Early Science from POSSUM: Shocks, turbulence, and a massive new reservoir of ionised gas in the Fornax cluster
C. S. Anderson, G. H. Heald, J. A. Eilek, E. Lenc, B. M. Gaensler, Lawrence Rudnick, C. L. Van Eck, S. P. O'Sullivan, J. M. Stil, A. Chippendale, C. J. Riseley, E. Carretti, J. West, J. Farnes, L. Harvey-Smith, N. M. McClure-Griffiths, Douglas C. J. Bock, J. D. Bunton, B. Koribalski, C. D. Tremblay, M. A. Voronkov, K. Warhurst
PPublications of the Astronomical Society of Australia (PASA)doi: 10.1017 / pas.2021.xxx. Early Science from POSSUM: Shocks, turbulence, and a massivenew reservoir of ionised gas in the Fornax cluster
C. S. Anderson , , , G. H. Heald , J. A. Eilek , , E. Lenc , B. M. Gaensler , Lawrence Rudnick , C. L. VanEck , S. P. O’Sullivan , J. M. Stil , A. Chippendale , C. J. Riseley , , E. Carretti , J. West , J. Farnes , L.Harvey-Smith , , N. M. McClure-Gri ffi ths , Douglas C. J. Bock , J. D. Bunton , B. Koribalski , , C. D.Tremblay , M. A. Voronkov , K. Warhurst Jansky fellow of the National Radio Astronomy Observatory, 1003 Lopezville Rd, Socorro, NM 87801 USA CSIRO Astronomy and Space Science, PO Box 1130, Bentley WA 6102, Australia ATNF, CSIRO Astronomy and Space Science, PO Box 76, Epping, New South Wales 1710, Australia Physics Department, New Mexico Tech, Socorro NM 87801 USA Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St. SE, Minneapolis, MN 55455 USA School of Physical Sciences and center for Astrophysics & Relativity, Dublin City University, Glasnevin, D09 W6Y4, Ireland Department of Physics & Astronomy, The University of Calgary, 2500 University Drive NW, Calgary AB, T2N 1N4, Canada Dipartimento di Fisica e Astronomia, Università degli Studi di Bologna, via P. Gobetti 93 /
2, 40129 Bologna, Italy INAF - Istituto di Radioastronomia, Via Gobetti 101, 40129 Bologna, Italy Oxford e-Research center (OeRC), Department of Engineering Science, University of Oxford, Oxford, OX1 3QG, UK School of Physics, University of New South Wales, Sydney, NSW 2052, Australia Western Sydney University, Locked Bag 1797, Penrith, NSW, 2751, Australia Research School of Astronomy & Astrophysics, Australian National University, Canberra ACT 2611 Australia
Abstract
We present the first Faraday rotation measure (RM) grid study of an individual low-mass cluster — the Fornaxcluster — which is presently undergoing a series of mergers. Exploiting commissioning data for the POlarisationSky Survey of the Universe’s Magnetism (POSSUM) covering a ∼
34 square degree sky area using the AustralianSquare Kilometre Array Pathfinder (ASKAP), we achieve an RM grid density of ∼
25 RMs per square degree from a280 MHz band centred at 887 MHz, which is similar to expectations for forthcoming GHz-frequency ∼ π -steradiansky surveys. These data allow us to probe the extended magnetoionic structure of the cluster and its surroundingsin unprecedented detail. We find that the scatter in the Faraday RM of confirmed background sources is increasedby 16 . ± . − within 1 degree (360 kpc) projected distance to the cluster centre, which is 2–4 times largerthan the spatial extent of the presently-detectable X-ray-emitting intracluster medium (ICM). The mass of theFaraday-active plasma is larger than that of the X-ray-emitting ICM, and exists in a density regime that broadlymatches expectations for moderately-dense components of the Warm-Hot Intergalactic Medium. We argue thatforthcoming RM grids from both targeted and survey observations may be a singular probe of cosmic plasma in thisregime. The morphology of the global Faraday depth enhancement is not uniform and isotropic, but rather exhibitsthe classic morphology of an astrophysical bow shock on the southwest side of the main Fornax cluster, and anextended, swept-back wake on the northeastern side. Our favoured explanation for these phenomena is an ongoingmerger between the main cluster and a sub-cluster to the southwest. The shock’s Mach angle and stand-o ff distancelead to a self-consistent transonic merger speed with Mach 1.06. The region hosting the Faraday depth enhancementalso appears to show a decrement in both total and polarised radio emission compared to the broader field. Weevaluate cosmic variance and free-free absorption by a pervasive cold dense gas surrounding NGC 1399 as possiblecauses, but find both explanations unsatisfactory, warranting further observations. Generally, our study illustrates thescientific returns that can be expected from all-sky grids of discrete sources generated by forthcoming all-sky radiosurveys. Keywords: galaxies: clusters: individual(Fornax) – galaxies: clusters: intracluster medium – magnetic fields – techniques:polarimetric – radio continuum: galaxies a r X i v : . [ a s t r o - ph . GA ] F e b C. S. Anderson et al.
The Universe’s baryons are mostly located outside the stel-lar envelopes of galaxies, in the vast expanses occupied byclusters of galaxies, and in filaments of tenuous plasma thatconnect them. The properties of gas in these di ff erent regimes— including their state of magnetisation — lie at the heart oftheories of cosmic evolution and ecology, but remain di ffi cultto pin down observationally. For instance, the hot intraclus-ter medium (ICM) contains about 4% of the baryonic massof the late-time Universe, which is (for example) a higherproportion than is contained in stars (de Graa ff et al., 2019).Magnetic fields break the isotropy of viscosity, pressure sup-port, and thermal conductivity of the ICM, thereby exertingan out-sized influence on cluster physics and evolution. Theycan trace ordered and turbulent flows in plasma (e.g. Ander-son et al., 2018), reveal interactions between the ICM andin-falling gas (e.g. Keshet et al., 2017), embedded galaxies(e.g. Dursi & Pfrommer, 2008; Pfrommer & Dursi, 2010) andgalactic outflows (e.g. Guidetti et al., 2011, 2012; Andersonet al., 2018), and help reveal how the broader cosmos becamemagnetised (e.g. Vazza et al., 2014; Bonafede et al., 2015).Beyond the ICM, the Warm-Hot Intergalactic Medium(WHIM) must contain around 80% of the Universe’s baryons(de Graa ff et al., 2019), though this material is comparativelyunstudied, with only recent claims of detection of its sparserphases (Nicastro et al., 2017; de Graa ff et al., 2019; Tanimuraet al., 2019; Macquart et al., 2020). Simulations suggest thatthe WHIM will be found in a diverse set of regimes, occupy-ing relatively dense agglomerations ( δ ∼ δ is theover-density factor of baryons compared to the cosmic mean,defined by δ ≡ ρ/ ¯ ρ −
1, and in turn, ρ is the baryon numberdensity at a given location, while ¯ ρ is the mean baryon num-ber density in the Universe, which is currently ¯ ρ ≈ × − cm − ; Planck Collaboration et al., 2016) around galaxy clus-ters in its densest and hottest manifestations, and in tenuousfilaments between massive galaxies in its sparsest and coolestregimes ( δ ∼ a few) (Davé et al., 2001). The magnetisationof this material is also consequential, since the predictions ofmodels for cosmic magneto-genesis di ff er most strongly here(e.g. Donnert et al., 2018 and references therein), which isjust now beginning to be revealed with extraordinary new lowfrequency radio measurements (Govoni et al., 2019; Botteonet al., 2020), and may also be probed via measurements ofradio polarisation and Faraday rotation (e.g. Akahori et al.,2018; Locatelli et al., 2018; O’Sullivan et al., 2020).Faraday rotation is an e ff ective tracer of the distributionand properties of rarefied, magnetised cosmic plasma, such asthe ICM and WHIM (e.g. Cooper & Price, 1962; Burn, 1966;Conway et al., 1974; Kronberg & Simard-Normandin, 1976;Taylor & Perley, 1993; Farnsworth et al., 2011; O’Sullivanet al., 2013; Johnston-Hollitt et al., 2015; Gaensler et al.,2015; Anderson, 2016). Consider that the linear polarisationstate of radio emission can be described by a complex vector P , related to the Stokes parameters Q and U , the polarisationangle ψ , the fractional polarisation p and the total intensity I as P = Q + iU = pIe i ψ (1)After being emitted at a location L , linearly polarised radia-tion will be Faraday rotated by magnetised thermal plasmaalong the line of sight (LOS) to an observer by an amountequal to ∆ ψ = φ ( L ) λ (2)where λ is the observing wavelength, and φ is the Faradaydepth, given by φ ( L ) = . (cid:90) L n e B · d s rad m − (3)and, in turn, n e [cm − ] & B [ µ G] are the thermal electrondensity and magnetic field along the LOS respectively.The observable polarisation spectrum P ( λ ) is obtained bysumming the polarised emission emerging from all possibleFaraday depths within the synthesised beam of the telescope: P ( λ ) = (cid:90) ∞−∞ F ( φ ) e i φλ d φ (4)The function F ( φ ) (the so-called Faraday Dispersion Spec-trum, henceforth FDS) specifies the distribution of polarisedemission as a function of Faraday depth along the LOS. Thisquasi-Fourier relationship can be inverted to reconstruct F ( φ )given observations of P ( λ ) (Burn, 1966; Brentjens & deBruyn, 2005). In the common situation where a point-likesource is viewed through an extended reservoir of magnetisedthermal plasma lying in the foreground (which we deal within this work), F ( φ ) shows a single peak at a well-definedFaraday depth φ peak = argmax( | F ( φ ) | ). This is then equiva-lent to the so-called Faraday rotation measure (RM) of thesource. Largely for historic reasons, we continue to use theterm “RM” in places in this work, though the measurementsthemselves are of φ peak — i.e. extracted through the methodof RM synthesis, rather than from the gradient of the polari-sation angle as a function of λ . Regardless of nomenclature, φ peak provides a direct measure of the amount of magnetisedthermal plasma that has been traversed along the line of sight.Ensembles of polarised radio sources can therefore back-illuminate the magnetoionic structure of extended plasmareservoirs in the foreground.Applying these ‘RM grid’ techniques to study the ICM orWHIM in individual galaxy clusters has historically been di ffi -cult, because past generations of radio instrumentation couldonly recover a relatively low density of polarised sourcesover the required multi-square-degree sky areas ( O (1) lin-early polarised source per square degree — e.g. Taylor et al.,2009), combined with the uncertainty of whether any givenRM grid source is located behind a target cluster, inside it,or in the foreground. Fortunately, these limitations will soonbe transcended using data from a new generation of radiointerferometers and optical redshift surveys. In the former ornax cluster magnetic fields ∼
25 per square degree over tens of square degrees injust a few hours (this work, West et al. in prep. ), and willsoon survey the entire southern sky at this or greater depthfor the Polarisation Sky Survey of the Universe’s Magnetism(POSSUM; Gaensler et al., 2010). At the same time, deeppointed observations like the MeerKAT (Jonas, 2009) FornaxSurvey (Serra et al., 2016) may soon recover ∼ hundreds ofpolarised sources per square degree. Both approaches willopen up the field of observational galaxy cluster astrophysicsto routine RM grid studies (Heald et al., 2020).This paper heralds the dawn of this era by exploitingASKAP’s unique imaging capabilities to study the ionisedgas in the Fornax cluster. The Fornax cluster is nearby (20.64megaparsecs; Mpc; Lavaux & Hudson, 2011), but muchpoorer than similarly well-studied clusters like the Virgo andComa clusters. It has only ∼
390 member galaxies (which aretypically low in mass; Maddox et al., 2019), and has a com-paratively low total mass of 6 + − × M (cid:12) (Drinkwater et al.,2001; Nasonova et al., 2011; Maddox et al., 2019), which isone and two orders-of-magnitude less massive than the Virgoand Coma clusters respectively. The (presently detectable)X-ray-emitting ICM is also small, extending asymmetricallyoutward from NGC1399 to a mere 15%–30% of the clus-ter’s 1.96 degree virial radius. Nevertheless, its halo mass ismore representative of that in which the majority of the galax-ies in the Universe reside and evolve (Haan & Braun, 2014and references therein). The dynamical state of the cluster,and associated astrophysical processes, are therefore of keeninterest.Our understanding of the dynamics of this system is evolv-ing rapidly. The core of the Fornax cluster is densely popu-lated with early-type galaxies that possess relatively uniformproperties and low velocity dispersion. This used to be citedas evidence that the Fornax cluster is virialised and well-evolved (see Iodice et al., 2019 and references therein), butit is now clear that the Fornax cluster possesses complexspatial sub-structure both in terms of its constituent gas andgalaxies (e.g. Drinkwater et al., 2001; Paolillo et al., 2002;Scharf et al., 2005; Su et al., 2017; Venhola et al., 2018;Sheardown et al., 2018), and is still assembling mass througha series of on-going mergers. At the largest scales, Drinkwa-ter et al. (2001) argue that there is a genuine mass partitionbetween northeast and southwest sub-components of the clus-ter, which are respectively dominated by the cD-type galaxyNGC 1399 and NGC 1316 — the host galaxy of the radiosource Fornax A — a few degrees ( ∼ . ff usegas there (Machacek et al., 2005). This appears to have in-duced sloshing in the ICM which is most apparent in the central ∼
30 kpc of the cluster (Su et al., 2017), and may havegenerated shocks and turbulence on scales up to more than adegree (Sheardown et al., 2018).Thus, the Fornax cluster di ff ers greatly in its propertiesfrom other relatively nearby massive clusters, including Virgoand Coma, and from the massive clusters from which ourcanonical understanding of the magnetised ICM were chieflyderived. While our understanding of the magneto-thermalplasma structures of even large clusters remain incomplete(e.g. Johnston-Hollitt et al., 2015; Heald et al., 2020), our ig-norance is much more pronounced at the important low-massend of the halo distribution. Sensitive new RM grid exper-iments can directly reveal the magnetised gas in such envi-ronments, providing sorely needed new data in this sphere.In this work then, our overarching aim is to search for Fara-day RM enhancements to trace the structure of magnetisedionised gas in an individual low-mass galaxy cluster for thefirst time. Our specific goals are to (a) estimate the mass andextent of any such material, and to compare these estimatesto those determined for ensembles of the more massive clus-ters previously probed in RM stacking experiments, (b) todetermine whether any material thereby revealed di ff ers inits properties or extent from that revealed by Bremsstrahlungradiation, thus establishing the complementarity of the twomeasurement techniques, and (c) demonstrate what uniqueinformation the RM measurements provide about the dynami-cal mass assembly processes that continue to take place in thesystem. The spatial density and areal sky coverage of our RMgrid, coupled the fact that it is dominated by confirmed back-ground radio sources (as we will show), is groundbreaking inthis field.Our paper is organised as follows. We describe our obser-vations, calibration, and imaging procedures in Section 2, andour polarimetric analysis in Section 3. Analysis of ancillaryredshift data is presented in Section 4. We present our results,discussion, and conclusions in Sections 5, 6 and 7 (respec-tively). In this paper, we adopt a distance to NGC 1399 ofD = / arcsec. Cardinal directions arereferred to by their usual abbreviations — e.g. NE, SW, Sfor northeast, southwest, and south, respectively. We use thespectral index convention S ∝ ν α . We observed the Fornax cluster region during commissioningtests of the ASKAP radio telescope (DeBoer et al., 2009;Johnston et al., 2007; Schinckel & Bock, 2016). ASKAPconsists of 36 × ∼
30 square degree instanta-neous field of view (depending on frequency) and high surveyspeed. We observed a single such pointing for six hours witha square_6x6 beam footprint (McConnell et al., 2016), us-ing a beam pitch (horizontal and vertical angular separation)of 0.9 degrees, covering the frequency range 747–1027 MHz
C. S. Anderson et al.
Table 1
Summary of observations
Target Fornax cluster regionScheduling block ID 8279Date of observations 23rd March 2019Field centre (J2000) 03 h m s , − d m s Field centre (J2000, Gal. l , b ) 235.988 ◦ , − ◦ No. telescope pointings 1Total integration time 6 hoursFull-band sensitivity † µ Jy beam − Recorded polarisations XX , XY , Y X , YY Beam footprint square_6x6
Beam pitch 0.9 degNumber of valid beams 30 paired X and Y pol. (of 36)FWHM of formed beams at 887 MHz ‡ ∼
34 deg Number of antennas 32Antenna diameter 12 mShortest baseline 22.4 mLongest baseline 6.4 kmAngular resolution (robust =
0) 11 ×
14 arcsecLargest recoverable angular scale ‡‡
30 arcminFrequency range (central frequency) 747–1027 MHz (887 MHz)Frequency resolution 1 MHz λ range 0.085–0.161 m Resolution in φ space a
46 rad m − Largest recoverable φ -scale ‡‡ a
37 rad m − Largest recoverable | φ | a
510 rad m − † Measured per Stokes parameter in multi-frequency synthesis images generatedwith a Briggs’ robust weighting value of 0.0. ‡ At centre frequency of band. ‡‡ At greater than 50% sensitivity. a Calculated from equations in Section 6 ofBrentjens & de Bruyn (2005). ornax cluster magnetic fields µ Jy beam − per Stokes pa-rameter. The ASKAP array configuration is shown in Figure1. Of the 36 beams formed for our observations, six in thesouth-west corner of the mosaic su ff ered from beamformingerrors leading to low sensitivity, and were discarded fromfurther analysis. It is coincidental that the bright radio galaxyFornax A appears in the vicinity of these beams for our ob-servations. The sky position of the remaining valid beamsare indicated in Figure 2. We note that the field centre waschosen to satisfy the competing demands of several scienceteams working in this sky area, and so while the field incor-porates the Fornax Cluster, Fornax A and several other radiogalaxies, it is not centred on any of them. Further details aresummarised in Table 1.We flagged and calibrated our data in the Common Astron-omy Software Applications ( CASA ; McMullin et al., 2007)package. We flagged radio frequency interference manually,which is feasible only because of the exceptionally RFI-quietconditions at the Murchison Radio-astronomy Observatory(e.g. Indermuehle et al., 2018). We calibrated the flux scale,instrumental bandpass, and (on-axis) polarisation leakage‘D-terms’ using standard methods applied to observations ofthe (unpolarised) standard calibrator source PKS B1934–638.The frequency-dependent instrumental XY-phase was nulledout at the beamforming stage using the ASKAP on-dish cali-bration system (ODC; Chippendale & Anderson, 2019). Theo ff -axis polarimetric instrumental response was not correctedfor this work. However, after the on-beam-axis D-term cor-rections are applied, and for the frequency and beam pitchemployed, we estimate that the leakage from Stokes I to Q and U is usually less than 1%, though it can be worse inisolated areas. We discuss this more in Section 3. The ab-solute polarisation angle was also left uncalibrated, but theinter-beam and inter-channel relative polarisation angle isguaranteed to be consistent by the beamforming procedure,which we subsequently verified by comparing polarisationspectra of sources observed in images of adjacent beams. Theabsolute flux scale is uncertain by up to 10%, and this canvary as a function of position in the field (McConnell et al.,2019).We imaged the data with WSClean (O ff ringa et al., 2014).For all Stokes parameters, we generated image cubes with5000 × σ and 3 σ respectively), and joined-channel CLEANing with8 MHz channelisation. We performed two rounds of phase-only self-calibration using CASA with a solution interval of300 seconds, and then one round of phase and amplitudeself-calibration with a solution interval of 60 seconds. We ex-perimented with shorter solution intervals, but this produced https://confluence.csiro.au/download/attachments/733676544/ASKAP_sci_obs_guide.pdf N o r t h e r n d i s t a n c e f r o m a k ( m ) Figure 1. O ff set ASKAP antenna positions in meters from antenna ak01(Longitude: 116.631424 ◦ E, Latitude: -26.697000 ◦ ; McConnell et al., 2019 )for the full ASKAP array. The inset panel zooms in on E-W o ff sets of -100mto + ff sets of -70m to + h m m m -32°-34°-36°-38° Right Ascension (J2000) D e c li n a t i o n ( J ) Figure 2.
The position (and FWHM at our maximum frequency of 1027MHz) of formed ASKAP beams used in this work (white circles), overlaidon a map of the local root-mean-squared (RMS) noise in peak- P (see Figure3 and Section 3 for an enlarged version containing further detail). The centreof the Fornax cluster is indicated with a red cross-hair, and the lobes ofFornax A are partially visible to the south west. C. S. Anderson et al. little e ff ect. We then re-imaged and c l e a n ed Stokes I MFSmaps independently, an then the Stokes Q and U datacubesusing WSClean ’s ‘join polarisations’ and ‘squared channeljoining’ modes. The individual beam images were then lin-early mosaicked for all channels and Stokes parameters us-ing the
SWarp package (Bertin et al., 2002), employing ascaled-width circular Gaussian beam, whose full-width-half-maximum scales as (1 . / λ (McConnell et al., 2019) ,truncated at the 10% power point. We then smoothed to thespatial resolution of our lowest frequency channel — 18 × λ .We note that in the final linear mosaics, nine or more beamscontribute to the data values at any point located inside theouter ring of beam centres, and that to our knowledge, thecluster centre is not in a ‘special’ or otherwise noteworthylocation with respect to the positions of the beam centres (seeFigure 2). We calculated the Faraday Dispersion Spectrum (FDS) overthe range -200 to +
200 rad m − using RM synthesis (Burn,1966; Brentjens & de Bruyn, 2005) applied to the Stokes Qand U data cubes with equal weighting per image channel.The result is a complex-valued FDS datacube with dimen-sions RA, Decl, and φ .We generated a map of the peak polarised intensity (peak- P ) across the field from the FDS cube using Miriad ’s (Saultet al., 1995) m o m e n t function (see Figure 3, which showsthe associated RMS noise map, since the resolution and skycoverage of our observations would render most sources in-visible in the peak- P map itself). We then identified polarisedradio sources in the field by applying the Aegean SoftwareTools source-finding package (Hancock et al., 2012, 2018)to our multi-frequency synthesis (MFS) Stokes I map and thepeak- P map, using seedclip [floodclip] values of 5 [4] and 7[5] respectively. With these settings, the nominal false detec-tion rate (FDR) expected from A egean is ∼
2% and ∼ . P images respectively, thoughwe note that the true FDR will be somewhat higher because(a) the peak- P image contains complicated non-Gaussiannoise structure (e.g. see Hales et al., 2012), which has thee ff ect of pushing noise peaks to higher apparent significanceunder the assumption of Gaussian noise statistics, and (b) thepeak- P and total intensity images each contain residual de-convolution artifacts around bright sources. We ameliorated https://confluence.csiro.au/download/attachments/733676544/ASKAP_sci_obs_guide.pdf https://github.com/brentjens/rm-synthesis , version 1.0-rc4 https://github.com/PaulHancock/Aegean , version 2.0.2 The A egean algorithm incorporates the generic F loodfill algorithm.In an image, source detections are ‘seeded’ at all locations where the pixelvalues exceeds the seedclip value. The algorithm then walks outwards fromthese locations, incorporating all adjacent pixels that exceed the floodclipvalue into the source model. Details are supplied in Hancock et al. (2012). these relatively high e ff ective FDRs by cross-matching thesource-finding results from the peak- P and total intensity im-ages. Assuming that the peak- P and total intensity images andassociated source finding results are statistically independent,the resulting nominal baseline FDR is a negligible ∼ . σ signal-to-noise cut in band-averaged linear polari-sation, which is required for reliable RM measurements (e.g.Macquart et al., 2012).For this background RM grid experiment, we extractedthe peak polarised intensity (peak- P ) and associated sensitiv-ity (see Figure 3), and the peak Faraday depth of the source( φ peak ), from the dominant peak in the Faraday spectrumfrom each source. In practice, almost all of sources only hada single peak in the FDS. The quality of the FDS (and theassociated Stokes Q and U spectra) are good throughout themosaic; representative examples of FDS and their associ-ated (Q,U) vs. λ spectra are shown in Figure 4, which wereselected at random to span the range of polarised signal-to-noise of the sources included in our RM grid sample. The fullcatalogue is provided online .Since the vast majority of sources detected were spatiallyunresolved or nearly so, we extracted the Stokes I , peak- P ,and φ peak values of each source at the location of the bright-est pixel in the peak- P map. For the few heavily-resolvedsources in the map (i.e. PKS B0336–35, which is actuallycomprised of the radio source inside NGC 1399, and a phys-ically un-associated source several arcminutes to the NE —see Killeen et al., 1988), we extracted the aforementionedquantities at the central coordinate location of the Gaussianemission components comprising the islands outputted by Aegean . This results in samples of a suitable number of in-dependent lines of sight towards these resolved sources. Thepolarisation state of some of these sources will be dominatedby o ff -axis polarisation leakage. Since a robust, frequency-dependent, o ff -axis polarisation calibration procedure has notbeen finalised for ASKAP, we proceeded by identifying andeliminating such sources from our sample. We estimated theposition-dependent, frequency- independent , Stokes I → Q and I → U leakages using field sources, as described in Ap-pendix A. The results are that the leakages are lower than 1%in most of the mosaic, but are greater in some areas, and inparticular, the mosaic edges and corners (see Appendix A).We eliminated sources from our sample that:1. were located more than 3 . ◦ from the mosaic centre2. were not located inside the half power point (at 1027MHz) of at least one formed beam3. had measured fractional Stokes q , u (we define q = Q / I , u = U / I , and use this nomenclature henceforth) valueswithin 3 σ uncertainty of our leakage map predictions atthat location < insert web address here > ornax cluster magnetic fields h m m m m m -32° -34°-36°-38° Right Ascension (J2000) D e c li n a t i o n ( J ) L o c a l n o i s e l e v e l ( u J y / b ) Figure 3.
The local root-mean-squared (RMS) noise in the peak- P map. This is supplied in lieu of the peak- P map itself, which renders point sourcese ff ectively invisible for our high resolution, large area map. This RMS map was generated by running a square sliding window of width and height both equalto five synthesised beamwidths over the peak- P map, and calculating the RMS values of the pixels inside the window. The image shown here has a square rootstretch applied. Linearly polarised radio sources are visible as a marked increase in the local RMS value. In source-free regions, the RMS is typically ∼ µ Jybeam − , except at the mosaic edges, and in the vicinity of bright sources, where the faint imprint of the synthesised beam manifests as narrow, diagonalfan–like structures. The centre of the Fornax cluster is indicated with a red cross-hair. Fornax A is partially visible in the bottom-right corner of the map,where six beams are missing due to beamforming errors. The white dashed box approximately indicates the region shown in Figure 8. The white dashed lineindicates an angular radius of one degree, while the white dotted line indicates the 705 kpc (1.96 degree) virial radius of the cluster. C. S. Anderson et al.
J033848-354206RA: 54.702Dec: -35.370Pol. SN: 706.1 3 h m s s m s s s -35°24'22'20' h m s s m s s s -35°24'22'20' D e c li n a t i o n ( J ) J033844-354102RA: 54.684Dec: -35.388Pol. SN: 271.4 3 h m s m s s s -35°26'24'22' h m s m s s s -35°26'24'22' D e c li n a t i o n ( J ) J033529-365222RA: 53.873Dec: -36.494Pol. SN: 115.3 3 h m s s s s -36°32'30'28' h m s s s s -36°32'30'28' D e c li n a t i o n ( J ) J033826-353636RA: 54.610Dec: -35.858Pol. SN: 62.6 3 h m s s s s -35°54'52'50' h m s s s s -35°54'52'50' D e c li n a t i o n ( J ) J034054-341334RA: 55.226Dec: -34.381Pol. SN: 24.5 3 h m s s m s s -34°26'24'22'20' h m s s m s s -34°26'24'22'20' D e c li n a t i o n ( J ) -200 +200J033738-342432RA: 54.409Dec: -34.005Pol. SN: 12.2 0.09 0.16 3 h m s m s s s -34°02'00'-33°58'Right Ascension (J2000) h m s m s s s -34°02'00'-33°58'Right Ascension (J2000) D e c li n a t i o n ( J ) [rad m ] [m ] Figure 4.
The calculated dirty (i.e. no rmclean (Heald et al., 2009) performed; see Section 3) FDS (first column), corresponding Stokes Q (red) and U (blue)spectra (second column), peak- P image (third column), and total intensity image (fourth column) , for selected sources showing a range of polarised signal-to-noise. For columns 1 & 2, the horizontal axes range from -200 to +
200 rad m − for the FDS plots (first column), and 0.08 to 0.16 m for the Stokes ( Q , U ) plots (second column); note that ticklabels are included on the bottom-most horizontal axes only. The vertical axes limits are all scaled to the maximum amplitudeof the data points in individual plots. The J2000 name, right ascension, declination, and band-averaged polarisedsignal-to-noise ratio (SN) are all written in the respective FDS plots. The error bars on the ( Q , U ) data points indicate thestandard deviation measured per image channel from the Stokes ( Q , U ) datacubes in a small region adjacent to each source. Thepeak polarised intensity of the sources are (from left to right, top to bottom) 212, 81, 3.5, 1.9, 0.7, and 0.4 mJy / beam / RMSF.Note that because the FDS have not been deconvolved with rmclean , the emission-free regions of the FDS cannot be used asa guide to the underlying noise level. The RMSF (which is common to all of our sources, given our method) is plotted as amagenta dot-dashed line in the top-most FDS plot, scaled to the magnitude of the accompanying FDS. Note that thebottom-most source is a possible example of a source with multiple FDS emission peaks, but the 6 σ S / N of the secondary peakis barely significant due to polarisation bias (Macquart et al., 2012; Hales et al., 2012). The peak- P and total intensity imagespresented in columns 3 & 4 each span 6 . × . ornax cluster magnetic fields
94. had measured Stokes q and u values that were simultane-ously within a factor of 2 of our leakage map predictionsat that locationIn combination, the first two criteria ensure that sourcesare observed close to at least one beam centre, that multiplebeams contribute to the final mosaic at the source locations,and that regions of high I → U leakage found outside thecentres of the corner beams in the square_6x6 beam foot-print are excluded from our analysis (see Appendix A, Figure13). In turn, this ensures that the o ff -axis response is averageddown, and that the polarisation of the sources are measuredin multiple beams that can be evaluated for consistency. Thelatter two criteria (respectively) ensure that the polarisationstate of a source is not either (a) consistent with pure instru-mental leakage, or (b) dominated by instrumental leakage.We note that we also tested other methods to exclude spuriousleakage-dominated sources, including local cuts on fractionalpolarisation based on predictions from our leakage maps, anduniform cuts on sources with fractional polarisations as highas 1.5%. Our results were not significantly a ff ected by thechoice of method. After the cuts listed above, our sampleconsists of 870 linearly polarised sources, with a medianfractional polarisation of 4.8% (uncorrected for Ricean po-larisation bias; see e.g. Hales et al., 2012, and noting theadditional upward bias on the sample median fractional polar-isation imposed by our polarised intensity cuto ff ; see Figure5). Figure 5 plots the distribution of polarised vs. total inten-sity for this sample, which appear broadly consistent withdistributions derived from several similar ∼ GHz-frequencystudies (Feain et al., 2009; Banfield et al., 2014; Hales et al.,2014). Moreover, the sample yields an average polarisedsource density of 27 per square degree. This is consistentwith several predictions for the number density of linearly po-larised sources for GHz-frequency surveys with similar depthand resolution (Stil et al., 2014; Rudnick & Owen, 2014a,b),and is somewhat lower than others (e.g. Hales et al., 2014).We are therefore confident that spurious leakage-dominatedsources do not significantly contaminate our sample, and donot a ff ect our analysis or conclusions in any important way.The Galactic contribution to Faraday rotation measure is oforder 10 rad m − in this region (refer to Table 1 for Galacticcoordinates), but varies over the field (Anderson et al., 2015,and see below). We attempted to remove this foreground con-tribution by fitting and subtracting a 2nd degree polynomialsurface to the position-dependent φ peak values of our sourcesto yield φ peak , res — the residual peak Faraday depth. Sourceslocated within 1.5 degrees projected distance of the Fornax Aradio core were excluded from the fit. We tested alternativefitting approaches, such as using a planar surface instead ofthe 2nd degree polynomial surface, and both the planar and2nd degree polynomial surfaces after excluding data pointslocated within 1.5 degrees of the cluster centre (the reasonfor which will become apparent in Section 5.1). In all cases,the residual RMs did not di ff er substantially in the vicinityof the cluster or throughout the larger field. Denoting the Total flux density (mJy / beam)10 P o l a r i z e d f l u x d e n s i t y ( m J y / b e a m ) Figure 5.
Linearly polarised (un-debiased) vs. total flux density for the 870sources in our sample. The red points represent sources inside a projectedcluster-centric distance of 1 degree, while the blue points represent theconverse. This distinction becomes relevant in Section 5.1.1. The dasheddiagonal lines are lines of constant fractional polarisation (from top left tobottom right: 100%, 10%, 1%, 0.1%). right ascension and declination a given source in decimaldegrees in the J2000 epoch as x and y , we define a 2nd de-gree polynomial surface as p ( x , y ) = (cid:80) i , j c i , j ∗ x i ∗ y j with i , j ≤
2, then fitting over the field as described above, we de-rive best-fit model coe ffi cients of c , = − . × , c , = − . × , c , = − . × , c , = . × , c , = . × , c , = . × , c , = − . × , c , = − . c , = − . ∼ +
10 rad m − , showing a slight gradientrunning almost directly N-S through the field, from ∼ + − for the northernmost sources down to ∼ + − for the southernmost sources. Our model is systematically ∼ − lower than the Hutschenreuter & Enßlin (2020)model in the very northern-most part of our field, but the dis-crepancy is generally less than or equal to the Hutschenreuter& Enßlin (2020) model uncertainty in this region, and wehave verified that the di ff erence does not a ff ect our results orconclusions in any case.The uncertainty in φ peak , res was calculated as per Brent-jens & de Bruyn (2005), based on the peak- P value of eachsource, the RMS noise measured from band-averaged mapsof Stokes Q and U in an adjacent source-free region (typi-cally 30 µ Jy beam − per Stokes parameter), and the rotationmeasure spread function (RMSF, which is the point-spreadfunction in Faraday depth space; see Brentjens & de Bruyn,2005) width measured directly from our data accounting forour channelisation scheme. We have multiplied the uncertain-ties in φ peak , res by an additional factor of 1.2, to capture theaggregate e ff ect of uncorrected widefield polarisation leakage0 C. S. Anderson et al. (see Section 5.2 of Ma et al., 2019).
The vast majority of radio sources brighter than ∼ ∼ GHz-frequencies are powerful AGN that lie at far greaterdistance than the Fornax cluster (e.g. Magliocchetti et al.,2000; Gendre & Wall, 2008; de Zotti et al., 2010). Never-theless, it is desirable to confirm this for the sources used inour particular RM grid experiment, for reasons described inSection 1.Maddox et al. (2019) have compiled a catalogue of reliablespectroscopic redshifts towards the Fornax cluster, drawnfrom deep optical imaging surveys in the literature as well astheir own data. This catalogue is complete within a degree ofNGC 1399, down to brightness levels typical of faint ultra-compact dwarf galaxies and globular clusters. The objects inour sample are all brighter than 0.6 mJy / beam in total radiointensity (see Figure 5) and will, if located in the Fornaxcluster redshift range (600 < cz < − ), have opticalcounterparts at least as bright as a star-forming galaxy (e.g.Padovani, 2016). It follows that any of our sample sourcesinside the Fornax cluster will have a spectroscopic redshift inthe Maddox et al. catalogue.We cross-matched our sample against the Maddox et al. catalogue for objects which (1) lie within 1 degree of thecentre of NGC 1399 (this radius becomes relevant in Section5.1.1), (2) had redshifts consistent with lying inside the For-nax cluster volume, and (3) were not associated with ‘Galacticstars’ or ‘globular clusters’ in Maddox et al. . We used an ini-tial matching radius of 90 arcseconds to account for possibleo ff sets between steep spectrum double radio sources and theiroptical counterparts (e.g. Hammond et al., 2012). This pro-duced three candidate matches, apart from the radio sourceassociated with NGC 1399 itself. However, each candidatewas then found to be a single, isolated, spatially-unresolvedradio source. For such sources, a matching radius equal to thesynthesised primary beam width (10 arcseconds) is more ap-propriate, but even a 30 arcsecond matching radius eliminatesall of the initial candidate matches. This complete lack ofoptical redshift counterparts confirms that our entire sample(with the exception of the radio source hosted by NGC 1399)lies beyond the Fornax cluster, and that their RMs are accu-mulated along lines-of-sight that traverse the entire distancethrough the cluster.Relaxing the cluster volume redshift range constraint, butotherwise cross-matching using the same methods against thefull Maddox et al. . catalogue, we obtain 21 matches satisfying0 . < z < .
41, with < z > = .
65. Six of these sourcesare located at a projected distance of less than one degree,and have 0 . < z < .
606 and < z > = . z = . . < z < .
41 and < z > = .
55. Therefore, to the extentpossible, we confirm that our sample sources typically re-side well beyond the Fornax cluster, though somewhat closerthan is typical for moderately bright ( >
10 mJy / beam) radiosources in the NRAO VLA Sky Survey (NVSS, for which < z > ≈ .
2; see Brookes et al., 2008 and Figure 11 of deZotti et al., 2010). This is not unexpected, given the complexdi ff erences in strategy used by the redshift surveys involved.Finally, a 2-sample Kolmogorov-Smirnov test shows that theredshift distributions of cross-matched sources located insideversus outside 1 degree do not di ff er significantly from eachother (D-value = = Figure 6 plots φ peak , res as a function of distance from thecentre of the cD-type galaxy NGC 1399, which we taketo be the position of the centre of the cluster (Drinkwateret al., 2001; i.e. located at 03 h m . s , − d m . s (J2000), and indicated on Figure 3 with a red cross-hair).Note that our sample selection criteria (with respect to themosaic beam centres; see Section 3) mean that sources aretruncated eastward of RA = φ peak , res within ∼ σ = . − ), compared to sources outsidethis radius ( σ = . − ). Figure 7 shows a similarresult, but with finer granularity. Here, we have calculated themedian of | φ peak , res | in a sliding window of maximum width0.5 degrees as a function of the cluster-centric radius of theouter bound of this window. A sharp decrease in the medianof | φ peak , res | is clearly evident as the outer bound of the slidingwindow crosses 1 degree, and has dropped to a more-or-lessconstant lower value at 1.5 degrees, indicating that a sharptransition in the degree of observed Faraday rotation occursat the former distance.The di ff erence in Faraday rotation inside vs. outside 1 de-gree cannot be accounted for by the measurement uncertain-ties. A 2-sample K-S test applied to the cumulative distribu-tions for these sub-samples (also shown in Figure 6) confirmsthat they di ff er both substantially and significantly, yieldingD- and p-values of 0.32 and 3 × − respectively. The sharpbreak in φ peak , res dispersion, and the relative enhancement inthis dispersion towards smaller cluster-centric radii, persist re-gardless of how the data are binned or the dispersion is param-eterised — see for example the half-interdecile range plot cal-culated in 0.56 degree (200 kpc) -wide bins in Figure 6. Thus, ornax cluster magnetic fields σ φ peak , res , cluster = √ . − . = . ± . − , where the quoted uncertainty range corresponds to the95% confidence interval calculated via bootstrap re-sampling.Apart from their di ff erence in φ peak , res dispersion, the distri-butions are otherwise similar — the skew and excess kurtosisof both do not significantly di ff er from the values expectedfor the Normal distribution (i.e. zero), for example. The morphology of the φ peak , res enhancement is revealed inFigure 8, where we interpolate (using the nearest neighbourmethod) and plot φ , res as a function of position. Contoursshowing the observable extent of the X-ray-emitting ICM asseen by Chandra (Scharf et al., 2005) and
ROSAT (Jones et al.,1997) are overlaid, as are contours for the radio galaxy FornaxA (see Norris et al. submitted ). We note that the
Chandra and
ROSAT
X-ray maps are smoothed to 2.5 and 3 arcminutesrespectively to reveal the faint di ff use emission. Particularlyfor the ROSAT contours, the apparent degree of extensiontowards the southwest is a ff ected by the smoothing requiredcombined with the presence of bright point sources unrelatedto the cluster medium. The ICM is therefore more asymmetricaround NGC 1399 — more ‘swept back’ towards northeast— than the ROSAT contours initially seem to imply (echoingthe morphology of the
Chandra contours). The dispersion in φ peak , res is clearly enhanced in the vicinity of the main cluster,extending to a radius of one degree in most directions, and to1.5–2 degrees towards the N and NW. The radial extent of theenhanced region exceeds that of the currently observable X-ray emitting ICM by a factor of 2–4 depending on azimuthalbearing, but lies within the 1.96 degree (705 kpc) virial radiusof the cluster (Iodice et al., 2017; indicated on Fig. 8).The global φ peak , res enhancement appears to be comprisedof two smaller sub-regions: the first, a circular sector of angle ∼ ◦ , with its vertex located near NGC 1399, and its twoenclosing radii oriented slightly clockwise of N-S and E-W(respectively), and the second region, a ∼ . ◦ -wide stripcentred ∼ . ◦ SW of NGC 1399, slightly concave towardsit. The sharp decline in φ peak , res dispersion at 1 degree cluster-centric radius is particularly evident at the outer edge of thisfeature. This ‘two region’ interpretation is bolstered whenthe sign of the φ peak , res values are considered (see Figure 9).The SW enhancement shows predominantly negative φ peak , res values, indicating that the magnetic field in this structure isoriented predominantly away from the observer. Conversely,the NE enhancement does not reveal an obvious bias towardseither positive or negative values, implying that the magneticfield in this region is more isotropic.We note the existence of another possible region of en-hanced φ peak , res dispersion, which runs adjacent to the FornaxA lobes to their NE, and which is not obviously attributableto calibration or image artifacts. While comprised of onlysix sources, the φ , res values are clearly elevated abovethe typical surrounding values for field sources — values for four of the sources lie at > σ , with two more at > σ .The probability of this happening in a contiguous region iscorrespondingly small. An apparent paucity of bright polarised sources in the vicinityof NGC 1399 (see the RMS map shown in Figure 3) moti-vated us to consider whether small-scale structure in the clus-ter medium could be depolarising background sources (e.g.Burn, 1966; Murgia et al., 2004; Bonafede et al., 2011). A2-sample Kolmogorov–Smirnov test comparing the polarisedintensity distribution of our sample inside versus outside 1degree results in a D-value of 0.22 with a p-value of 0.001,suggesting the lower apparent polarised flux near the clusteris statistically significant at the ∼ . σ level. The questionis then whether sources near the cluster are fewer, fainter, orboth, and whether depolarisation or some other mechanismis responsible for this.We investigated this by calculating the polarised sourcecounts, and the integrated and median polarised and total flux,in equal-area ( π -square degrees) annular bins centred on NGC1399. The experiment is described in more detail in AppendixB, while the results are shown in Figure 10. The polarisedsource counts (top panel of Figure 10) show a 2 σ decrementinside one degree radius (averaging 17 polarised sources persquare degree), a 2 σ enhancement between 1 and 2 degreesradius (averaging 34 polarised sources per square degree),but are consistent with our average 27 polarised sources persquare degree thereafter. Taken on their own, these deviationsare not statistically significant in a sky area the size of ourmosaic. However, the plots of the integrated and median fluxdensities (middle and lower panels of Figure 10, respectively)mirror the behaviour of the source count plot, and here thedeviations are significant. The integrated polarised and totalfluxes (respectively) show ∼ σ and ∼ σ decrements relativeto the expectation from the broader mosaic inside 1 degreeradius, corresponding to a 50% decrement in polarised fluxin the former case. The data then show a ∼ . σ and ∼ σ enhancement in the integrated polarised and total flux (respec-tively) between 1 and 2 degrees radius. In total intensity only,the enhancement continues to fall outside the 99.7% confi-dence interval until a radius of 2.3 degrees, beyond which itreturns to low-significance deviations from the expectationvalue, along with the polarised flux. The median polarised andtotal fluxes also show ∼ . σ and ∼ σ decrements (respec-tively) inside 1 degree radius, but less significant deviationsin other bins. This may indicate that the flux decrement inside1 degree is driven by the bulk of the sources therein, whilethe flux enhancement from 1–2.3 degrees may be driven bya smaller proportion of brighter sources. Finally, the medianfractional polarisation shows no evidence for a decrement atsmall cluster-centric radii, as was found by Bonafede et al.(2011) for a sample of clusters, who attributed the e ff ect todepolarisation by turbulent cells in the ICM as per our mo-2 C. S. Anderson et al. p e a k , r e s [ r a d m ] . . . . . CDF (Normalized)
Figure 6.
Foreground-corrected Faraday depth ( φ peak , res ) versus projected distance from NGC 1399. The foreground was removed as described in Section 5.1.Data points within one degree (indicated by the red shaded region) show an excess dispersion, as described in Section 5.1. Sources that are located inside theFornax cluster volume, instead of behind it, are indicated with magenta crosses (see Section 4). Note that all such sources are in fact sub-components of thecentral radio source in NGC 1399 (following from our approach for dealing with heavily resolved sources, discussed in Section 3). The blue step plot shows the half-interdecile range (i.e. the interdecile range divided by two) for the data points located withineach 0.56 degree (200 kpc) -wide step. The vertical blue bars indicate the associated 90% confidence interval for theunderlying population distribution in each bin, calculated using bootstrap re-sampling. The right-most axes show normalisedcumulative histograms of φ peak for sources located within (red) and outside (black) a projected distance of one degree. The redshading highlights the di ff erence between these distributions. ornax cluster magnetic fields M e d i a n | p e a k , r e s | [ r a d m ] Figure 7.
The median of | φ peak , res | in a sliding window of width 0.5 degreesas a function of the cluster-centric radius of the outer bound of this window(blue line). The blue-shaded region indicates the 95% confidence interval onthis value, calculated as ± . × IQR / √ n (McGill et al., 1978), where IQRand n are the interquartile range and number of measurements (respectively)of | φ peak , res | in the sliding window. A sharp and significant decrease in theplotted values is evident when the outer bound of the window passes acluster-centric radius of 1 degree, which is marked with a vertical red dashedline. The width of the sliding window is indicated by the gray shaded region. tivating hypothesis above. Instead, we find that the medianfractional polarisation is ∼ ff ective core radii (see figure 2 ofthat work). However, this comparison comes with the caveatsthat (a) our polarised sources at small cluster-centric radii isinsu ffi cient to probe the core ICM regions where Bonafedeet al. (2011) observed the depolarisation e ff ect, and (b) ourRM grid sources are confirmed to lie exclusively behind theFornax cluster, whereas Bonafede et al. (2011)’s sample wasa heterogeneous mixture of sources embedded in the clustersbeing measured, as well as in the background (though seetheir Appendix A.1 for arguments that this cannot explaintheir results). In the future, it might be possible to probe closerto the core of the Fornax cluster using the central radio sourcehosted in NGC 1399 (e.g. Killeen et al., 1988), at which pointa more detailed comparison would be appropriate.We note that the decrement and enhancement structuresdescribed above are visually apparent in Figure 3 (in polari-sation). The results are unusual for the Stokes I emission inparticular, for it is not obvious how emission or transmissionprocesses linked to the cluster could produce them (see dis-cussion in Section 6.7). A mundane possibility is that, giventhe fact that the data were collected during ASKAP’s EarlyScience phase, the e ff ect could be instrumental. We rule thisout conclusively by including data from the GaLactic andExtragalactic All-sky Murchison Widefield Array (GLEAM;72–231 MHz; Wayth et al., 2015; Hurley-Walker et al., 2017)and NVSS (1.4 GHz; Condon et al., 1998) survey cataloguesin the middle panel of Figure 10. We applied the same spatialtruncations to these data as to our sample, and then scaledtheir fluxes to those expected in the ASKAP band assum-ing a spectral index of − .
7. Evidently, the modified total intensity data from GLEAM and NVSS track the ASKAPdata closely, as does the polarised intensity data from NVSS,ruling out instrumental e ff ects. A final question is whetherthese e ff ects are observed over a range of flux densities. InFigure 11, we plot the normalised integrated source countsversus flux density, which we calculate both inside and out-side 1 degree cluster-centric radius, for both polarised andtotal intensity. The data show that the decrement inside 1degree radius persists over a wide range in flux density.Thus, we draw the following conclusions: (1) the polarisedsource counts, the polarised flux densities, and the total fluxdensities all show decrements inside 1 degree projected radiusfrom the cluster; (2) the average magnitude of the decrementis ∼
50% for the polarised flux, and ∼
30% for the totalintensity; (3) between 1 and 2.3 degrees projected radius,there is a surfeit of flux in one or both quantities; (4) noneof these results can be attributed to a normalisation problem,instrumental e ff ect, or the modest ∼
50% increase in imagenoise that occurs in a small ∼ ×
10 arcminute regionaround PKS B0336–35 (see Figure 3 and Section 3); (5) thecoexistent decrements in Stokes I and P are inconsistent withour initial hypothesis that depolarisation by turbulent cells inthe Fornax ICM could cause the decrement in P (cf. Bonafedeet al., 2011). We discuss these results further in Section 6.7. We summarise our observational results as follows: • The distribution of peak Faraday depths for discreteradio sources shows an excess scatter of σ φ peak , res , cluster = . ± . − within 1 degree (360 kpc) of theFornax cluster centre. In more spatially-limited areas,the excess can be traced out to the ∼ .
96 degree (705kpc) virial radius of the cluster. • The projected area of the Faraday depth enhancementextends 2–4 times the projected distance of the X-rayemitting ICM, though is mostly contained within thecluster’s virial radius. • The global Faraday depth enhancement naturally dividesinto two distinct (projected) morphological sub-regions:(1) A triangular region extending from its vertex nearNGC 1399 towards its apparent base about ∼ . ◦ to theNE, with a mix of both positive and negative φ peak , res values, and (2) a banana-shaped strip of width ∼ . ◦ and length ∼ . ◦ , curving slightly around NGC 1399,but centred ∼ . ◦ to its SW, and having predominantlynegative φ peak , res values. • On average, the areal total and polarised radio emissiondensity is ∼
30% and ∼
50% lower within 1 degree(360 kpc) of the Fornax cluster (respectively) comparedto outside this radius. Cumulative source counts versusflux density show that the emission decrement persistsover the full range of flux densities that are e ff ectivelyprobed by our observations and sample.4 C. S. Anderson et al. h m m m m m -33°-34°-35°-36°-37°-38° RA (J2000) D e c l . ( J ) p e a k , r e s [ r a d m ] Figure 8.
A map of φ , res across the field, employing nearest neighbour interpolation, as described in Section 5.1. The region shown is indicated in itsbroader context in Figure 3 with a white dashed box. Each cell contains a single polarised source, and is colorised by the sources’ value of φ , res . The extentof X-ray emission from the Fornax cluster ICM as seen by Chandra (0.3–1.5 keV bandpass; light blue contours; smoothed to 2.5 arcminute resolution; Scharfet al., 2005) and the
ROSAT
Position-Sensitive Proportional Counter (PSPC; 0.1—2.4 keV; smoothed to 3 arcminute resolution; pink contours; Jones et al.,1997) is indicated. White contours show Fornax A. The white dashed circle indicates 1 ◦ projected distance — the projected distance inside which the varianceof φ peak , res was found to be enhanced in Figure 6. The white dashed ellipse roughly indicates where φ , res values appear to be elevated in a contiguousregion near Fornax A. The white dotted line indicates the 1.96 degree (705 kpc) virial radius of the cluster (Iodice et al., 2017). The blacked-out polygonsindicate sources which fall more than 3 . ◦ from the mosaic centre, and which are therefore excluded from our polarimetric analysis (Section 3). ornax cluster magnetic fields Figure 9.
Left:
As for Figure 8, but zoomed on the main Fornax cluster, and with | φ , res | <
200 rad m − masked (appearing black). The two distinct regionsof enhancement described in the main text are delineated by white dashed lines. Right:
As for the left panel, but showing sign( φ peak , res ) × φ , res . There are two possible locations for the excess Faraday ro-tating material identified in Section 5.1: In our Galaxy, or inthe Fornax cluster. The field contains intervening Galacticemission in H i , H α and soft X-rays. The interstellar mediumthereby traced is Faraday-active, appearing capable of induc-ing mild depolarisation via di ff erential Faraday rotation inspatially-limited regions due to its arcsecond-scale ionisationstructure (Anderson et al., 2015). The question is whetherdegree-scale Galactic foregrounds can enhance variance in net
Faraday rotation over arcminute scales. We consider thisunlikely, because: • Anderson et al. (2015) showed that in this field (i.e. cen-tred on Galactic l , b of 235.988 ◦ , − ◦ ), over spatialscales of several arcminutes, the expected contributionof the Galactic foreground to RM variance is only ∼ m − (see Figure 36 and Section 7.2.1 of that work).The 282 + − rad m − variance in the vicinity of the clus-ter is ∼ ± • We cannot identify any foreground structures in mapsof Parkes Galactic All Sky Survey (GASS; McClure-Gri ffi ths et al., 2009) H i column density, Planck spec-tral brightness,
ROSAT soft X-rays, or H α photon fluxthat map to precisely the same region in which the Fara-day depth enhancements occur (though structure in suchemission is present in the field — see Figure 37 of An-derson et al., 2015). • The prior probability that a degree-scale Galactic Fara-day depth enhancement would happen to centre pre-cisely on a pre-existing and well-defined position of interest is not well known, but must surely be small.In what follows then, we assume that the Faraday activematerial is physically associated with the Fornax cluster.
Little is concretely known about the structure of magnetisedplasma in the periphery of low-mass galaxy clusters, includ-ing the strength and characteristic scale-length of the turbu-lent and regular magnetic fields in the rarefied plasma. In thecase of the Fornax cluster, our di ffi culties are compoundedby the fact that the Fornax cluster is not relaxed, but is beingdisturbed by ongoing mass-assembly processes. This can dis-tribute µ G-level magnetic fields throughout cluster volumes(e.g. Xu et al., 2009), inducing significant variability in theFaraday rotation signal of clusters with otherwise similarproperties (Xu et al., 2011), and degeneracies in the inter-pretation of such data (Johnson et al., 2020). Nevertheless,following Anderson et al. (2018), we can crudely estimate thebaryonic gas mass generating the Faraday depth enhancementas follows. The peak Faraday depth of a column of thermalelectrons threaded by a uniform magnetic field is (e.g. Heiles& Haverkorn 2012): φ = . n e B u , || L = N e , B u , || rad m − (5)where B u , || is the strength of the magnetic field projectedalong the line of sight [ µ G], and N e , is the electron columndensity in units of 10 cm − . From Figure 8, we estimate thesolid angle occupied by the Faraday depth enhancements tobe 4 . × square arcseconds, corresponding to a projected6 C. S. Anderson et al. p o l a r i s e d s o u r c e c o un t [( s q . d e g . ) ] T o t a l P f l u x [ J y ( s q . d e g . ) ] T o t a l I f l u x [ J y ( s q . d e g . ) ] M e d i a n P f l u x [ m J y ( s q . d e g . ) ] M e d i a n I f l u x [ m J y ( s q . d e g . ) ] M e d i a n P / I Figure 10.
Binned polarised source counts, polarised and total radio flux,and fractional polarisation statistics, calculated in equal π -square-degreeannular bins centred on NGC 1399, and plotted against the bounding radiusof each annulus. Details of the experiment are described in Appendix B. Panel 1 (top):
The observed polarised source counts in each annular bin,expressed as the average number per square-degree. The grey bands indicateconfidence intervals of 67% (dark grey), 95% (mid grey), and 99.7% (lightgrey) around the expected count of 27 polarised sources per square degree(black horizontal line).
Panel 2:
Integrated polarised (red) and total (blue) fluxfor ASKAP (joined dots), NVSS (‘ + ’ symbols) and GLEAM (‘x’ symbols;total intensity only) in each annular bin, with the NVSS and GLEAM fluxesscaled to those expected in the ASKAP frequency band by assuming aspectral index of − .
7. The fractional uncertainty on the plotted quantities isgenerally less than 1%, and so are not indicated. The shaded areas indicateconfidence intervals of 67% (dark shading), 95% (medium shading), and99.7% (light shading) for the ASKAP-derived polarised (red-shaded) andtotal intensity (blue-shaded) quantities, which have each been truncatedhorizontally in the plot for clarity.
Panel 3:
As for panel 2, but here forthe median flux in each annulus rather than its sum.
Panel 4 (bottom):
Themedian fractional polarisation of sources in each annulus, calculated on aper-source basis. Confidence intervals are represented as above. N ( > S ) Figure 11.
Normalised integrated source counts versus the logarithm ofpolarised (dashed lines) and total (solid lines) flux density inside (red lines)and outside (black lines) 1 degree projected cluster-centric radius. area A = . × cm at the distance of the cluster. As-suming the Faraday-active plasma is dominated by ionisedhydrogen and helium nuclei with a typical ICM abundance ra-tio of 9:1 (respectively), and thus a mass density of 1 . n e m p (where m p is the mass of a proton), the total mass of baryonicmaterial is roughly: M Thermal ≈ . × N e , Am p (6)Defining the characteristic Faraday depth of the material as φ peak , res , char , then combining Eqns. 5 and 6 yields: M Thermal ≈ . × (cid:18) φ peak , res , char B u , || (cid:19) M (cid:12) (7)Using φ peak , res , char ∼ σ φ peak , res , cluster ≈
17 rad m − , we get M Thermal ≈ . × (cid:0) B µ G (cid:1) M (cid:12) , which for comparison, isapproximately three times the mass of the X-ray-emitting hotICM (but see Johnson et al., 2020 for discussion of inherentuncertainties in such measurements). If there are typically N magnetic field reversals along the line of sight to sources inour sample, M Thermal will be larger by a factor of ∼ N / .The material extends well beyond the presently-detectablehot ICM, typically to a distance of 360 kpc. This yields anaverage thermal electron density inside this volume of n e ≈ . × − (cid:0) B µ G (cid:1) N / f − cm − , where f is the volume-fillingfactor. If B , N , and f are equal to 1, it represents a baryonicover-density of δ ∼
215 — a regime which is obviously verydi ff erent to the hot ICM, for which δ (cid:29) ff precipitously to δ ∼
50 by 180 kpc from the cluster centre, and which isprojected to drop by a further two orders of magnitude tonegligible levels by 360 kpc (based on
ROSAT measurementsof soft X-ray emission; see Sections 2.6 and 2.6 of Paolilloet al. 2002). Instead, it is comparable to the radially-averagedcharacteristic density of the intergalactic medium expectedto inhabit ∼ M (cid:12) galaxy groups and poor clusters (Davéet al., 2010; Haan & Braun, 2014), and the moderately-dense ornax cluster magnetic fields B is lower than 1 µ G, or that the number of magnetic fieldreversals along typical lines of sight N is large, or that thevolume filling factor f is small, or some combination of theabove. But it each case, this would tend to raise our totalgas mass estimate. While this might bring the baryonic over-density more into line with expectations for a hot ICM phasein a cluster environment, its radial distribution would berendered even more inconsistent with direct measurementsof radial gas densities in this hot phase reported by Paolilloet al. (2002). Thus, we claim to have directly detected amoderately-dense phase of the di ff use WHIM via Faradayrotation, which is either too cool, too di ff use, or both, tohave been detected by X-ray observatories to date (thoughthis may be addressed with future observations by eROSITAfor example; Merloni et al., 2012). This appears to be madepossible by cluster dynamic processes that act to organizeand amplify the embedded magnetic field. We discuss thisfurther in Section 6.3. The morphology of the Faraday depth enhancement (Section5.1.2; Figures 9,12) is reminiscent of the bow shocks seenaround merging cluster cores (e.g. Markevitch & Vikhlinin,2007), and astrophysical bow shocks more generally. If ashock system does exist, it could be either a stationary bow-shock caused by interaction between the NE and SW sub-clusters (Drinkwater et al., 2001; Scharf et al., 2005), or apropagating shock, set up by merger activity in the main (i.e.NE) sub-cluster itself (Sheardown et al., 2018). We considerthese possibilities in turn.
Drinkwater et al. (2001) proposed that the Fornax clustercan be partitioned into NE and SW clumps, which are likelymerging at speeds between 100 and 500 km s − . Scharf et al.(2005) interpreted the swept-back (to the NE) morphology ofthe X-ray-emitting main cluster ICM as evidence to supportthis. Extrapolating X-ray-derived temperature and densitymeasurements from Jones et al. (1997) to the approximateradius of the shock front (1 degree) yields an estimated soundspeed of c s = (cid:112) T / K ≈
420 km s − (Sarazin, 2002),and an Alfvén speed of c A = (cid:112) B /ρ ≈
320 km s − . Themerger speed V may therefore be transonic, in which casea bow shock could form in di ff use gas between the mergingcomponents.We propose that the features apparent in our maps of φ , res (Figure 9) may correspond to the canonical featuresof a stationary shock leading a blunt object as illustrated inFigure 12 (left panel). That is, in this instance (a) a concaveshock front centred around the X-ray-emitting ICM, whose point of closest approach is located 360 kpc to its SW, (b) acontact discontinuity between the main cluster gas and that ina more di ff use extended envelope, located perhaps one thirdof the way from NGC 1399 to the leading shock, and (c) atriangular extension of the X-ray-emitting ICM to the NE,representing a less-dense and less-hot phase of the magneto-ionised ICM stripped from the NE cluster. The boundary ofthis region may be associated with magnetic fields drapedover the X-ray emitting ICM and amplified there — expectedto appear for any super-Alfvénic merger in magnetised media(Lyutikov, 2006).If the features described in the previous paragraph are cor-rectly identified, then since the radius of the X-ray-emittingmedium is small compared with the length of the shock front,we can estimate the Mach number of the shock via its Machangle and stand-o ff distance (see Figure 12). The Mach angleis given by µ = sin − (1 / M s ), where M s is the sonic Machnumber. From visual inspection of Figure 9, µ ≈ ± ◦ yielding M s = . + . − . , placing the merger in the transonicregime. The shock stand-o ff distance d s is a sensitive andindependent measure and test of this claim (Sarazin, 2002) —it depends only on the value of M s and the e ff ective shape ofthe supersonic object. A prediction for the stand-o ff distanceversus Mach number is given by Sarazin (2002, Figure 4). Forour best estimate of M s = .
06, we expect d s / R ≈
7, where R is the radius of curvature of the dense core. For the denseX-ray-emitting ICM, we estimate R ≈ ∼
49 arcminutes SWof the cluster. This is essentially consistent with the locationof the proposed shock front in our maps (1 degree to the SWof the cluster core).This sub-cluster merger model predicts several featuresthat could be used to confirm or refute it in future, and whichmight then be used to measure the properties of the gas. First,a generic feature of super-Alfvénic mergers is that magneticfields should be ‘collected’ and amplified along a thin coniclayer by the dense cluster ICM upon its passage through themore extended di ff use envelope. This is known as magneticdraping (Lyutikov, 2006), and is expected to occur for a widerange of merger speeds and magnetic field configurations.The expected minimum thickness for the magnetic field am-plification layer is ∼ Rc A / V ≈
10 arcminutes (Lyutikov,2006), presumably draped over the leading edge of the densecore ∼ B ∼ πρ V . For the NE-SW merger speed and ICMdensities cited above, this implies a magnetic field strengthof ∼ µ G. Both expectations are interesting, for they havebeen raised by Su et al. (2017) in the context of a sloshingcold front identified in this system at approximately the ex-pected location (identified as the "F2" front in that work),8
C. S. Anderson et al.
Figure 12.
Physical features for the NE-SW sub-cluster merger (left panel) and NGC 1404 merger (right panel) scenarios, described in Section 6.3.
Left panel:
Light blue filled circle: X-ray emitting ICM; Light blue arrows: Turbulent eddies in stripped ICM; Black lines: Canonical features of astrophysical shocks, asdiscussed in the main text; X-ray emitting ICM; Red dotted line: Shock stand-o ff distance d s ; Purple dashed line: Projected angle of shock front. Note that theangle between the red-dotted and purple-dashed lines is the Mach angle referred to in Section 6.3.1. Right panel:
Large light blue filled circle: NGC 1399;Small light blue filled circle: NGC 1404; Light blue blobs: Wake features generated by NGC 1404 in-fall, as described in the main text; Red line and arrows:Path of in-falling NGC 1404; Black line: Detached moving bow shock generated by NGC 1404 in-fall. and the hypothesis that such a cold front can be stabilisedagainst Kelvin-Helmholtz instabilities via magnetic tension,if only strong enough fields can be generated. The stabilisa-tion requires a magnetic field running locally parallel to thefront with strength ∼ µ G (Vikhlinin et al., 2001), whichis evidently similar to the value we obtain for ram-pressurebalance in the system. Thus, in our merger model, we suggestthat the cold front identified by Su et al. (2017) may act asthe e ff ective surface of ram-pressure balance with a di ff useionised medium through which the dense core of the clustermoves with transonic speed. The cold front might stabilizeitself via the very magnetic draping and compression that theNE-SW sub-cluster merger induces.A second feature that might be sought to furnish evidencefor or against our model is as follows. In the wake of blunt ob-jects embedded in a hydrodynamic flow where the Reynoldsnumber exceeds ∼
50 (most likely applicable throughoutgalaxy clusters — e.g. Zhuravleva et al., 2019), vortex shed-ding occurs (e.g. Lienhard, 1966). This terms refers to aphenomenon where vortices are created behind a blunt objectembedded in a fluid flow, and are periodically jettisoned intothe flow. The vortex shedding frequency ( f ) is related to L and the flow speed of the external fluid ( U ) by the Strouhalnumber ( S t ) as
S t = ( f L ) / U , where S t ≈ . L ).Thus, in the wake of the dense Fornax cluster ICM, we expectto see coherent vortical structures ranging in size from ∼ ff ective Reynolds number of the medium (among otherfactors) (e.g. Subramanian et al., 2006; Zhuravleva et al.,2019). These observational signatures are not detectable inour present observations, but may be in pending deep obser-vations of the region (see Section 7).Finally, we note that in Section 5.1.2, we proposed that anenhancement in Faraday depth can be seen running adjacentto the NE of the long axis of the Fornax A lobes. Ekerset al. (1983) previously argued that the Fornax A system wasmoving to the N or NE due to a ∼ southerly o ff set of a di ff useradio bridge between the lobes and its radio core. Both thisfeature, and the purported Faraday depth enhancement to theNE, might be naturally explained as a consequence of gas andmagnetic field compression in the sub-cluster merger model. Recently, Sheardown et al. (2018) simulated the in-fall andmerger of the galaxy NGC 1404 to the main Fornax cluster,and highlighted several features that bear an intriguing cor-respondence with features in our data. Their preferred simu-lated in-fall scenario produces: (a) a detached bow shock fromNGC 1404’s previous orbit in the cluster potential, having aMach number in the range 1.3–1.5, currently propagating out-wards between 450 and 750 kpc S and SW of NGC 1399, and(b) regions of relatively cold turbulent material distributedthrough much of the cluster, but particularly towards the NE,again stirred up by NGC 1404’s previous orbits through thesystem (see Figure 12, right panel).Qualitatively, these predictions are similar to the sub-cluster merger scenario above, and can explain our resultsalmost equally well. A minor point of disagreement is that ornax cluster magnetic fields
The excess scatter ( σ φ peak , res , cluster = . − ) and spatialextent (360 kpc radius) of the RM enhancement are bothsmaller than reported for ensembles of galaxy clusters in RMstacking experiments. Clarke et al. (2001) report a standarddeviation in RM of 114 rad m − for sources located within theprojected radius of galaxy clusters, compared to 15 rad m − for a control sample, which we note is similar to our value of11.8 rad m − for our field sources. More recently, Böhringeret al. (2016) report a value of 120 rad m − for sources locatedwithin the projected radius of clusters. However, Böhringeret al. (2016) also show that this scatter is driven mainly bymassive clusters: When their sample is split by the medianX-ray luminosity of their associated cluster (correspondingto a total mass of 1 . × M (cid:12) ), the standard deviation inRM increases to 158 ±
34 rad m − for sources associated withclusters in the upper half of the mass range, and decreases to62 ±
11 rad m − for the converse sources. Our lower derivedvalue of of 16 . ± . − for the RM scatter seemsbroadly consistent with this coarse mass dependence, giventhat the total mass of the Fornax cluster is only 6 + − × M (cid:12) (Drinkwater et al., 2001; Nasonova et al., 2011; Maddox et al.,2019) inside a few Mpc, which is half the mass cut value usedby Böhringer et al. (2016). It is also comparable to resultsfrom simulations for unrelaxed clusters of approximately thesame mass (see Figure 14 of Xu et al., 2011, for example).However, in light of our conclusions about the nature of theionised gas from Section 6.2, Böhringer et. al ’s statementthat the relationship between RM scatter and cluster massconfirms "that the observed excess scatter in the RM in thelines of sight of galaxy clusters is due to the cluster ICM" may require a minor qualification, in the sense that someportion of the RM scatter may be driven by plasma regimesthat di ff er from the canonical hot ICM.The Clarke et al. (2001) and Böhringer et al. (2016) stud-ies, and results from other recent works of simulation andobservation (Marinacci et al., 2018 and references therein),show that cluster-based RM enhancements are typically astrong function of radius. The central 200 kpc of the clusterensemble shows | RM | values often exceeding 100 rad m − ,but these values decrease roughly exponentially until they be-come indistinguishable from field source RMs beyond ∼ ff erent: The degree of RM scatter is quite uni-form out to a projected radius of 360 kpc, at which point it drops precipitously to roughly half its value (Figures 6and 7), and thereafter remains constant with projected radius.This qualitative di ff erence could be due to several factors,possibly including that (a) the plasmas traced by our RMscompared to the stacking experiments di ff er in their phaseor properties at various fiducial cluster-centric radii, mostplausibly because the Fornax cluster is exceptionally poorin terms of the number of member galaxies, gas mass, andtotal mass (b) the Fornax ICM is being disturbed by ongoingmass assembly, or (c) clusters that contribute to stacking ex-periments may individually show similar behaviour, but thissignal is averaged out in the stacking. Further observations ofa range of individual clusters — now possible with ASKAPand other instruments — are obviously the key to exploringthese possibilities. What studies do exist of the magnetised ICM in individuallow-mass clusters generally involve mapping the RMs acrossthe lobes of the central dominant radio galaxy (e.g. Perleyet al., 1984; Laing et al., 2008; Guidetti et al., 2010; Govoniet al., 2017). This provides an exquisite view of magneticstructure in the inner-most regions of the ICM, but little in-formation beyond the range where the the radio lobes arebright enough to calculate reliable RMs (10s–100 kpc). Inaddition, the fields are likely modified by interactions withthe radio galaxies themselves (Guidetti et al., 2012). RMgrid studies avoid both of these problems, since the sourcesare not in physical proximity to the medium being probed,and generally provide abundant information beyond 100 kpc,but limited information inside this distance. While there arenot yet su ffi cient data to connect the results of these exper-iments across the gap in scales, some brief comments arenevertheless warranted.Laing et al. (2008); Guidetti et al. (2010) and Govoni et al.(2017) mapped the RMs of centrally-located radio lobes tostudy the magnetised ICM of poor clusters with ∼ hundredsof member galaxies, masses in the range 4–9 × M (cid:12) (Ko-mossa & Böhringer, 1999; Nikogossyan et al., 1999), andcentral magnetic fields strengths of 3–10 µ G, making thembroadly comparable to the Fornax cluster. These studies mea-sure RM dispersions of 0–40 rad m − , which our measuredenhancement of 17 rad m − falls squarely inside. For thosestudies however, the RM dispersion measured against thelobes generally drops to a few rad m − by cluster-centricdistances of 100 kpc (see Figures 9 and 12 of Laing et al.,2008 and Guidetti et al., 2010 respectively, and Figure 14 ofGovoni et al., 2010), whereas the Faraday depth enhancementin the Fornax cluster is maintained out to at least 360 kpc.The studies cited above also attributed the enhanced Faradaydispersion to the cluster ICM, and indeed, the scale-size ofX-ray emission from the hot ICM and region of enhancedFaraday depth are well matched, unlike the case for the For-nax cluster. It is not clear how to reconcile these results with0 C. S. Anderson et al. the present data. It is possible that the Fornax cluster is beingfed with more warm-hot gas from filaments of large-scalestructure, or that similar reservoirs of gas exist in the vicinityof the other clusters but have not been detected yet, or thatthis gas exists but can only be detected in certain situations— in the case of the Fornax cluster we speculate, because itsongoing merger status organises the magnetic field structureto as to induce a detectable Faraday rotation signature over asu ffi ciently large area of sky. Further observations of a largersample of similar clusters are clearly needed.Laing et al. (2008); Guidetti et al. (2010) speculate that theouter scale of magnetic field fluctuations — of order 70 kpcin both cases — could be set by the characteristic separationof interacting cluster members. If this picture is correct, thenthe ∼ ∼ degree-scale Faraday depth enhancements that we have detected inthe cluster a priori . In turn, this may suggest that clustersundergoing similar mergers of massive sub-components, suchas the nearby Antlia (e.g. Caso & Richtler, 2015, and refer-ences therein) and Centaurus (Churazov et al., 1999) clusters,may represent particularly valuable targets for future RMgrid studies, since the detectable x-ray-emitting ICM maynot provide the whole picture. Finally, in Section 6.3.1, wepredicted that if the Faraday depth enhancement to the NE ofthe cluster is associated with vortex shedding of the clustergas, we might expect to see coherent associated RM struc-tures ranging in size from ∼ Given our conclusions that the Faraday-active ionised gasis associated with the WHIM, it is interesting to considerwhether Faraday rotation measure grids (e.g. Gaensler et al.,2004) and associated advanced analysis techniques (e.g. Vern-strom et al., 2019; O’Sullivan et al., 2020; Stuardi et al.,2020) might e ff ectively probe such material. The thermalelectron density drops rapidly with cluster-centric radius intypical ICM models, and the e ffi ciency of Bremsstrahlung asa tracer of this gas drops more precipitously, since its emis-sivity is proportional to n e . In contrast, the Faraday e ff ectis proportional to n e BL , assuming no significant separationof magnetic fields and thermal electrons along the line ofsight. It is not clear what structure magnetic fields generallyhave at the periphery of clusters, but it is clear that certainprocesses can amplify magnetic fields, increase their degreeof order, push their auto-correlation lengths to larger charac-teristic scales, or simply inject large-scale magnetic fields tobegin with (e.g. sub-cluster mergers; e.g. Govoni et al., 2005; Bonafede et al., 2009; Girardi et al., 2016, magnetic draping;e.g. Lyutikov, 2006, shocks; e.g. van Weeren et al., 2010;Brüggen et al., 2011, subsonic gas motions and shear flows;e.g. Keshet et al., 2010; Zuhone & Roediger, 2016; Donnertet al., 2018, also this work). Finally, the periphery of clustersprovides Mpc-scale path lengths through which polarisedemission can propagate through such plasmas. Therefore, itseems reasonable to conclude that Faraday rotation measuresshould provide a sensitive means of detecting and studyingrarefied warm plasma phases, assuming a su ffi cient densityof background sources over a wide enough area. The currentgeneration of radio telescopes will soon provide this routinelyfor many galaxy clusters. Following the results and arguments presented in Section 5.2,there are two two possible causes for the polarised and totalintensity emission decrements observed inside one degreecluster-centric radius: (1) scattering or absorption by fore-ground material, or (2) a genuine paucity of radio emissiondue to cosmic variance.The former possibility requires that cool, dense gas liesalong the line of sight. While it can be shown that the requiredgas could plausibly exist in the cluster, perhaps in the form ofcloudlets of ∼ K photoionised gas that often envelop el-liptical galaxies (e.g. Gauthier et al., 2010; Thom et al., 2012;Prochaska et al., 2013; Farnes et al., 2017; Lan & Fukugita,2017; Berg et al., 2019; Pradeep et al., 2019; Werner et al.,2019; Liang & Remming, 2020), we can test this scenariousing the frequency-dependence of the e ff ect. Consider thatthe free-free optical depth is given by τ ff ≈ . × − (cid:18) T e K (cid:19) − . (cid:18) ν GHz (cid:19) − . (cid:18) EMpc cm − (cid:19) (8)where T e is the electron temperature, ν is the observing fre-quency, and EM is the emission measure.We therefore cross-matched the discrete sources from oursample found within 1 degree of the cluster centre with ra-dio surveys over a wide range of frequencies (including theGLEAM survey (72–231 MHz; Wayth et al., 2015; Hurley-Walker et al., 2017) survey, the VLA Low-frequency SkySurvey redux (VLSSr; 74 MHz; Lane et al., 2014), the TIFRGMRT Sky Survey (TGSS; 150 MHz; Intema et al., 2017),the Westerbork in the Southern Hemisphere (WISH; 352MHz; De Breuck et al., 2002) survey, the Molonglo Ref-erence Catalogue (MRC; 408 MHz; Large et al., 1981), theSydney University Molonglo Sky Survey (SUMSS; 843 MHz;Bock et al., 1999; Mauch et al., 2003), the NVSS (1.4 GHz;Condon et al., 1998), the Parkes-MIT-NRAO (PMN; 4.85GHz; Gregory et al., 1994; Wright et al., 1994) survey, theAustralia Telescope Parkes-MIT-NRAO (ATPMN; 5 and 8 ornax cluster magnetic fields / beam at 887 MHz in this sub-sample possess a spectral peak at frequencies above ∼ π square degrees of sky down to ∼ mJy beam − sen-sitivity (at which we continue to see the emission decrementof up to ∼ σ uncertainty insource counts of only ∼
15% from cosmic variance (Hey-wood et al., 2013, Figure 2), corresponding to only a ∼ . ∼ ffi cult to explain.The handful of redshift cross-matches in this region indicatedistances much greater than the cluster, making it appear tobe a chance e ff ect. We are unaware of known clusters in theselocations, but redshift coverage here is currently relativelysparse.Nevertheless, remarkable large-scale cosmic structure doesappear to exist in both the foreground and background of theFornax cluster: Purportedly, a dense filament of dark matterextends along the entire line of sight between the Fornax clus-ter and the Milky Way Galaxy (see Figure 4 of Hong et al.,2020), while the ∼ × ×
140 Mpc diameter Sculptor voidlurks immediately behind (Tully et al., 2019). At a near-sidedistance of only ∼
30 Mpc, the latter possesses an apparentangular diameter which is far too large to explain our sourcedecrement / enhancement structures, which cover less than 10square degrees. Nevertheless, such voids appear to containsignificant substructure, and are linked to other voids in asponge-like lattice which cannot yet be mapped out in detailto the typical distance of powerful radio sources. We spec-ulate that a lattice of connected under-dense regions couldresult in smaller-scale ‘tunnels’, through which the averagedensity and brightness of radio sources is lower on average,and perhaps chance alignments of higher-density filaments orwalls where the opposite is true. With the available evidencefailing to support scenarios involving instrumental e ff ects, de-polarisation, or absorption, we tentatively conclude that cos-mic variance due to such large scale structure may be the mostviable explanation for our results. Over the next several years,the Evolutionary Map of the Universe (EMU; Norris et al.,2011) and POSSUM surveys will map the radio sky withan unprecedented combination of sky coverage, depth, anddetail. This will shed much new light on the 3-dimensionaldistribution of radio sources and large-scale cosmic structure,as well as on Faraday rotation associated with the gas in thiscosmic web. Our result can then be revisited and reinterpreted if necessary. We have conducted the first Faraday rotation measure gridstudy of an individual low mass galaxy cluster, achieving apolarised source density of 27 per square degree using the rev-olutionary new survey capabilities of the ASKAP telescope.Our key results are that: • The distribution of peak Faraday depths for confirmedbackground radio sources shows an excess dispersion of ∼
17 rad m − within 1 degree (360 kpc) of the Fornaxcluster centre, and in more spatially-limited regions outto the 705 kpc virial radius of the cluster. This is between2 and 4 times farther than the projected distance of thecurrently observable X-ray emitting ICM. • We estimate that the mass of the Faraday-active gas is2 . × M (cid:12) , which is approximately triple the massof the hot ICM so far detected in X-rays, but with alow average density of n e ≈ . × − cm − . Thisrepresents a baryonic over-density (compared to thecosmic average) of δ ∼
215 found at cluster-centric radiiout to 360 kpc. This appears to be markedly di ff erentfrom the hot ICM phase in Fornax, for which δ (cid:29) δ ∼
50 by 180 kpc, and projected to drop to negligibledensities much beyond this. • Morphologically, the Faraday depth enhancement di-vides into two regions. We interpret one as an astrophys-ical shock front, and the other as the turbulent main-cluster wake, in a scenario in which NE and SW sub-clusters are merging at transonic speeds. Alternatively,it may be that the protracted merger of the dominantcluster galaxy NGC 1399 and the in-falling galaxy NGC1404 has produced a detached shock moving to the SW,and has redistributed cold turbulent gas from the clustercentre and the ISM of NGC 1404 throughout the cluster. • On average, the total and polarised radio emission arealdensity is ∼
30% and ∼
50% lower (respectively) within1 degree of the Fornax cluster compared to outside thisradius. Consistent with this, cumulative source countsversus flux density show the ∼
50% emission decrementpersists over a large range of flux densities e ff ectivelyprobed by our observations and sample. Depolarisation,instrumental e ff ects and image artifacts, and free-freeabsorption by a cold and dense gas, are all ruled out aspossible causes or found to be unlikely. Cosmic vari-ance also appears to be an unlikely explanation, but onewhich we tentatively favour in lieu of more compellingevidence. This result should be examined using future,deeper observations.We argued that the Faraday-active gas is associated witha moderately dense phase of the WHIM, in which ongoingmerger processes in the cluster continue to amplify and or-ganize magnetic fields, thereby providing ideal conditions2 C. S. Anderson et al. to trace this material with the Faraday e ff ect. In particular,a shock system traced by Faraday RMs may confirm thatthe NE and SW Fornax appear to be undergoing a transonicmerger, as previously described.These results demonstrate that deep, wide-field RM gridstudies have the capacity to reveal the gas in and aroundgalaxy clusters in a diverse set of regimes. This being the case,impending deep all-sky linear polarisation surveys like POS-SUM, the VLA Sky Survey (VLASS; Lacy et al., 2019), thePOlarised GLEAM survey (POGS; Riseley et al., 2018, 2020),and the LOFAR Two-Metre Sky Survey (LoTSS; Shimwellet al., 2017) will all help to revolutionize our understandingof large samples of such objects, while much deeper targetedobservations like the MeerKAT Fornax Survey (Serra et al.,2016) will reveal a wealth of structure in individual clustersthat has gone heretofore unseen.Finally, in addition to the RM grid analysis presented here,Anderson et al. (2015) demonstrated the value of depolarisa-tion grids to study small-scale magnetoionic structure alongthe line of sight. In this work, we initially postulated that ICMdepolarisation may be responsible for the reduced counts andpolarised flux we observed in the vicinity of the Fornax clus-ter, but then recognised that this signal was largely reflectedin total intensity emission, too. It remains unclear wherethis underdensity comes from, but it is reasonable to assumethat such fluctuations will be found on these angular scaleselsewhere on the sky, for similarly uncertain reasons (e.g.see Rudnick et al., 2007). Now that deep polarised sourcegrids are becoming available, which provide RM and depo-larisation information at areal densities of ∼ several tens persquare-degree, we must be aware of these fluctuations, andpursue a better understanding of the clustering scales forextragalactic radio sources. ACKNOWLEDGEMENTS
The authors would like to thank the anonymous reviewer fortheir time, and for their very helpful comments. Our paperhas benefited significantly from this input. C. S. A. is a JanskyFellow of the National Radio Astronomy Observatory. C. S.A. thanks Phil Edwards for helpful feedback which has im-proved this paper, and Joe Callingham for curating the multi-survey spectral measurements discussed in Section 4.2. TheAustralian SKA Pathfinder is part of the Australia TelescopeNational Facility which is managed by CSIRO. Operation ofASKAP is funded by the Australian Government with supportfrom the National Collaborative Research Infrastructure Strat-egy. ASKAP uses the resources of the Pawsey Supercomput-ing centre. Establishment of ASKAP, the Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Cen-tre are initiatives of the Australian Government, with supportfrom the Government of Western Australia and the Scienceand Industry Endowment Fund. We acknowledge the WajarriYamatji people as the traditional owners of the Observatorysite. The POSSUM project has been made possible throughfunding from the Australian Research Council, the Natural Sciences and Engineering Research Council of Canada, theCanada Research Chairs Program, and the Canada Founda-tion for Innovation. The Dunlap Institute is funded throughan endowment established by the David Dunlap family andthe University of Toronto. B.M.G. acknowledges the supportof the Natural Sciences and Engineering Research Coun-cil of Canada (NSERC) through grant RGPIN-2015-05948,and of the Canada Research Chairs program. CIRADA isfunded by a grant from the Canada Foundation for Innova-tion 2017 Innovation Fund (Project 35999), as well as by theProvinces of Ontario, British Columbia, Alberta, Manitobaand Quebec. C. J. R. acknowledges financial support from theERC Starting Grant “DRANOEL”, number 714245. NMc-Gacknowledges funding from the Australian Research Coun-cil via grant FT150100024. S.P.O. acknowledges financialsupport from the Deutsche Forschungsgemeinschaft (DFG)under grant BR2026 /
23. Partial support for LR is provided byU.S. National Science Foundation grant AST-1714205 to theUniversity of Minnesota. J. M. S. acknowledges the supportof the Natural Sciences and Engineering Research Councilof Canada (NSERC) Discovery Grants program.
A ESTIMATING THE UNCORRECTEDOFF-AXIS POLARISATION LEAKAGE
The magnitude of uncorrected o ff -axis Stokes I → Q and I → U polarisation leakage can be estimated for ASKAPdata using field sources themselves as probes, by adoptinga modified version of the approach described by Lenc et al.(2017), as follows.Within the ∼
34 square degrees covered by the ASKAPfootprint, we detect 18640 sources in Stokes I — approx-imately 550 sources per square degree on average. We ex-tracted the Stokes I , Q , and U values at the location of eachof each of these sources in multi-frequency synthesis mosaicsof the field, and calculated the fractional Stokes quantities q = Q / I and u = U / I . These data points provide a localpoint-probe of the e ff ective frequency-independent leakagebetween the relevant Stokes parameters in our linear mosaics.We call them ‘local leakage estimators’ here.We create maps of the Stokes I → Q and I → U polari-sation leakage over the ASKAP footprint by first forming adense, regular grid of coordinate locations covering the field.At each coordinate location, we then:1. select all Stokes I sources with a full-band (i.e. 288MHz) S / N >
10 in an 0 . ◦ radius aperture around thepoint, corresponding to one quarter of the FWHM ofthe formed beams, and typically netting ∼
300 sourcecomponents2. calculate the inverse-variance-weighted mean of Stokes[Q,U] / I for the sample, providing an initial estimate ofthe local polarisation leakage, which will be a ff ectedtrue polarised sources3. calculate the standardized residuals (SRs) of Stokes[Q,U] / I from the initial leakage estimate for each source ornax cluster magnetic fields / I value lies awayfrom the initial leakage estimate in both the positive andnegative directions4. identify sources whose SR falls in the upper and lower5% of the SR distribution, and remove these from sub-sequent calculations. These ∼
30 source componentsare assumed to be genuinely polarised sources (i.e. theirpolarisation is inconsistent with the leakage model). Theremaining ensemble of sources are assumed to be po-larised only insomuch as they are a ff ected by the localpolarisation leakage, which will be roughly similar inmanner and degree, and can therefore provide a reason-able estimate of such.5. perform step (2) again with the trimmed sample, whichresults in our final estimate of the local polarisationleakage at the coordinate location in questionThe resulting maps for Stokes I → Q and I → U polarisationleakage over the full ASKAP beam footprint are shown inFigure 13. Before highlighting the salient features of thesemaps, we first describe a set of simulations that we undertookto assess the accuracy of our estimates and methods. Thesimulator was set up to answer the following question: Fora given grid location in our mosaic, and given (a) specifiedStokes I → [ Q , U ] leakage value, (b) a randomly generatedpopulation of sources with realistic distributions of Stokes I , Q , and U values and fractional polarisations, (c) the sen-sitivity of our observations, and (d) the leakage estimationprotocol described above, what is the resulting distributionin the derived leakage values for 10,000 independent reali-sations of the simulation? The results were that our medianestimated leakage value was almost identical to the specifiedinput value (0 . × the specified input value, to be precise),while the standard deviation was 0.5% — that is, the uncer-tainty on the fractional leakage maps in Figure 13 is ∼ . ff set by 45 ◦ for Stokes q andu), which is characteristic of linear feeds. In the body of themosaic, the leakage is typically less than 1%, though valuesof up to 2% are commonly observed in isolated regions, andcan become as severe as 5% for a handful of sources. Weeliminated leakage-dominated sources from our sample asdescribed in Section 2. h m m m m m -32°-34°-36°-38° Right Ascension (J2000) D e c li n a t i o n ( J ) h m m m m m -32°-34°-36°-38° Right Ascension (J2000) D e c li n a t i o n ( J ) F r a c t i o n a l l e a k a g e F r a c t i o n a l l e a k a g e Figure 13.
Position-dependent Stokes I → Q (top) and I → U (bottom)leakage maps, derived as described in the main text. The centre of the Fornaxcluster is indicated with a red cross-hair. The white dashed circle indicatesan angular radius of one degree, the smaller of the two white dotted circlesindicates the 705 kpc (1 . ◦ ) virial radius of the cluster, and the larger of thetwo white dotted circles indicates 3 . ◦ distance from the centre of the mosaic.We do not consider sources in the main analysis of this paper, in order toreject regions of large I → U leakage from the corner beams. The white dotsare the formed beam centres. For reference, the half-width-at-half-maximumof the formed beams is approximately equal to the separation of the beamcentres (see Figure 2). C. S. Anderson et al.
B DETAILS OF THE BINNING EXPERIMENTFROM SECTION 5.2
For the equal-area annular binning experiment described inSection 5.2, the bin radii cannot be calculated analytically,because some of the annuli overlap truncated regions nearthe edge of our mosaic (see Sections 2 and 3). Therefore, tosimplify the experiment, and to ensure that the annular bound-ing radii were as uniformly spaced as possible, we started byselecting an appropriate sub-set of our sample. Consider thefollowing logical statements about the possible locations ofsources in our mosaic. A source may be: (1) located outside aprojected cluster-centric radius of 10 arcminutes, (2) locatedoutside a projected cluster-centric radius of 10 arcminutes,but inside a cluster-centric radius of 1.014 degrees (corre-sponding to the first π square degree annulus), (3) locatedoutside a cluster-centric radius of 1.014 degrees, (4) locatedeastward of the western-most source satisfying condition 2above, (5) located northward of the southern-most sourcesatisfying condition 2 above, (6) located in the southeastquadrant relative to the cluster centre. We selected sourcesfor this experiment satisfying the following logical combina-tion of these conditions: (1 and 2) or ( (3 and 4 and 5) andnot 6). The positions of the selected sources, and the NVSSand GLEAM sources also used in the experiment, are shownin Figure 14. Note that condition 1 ensures that we excludeknown Fornax cluster sources from the analysis, and thatthese selection criteria were applied after, and in addition to,the selection criteria described in Sections 2 and 3.Next, we calculated the bin radii corresponding to an ef-fective (i.e. post-spatial-truncation) enclosed area of π squaredegrees in each annulus. We did so by generating a densegrid of 10 points over the entire mosaic area, being randomin location but uniform in their average spatial density. Wethen applied the same spatial truncations to these points as tothe sample. By tallying up these random points, it is trivialto define the bin radii corresponding to the desired π squaredegree e ff ective bin areas. The resulting bounding radii forthe annular bins are located 0.167, 1.014, 1.737, 2.324, 2.826,3.313, 3.764 and 4.309 degrees from the cluster centre, andare shown in Figure 14.The outcome of the experiments depend on the confidenceintervals plotted in Figure 10. Note that our aim is to establishwhether the observed properties of sources behind the clusterdi ff er significantly from those of the broader radio sourcepopulation, based on our estimates of the mean and varianceof the latter. We are not trying to estimate the characteristicsof the broader radio source population from the statistics inour individual π square degree annuli, nor the probabilitythat the measurements in each bin could fluctuate towardsthe expectation value of the broader radio population. There-fore, the appropriate confidence intervals are attached to thesky model, not to the individual data points (for which theobserved counts, median and sum have zero or negligibleuncertainties for the purpose of this analysis), and it is thedegree to which the latter fall outside the former that provide D e c [ d e g ] Figure 14.
Locations of the sources and bins used in the experiment de-scribed in Section 5.2 and Appendix B. Dots indicate the locations of po-larised ASKAP (large red), polarised NVSS (medium blue), and GLEAM(small green) sources after the spatial truncations described in this appendix.The black dashed lines indicate the locations of the annular bins, each in-corporating an e ff ective area of π square degrees (with the exception of thecentral and outer bins, which are not included in the analysis). The red ‘x’indicates the position of the Fornax cluster centre. the measure of statistical significance which is appropriatefor our aims.We estimated the expectation values and confidence inter-vals for the broader population statistics di ff erently dependingon the statistic in question. For the polarised source counts(plotted in the uppermost panel in Figure 10), we assume theprobability distribution corresponds to a spatial Poisson pointprocess with an expected source count of 27 polarised sourcesper square-degree — this value being the average polarisedsource density outside 2 degrees radius from the cluster cen-tre. The confidence intervals then follow from the standardproperties of Poisson processes. For the sums and mediansof the polarised and total flux in each annular bin (middleand lower panels of Figure 10), we derived the confidenceintervals from a bootstrap analysis of our full sample. Thatis, we randomly select (with replacement) 10 independentsub-samples of 76 radio sources — the number of polarisedsources closer than 1 degree to the cluster centre — situatedfurther than 2 degrees from the cluster centre in the mosaic.The relevant confidence intervals follow from the percentilesof these data. Ideally, we should also impose the constraintthat each sample be taken from a contiguous π square degreearea, but our mosaic is too small to provide a su ffi cient num-ber of independent samples for this purpose. Moreover, wecaution that our mosaic region may not be representative ofthe broader extragalactic sky, which would a ff ect our calcu-lated confidence intervals. Future ASKAP surveys are neededto provide crucial new information about the global clusteringproperties of radio sources, particularly in polarisation, at thiscombination of survey depth, resolution, and frequency (seeSections 6.7 and 7). ornax cluster magnetic fields REFERENCES
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