVSS)10 S o u r c e c o un t s p-value: 0.447 NVSS pol (no LOFAR)NVSS+LOFAR polLOFAR pol (no NVSS)3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 1.0 α S o u r c e c o un t s p-value: 0.015 NVSS pol (no LOFAR)NVSS+LOFAR polLOFAR pol (no NVSS)
Figure 10.
Distributions in total flux density at 150 MHz (top), 1400 MHz(middle) and spectral index (bottom) for our NVSS-LOFAR cross-matchedsources. NVSS polarized sources that are not polarized at 150 MHz areshown in hatched beige and those that are polarized at 150 MHz are shownin blue. Sources that are polarized at 150 MHz but not at 1400 MHz areshown in black dashed lines. Note the 𝑝 -values refer to the comparisonbetween blue and hatched beige distributions only.MNRAS , 1– ????
Distributions in total flux density at 150 MHz (top), 1400 MHz(middle) and spectral index (bottom) for our NVSS-LOFAR cross-matchedsources. NVSS polarized sources that are not polarized at 150 MHz areshown in hatched beige and those that are polarized at 150 MHz are shownin blue. Sources that are polarized at 150 MHz but not at 1400 MHz areshown in black dashed lines. Note the 𝑝 -values refer to the comparisonbetween blue and hatched beige distributions only.MNRAS , 1– ???? (2020) olarization properties of radio galaxies Π (1400 MHz;NVSS) Π ( M H z ) Detections
Figure 11.
LOFAR fractional polarization at 150 MHz against NVSS frac-tional polarization at 1400 MHz for 28 sources in our sample with bothLOFAR and NVSS detections. The red line shows the line of equality.NVSS error bars are taken from the catalogue of Taylor et al. (2009). so that their flux densities have decreased beyond detection at 1400MHz, while still being polarized at 150 MHz. Note that the medianerror in the spectral indices in our sample is Δ 𝛼 = .
11, takinginto account 3 𝜎 errors on the total flux density measurements.In Figure 11 we plot the fractional polarization at 150 MHzagainst that at 1400 MHz for our cross-matched sources. We see thatall sources, except one, have a lower fractional polarization at 150MHz, showing depolarization at low frequencies. For the source notdepolarized at 150 MHz relative to 1400 MHz (at Π ∼ Π to beam depolarization in NVSS – uponvisual inspection the LOFAR data show resolved components in thelobes which are shown as a single component in the NVSS image. In this section we analyse the 𝑅𝑀 s of our sample. The 𝑅𝑀 arisesfrom the superposition of the line of sight contributions fromthe Galaxy, the intergalactic medium, the intragroup/intraclustermedium and the source itself. We are more interested in the sourceand local environment properties, and so we subtract the Galactic 𝑅𝑀 measured at the location of each source in our sample. To dothis we positionally cross match the sources in our sample with theGalactic Faraday sky map made by Oppermann et al. (2015). Thepixel size in this map is around 30 arcmin, and hence all our sourcesare spatially coincident within single pixel regions in this map. Wesubtract the pixel 𝑅𝑀 value from the 𝑅𝑀 value we measure at 150MHz, as well as from the 𝑅𝑀 s at 1400 MHz from the Taylor et al.(2009) catalogue, giving Galaxy-subtracted values. For each sourcewe propagate the LOFAR and NVSS 𝑅𝑀 errors (Section 2.2) withthe 𝑅𝑀 errors catalogued by Oppermann et al. (2015).In Figure 12 we plot the distribution in observed 𝑅𝑀 at 150MHz and the Galaxy-subtracted 𝑅𝑀 for our sample. The average 𝑅𝑀 in our sample is positive, with a mean observed value of + . ± .
15 rad m − , and the mean Galaxy subtracted value is + . ± .
14 rad m − (with an rms of 7.56 rad m − ). This shows that Uncertainties quoted are the standard errors of the mean
20 10 0 10 20 30 40 RM rad m − S o u r c e c o un t s p-value: 9.5e-14 Observed RMGalaxy-subtracted RM
Figure 12.
Rotation measure distribution of our sample. The yellow his-togram shows our observed rotation measures, and the blue histogram showsthe same data after being corrected for the Galactic contribution. Dashedlines represent medians. the bulk of our sample do not have large magnitudes of 𝑅𝑀 fromnon-Galactic Faraday screens. It is likely then that the dominantcontributor to our 𝑅𝑀 s comes from multiple Faraday screens withmultiple magnetic field reversals, which acts to reduce the 𝑅𝑀 mag-nitude, or that our sources are preferentially located in low densityenvironments which lead to lower depolarization, or a combinationof both factors.We also compare the distributions in Galaxy-subtracted 𝑅𝑀 at 150 MHz and 1400 MHz in Figure 13. In the top panel we showthe 1400 MHz 𝑅𝑀 s of those sources that are polarized (blue) anddepolarized (hatched beige) with LOFAR. We see that there aresimilar distributions and medians in 1400 MHz subtracted 𝑅𝑀 sbetween LOFAR polarized and depolarized sources, with a similarrange. This suggests, on a statistical level, that the depolarization ofRLAGN at low frequencies is not solely driven by the magnitude ofFaraday rotation, as expected. Rather, it is the large spatial and/orline of sight dispersion of Faraday rotation that causes depolariza-tion at low frequencies, and since small-scale variations (i.e internalFaraday rotation) will cause depolarization, it is more likely that thesources we detect with little 𝑅𝑀 variation across the detected re-gions have significant contributions from the foreground mediumlocal to the source (i.e an ICM). Moreover, as shown by the bottompanel of Figure 13, the Galaxy subtracted 𝑅𝑀 s have similar peaksbetween LOFAR and NVSS data for those sources polarized withLOFAR, while there is a much larger spread in NVSS 𝑅𝑀 as ex-pected due to the lower 𝑅𝑀 resolution. This also shows a generalconsistency between Faraday screens in the foreground responsiblefor depolarization in our sample. These results imply that the ab-sence of polarized emission with LOFAR for these sources is mostlydriven by the combination of their total flux density at 150 MHzand their individual Faraday-rotating media. In Figure 14, wherewe plot the 𝑅𝑀 s at 1400 MHz against those at 150 MHz for thecross-matched LOFAR polarized sources, the red diagonal line ofequality shows that there is a general lack of a correlation, evenwith the large errors (calculated using propagation of errors duringsubtraction). The lack of a clear correlation implies that we maybe tracing components of different Faraday screens, rather than dif- MNRAS , 1– ?? (2020) V. H. Mahatma
80 60 40 20 0 20 40 60 RM (rad m − ) S o u r c e c o un t s p-value: 0.179 NVSSLOFAR and NVSS60 40 20 0 20 40 60 RM rad m − S o u r c e c o un t s p-value: 0.146 LOFAR RMNVSS RM
Figure 13. 𝑅𝑀 s for our LOFAR-NVSS cross-matched sample. Top panelshows the 1400 MHz 𝑅𝑀 s between those polarized with LOFAR (blue)and those depolarized with LOFAR (hatched beige). Bottom panel shows theLOFAR (hatched beige) and NVSS (blue) 𝑅𝑀 s for the sources polarizedwith LOFAR. Medians are shown as dashed lines. ferent components of the same Faraday screen. Since we infer thatour 𝑅𝑀 s are sensitive to external Faraday screens such as the ICM,we may predict 𝑅𝑀 s toward realistic ICM environments aroundRLAGN and compare them with our observations. X-ray data have long been used to determine environmental prop-erties of radio galaxies (e.g. Croston et al. 2008, 2011; Hardcastleet al. 2016). However, these are difficult to obtain for large samples,particularly in probing the high-redshift regime ( 𝑧 > 𝑅𝑀 mapscan provide an independent method of determining the line-of-sightenvironmental properties that may be used to infer the environmentsof large samples of radio galaxies. While it is difficult to infer theenvironment from the 𝑅𝑀 without information on the electron den-sity, magnetic field strength or the magnetic field reversal scale (the
60 40 20 0 20 40 60
150 MHz Galactic-subtracted RM (rad m − ) M H z G a l a c t i c - s u b t r a c t e d R M ( r a d m − ) Detections
Figure 14.
150 MHz 𝑅𝑀 against 1400 MHz 𝑅𝑀 for our cross-matchedsample, after Galaxy 𝑅𝑀 subtraction. Calculation of error bars are statedin Section 2.2. The red line is the line of equality, and not a regression linefit to the data. typical physical length between magnetic field direction reversalsin the line of sight), we may instead use a model to predict 𝑅𝑀 sbased on realistic radio galaxy environments. In particular, assum-ing purely external Faraday rotation due to a local environment,with plausible assumptions about thermal gas distributions, mag-netic field strengths, reversal scales and geometry, we test whetherit is possible to reproduce the 𝑅𝑀 distribution that we observe withLOFAR. If such a distribution is obtained (by way of a two-sampleKS test between modelled and observed 𝑅𝑀 distributions), we maythen compare the physical environmental properties of models thatLOFAR is sensitive to and those that LOFAR is not sensitive to.We also compare the fraction of models that have 𝑅𝑀 s in our ob-served range against our polarized detection fraction, and discussany discrepancies between the two. We create an analytic model which predicts 𝑅𝑀 s using Equation2, which relies on the electron density 𝑛 𝑒 and the magnetic field (cid:174) 𝐵 through the line of sight toward each polarized source in oursample. A calculation of these properties requires knowledge of thephysical environment of each source. Recent studies have shownthat the radio lobe properties can be reliable indicators of the ICMpressure at a fixed distance (Ineson et al. 2017; Croston et al. 2017),but such associations based on large samples of the overall RLAGNpopulation have large uncertainties when predicting the propertiesof any given source. Instead, to determine the physical informa-tion needed to predict 𝑅𝑀 s, we draw cluster/group masses froma distribution appropriate for radio galaxy environments. We alsoinclude prescriptions for the magnetic field reversal scale (whichaffects whether the incremental 𝑅𝑀 is positive or negative) and theorientation of the radio source (which affects the line of sight pathlength), both of which are unknown, but we use appropriate proba-bility distributions for these input parameters and sample them as amonte carlo simulation. Our 𝑅𝑀 prediction model is as follows: • We generate distributions of group/cluster masses using the
MNRAS , 1– ????
MNRAS , 1– ???? (2020) olarization properties of radio galaxies mass function of Girardi & Giuricin (2000), who show a goodagreement between a single Schechter function at 𝑧 = 𝛼 = − .
5) for group/cluster masses inthe range 10 − 𝑀 (cid:12) , which gives a bias towards masses ofgroups/clusters which tend to host RLAGN based on optical andX-ray studies (Hill & Lilly 1991; Hardcastle & Worrall 1999; Best2004; Ineson et al. 2015). For each polarized source in our sample,we draw a sample of 1000 values from this function. • We assume an equivalence between the group/cluster massand 𝑀 , the mass enclosed in a sphere within which the meandensity is 500 times the critical density at 𝑧 =
0. For each 𝑀 for each source, we determine a radial pressure profile 𝑝 ( 𝑙 ) of theenvironment, parameterised by 𝑀 , using the universal pressureprofile of Arnaud et al. (2010). The physical size of the pressureprofile is determined by calculating the distance from the polarizedsource at its redshift to 𝑧 = • We determine a density profile 𝑛 𝑒 ( 𝑙 ) for each environmentby scaling the pressure profile with a single temperature 𝑘𝑇 = . × (cid:16) 𝑀 [ 𝑀 (cid:12) ]/ . × (cid:17) . / . keV, based on the empiricalrelationship determined by Arnaud et al. (2010). • For each model we assume a central peak magnetic fieldstrength (cid:174) 𝐵 , following the prescriptions in the numerical radiogalaxy simulations by Hardcastle & Krause (2014), of | (cid:174) 𝐵 | = √︁ 𝑘𝑇 [ keV ]/ 𝜇 G (calibrated by observations of groups and clus-ters, see e.g. Guidetti et al. 2012), with a randomly chosen direction(positive or negative). We then determine the magnetic field profile (cid:174) 𝐵 ( 𝑙 ) by scaling peak field strength with the density profile using 𝐵 ( 𝑙 ) ∝ 𝑛 𝑒 ( 𝑙 ) 𝛾 , where we use 𝛾 = .
9, as found by Dolag et al.(2001) and Dolag (2006) using correlations between rms 𝑅𝑀 s andX-ray surface brightnesses for groups and clusters. We then accountfor the fact that we only consider the line of sight component of thetotal magnetic field, so that (cid:174) 𝐵 ( 𝑙 ) (cid:107) = (cid:174) 𝐵 ( 𝑙 )/√ • We perform the integral 𝑅𝑀 model = . ∫ 𝐿 (cid:48) 𝑛 𝑒 (cid:174) B (cid:107) d (cid:174) l (cid:48) in-crementally for each model to calculate the total 𝑅𝑀 , where 𝐿 (cid:48) isthe distance from the polarized emission (either core or hotspot(s)for our sources) to the observer. We visually classified sources ashaving either; one polarized hotspot, two polarized hotspots or apolarized core. We assume in this model that the AGN is locatedat the centre of the ICM/IGM, and hence the location of a hotspotis half the linear size of the source in projection from the centre ofthe ICM/IGM, from where the radial profiles 𝑛 𝑒 ( 𝑙 (cid:48) ) and (cid:174) 𝐵 ( 𝑙 (cid:48) ) (cid:107) aretaken. For core-polarized sources we assume a jet with a polarizedhotspot at an arbitrarily small distance of 1 pc from the center ofthe environment, from where the profiles are taken. Due to spher-ical symmetry of the environment the choice of hotspot (east orwest), for core-polarized sources and for sources with one detectedhotspot, does not change our results. For models with two polar-ized hotspots, we calculate the 𝑅𝑀 from both hotspots and take themean, as is done for our observations. In Figure 15 we display thedistribution of projected physical distances of the polarized emis-sion from the cluster/group centre (i.e half the projected physicalsize) for the sources in our sample. Note we do not plot the core-polarized sources as their polarized emission has been fixed at 1 pcfrom the centre of their environments. We immediately see that thesources where both hotspots are polarized are significantly larger(in projection) than sources with a polarized hotspot in one lobe(note the 𝑝 -value from a WMU test in the figure heading). This im-plies that detecting polarized hotspots in both lobes requires largersources where, assuming an environment with radially decreasing log ( D proj [pc]) N u m b e r o f s o u r c e s p-value: 3.31e-22 Matched RM s (One hotspot)Matched RM s (Two hotspots) Figure 15.
Distribution of projected physical distance of the polarizedhotspot(s) from the centre of the ICM/IGM for sources with one polarizedhotspot (orange hatched) and polarized hotspots in both lobes (blue). density (as in our model), the hotspots are located in a less densemedium where the effects of Faraday rotation are less severe. • The values in the integral above depend on the field reversalscale and orientation 𝜃 . We sample a uniform distribution of scalesbetween 10 pc and 10 pc. The choice in field reversal scales werechosen so that they sample the range of scales consistent with obser-vations of groups and clusters (e.g. ∼ pc; Laing et al. 2008) andwith cosmological magnetohydrodynamic simulations of clusters(e.g. 1 Mpc; Dolag et al. 2002). In each 𝑅𝑀 integral calculated, theinitial sign of (cid:174) 𝐵 (cid:107) is changed every time the incremental path lengthin the integral reaches the reversal scale. For the orientation angle 𝜃 we draw 1000 values from the distribution 𝑝 ( 𝜃 ) = / ( 𝜃 ) within the range 0 ◦ (cid:54) 𝜃 (cid:54) ◦ , with 0 ◦ being perpendicular tothe plane of the sky and towards the observer and 180 ◦ being awayfrom the observer. • We then truncate each resulting distribution of modelled 𝑅𝑀 sto lie only in the range of those that we sample through 𝑅𝑀 syn-thesis: − (cid:54) 𝑅𝑀 ( rad m − ) (cid:54) + 𝑅𝑀 s that LOFAR can be sensitive to in our analysis.There are caveats to this model which we address before describingour results. The first is in the use of a uniform distribution of fieldreversal scales, the values of which are relatively unconstrained forthe environments around the population of radio galaxies, though wereiterate that they are in approximate agreement with the few studiesthat do constrain them. Another caveat is that our observationshave a finite beam size, whereas we have modelled our sourcesthrough single line(s) of sight towards a hotspot(s) with infiniteresolution. This is likely to be a very minor affect on our resultsas the polarized emission we observe is predominantly unresolved,and we take pixel-averaged values as the observed 𝑅𝑀 within thebeam. The final caveat is that we have assumed all sources liein the geometric centres of their environments. This is supportedobservationally by studies finding that the majority of X-ray-selectedclusters host a central RLAGN (e.g. Magliocchetti & Brüggen 2007;Best et al. 2007), though it is possible that a small number of oursources do not lie in the geometric centers of their environments.In general, while our results (discussed below) are clearly related toour choice of input distributions, we use observationally calibrated MNRAS , 1– ?? (2020) V. H. Mahatma
20 10 0 10 20 30 RM (rad m − ) N o r m a li z e d nu m b e r o f m o d e l s p-value: 0.0581 ModelsObservations150 100 50 0 50 100 150 RM (rad m − ) N o r m a li z e d nu m b e r o f m o d e l s Matched modelsUnmatched models
Figure 16.
Top: normalised 𝑅𝑀 distributions of our matched models (yel-low) and our observations (grey). Note the superposition of grey and yellowgives a brown colour. Dashed lines indicate median values. Note that thenormalised distribution is such that the integral of the distribution is equalto one. Bottom: normalised 𝑅𝑀 distributions of our matched (yellow, as intop panel) and unmatched (grey) models. results where possible with currently available data. Furthermoreour choice of 1000 values drawn from each unknown parameterdistribution was made to ensure the models are stochastic.We separated our models into those which lead to 𝑅𝑀 s withinthe range of the observed Galaxy-subtracted 𝑅𝑀 distribution of oursample (‘matched’ 𝑅𝑀 s; − (cid:54) 𝑅𝑀 ( rad m − ) (cid:54) +
25, see Figure12) and those that are not (‘unmatched’ 𝑅𝑀 s; outside our observedrange but within those that we sample with 𝑅𝑀 synthesis and thatLOFAR is sensitive to, i.e. − (cid:54) 𝑅𝑀 ( rad m − ) (cid:54) + ∼ 𝑅𝑀 synthesis range, of which ∼ 𝑅𝑀 range. Given our observed detection fraction of 18 per cent, themodel predicts a factor of three higher detection fraction in the 𝑅𝑀 range that we observe. We partly associate this with our selectionbias for our sample: our models have a matched- 𝑅𝑀 fraction of ∼
58 per cent for core-polarized sources, compared to our observeddetection fraction for such sources of 3.4 per cent. While in realitythese are mostly based on the FR-I radio galaxies in our sample,such modelled 𝑅𝑀 s would also come from polarized blazars (e.g. Log M ( M fl ) M o d e ll e d R M ( r a d m − ) O r i e n t a t i o n ( ◦ ) Figure 17.
Group/cluster mass against the modelled 𝑅𝑀 for the polarizedsource ILTJ112543.21+543903.2 in our sample in an environment with amodelled field reversal scale of ∼ . pc. Models are color-coded by theorientation angle of the jet with the polarized hotspot (0 ◦ is the jet pointingdirectly at the observer). Note that for this source angles above 90 ◦ produced 𝑅𝑀 s too extreme to be observed in our sample. as found by O’Sullivan et al. 2018 in LoTSS), which have been ex-cluded from our sample through our selection of large angular size(>100 arcsec) sources. Hence, the incompleteness in our sample re-moves polarized sources that we may detect, whereas our models donot take into account any flux or angular size limit. However, moreimportantly, core-polarized sources in our models that have matched 𝑅𝑀 s produce similar 𝑅𝑀 s based on all orientation angles (sincethe 1 pc distance of their polarized emission at any orientation fromthe centre of the environment profile does not significantly affectthe final aggregated 𝑅𝑀 ), our models are already biased towards avery high matched fraction. Further, since FR-I sources (which tendto have polarized cores) live in rich environments relative to FR-IIs, it is possible that the Schechter function we use for all modelsunderestimates the cluster/group masses for FR-Is as a population.In top panel of Figure 16 we compare the resulting distributionof 𝑅𝑀 for matched models and our observations. We see a fairlygood agreement between the distributions, with a KS test betweenboth distributions having a 𝑝 -value of ∼ .
05. Given this statisticalsimilarity, we can analyse the observable and physical propertiesof the matched models to give inferences of the polarization de-tectability at low frequencies. For completeness we also show thedistributions between matched and unmatched 𝑅𝑀 s for our models(bottom panel of Figure 16), showing a clear peak for models in ourobservational range and a strong decrease in model counts beyondthis range, highlighting that our model inputs are appropriate inpredicting 𝑅𝑀 s that we observe with LOFAR. To give an example of the effects of the 𝑅𝑀 with 𝑀 we displayour models for ILTJ112543.21+543903.2, a polarized source in oursample with a projected size of 673 kpc and with one polarizedhotspot, modelled with a field reversal scale of 10 . pc, color-coded by the orientation angle in each model in Figure 17. For thistype of source we see that there is a preference for the jet with apolarized hotspot to be inclined toward the observer ( (cid:54) ◦ ) and as MNRAS , 1– ????
05. Given this statisticalsimilarity, we can analyse the observable and physical propertiesof the matched models to give inferences of the polarization de-tectability at low frequencies. For completeness we also show thedistributions between matched and unmatched 𝑅𝑀 s for our models(bottom panel of Figure 16), showing a clear peak for models in ourobservational range and a strong decrease in model counts beyondthis range, highlighting that our model inputs are appropriate inpredicting 𝑅𝑀 s that we observe with LOFAR. To give an example of the effects of the 𝑅𝑀 with 𝑀 we displayour models for ILTJ112543.21+543903.2, a polarized source in oursample with a projected size of 673 kpc and with one polarizedhotspot, modelled with a field reversal scale of 10 . pc, color-coded by the orientation angle in each model in Figure 17. For thistype of source we see that there is a preference for the jet with apolarized hotspot to be inclined toward the observer ( (cid:54) ◦ ) and as MNRAS , 1– ???? (2020) olarization properties of radio galaxies Figure 18.
Jet orientation (top) and reversal scale (bottom) against 𝑀 forour 𝑅𝑀 models. Grey hexagons are our unmatched models (color-codedby density of counts), yellow points are matched models with a polarizedcore, orange points are matched models with one polarized hotspot and bluepoints are matched models with polarized hotspot from both lobes. a function of group/cluster mass, meaning that at high cluster/groupmasses, sources will tend to be depolarized unless one of the jets isorientated towards the observer (as it will experience less Faradayrotation).In Figure 18, we plot the input physical parameters of ourmatched and unmatched models. In the top panel we plot the sourceorientation against 𝑀 where we see that for any given orien-tation, there is a higher matched model fraction at masses below ∼ . 𝑀 (cid:12) , i.e sources tend to be depolarized in higher mass en-vironments as the resulting | 𝑅𝑀 | would be too high to detect inour observed range (and in reality they would cause higher 𝑅𝑀 dispersion resulting in depolarization at 150 MHz). As a compari-son with sources for which spatially-resolved 𝑅𝑀 images have beenobtained (at high frequencies), the clusters surrounding Cygnus Aand Hydra A are at 𝑀 = . × 𝑀 ◦ (Wilson et al. 2002) and 𝑀 = . × 𝑀 ◦ (Zhang et al. 2017) respectively, while a lessrich group such as that surrounding 3C31 has a mass of 6 . × 𝑀 ◦ (Komossa & Böhringer 1999). This implies that LOFAR is prefer-entially sensitive to polarized sources in less rich clusters and poor group environments, and is consistent with our earlier remarks thatwith LOFAR we are sensitive to polarized radio galaxies with lowdispersion in Faraday depth. Interestingly we see that, for sourceswith a polarized hotspot in one lobe (orange circles), there is astrong preference for angles (cid:54) ◦ , meaning that we are seeing theapproaching jet which is inclined towards the observer (as seen inFigure 17 for one source). This is due to the fact that such sourceswill tend to have relatively low | 𝑅𝑀 | due to smaller path lengthsthrough the line of sight and they experience less Faraday rotation,such that they are within our observed 𝑅𝑀 range with LOFAR.On the other hand, core-polarized sources (yellow) are populatedat all orientation angles, since the jet orientation of their assumedpolarized emission at a distance of 1 pc from the centre does not sig-nificantly affect the final aggregated 𝑅𝑀 at 𝑧 =
0. Double polarizedsources (polarized hotspots in both lobes of an FR-II radio galaxy;blue points) seem to be almost exclusively populated at angles ∼ ◦ (i.e on the plane of the sky), as would be expected since the hotspotfrom the receding jet at a larger angles from the plane of the sky canbecome more easily depolarized (Laing-Garrington effect; Laing1988; Garrington et al. 1988). Hence, according to our model, LO-FAR would tend to only detect both hotspots in polarization if thesource is on the plane of the sky.In the bottom panel, showing 𝑀 against the field reversalscale, we see no clear correlation and that the range of the reversalscales we sample are equally likely to produce the 𝑅𝑀 s we observefor a given 𝑀 . Intuitively one expects smaller field reversal scalesto produce smaller 𝑅𝑀 s in the range expected for LOFAR data, butmany of our sources are very large in physical size (see Figure 15),so that their hotspots in the periphery of the ICM do not requiremany reversals to keep the 𝑅𝑀 low. The core-polarized sources,which are located at the centre of their environment, even with thelargest reversal scales, produce the highest 𝑅𝑀 s in our models atthe tail of the 𝑅𝑀 distribution in Figure 16. This means that ourchoice of reversal scales and 𝑀 are very appropriate for radiogalaxies observed with LOFAR, and that more extreme environ-mental parameters (i.e. 𝑀 ≈ 𝑀 (cid:12) or reversal scales (cid:62) pc) do not produce the distribution of 𝑅𝑀 s we observe, consistentwith the bottom panel of Figure 16. We note that FR-I sources inreality likely have a different distribution of 𝑀 , more appropriatefor higher mass environments, than is modelled here. While obser-vational evidence for the values of reversal scales at the centres ofclusters and groups are unavailable, we note more robust numericalmagnetohydrodynamic model are needed to understand the typicalfield reversal scales required to detect sources at low frequencies.In summary, we find that, in a model with only external Fara-day rotation from the local environment of a source, polarized radiogalaxies at low frequencies are predominantly detected in clus-ter/group masses (cid:54) . 𝑀 (cid:12) , while polarized hotspots are pref-erentially seen when the jets are on the plane of the sky, otherwiseonly one hotspot from the approaching jet is seen (Laing 1988; Gar-rington et al. 1988). We reiterate that our model distributions are adirect product of the assumed input parameter distributions, and indepth analyses of cluster 𝑅𝑀 s are needed to test the robustness ofour inputs. We have analyzed 20 arcsec resolution polarization data of radiogalaxies from part of the upcoming LoTSS DR2. This statisticalstudy of the bulk properties has extended the work of OS18 and
MNRAS , 1– ?? (2020) V. H. Mahatma
Stuardi et al. (2020) with the use of an optically identified sampleof 382 classified radio galaxies, with 67 detected in polarization.We find that at 150 MHz the polarization detection fractionincreases with total flux density, as expected; however, the distri-butions in angular size between detected and non-detected sourcesare statistically indistinguishable for sources >
100 arcsec. Thistrend may be biased due to our selection criteria, and it is possi-ble that the polarized detection fraction for RLAGN increases withsmaller angular size due to the presence of blazars. We confirmthe conclusions of OS18 that, in terms of resolved sources, thehotspots of FR-II radio galaxies are predominantly detected evenat low frequencies. FR-II radio galaxies are not only brighter andmore luminous, but they are known to reside in less rich environ-ments than FR-Is, and so physical depolarization due to the ambientmedium is less prominent, particularly since the brightest emissionis in the hotspots which are far away from the densest part of theIGM/ICM, contrary to the case for FR-Is. The morphologically-classed FR-IIs in our sample generally have a higher polarized fluxand fractional polarization than the FR-I sources over the range intotal flux density, though with large overlap.The comparison of host galaxy photometry between polar-ized and depolarized sources further highlights the importance ofmorphology in polarization – without accounting for morphology,host galaxies with higher values of WISE colour (more AGN-likeon a WISE colour-colour diagram) seem to drive RLAGN witha higher detection fraction of polarization. The observed low fre-quency polarization is related to FR morphology rather than WISEcolour, with the more powerful FR-IIs having a high detection frac-tion, though this case may be unrelated for intrinsic polarization,for which past studies have found significant differences betweenHERGs and LERGs (which at low redshift tend to be associated withFR-IIs and FR-Is, respectively). More dense cluster environmentscontributing to higher internal depolarization via entrainment of thethermal material is a possible explanation for the lack of polarizedFR-Is, but our data provide no direct evidence for this hypothesis.For the sources that have polarized counterparts to the sourcesin our sample at 1400 MHz, we find that they are de-polarized(weaker but detectable polarization) at 150 MHz for all but onesource. This is further confirmed by Figure 10, which shows thatthe distribution in 150 MHz total flux density is significantly higherfor those NVSS sources that are detected with LOFAR, whereas thenon-detected sources are not bright enough to produce sufficientpolarized emission to be detected. The spectral index distributionsimply that the sources detected by LOFAR have significantly steeperspectral indices on average, explaining the lack of polarized NVSScounterparts to the polarized sources in our sample.Modelling of the environments toward radio galaxies and theirsubsequently integrated 𝑅𝑀 s shows that, for a range of cluster/groupmasses, field reversal scales and jet orientation angles, we wouldexpect to preferentially observe polarized hotspots that are inclinedtowards the observer, for the case where a hotspot from one lobeis detected in polarization. For the case where hotspots in bothlobes are detected, our models indicate that the jets are on theplane of the sky, consistent with the Laing-Garrington effect. Core-polarized sources are generally favoured at all orientation angles asa function 𝑀 and reversal scale (due to our model assumptionthat they have a compact polarized component at 1 pc from thecentre). Our results generally imply that there is a very low chanceof detecting a polarized radio galaxy at 150 MHz if it is in even amoderately rich environment ( 𝑀 (cid:62) . 𝑀 (cid:12) , depending on itsorientation angle or physical size (Figure 15), as the 𝑅𝑀 s would betoo high to observe at low frequencies. We reiterate that our results are dependent on our input model parameters, which are based onempirical relationships and observations, but must be validated bymore robust numerical modelling.Our overall results imply that detecting polarized radio galaxieswith LOFAR at 150 MHz is related to the combination of totalflux density, environment and jet orientation. These results will beuseful in determining the properties of polarized sources in the fullLoTSS survey, which is expected to contain around ten million radiosources. ACKNOWLEDGEMENTS
We thank Aritra Basu, Ettore Carretti, Rainer Beck, Błażej Nikiel-Wroczyński and the anonymous referee for helpful comments inimproving this paper.VHM thanks the University of Hertfordshire for a researchstudentship [ST/N504105/1]. MJH acknowledges support from theUK Science and Technology Facilities Council [ST/R000905/1].This paper is based (in part) on data obtained with the In-ternational LOFAR Telescope (ILT). LOFAR (van Haarlem et al.2013) is the LOw Frequency ARray designed and constructed byASTRON. It has observing, data processing, and data storage fa-cilities in several countries, which are owned by various parties(each with their own funding sources), and are collectively oper-ated by the ILT foundation under a joint scientific policy. The ILTresources have benefitted from the following recent major fund-ing sources: CNRS-INSU, Observatoire de Paris and Universitéd’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; ScienceFoundation Ireland (SFI), Department of Business, Enterprise andInnovation (DBEI), Ireland; NWO, The Netherlands; The Scienceand Technology Facilities Council, UK; Ministry of Science andHigher Education, Poland.This research made use of the Dutch national e-infrastructurewith support of the SURF Cooperative (e-infra 180169) and theLOFAR e-infra group. The Jülich LOFAR Long Term Archive andthe German LOFAR network are both coordinated and operated bythe Jülich Supercomputing Centre (JSC), and computing resourceson the supercomputer JUWELS at JSC were provided by the GaussCentre for Supercomputing e.V. (grant CHTB00) through the Johnvon Neumann Institute for Computing (NIC).This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computingfacility located at the University of Hertfordshire and supported bySTFC [ST/P000096/1], and of the Italian LOFAR IT computinginfrastructure supported and operated by INAF, and by the PhysicsDepartment of Turin university (under an agreement with ConsorzioInteruniversitario per la Fisica Spaziale) at the C3S SupercomputingCentre, Italy.
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author, after the LoTSS DR2 data is madeavailable to the public in early 2021.
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APPENDIX A: FARADAY SPECTRA
MNRAS , 1– ?? (2020) V. H. Mahatma
150 100 50 0 50 100 150Faraday depth (rad m − )0.00.20.40.60.81.01.21.41.61.8 P e a k p o l a r i z e d i n t e n s i t y ( m J y b e a m − ) ILTJ105033.36+553000.7
150 100 50 0 50 100 150Faraday depth (rad m − )0.00.20.40.60.81.01.2 P e a k p o l a r i z e d i n t e n s i t y ( m J y b e a m − ) ILTJ123129.30+491541.4
150 100 50 0 50 100 150Faraday depth (rad m − )0.00.51.01.52.02.5 P e a k p o l a r i z e d i n t e n s i t y ( m J y b e a m − ) ILTJ145352.84+500404.6
Figure A1.
Polarized intensity maps (left; see Figure 1 for details) and the Faraday spectrum (right) of their peak polarized intensity pixel. The red crossdenotes the 𝑅𝑀 of the pixel as found using 𝑅𝑀 synthesis (neglecting − (cid:54) 𝜙 (rad m − ) (cid:54) . , 1– ????