Observations of the galaxy cluster CIZA J2242.8+5301 with the Sardinia Radio Telescope
F. Loi, M. Murgia, F. Govoni, V. Vacca, L. Feretti, G. Giovannini, E. Carretti, F. Gastaldello, M. Girardi, F. Vazza, R. Concu, A. Melis, R. Paladino, S. Poppi, G. Valente, W. Boschin, T.E. Clarke, S. Colafrancesco, T. Enßlin, C. Ferrari, F. de Gasperin, L. Gregorini, M. Johnston-Hollitt, H. Junklewitz, E. Orrù, P. Parma, R. Perley, G.B Taylor
aa r X i v : . [ a s t r o - ph . C O ] A ug MNRAS , 1–20 (2017) Preprint 30 July 2018 Compiled using MNRAS L A TEX style file v3.0
Observations of the galaxy cluster CIZA J2242.8 + F. Loi, , ⋆ M. Murgia, F. Govoni, V. Vacca, L. Feretti, G. Giovannini, , E. Carretti, F. Gastaldello, M. Girardi, , F. Vazza, , R. Concu, A. Melis, R. Paladino, S. Poppi, G. Valente, , W. Boschin, , , T.E. Clarke, S. Colafrancesco, T. Enßlin, C. Ferrari, F. de Gasperin, L. Gregorini, M. Johnston-Hollitt, , H. Junklewitz, E. Orrù, P. Parma, R. Perley, G.B Taylor, INAF-Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius (CA), Italy Dipartimento di Fisica, University of Cagliari, Strada Prov.le Monserrato-Sestu Km 0.700,I-09042 Monserrato (CA), Italy INAF - Istituto di Radioastronomia, Via Gobetti 101, I–40129 Bologna, Italy Dip. di Fisica e Astronomia, Università degli Studi Bologna, Viale Berti Pichat 6 /
2, I–40127 Bologna, Italy INAF - IASF Milano, Via Bassini 15, I-20133 Milano, Italy Dip. di Fisica dell’Università degli Studi di Trieste - Sezione di Astronomia, via Tiepolo 11, I-34143 Trieste, Italy INAF - Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34143 Trieste, Italy Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029, Hamburg, Germany Agenzia Spaziale Italiana (ASI), Roma Fundación G. Galilei - INAF TNG, Rambla J. A. Fernández Pérez 7, E-38712 Breña Baja (La Palma), Spain Instituto de Astrofísica de Canarias, C / Vía Láctea s / n, E-38205 La Laguna (Tenerife), Spain Dep. de Astrofísica, Univ. de La Laguna, Av. del Astrofísico Francisco Sánchez s / n, E-38205 La Laguna (Tenerife), Spain Naval Research Laboratory, Washington, District of Columbia 20375, USA School of Physics, University of the Witwatersrand, Private Bag 3, 2050, Johannesburg, South Africa Max Planck Institut für Astrophysik, Karl-Schwarzschild-Str.1, 85740 Garching, Germany Laboratoire Lagrange, UCA, OCA, CNRS, Blvd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France University of Leiden, Rapenburg 70, 2311 EZ Leiden, the Netherlands Peripety Scientific Ltd., PO Box11355 Manners Street, Wellington, 6142, New Zealand School of Chemical & Physical Sciences, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand Argelander-Institut für Astronomie, Auf dem Hügel 71 D-53121 Bonn, Germany ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801, USA Department of Physics and Astronomy, University of New Mexico, Albuquerque NM, 87131, USA
Accepted XXX. Received YYY; in original form ZZZ © F. Loi et al.
ABSTRACT
We observed the galaxy cluster CIZA J2242.8 + ′ , 2.9 ′ and 1 ′ respectively. These single-dish data were also combined with archival inter-ferometric observations at 1.4 and 1.7 GHz. From the combined images, we measured a fluxdensity of S . = (158 . ± .
6) mJy for the central radio halo and S . = (126 ±
8) mJyand S . = (11 . ± .
7) mJy for the northern and the southern relic respectively. After thespectral modelling of the discrete sources, we measured at 6.6 GHz S . = (17 . ± .
2) mJyand S . = (0 . ± .
3) mJy for the northern and southern relic respectively. Assuming sim-ple di ff usive shock acceleration, we interpret measurements of the northern relic with a con-tinuous injection model represented by a broken power-law. This yields an injection spectralindex α inj = . ± . = . ± .
9, consistent with recent X-ray esti-mates. Unlike other studies of the same object, no significant steepening of the relic radioemission is seen in data up to 8.35 GHz. By fitting the southern relic spectrum with a simplepower-law (S ν ∝ ν − α ) we obtained a spectral index α ≈ . ≈ .
8) in agreement with X-ray estimates. Finally, we evaluated the rotation measure ofthe northern relic at 6.6 GHz. These results provide new insights on the magnetic structureof the relic, but further observations are needed to clarify the nature of the observed Faradayrotation.
Key words: galaxies: clusters: intracluster medium – magnetic fields – acceleration of parti-cles
In the standard scenario of hierarchical formation of the Universelarge-scale structures form and grow through merger events involv-ing dark matter dominated clumps like galaxy clusters and galaxygroups. An example of these processes are gravitational driven col-lisions between two sub-clusters of galaxies that end up with theformation of a more massive galaxy cluster. Such merging eventsrepresent the most spectacular and energetic processes since theBig Bang: they can release enormous amounts of energy in the in-tracluster medium (ICM), as much as & erg (Sarazin 2002).In these environments some galaxy clusters show di ff usesynchrotron radio sources called radio haloes and relics (e.g.,Feretti et al. 2012) found at the centre and at the periphery of thecluster respectively. These sources are not associated with specificoptical counterparts so they reveal the existence of a non-thermalcomponent in the ICM made up of relativistic particles and mag-netic fields spread over the cluster volume (e.g., Carilli & Taylor2002). Radio haloes and relics have a typical size of ∼ ∼ . − µ Jy / arcsec at 1.4 GHz) and aresteep-spectrum ( α & + ∼ − ⋆ E-mail: fl[email protected] discontinuities in the temperature and surface brightness distribu-tions inferred from X-ray observations of galaxy clusters. In par-ticular, Enßlin et al. (1998) proposed a di ff usive shock accelerationmechanism (DSA, Drury 1983) to explain the re-acceleration ofrelativistic particles in relics. This mechanism does not put con-straints on the nature of the injected relativistic particles. In thisrespect, recent observations are consistent with a scenario in whichold electrons from nearby radio galaxies are re-accelerated throughthe DSA mechanism (e.g., Bonafede et al. 2014; van Weeren et al.2017). However, a single acceleration of thermal electrons byshocks or a combination of acceleration and re-acceleration havebeen shown to produce quite similar results in a few specific cases(e.g., Kang & Ryu 2016). Radio observations of relics are also im-portant to understand the evolution of large scale magnetic fields.Shock waves amplify the fields to µ G-levels and align the mag-netic field with the shock plane, as predicted by the aforemen-tioned models and observed in terms of strong linearly-polarizedsynchrotron emission associated with relics. Relics are usually ob-served at low frequencies with interferometers. However, due tothe fact that interferometers are only sensitive to angular scales ac-cording to their minimum baseline length, single-dish telescopesare essential for the study of di ff use radio sources, especially athigh frequencies (Emerson 2002). There are many examples ofsingle-dish telescopes being used to investigate di ff use radio relicsand haloes in literature (Farnsworth et al. 2013; Carretti et al. 2013;Kierdorf et al. 2016).The Sardinia Radio Telescope (SRT) is a new 64-m single-dish radio telescope, designed to operate in the frequency range0.3-116 GHz, and currently working between 0.3 and 26 GHz(Bolli et al. 2015; Prandoni et al. 2017). It has recently been suc-cessful in spectro-polarimetric observations of galaxy clusters(Murgia et al. 2016). In this paper we present the SRT observationsof the galaxy cluster CIZA J2242.8 + , 1–20 (2017) bservations of CIZA J2242.8 + observed CJ2242 with the SRT at 1.4 GHz, 6.6 GHz and 19 GHzas part of of the early science project SRT Multi-frequency ob-servations of galaxy clusters (SMOG, project code S0001, PI M.Murgia). The SMOG program consists of wide-band and wide-field spectral-polarimetric observations of a sample of galaxy clus-ters (Govoni et al. 2017). The aim of the project is to improve ourknowledge of the non-thermal components (relativistic particlesand magnetic fields) of the ICM on large scale and to shed lighton the interplay between these components and the life-cycles ofcluster radio galaxies. This can be done through the comparison ofSRT observations with radio observations at higher resolution andat di ff erent frequencies, and with observations in the mm, sub-mm,optical and X-ray.The galaxy cluster CJ2242 has been included in the SMOGsample because it is an interesting case of system hosting a faintcentral halo and a double relic system (van Weeren et al. 2010) andit is located at a relatively low redshift of z = ff use radio emission easily exceeds 15 ′ , makingsingle-dish observations with the SRT essential to measure theemission at all relevant angular scales.The paper is organized as follows. In Section 2, we briefly il-lustrate the current knowledge about this cluster. In Section 3, wedescribe the details of the observations, the data reduction and theimaging of CJ2242 with the L-band, C-band and K-band receiversof the SRT. Total intensity images are shown in Section 4, where weinclude the combination of single-dish and interferometric maps at1.4 GHz for the galaxy cluster. We also estimate the flux densityof the di ff use and discrete sources and their spectral behaviour. InSection 5 we present the linearly-polarized emission and the appli-cation of the rotation measure synthesis technique to C-Band ob-servations. Finally, the conclusions are presented in Section 6.Throughout this paper we assume a Λ CDM cosmology withH = · s − Mpc − , Ω m = . Ω Λ = .
73. At the redshift ofCJ2242, 1 ′ corresponds to 189.9 kpc. + The galaxy cluster CJ2242 was discovered with X-rays byKocevski et al. (2007) during a survey aiming at finding new clus-ter candidates at low Galactic latitudes (l = = − = X = . × ergs − ) in the energy band 0.1 − ∼ ∼
55 kpc and located 1.5 Mpc from the centre ofthe cluster. The radio morphology, together with the spectral indexgradient of the northern relic toward the cluster centre, have beeninterpreted as signatures of acceleration and spectral aging of rela-tivistic electrons due to the passage of a shock. Assuming the DSAmodel they found a Mach number M ∼ . ◦ ) between two sub-clusters with a massratio of 2:1 (confirmed by Okabe et al. 2015 using gravitationallensing) and an impact parameter .
400 kpc. The core passage ofthe sub-clusters likely happened about 1 Gyr ago (van Weeren et al.2011). Association of the relics with shock fronts has been confirmedfrom Suzaku observations - Akamatsu & Kawahara (2013) mea-sured a drop in temperature at the position of the northern relic,while the jump in the X-rays surface brightness was not detected,probably because of resolution limits. However, even with the high-est spatial resolution X-ray data available (i.e. the Chandra data,Ogrean et al. 2014), the surface brightness discontinuity is still notdetected. This aspect is very peculiar since at these high Machnumbers (M ∼ ff ects can be invoked but the optical analysis by(Dawson et al. 2015) points to the systems being in a nearly plane-of-the-sky merger configuration. Evidence for shock compressioneast of the southern relic has been observed with XMM-Newtonby Ogrean et al. (2013). Recent estimates (Akamatsu et al. 2015)of temperature drops from Suzaku observations suggest a Machnumber M ∼ ∼ ∼ α = α = ff ected by the Sunyaev − Zel`dovich e ff ect (see Basu et al.2016). These aspects have been taken into account in a recent workwhere the relic has been studied with single-dish observations con-ducted with the E ff elsberg telescope (Kierdorf et al. 2016). Theyinferred a relic spectral index α = (0 . ± .
04) between 150 MHzand 8.35 GHz and suggest that models describing the origin ofrelics have to include e ff ects beyond the DSA mechanism that re-quires α >
1, in order to physically model the relic. Similar findingshave been reported for the cluster A2256 by Trasatti et al. (2015).From this picture, it is clear how new, accurate high frequency ob-servations and estimates of the flux density of the northern relic areimportant to constrain the physical scenario of CJ2242.
We observed the galaxy cluster CJ2242 at the SRT in three fre-quency ranges: L-band (1.3-1.8 GHz), C-band (6-7.2 GHz) and K-band (18-20 GHz). L-band and C-band observations were centred
MNRAS , 1–20 (2017)
F. Loi et al.
Table 1.
Details of the observations of the galaxy cluster CIZA J2242.8 + [GHz] FWHM [ ′ ] FOV OTF scan axis Calibrators TOS [h]
08 Jul 2016 L-Band 1.3-1.8 14 3 ◦ × ◦ × RA + × DEC 3C147 2.212 Jul 2016 L-Band 1.3-1.8 14 3 ◦ × ◦ × RA + × DEC 3C147 2.206 Feb 2016 C-Band 6.0-7.2 2.9 1 ◦ × ◦ × RA + × DEC 3C286, 3C84 2.301 Jun 2016 C-Band 6.0-7.2 2.9 1 ◦ × ◦ × RA + × DEC 3C48, 3C84 2.524 Jun 2016 C-Band 6.0-7.2 2.9 30 ′ × ′ × RA + × DEC 3C138, 3C48, 3C84 4.226 Jun 2016 C-Band 6.0-7.2 2.9 30 ′ × ′ × RA + × DEC 3C138, 3C48, 3C84 5
Table 2.
Details of the observations of some discrete sources, in the field of view of the galaxy cluster CIZA J2242.8 + ′ . Columns report from left to right: the source name, the source J2000 coordinates, the field of view (FOV) of the scans, the number of the cross scans, thecalibrators used for the data reduction.Source RA [ h m s ] DEC [ ◦ ′ ′′ ] FOV Cross Scans CalibratorsA 22 43 38.027 +
53 09 19.47 6 ′ x6 ′
20 3C147B 22 42 44.666 +
53 08 04.98 6 ′ x6 ′
21 3C147C 22 43 17.995 +
53 07 19.84 6 ′ x6 ′
22 3C147D 22 42 48.004 +
53 05 34.99 6 ′ x6 ′
23 3C147E 22 42 53.000 +
53 04 50.00 6 ′ x6 ′
11 3C147G 22 42 51.338 +
53 00 35.00 6 ′ x6 ′
23 3C147H 22 42 04.820 +
52 59 34.39 6 ′ x6 ′
11 3C147 at the J2000 coordinates RA 22 h m s and DEC + ◦ ′ ′′ ,while K-band observations were centred on individual galaxies ofthe system. The details of the observations are reported in Table 1(L, C-band observations) and Table 2 (K-band observations).We acquired spectral-polarimetric data in full-Stokes parameterswith the SArdinia Roach2-based Digital Architecture for Radio As-tronomy back-end (SARDARA, Melis et al. in prep.) for the L andC-band observations, while for the K-band observations only totalintensity continuum observations were performed. For the data re-duction and the imaging we used the proprietary software packageSingle-dish Spectral-polarimetry Software (SCUBE, Murgia et al.2016). In the following we describe, for each band, the observa-tional set up and the procedure adopted for the data reduction andimaging. L-Band
We observed an area of 3 ◦ × ◦ with the entire 1.3 − ′ at a frequencyof 1.55 GHz. We performed several On-The-Fly (OTF) maps inequatorial coordinates along the two orthogonal directions of RAand DEC. The telescope scanning speed was set to 6 ′ / s and thescans were separated by 3.5 ′ to properly sample the SRT beam.We recorded the data stream by sampling at 10 spectra per secondthereby producing individual samples separated by 36 ′′ along thescanning direction.For our purposes, we calibrated only the total intensity. Band-passand flux density calibration were performed by observing 3C 147assuming the flux density scale of Perley & Butler (2013). Thosefrequency windows a ff ected by persistent radio-frequency interfer-ence (RFI) were flagged by hand. We also applied an automatic flagging procedure to excise the large amount of RFI randomlyspread in frequency and time. The flagged data were then used torepeat the baseline subtraction, bandpass, and flux density calibra-tion. At these frequencies, the gain-elevation curve can be assumedto be flat and therefore we did not apply any correction.We subtracted the baseline of the OTF maps of CJ2242, scan byscan, by fitting 10% of the data at the beginning and at the end ofeach scan. We projected the data in a regular 3-dimensional gridwith a spatial resolution of 180 ′′ / pixel. We then applied the au-tomatic flag procedure on the target and we repeated the baselinesubtraction and the projection. In total, we discarded about 30% ofthe data. The total intensity image of CJ2242 is obtained by stack-ing all the calibrated OTF maps. In the combination the individualimage cubes were averaged and de-striped by mixing their station-ary wavelet transform (SWT) coe ffi cients. Coe ffi cients on a spatialscale below 2 pixels were omitted in order to improve the signal-to-noise ratio without degrading the resolution. For further detailssee Murgia et al. (2016). C-Band
We decided to make a shallow and a deep map, over a field of viewof 1 ◦ × ◦ and 30 ′ × ′ , respectively. We used a 1.2 GHz band-width centred at 6.6 GHz. We acquired full-Stokes parameters ina bandwidth of 1500 MHz with the SARDARA back-end, with1024 channels of 1.46 MHz each. The beam FWHM at 6.6 GHzis 2.9 ′ . We performed several OTF maps setting a spacing betweenthe scans of 0.7 ′ using a scan rate of 6 ′ / s for the shallow map and3 ′ / s for the deep map. We acquired 33 spectra per second, there-fore, on the sky, the spatial separation between individual samplesalong the scanning direction was 10.9 ′′ and 5.45 ′′ , for the shallowand the deep maps respectively.We calibrated the band-pass and the flux density by observing3C 286, 3C 48 or 3C 138, depending on availability for each obser- MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + vation, assuming the flux density scale of Perley & Butler (2013).We removed RFI observed in a cold part of the sky and we repeatedthe calibration and RFI-flagging procedure until all the obvious RFIwas removed. Then, we applied the gain-elevation curve correctionto take into account the gain variations with elevation due to thetelescope structure’s gravitational stress change. For the polariza-tion we first corrected the delay between right and left polarizationof the receiver by using 3C 286, 3C 138 or 3C48. Next we used3C 84 to correct the instrumental polarization, and finally we cor-rected the absolute position of the polarization angle using 3C 286,3C 138 or 3C48.We subtracted the baseline of each scan of the OTF map of CJ2242.To take into account the presence of bright sources at the edge ofthe images we decided to refine the baseline removal from eachimage cube using a mask. The mask has been obtained from theobservation of CJ2242 at 1.4 GHz with the NRAO VLA Sky Sur-vey (NVSS, Condon et al. 1998): after a convolution of the mapwith the SRT beam we blanked all the pixels where the signal waslarger than 1 σ ( σ = / beam), in order to keep just the noiseregions. We proceeded by fitting the baseline of our images witha second order polynomial, excluding the blanked regions in themask. In this way, we could evaluate and subtract the noise moree ffi ciently. We flagged the remaining RFI and then we repeated thebaseline removal. The fraction of flagged data is ∼ ′′ / pixel. Afterwards, we stacked together all the RA-DECscans to obtain full-Stokes I, U, and Q cubes. In the combinationthe individual image cubes were averaged and de-stripped by mix-ing their SWT coe ffi cients. Coe ffi cients on a spatial scale below 2pixels were omitted to improve the signal-to-noise ratio without de-grading the resolution. The polarized intensity P and the observedpolarization angle Ψ were obtained from the U and Q maps by ap-plying the relation P = p Q + U and Ψ = . · arctan(U / Q). Thepolarization maps were corrected for the positive bias introducedwhen combining U and Q images (see Appendix B in Killeen et al.1986).
K-Band
At 19 GHz, the di ff use emission of CJ2242 is very faint becauseof its steep spectrum. For instance, to detect the northern relic at19 GHz with a S / N =
3, we would need to reach a sensitivity levelof σ = / beam in the SRT images. Even with the SRT K-bandmulti-feed, this would require more than 100 hours of exposuretime, too much to fit within the time allocated to the SMOG pro-gram.Indeed, the K-band observations were aimed at characterizing thespectral behaviour of a few discrete sources embedded in the dif-fuse emission of the galaxy cluster CJ2242. In this way we can havean accurate estimate of their flux densities at 6.6 GHz and disentan-gle the discrete and the di ff use emission of CJ2242 (see 4.3.2).We performed total intensity continuum observations, using a to-tal bandwidth of 2 GHz centred on 19 GHz, at which the FWHMis ∼ ′ . The coordinates of the cross-scans observations and otherdetails are reported in Table 2.After the baseline subtraction from each cross scan we calibratedthe flux density with 3C 147 corrected for the atmosphere opac-ity and the gain variation with elevation. We used sky-dip observa-tions to infer the opacity τ . The opacity during our observations was τ ≃ ′′ / pixel and we stacked all the cross scans together to improve the signal-to-noise ratio. We fitted the crossscans with a 2-dimensional Gaussian to derive the high frequencyflux density. The results obtained from the L-band observations of CJ2242are shown in Figure 1 (top panel): contours start at 3 σ with σ =
20 mJy / beam and colours refer to the NVSS image of the clus-ter. The central emission belongs to the galaxy cluster CJ2242. Inthe SRT image we note two additional features. About one de-gree north of CJ2242 we see a di ff use arc-shaped structure whichis likely due to a blending of discrete radio sources. North-eastof CJ2242, at ∼
10 Mpc from the cluster centre, we detect an ex-tended “L-shaped” structure which appears in the NVSS as a clus-tering of several point-like sources. In the bottom panel of Figure1 we show a zoomed figure including this extended structure andCJ2242. Colours refer to the X-ray image taken from the ROSATAll-Sky Survey (RASS, Trümper 1993) in the 0.1-2.4 keV band,corrected for the background, divided by the exposure map, andsmoothed with a Gaussian of σ = ′′ . We overlaid the SRT con-tours in blue and those from NVSS in black. The SRT L-shapedstructure seems to connect a few spots of X-ray emission: (1) onthe west side, the closest to CJ2242, hosts at its centre an NVSSsource; (2) another source, which is seen at the southern tip of theextended L-shaped structure, is somewhat fainter and overlaps inprojection with several NVSS sources.We wondered if the spatial coincidence between the radio and X-ray emission may possibly indicate the presence of one or moregalaxy clusters, nearby to CJ2242. The association with high hard-ness ratios of sources in the ROSAT Bright Source Catalogue(BSC, Voges et al. 1999) and in the Faint Source Catalogue (FSC),coupled with the presence of an optical over-density or Sunyaev-Zel`dovich (SZ) signal, is a good indication of the presence of acluster (e.g. Ebeling et al. 2002; Planck Collaboration et al. 2013).A bright source with a high hardness ratio, associated with opti-cal over-density, is the selection criterion of the CIZA catalogueitself (Kocevski et al. 2007, and references therein). This criteriacan be extended to faint sources (Ebeling et al. 2013). The sourceclosest to CJ2242 (labelled S1 in Sect. 4.2.1) is associated withthe FSC source 1RXS J224504.3 + ± + ± We combined our single-dish map together with interferometricmaps from Stroe et al. (2013), available online , taken withthe WSRT at 1.4 and 1.7 GHz. Data were collected in the fre-quency ranges between 1.303 − − . ′′ × . ′′ and15 . ′′ × . ′′ at 1.4 GHz and 1.7 GHz respectively. Theirsensitivity is σ = µ Jy / beam at 1.4 GHz and σ = µ Jy / beam at http: // vizier.cfa.harvard.edu / viz-bin / VizieR?-source = J / A + A / / A110MNRAS , 1–20 (2017)
F. Loi et al.
22 35 0022 40 0022 45 0022 50 0052 00 0053 00 0054 00 00 RIGHT ASCENSION (J2000) D E C L I N A T I O N ( J ) D E C L I N A T I O N ( J ) Figure 1.
Top:
NVSS image overlaid with the SRT total intensity contours of the galaxy cluster CIZA J2242.8 + ◦ x3 ◦ . The FWHM beam is 14 ′ and is shown in bottom-left corner. The noise level is 20mJy / beam. Contours start at 3 σ -level and increase by a factor of √ σ ) drawn in orange. Bottom:
A zoomed version including theL-shaped structure (see text) and CJ2242 is shown. The SRT contours in blue and the NVSS contours in black are overlaid on the X-ray image taken from theRASS in the 0.1-2.4 keV band. MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + Figure 2.
Results of the single-dish interferometer combination: on the left we show the WSRT maps at 1.4 GHz (top) and 1.7 GHz (bottom) taken fromStroe et al. (2013) and on the right the WSRT and SRT combination maps. Contours start at 3 σ -level, where σ = µ Jy / beam at 1.4 GHz and σ = µ Jy / beamat 1.7 GHz, and increase by a factor of √
2. Negative contours (-3 σ ) are drawn in orange. The beam sizes of the images are 20 . ′′ × . ′′ at 1.4 GHz and15 . ′′ × . ′′ at 1.7 GHz. ff use emission in CJ2242 (radio halo and relics) exceeds 15 ′ . Themaximum structure that can be recovered by the WSRT at L-band,given the minimum baseline of b min =
36 m between the antennasof the array, is about 16 ′ for a source at the zenith. As a result, a fraction of the flux density from the radio halo and the relics couldhave been missed by the WSRT, due to the lack of information inthe inner portion of the (u , v)-plane. The single-dish SRT L-bandimage does not su ff er from this limitation, since structures as largeas the angular scale of the SRT image are retained (3 degrees).Therefore we combined the SRT with the WSRT images to MNRAS , 1–20 (2017)
F. Loi et al. reconstruct the correct large scale structure while preserving theangular resolution of the interferometric observations (see e.g.Stanimirovic et al. 1999).We did this in the image plane using the SCUBE softwarepackage, in a similar way as the Astronomical Image ProcessingSystem (AIPS) task IMERG or the Miriad (Sault et al. 1995) taskIMMERGE. In particular, we used the WSRT images which arealready corrected for the primary beam attenuation. These imagesconsist of a single pointing and are blanked outside a circularregion of 55.3 ′ and 45 ′ , at 1.4 and 1.7 GHz, respectively. Weextracted two smaller sub-bands from the full SRT bandwidth(1.3 − ff erent resolution of the twoinstruments, we deconvolved the images, by dividing both of themby the Fourier transforms of the corresponding Gaussian beams,before calculating the scaling factor.Due to the superior signal-to-noise ratio the scaling factor wascalculated at 1.7 GHz. The required adjustment resulted in ascaling-up factor for the SRT image of 1.23 that we also applied tothe SRT 1.4 GHz image. After this scaling the two power spectrawere merged using a weighted sum of the Fourier transforms.For the single-dish observations, data weights are set to 0 for allwave-numbers larger than the outer ring of the annulus, while theyare set to 1 in the inner portion of the Fourier plane. In the annulusthe weights linearly vary from 0 to 1. The interferometric data areweighted in a similar way but with swapped values for the weights.The combined Fourier spectrum was then tapered by multiplyingby the transform of the interferometer beam. The combined image,obtained by the anti-transform, has the same angular resolution ofthe original WSRT image and includes the large scale structuresdetected by the SRT.Results are shown in Figure 2: at left we present the WSRTmaps at 1.4 GHz (top) and 1.7 GHz (bottom) and on the rightwe show the WSRT and SRT combined maps. Contours startat 3 σ -level. Thanks to the combination we can recover the fluxdensity associated with the di ff use sources of the galaxy clusterCJ2242, revealing a greater extension of the central radio halo,especially at 1.4 GHz. At 1.7 GHz we do not see a significantenhancement of the radio halo emission. This could be consis-tent with the fact that typically these sources have a steep spec-trum ( α = h I . i = h I . i × . ff erent beam areas of the two instruments. At 1.4 GHz, h I . i ∼ . × σ . that implies h I . i ∼ .
074 mJy / beam.Thus, in order to detect the radio halo at 1.7 GHz, we would need anoise level of σ = µ Jy / beam, lower than the rms of the image. Figure 3.
This image shows the area we considered to measure the flux ofthe di ff use sources hosted by CIZA J2242.8 + ff use sources We measured the flux density of the di ff use emission of the galaxycluster CJ2242 at 1.4 GHz using the combination of SRT andWSRT data.As we do not observe radio halo emission in the WSRT 1.7 GHzimage of Figure 2 at the 3 σ -level we used this image to blank thestrong sources in the field of CJ2242 from the 1.4 GHz images. Weended up with an image where the discrete sources and the relicsare blanked as shown by blue contours in Figure 3.In this image black represents the emission above the 3 σ -level ofthe combined map at 1.4 GHz. We assumed that this is the extentof the radio halo and that the relics are located inside the redcontours. We defined the northern relic region by taking all thosepixels inside the same area considered by Stroe et al. (2016) inFigure A1 with a flux density greater than 5 σ , excluding obviousdiscrete sources. The southern relic emission is fainter than thatof the northern relic. Thus, to isolate the southern relic from theradio halo, we used a stronger limit in flux by drawing a 8 σ -levelcontour around the relic. We used the black area outside the bluecontours (equivalent to ∼
451 times the beam area) to evaluate amean surface brightness of the radio halo. Then, we multiplied thisvalue with the total area (equivalent to ∼
869 times the beam area),as we assume that the halo extends even in the relic regions andthat of the discrete sources.We found that the radio halo hosted by CJ2242 has a total fluxdensity of S
S RT + WS RT . GHz = (158 . ± .
6) mJy. We noticed that ifwe measure with the same procedure the radio halo flux fromthe WSRT 1.4 GHz image we find S
WS RT . GHz = (115 ±
7) mJy. Inour estimates we included statistical and systematic (6% of theflux to include calibration uncertainties) errors. The northernrelic has a total flux density of S
WS RT . GHz = (121 ±
7) mJy andS
WS RT + S RT . GHz = (126 ±
8) mJy as calculated from the interferometric
MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + Figure 4.
Radio halo power at 1.4 GHz versus the cluster X-ray luminosityin the 0.1-2.4 keV band (top) and versus the largest linear size of the radiohalo measured at 1.4 GHz (bottom). Full dots are observed clusters takenfrom the literature. We added to the compilation by Feretti et al. (2012)new radio haloes in merging galaxy clusters revealed through pointed inter-ferometric observations at ≃ and combined maps respectively. Here we have subtracted thecontribution of the extended radio halo in order to take into accountonly the flux density of the northern relic. Finally, we found thatthe southern relic has a flux density S WS RT + S RT . GHz = (11 . ± .
7) mJy,a value consistent, within errors, with that calculated from theinterferometric map, S
WS RT . GHz = (11 . ± .
7) mJy.For the radio halo we find an enhancement of the flux density ofabout ∼
38% when we combine single-dish and interferometricimages, whereas for the relics we obtain no significant di ff erences.This demonstrates how the interferometer has poor sensitivity to extended and di ff use emission while it performs better with narrowstructures such as the northern relic.The statistical properties of radio haloes in galaxy clusterare important in order to understand the nature of these sources.Thanks to our measurements, we can now compare the prop-erties of CJ2242 with other clusters that host radio haloes. InFigure 4, we plot the 1.4 GHz power of the radio halo ver-sus the X-ray luminosity between 0.1 − ≃ In Figure 5 (bottom) we show the resulting total intensity contourmap in the frequency range between 6 and 7.2 GHz over a regionof 1 ◦ x1 ◦ . We reached a noise level of σ = / beam with a beamsize of 2 . ′ × . ′ . The radio contours at 6.6 GHz are overlaid onthe same X-ray image as Figure 1, taken from the RASS in the 0.1-2.4 keV band. The central cluster is bright both in the X-ray andradio band and we detected the di ff use radio emission associatedwith CJ2242.Among the external sources, marked with a letter in the image, themost interesting is S1. As already pointed out in Section 4.1.1,the X-ray emission has the right hardness ratio to be classifiedas a galaxy cluster candidate. We show in Figure 5 (top), con-tours of the 323 MHz GMRT image of Stroe et al. (2013). Thesecontours are drawn starting from 2 mJy / beam and increase by afactor of 2. Thanks to the higher resolution of the GMRT wecan appreciate the head-tail morphology of the source which isfurther indication of the presence of a dense external mediumsimilar to what is typically found in galaxy clusters. The radiocontours are overlaid on an optical Canada-France-Hawaii Tele-scope (CFHT) image , where two blue crosses indicate the po-sition of two optical galaxies: 2MASX J22445464 + ′ from S1, and 2MASX J22445565 + ′ . The galaxies have a K-band magnitude of M = (13.5 ± = (12.67 ± ∼ z ∼ . − .
2) when consid-ering the K-band magnitude-redshift relation for brightest clustergalaxies (see Fig.5 in Stott et al. 2008).Even if at the moment there are only two optical galaxies iden-tified in the vicinity of S1, this fact, together with its X-ray prop-erties and the fact that S1 is an head-tail radio source, corroboratesthe hypothesis of S1 as a cluster candidate. http: // / en / search / MNRAS , 1–20 (2017) F. Loi et al.
22 44 5022 44 5522 45 0022 45 0522 45 1053 28 0053 28 3053 29 0053 29 30 RIGHT ASCENSION (J2000) D E C L I N A T I O N ( J )
22 40 0022 42 0022 44 0022 46 0052 45 0053 00 0053 15 0053 30 00 RIGHT ASCENSION (J2000) D E C L I N A T I O N ( J ) S3 S4 S1 S2H
S6 S5
Figure 5.
Top:
CFHT optical image of S1 with the two optical galaxies indicated by the crosses and contours from the 323 MHz GMRT image that start at2 mJy / beam and increase by a factor 2. Bottom:
Shallow SRT total intensity contour image of the galaxy cluster CIZA J2242.8 + − ◦ × ◦ . The FWHM beam is 2.9 ′ and is shown in bottom-left corner. Contours start at 3 σ -level, with σ = / beam, andincrease by a factor of √
2. MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + Table 3.
Flux measurements of the sources marked in Figure 5 obtainedfrom the NVSS 1.4 GHz (Condon et al. 1998) and the SRT 6.6 GHz images(this work).Label Name S mJy1 . S mJy6 . α S1 NVSS J224455 + ± ± ± + ± ± ± + ±
11 26 ± ± + ± ± ± + ± ± ± + ± ± ± + ± ± ± In Table 3 we give the flux density of the sources identified in thefield and marked with a letter in Figure 5, measured from the NVSS1.4 GHz and the SRT 6.6 GHz images. We also calculated the spec-tral index α of the sources assuming for the flux density S ν a powerlaw behaviour with the frequency ν , S ν = S (cid:18) νν (cid:19) − α . (1)For source S1 we found α = . ± .
09 which is typical for head-tail sources as pointed out in the previous Section.
In Figure 6 we show the total intensity map resulting from all theobservations at 6.6 GHz in a field-of-view of 30 ′ × ′ centred onthe cluster centre. In this image we reached a noise level of σ = . / beam. Here the two relics are clearly detected. We characterize the spectral behaviour of the discrete sources, atless than 15 ′ from the cluster centre, by using the following multi-frequency high resolution images of the galaxies:(i) from the NRAO archive we retrieved observations from theprogram AV312 presented by van Weeren et al. (2010), which usedthe VLA in C configuration at 4835 MHz and 4885 MHz. We cali-brated data following standard procedures using the AIPS softwarepackage;(ii) we used GMRT 323 MHz, 608 MHz and WSRT 1714 MHz,2272 MHz images from Stroe et al. (2013) available online ;(iii) we included in our sample the Westerbork Northern SkySurvey (WENSS) at 325 MHz (Rengelink et al. 1997) and theNVSS at 1400 MHz (Condon et al. 1998) maps;(iv) we also added the SRT 19 GHz observations reported in Ta-ble 2.We considered the nine sources marked in Figure 7 whose flux ismixed with the di ff use sources at the SRT resolution. In this im-age colours represent the SRT total intensity image at 6.6 GHz,and contours are from the VLA 4.8 GHz contours at 5 σ -level. We http: // vizier.cfa.harvard.edu / viz-bin / VizieR?-source = J / A + A / / A110 measured the flux density of each point-like source using a two-dimensional Gaussian fit, while for the extended sources we in-tegrated the radio brightness down to the first isophote above thenoise level.In Table 4 we present the values obtained including asystematic error of 10% of the source flux, to take into accountthe di ff erent calibration scales of the images. Figure 7 showsthe resulting spectra: in each panel the corresponding sourceis indicated in the bottom left corner with red dots indicatingSRT 19 GHz measurements listed in Table 4 together with othermeasurements shown by black dots. Spectra are modelled by usingthe software SYNAGE (Murgia et al. 1999). The continuous blueline is the result of the fit using parameters as reported in the topright corner of each panel.The spectra of A, B, C, D, E, G, and I are well described bya continuous injection (CI) model (Pacholczyk 1970), where thesources are continuously and constantly replenished with new rel-ativistic electrons by the AGN and the power-law spectrum breaksdue to energy losses caused by the synchrotron radiation itselfand inverse Compton scattering with the Cosmic Microwave Back-ground (CMB) photons. The CI model includes three free param-eters: the injection spectral index, α inj , that characterizes the spec-trum below the break frequency, ν b , and the normalization. Above ν b , the high-frequency spectral index is: α h = α in j + . s , i.e. the time elapsed since the start of the injection: t s = B . ( B + B IC )[(1 + z ) ν b ] . Myr (3)where B is the magnetic field in µ G of the source and B IC isthe equivalent magnetic field due to the inverse Compton of theCMB that depends on redshift B IC = . + z) µ G. The breakfrequency is in GHz. We calculated the synchrotron age by adopt-ing the equipartition value B min for the magnetic field strength (seeEq. A.12 in Murgia et al. 2012). Since this value depends on thesource volume we derived B min and hence the age only for the ex-tended sources B, C, D, E and G. The results of the spectral mod-elling and the source ages are listed in Table 5.
Source A:
It is point-like, the spectrum is fitted by a CI-modelwith α inj = .
5, and ν b = . Source B:
The spectrum for this source is described by a CI-model, with α inj = .
43 and ν b = . min ≈ . µ G, and we deduce anage of t s =
76 Myr.
Source C:
This is a narrow-angle-tail source, seen in projectionover the northern relic. The tail, which has a linear size of 146 kpc,extends toward the north-east. We calculate for this source an ageof t s =
70 Myr.
Source D:
This source is seen in projection close to the clus-ter centre, and is slightly extended at the resolution of the VLA4.8 GHz image. The spectrum is well fit by a CI-model. We esti-mate an age of 46 Myr.
MNRAS , 1–20 (2017) F. Loi et al.
22 41 0022 42 0022 43 0022 44 0052 50 0053 00 0053 10 00 RIGHT ASCENSION (J2000) D E C L I N A T I O N ( J ) Figure 6.
Deep SRT total intensity image of the galaxy cluster CIZA J2242.8 + − ′ × ′ . The FWHM beam is 2.9 ′ and is shown in bottom-right corner. The noise level is 0.5 mJy / beam. Contours start at3 σ -level and increase by a factor of √ Table 4.
Flux density measurements obtained from the following maps: GMRT 323 MHz (Stroe et al. 2013), WENSS 325 MHz (Rengelink et al. 1997),GMRT 608 MHz (Stroe et al. 2013), NVSS 1400 MHz (Condon et al. 1998), WSRT 1714 MHz (Stroe et al. 2013), WSRT 2272 MHz (Stroe et al. 2013), VLA4835 MHz and 4885 MHz (van Weeren et al. 2010), SRT 19 GHz (this work). We report the expected flux density of each source at 6.6 GHz in the last column.
Source S mJy323MHz S mJy325MHz S mJy608MHz S mJy1 . S mJy1 . S mJy2 . S mJy4 . S mJy4 . S mJy19GHz [ S mJy6 . ] exp A 56 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
36 - 248 ±
25 - 106 ±
11 82 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
10 - - 102 ±
10 80 ± ± ± ± ± ± ± ± ± ± ± ± Source E:
This source is located in projection close to the clustercentre. Its morphology shows two bright lobes and two faint tailsextending in the N-S direction. The spectrum is fitted by a CI-modelwith ν b =
22 GHz and has an estimated age of t s =
45 Myr.
Source F:
This source is located at the Eastern tip of the north-ern relic. For this source we added the flux density measurements we derived from the 150 MHz TIFR GMRT Sky Survey (TGSS )(Intema et al. 2017) and the WSRT 153 MHz (Stroe et al. 2013)images: S = (65 ±
6) mJy and S = (67 ±
2) mJy. Theradio spectrum shows a sharp high frequency exponential cut-o ff that cannot be explained by the smooth steepening of the CI-model. This source seems to be an example of a dying source http: // tgssadr.strw.leidenuniv.nl / doku.php MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + C BDE HAF IG
Figure 7.
The image is the deep 6.6 GHz SRT total intensity map of the galaxy cluster CIZA J2242.8 + σ -level ( σ = / beam). Each plot around the image refers to the spectrum of the discrete source specified in the bottom left corner. Black points are the flux densitymeasurements from GMRT, WSRT, WENSS, NVSS and VLA images, while red points indicate the 19 GHz SRT measurements (see text for details). Thecontinuous blue line is the result of the fit whose parameters are reported in the top right corner of each panel. where the central black hole of the galaxy has stopped its activ-ity (Murgia et al. 2011). Following these authors, we fitted the ra-dio spectrum using the CI OFF model. This model assumes that theCI phase is followed by a remnant (or dying) phase during whichthe radio jets are switched o ff . In the absence of the injection ofnew electrons the sources spectrum develops an exponential highfrequency cut-o ff . By fitting the CI OFF model we derived the break frequency which gives the total source age, and t
OFF / t s , which givesthe relative duration of the dying phase. We found a total source ageof 149 Myr. The source has been in the active phase for 45 Myr andin the dying phase for 104 Myr. The morphology is relaxed, as ex-pected for dying sources, but a weak point-like core is present. Thisweak core seems however to be disconnected from the fading lobesas no jets are visible. MNRAS , 1–20 (2017) F. Loi et al.
Table 5.
Results of the spectral modelling and source ages.Source Model α inj ν b [GHz] B min [ µ G] t s [Myr]A CI 0.5 ± ± ± ± ±
36C CI 0.5 ± ± ±
24D CI 0.6 ± ± ±
22E CI 0.7 ± ±
14 10.2 45 ±
16F CI
OFF ± ±
60G CI 0.4 ± ± ±
58H SSA + PL 0.7 ± < ± ± Source F could be a potential source of seed electrons for the north-ern relic (e.g., Bonafede et al. 2014; van Weeren et al. 2017). Bylooking at the top-right panel of Figure 2 we see that the source isclose to an arc-like feature which appears to be a secondary shockor a possible extension of the northern relic, although a discontinu-ity between these two structures is present.
Source G:
This is a narrow-angle tail with a linear size of 174 kpc.The spectrum is well described by a CI model, with ν b ≈ ± · km / s, where i is the incli-nation of the source with respect to the line-of-sight. Source H:
For this source we added the flux densitymeasurement derived from the 150 MHz TGSS image:S = (5 . ± .
3) mJy. This source exhibits a spectralturn-over at low frequencies, that could be due to synchrotronself-absorption (SSA). In the optically thick part of the spectrumwe fixed the spectral index to α thick = -2.5, while we modelled theoptically thin regime using a power-law. The source is unresolvedand could be intrinsically a compact steep spectrum source wherethe break frequency is below the SSA peak: ν b « ν SSA . For thisreason the observed spectral index in the optically thin part of thespectrum is interpreted as α = α inj + . Source I:
The spectrum of this source is well fit by a CI modelwith the break at 1.5 GHz and α inj ≈ ν = ff use sources As mentioned in the introduction, single-dish telescopes can beused to accurately infer the size and flux density of di ff use sources.They are not a ff ected by the missing zero spacing problem thatplagues radio interferometers, especially at high frequency wherethe primary beam is usually smaller than the cluster size in the localUniverse. Unfortunately, the typical beam of single-dish telescopesis far larger than the beam synthesised by the interferometer, so itis di ffi cult to distinguish between di ff use and discrete sources.Thanks to the spectral modelling of the discrete sources from theprevious section we have a firm prediction of their flux densities at6.6 GHz (see last column of Table 4).We modelled these sources with Dirac delta functions normalizedto the expected fluxes. We then convolved these functions with theSRT beam and finally we subtracted the resulting image from our Table 6.
Flux density measurements of the northern relic of CIZAJ2242.8 + ν [GHz] S ν [mJy] Reference0.15 780.4 ±
80 Stroe et al. (2016)0.325 315.7 ± ±
21 This work, WENSS image0.61 222.3 ± ± ± ± ± ± ± ± ± SRT 6.6 GHz image.Figure 8 shows in grey-scale and magenta contours the total inten-sity deep image on the right and, on the left, the image with thesources subtracted, where we expect to observe the contribution ofdi ff use emission only. The noise is σ = / beam. Both imagesshow yellow contours of the combined image at 1.4 GHz presentedin Figure 2. At the 3 σ -level the northern emission seems to ex-tend beyond the strong galaxy C covering a total extension of ∼ ∼
800 kpc. However, the extra-component inthe north-east direction could be either due to a real extension ofthe northern relic or to the residual flux from source F (see noteson Sect. 4.3.2). For these reasons, and to be consistent with theother measurements (see Fig. A1 of Stroe et al. 2016), we evalu-ated the northern relic flux density inside the ellipse drawn with adashed line in Figure 8. At the 5 σ -level (a cut consistent with thatof Kierdorf et al. 2016), we found S . = (17 . ± . . = (0 . ± . σ -level. Our results regarding the flux of the northern relic are reported inTable 6 together with flux density measurements at di ff erent fre-quencies taken from literature up to 8.4 GHz. We included the valuewe inferred from the WENSS 327 MHz image after the subtractionof sources A, B and C, with the flux densities expected from ourmodels at 327 MHz.In Figure 9 we plot the values of Table 6. The red points rep-resent our measurement obtained with the SRT observations. We fitthe spectrum of the northern relic with a continuous injection model(blue line). This model takes into account the presence of relativis-tic particles injected at early stages of the shock passage that havelost their energy resulting in a break in the spectrum. From the fitwe obtain a value of the injection spectral index α inj . This value isrelated to the spectral index α h as already shown in Eq. 2.From the fit we know that the spectrum breaks at ν b = . + . − . GHzand that α inj = (0 . ± . ν >> ν b),where radiative losses are balanced by the injection of new par-ticles, the resulting spectral index is α h = (1 . ± . M = s α h + α h − MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + JY/BEAM JY/BEAM
Figure 8.
Left:
The original SRT image at 6 − + magenta contours) overlaid with the higher resolution WSRT + SRT 1.4 GHz contours(yellow).
Right:
The residual 6 − ff use emission after the subtraction of modelled discrete sources (see text for details). Again theWSRT + SRT 1.4 GHz contours are overlaid in yellow.
Figure 9.
Total flux measurements of the northern relic at di ff erent frequen-cies from Table 6. Red points are the new measurements from this paperobtained with the SRT observations. The blue line represents the continu-ous injection model fit whose parameters are shown in the top-right cornerof the image. Dot and a dashed lines have been drawn to show the flux den-sity decrement due to the SZ e ff ect as predicted for the northern relic ofCJ2242 by Basu et al. (2016) assuming M = = Figure 10.
Total flux measurements of the southern relic obtained with theSRT observations. we inferred a Mach number M = (3 . ± .
9) in agreement withinthe errors of the value M = . + . − . presented in Akamatsu et al.(2015). However, we noticed that there is not yet a clearly detectedjump in the X-ray surface brightness as expected at these Machnumbers (Donnert et al. 2017) (see discussion in Sect.2). MNRAS , 1–20 (2017) F. Loi et al.
In the frequency range probed by our observations no signifi-cant evidence of steepening in the radio spectrum is found beyondthat predicted by the CI model. From our analysis based on a widefrequency range (from 150 MHz to 8.35 GHz) we can exclude thesteepening found by Stroe et al. (2016) beyond 2.5 GHz. Moreover,we find that the continuous injection model is consistent with thedata. Thus, the physics of the northern relic of CJ2242 does notseem to require models beyond the standard DSA mechanism,although only new accurate measurements at frequencies higherthan 10 GHz can definitively exclude alternative scenarios.It should be noted that Stroe et al. (2016) presented interfer-ometric measurements at 16 GHz and 30 GHz taken with the Ar-cminute Microkelvin Imager (AMI) and with the Combined Ar-ray for Research in Millimeter-wave Astronomy (CARMA). Thesemeasurements are represented as open dots in Figure 9. We do notinclude them in our fit procedure since these measurements aremade with interferometers that could have lost a significant frac-tion of the flux density from the extended structure. Nonetheless,we compare them with the best fit of the CI model taking into ac-count the SZ decrement. Extrapolating the CI model at frequencieshigher than 10 GHz we show as a dot and dashed lines in Figure9 the SZ decrement as expected by Basu et al. (2016) for this relicassuming a Mach number of M = ∼
16 GHz. Above thisfrequency the SZ decrement is increasingly significant, but notenough to explain the measurements at 16 and 30 GHz.The observed gap could be due to a missing flux problem, aspreviously mentioned, or it could be real. In the latter case amodification from the basic CI model is required. Donnert et al.(2016) showed that a non uniform magnetic field in the regionof the relic could explain the flux densities measured at 16 and30 GHz. Future single-dish observations at frequencies higher than10 GHz, which could be obtained with the SRT 7-feed K-bandreceiver, could help to shed light on the claimed high frequencysteepening.It should be noted that the break frequency of the CI modelcorresponds to the spectral break of the oldest electron populationinjected only if the particles are confined within the volume of theradio source, and the radio spectrum is extracted from a regionthat encloses the entire emitting region. In this case, we can thinkat the CI model as the sum of all electron populations from theyoungest to the oldest ones. Below the break frequency (whereradiative losses are negligible) particles accumulate and the sourceluminosity grows linearly with time. Above the break frequencya steady state is reached and the high-frequency spectrum staysunchanged since radiative losses are compensated by the freshlyinjected particles (Kardashev 1962; Pacholczyk 1970). If themagnetic field has been constant in time and uniform in spaceinside the radio source we can use Eq. 3 to estimate the time sincethe start of the injection, provided that we know the magneticfield strength. This assumption was used to estimate the ages ofthe discrete sources embedded in the di ff use emission in Section4.3.2. However, this basic scenario needs to be modified if theconfinement time τ c of the particles inside the source is finitewhich is likely the case for relics. We can make the oversimplifiedassumption that the shocked region consists of a slab of enhancedmagnetic field strength of width l relic . Particles are acceleratedin the outer rim of the slab at the edge of the upstream regionby the shock wave and then they flow and age backwards in the downstream region. As the particles exit the slab their radioemission rapidly disappears even at low-frequencies due to thedrop in the magnetic field strength. Indeed, the confinement timeis related to the relic width by τ c = l relic / v d , where v d is the down-stream velocity. Note that a similar argument has been advocatedin Carilli et al. (1991) to explain the spectra of the hot spots inCygnus-A, where particles are injected (or re-accelerated) at thetermination shock inside the hot spots and then they back-flowinto the radio lobes. By definition, the age of the oldest electronsstill present in the relic region and that produce the spectral breakseen in the CI spectrum should be exactly τ c . The magnetic fieldstrength inside the relic is not known, however, from Eq. 3 itcan be shown that the maximum age allowed for the electronsis t max = = B IC / √ ≃ . µ G.We highlight that this value is in agreement with the minimumenergy field strength of B min = . µ G estimated by Kierdorf et al.(2016). Therefore, by assuming a the relic width l relic ≃ d > / s or M >
3. We note that this lower limitis high but still compatible, within the measurement errors, withthe Mach number derived both from the X-rays and from theDSA model (see Eq. 4). It is reasonable to assume (see Sect. 5.2)that the ambient magnetic field in the proximity of the relic isof the order of 1 µ G. Indeed, the average magnetic field strengthinside the relic region would be amplified by a factor &
2. Thisrepresents the average magnetic field strength in the compressionregion, while outside we suppose that the magnetic field drops tothe background level. The particles that flow in the de-compressedregion disappear rapidly, even at low frequencies, because of thedrop in the spectrum normalization due to the weaker magneticfield. We stress that, according to this simple scenario, the breakfrequency of the CI model is not related to the time necessary to theshock to propagate from the cluster centre to the observed position( ∼ τ c ) since the very first injected particles are notcontributing anymore to the current observable radio spectrum.We underline that in this calculation we assumed that the magneticfield strength profile is described by a simple step function. Amore detailed treatment of this issue is beyond the scope of thiswork; we refer to Donnert et al. (2016) for a more sophisticatedmodelling. These authors consider much smoother profiles for themagnetic fields after the shock (resulting from their assumptionof a small-scale dynamo in the downstream region), which resultsin a curvature for the high-frequency spectrum more pronouncedwith respect to that of the CI model.In any case, it is important to point out that a steep-spectrumpower-law behaviour is expected only if the confinement time isso long that the break frequency of the oldest population presentin the relic region shifts below the lower end of the observedwindow. Attempts to fit the spectrum with a single power-law havebeen presented in Kierdorf et al. (2016). They found for CJ2242 α = . ± .
04 which is intermediate between α inj and α h in ourfit. However, this value of spectral index leads to problematicresults since the Mach number expected by the DSA modeldiverges. We therefore opt for the CI fit, under the assumption thatthe spectral curvature is real, since the missing flux problem is neg-ligible below 1 GHz. This is confirmed by the finding that the fluxdensity of the relic before and after the single-dish-interferometriccombination is roughly the same at L-band. MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + Concerning the southern relic: we fitted our estimates of theflux density at 1.4 GHz and 6.6 GHz with a simple power-law asshown in Figure 10. Because only two experimental points wereavailable the fit of the CI model is not applicable. The southernrelic has a spectral index α ≃ . M ≃ .
8. Even in this case the value is in agreement with thatfound by Akamatsu et al. (2015) ( M = . + . − . ).After the submission of our paper we became aware ofthe work of Hoang et al. (2017) where these authors presentLow-Frequency Array (LOFAR) observations between 115.5 and179 MHz and a study of the di ff use sources of CJ2242. Assumingthe DSA model and by evaluating the injection spectral index in theupstream region, they find Mach numbers for the southern and thenorthern relics in agreement with the ones obtained from X-rays byAkamatsu et al. (2015) and consistent with our results. Figure 11 shows, on the left, the SRT 6.6 GHz linearly-polarizedintensity image of CJ2242 in colours as detected from the deepobservations (FoV = ′ × ′ ). Contours refer to the total intensityimage (Figure 6) and vectors indicate the electric-field polarization.In this image the noise-level is σ = / beam.We detect the polarized emission of the northern relic: its averagefractional polarization is of ∼ ∼ We applied the Rotation Measure (RM) Synthesis technique (Burn1966; Brentjens et al. 2005) on the linearly-polarized data pre-sented in Figure 11 in order to recover the Faraday depth of therelic.In addition to the SRT data, for which the frequency band goesfrom 6.0 GHz up to 7.2 GHz with a channel width ∼ λ coverage. We smoothed the VLA U and Q images to theSRT resolution. However, the resulting RM transfer function hasstill a quite large FWHM ( ∼ / m ) since we are observing atrelatively high frequencies. We should also consider that the angu-lar resolution of our polarized images corresponds to a linear scaleof ∼
550 kpc, which could be larger than the autocorrelation lengthof the RM fluctuations. Indeed, it is hard to distinguish multiplecomponents in the Faraday depth space and as a consequence wecannot verify if the RM originates internally to the radio relic or inan external Faraday screen. For these reasons, in what follows weassumed that the RM originates entirely in the ICM between us andthe relic and that the internal Faraday rotation is negligible. In prac-tice we considered just one polarized component in Faraday spaceand we computed its RM from the RM Synthesis by measuring theFaraday depth of the polarization peak.Figure 11 shows, on the right, the results of the RM Synthe-sis applied on pixels with a polarized S / N ratio larger than 3. The top-right panel shows the resulting Faraday depth while the bottom-right panel shows the associated uncertainty.These errors have been evaluated with a Monte Carlo simula-tion. We injected 30 di ff erent components in Faraday depth, ran-domly distributed between − / m , with inten-sities ranging from 1 mJy / beam up to 4 mJy / beam to reproduce theS / N range of the observed polarization intensity. From these val-ues we produced simulated U and Q data in the selected frequencyband (SRT C-band plus the two VLA frequencies). We fixed therelic spectral index to what found in Sect. 4.4 and we assumed aweight w ch for each frequency channel (defined as w ch = / ( σ )where σ ch is the rms of the single channel), in order to accuratelyreproduce the e ff ect of the noise on data. We used w ch = ff erence between inputand “measured” Faraday depth. As expected, the higher the S / N ra-tio the lower the rms. For a S / N = / m , but it decreases down to 7 rad / m at the position with thebrightest polarized emission (S / N = −
150 at the east end to about −
400 rad / m at the west end. At the polarization peak we foundRM = ( − ± / m . Our Faraday depth image is in goodagreement with the values obtained by Kierdorf et al. (2016), butwe observe a RM gradient of ∼
250 rad / m over an angular scaleof 10 ′ , a factor of 2 larger than the gradient inferred from that work.We estimated the Galactic RM contribution in the position ofCJ2242 using the reconstruction of Oppermann et al. (2015) thatprovides a RM gal = ( − ± / m . Therefore, despite the largeuncertainties the Faraday depth shown in Figure 11 seems to ex-ceed the Galactic contribution by at least a factor of two. Further-more one could ask if the observed RM gradient is due to a gra-dient in the foreground Galactic RM since CJ2242 is very closeto the Galactic plane (latitude b = − / m / deg are possible along the Galactic plane.In order to explain the RM gradient observed along the north-ern relic in CJ2242 we would need a very high gradient of about1500 rad / m / deg.We therefore deduce that the RM gradient is not due to theGalactic foreground. Thus, we can subtract the constant value ofRM gal = − / m , and evaluate if the residual RM could becaused by the magneto-ionic medium in the galaxy cluster itself.Following Govoni et al. (2010), and assuming a cluster magneticfield with an autocorrelation length Λ B << L, where L is the inte-gration path along the gas density distribution, the observed RMalong a line of sight is a random walk process that involves a largenumber of cells with size Λ B . The distribution of the RM will be aGaussian with zero mean and a variance: σ RM = < RM > = (812) Λ B Z L ( n e B k ) dl (5)Assuming that the cluster magnetic field follows a η -profile withrespect to the density distribution B ( r ) = B ( n e ( r ) / n ) η and that thedensity distribution follows a β -profile n ( r ) = n (1 + r / r ⊥ ) − β/ ,we obtain that the RM dispersion at a given projected distance r ⊥ MNRAS , 1–20 (2017) F. Loi et al. D E C L I N A T I O N ( J ) -350 -300 -250 -200 -150RAD/M/M10 15 20 25RAD/M/M Figure 11.
Left:
SRT linearly-polarized intensity image of the galaxy cluster CIZA J2242.8 + ′ × ′ . The FWHM beam is 2.9 ′ and is shown in bottom-right corner. The noise level is 0.35 mJy / beam.Contours refer to the total intensity image starting at the 3 σ -level and increasing by factors of √
2. The vectors indicate the electric field polarization with theorientation corresponding to the polarization angle and the length proportional to the polarization percentage where 100% is shown in the top-left corner. Thevectors are traced only for pixels with a total and linearly-polarized intensity signal higher than 3 σ and an error of the polarization angle below 10 ◦ . Right:
Result of the application of the RM Synthesis technique. The top panel on the right represents the Faraday depth we obtained for the maximum polarizedsignal. In the bottom panel we report the associated uncertainties evaluated from simulations. is: σ RM ( r ⊥ , L ) = K ( L ) B Λ / B n r / c (1 + r ⊥ r c ) β (1 + η ) − s Γ [3 β (1 + η ) − ] Γ [3 β (1 + η )] (6)where K(L) depends on the integration path along the gas densitydistribution. We assume that the northern relic is located halfwaythe cluster so that K = and n are respectively the centralvalues of the magnetic field and thermal plasma density profiles, r c is the core radius of the cluster and Γ is the gamma function. Theobserved RM image is compatible with a magnetic field tangledon a scale equal or larger than the RM structure of Figure 11,so that we can assume Λ B ∼ = − / m . Assuming reasonable valuesfor the parameters of the hot ICM (n = − cm − , β = .
6, andr c =
500 kpc), we would need a magnetic field of B = . µ G atthe cluster centre with η = . σ RM ∼ / m at the relic, where we expect B = . µ G. Wenote however that even if the central magnetic field strength isin line with what typically found at the centre of galaxy clusters(Feretti et al. 2012), the magnetic field autocorrelation length ismuch larger than what expected for the turbulent ICM. We also note that the condition Λ B << L could not be verified in our case,since the scale of the magnetic field would be comparable with thesize of the cluster.Another possibility is to consider that the Faraday rotationis occurring in a cosmic web filament which includes CJ2242.As suggested by Planck Collaboration et al. (2016) the primordialmagnetic fields have a strength not larger than a few nG. Evenassuming a thermal density of n e = − cm − and a magneticfield tangled on a scale of 1300 kpc, the resulting RM would beonly ∼ / m , making the filament contribution irrelevant.Moreover we notice that magnetic fields of the order of ∼ . µ Gin filaments should be reached only in the presence of small-scaledynamo amplification in excess of what can be presently resolvedby simulation (Vazza et al. 2015). This may be verified in thepresence of small-scale vorticity and / or plasma instabilities ofvarious kinds (e.g. Mogavero & Schekochihin 2014), which wouldhowever make the magnetic field tangled on much smaller scalesthan what is inferred by our observations.For this analysis it is clear that high resolution polarized ob-servations are needed to clarify the nature of the observed Fara- MNRAS , 1–20 (2017) bservations of CIZA J2242.8 + day rotation in CJ2242. For instance the forthcoming Wester-bork Observations of the Deep APERTIF Northern-Sky (WODAN,Röttgering et al. 2011) project will give us a polarized image of thenorthern sky. The high resolution and sensitivity of this survey willmake it possible to better investigate the RM observed in the regioncovered by the galaxy cluster CJ2242 and will help to constrain theproperties of the intracluster magnetic field. We observed the galaxy cluster CIZA J2242.8 + ff use radio emission.We conducted observations in three frequency bands centred at1.4 GHz, 6.6 GHz and 19 GHz. These single-dish data were alsocombined with archival interferometric observations at 1.4 and1.7 GHz taken with WSRT.From the single-dish-interferometer combined imageswe measured a flux density of S . = (158 . ± . . = (131 ± . = (11 . ± . . = (19 . ± . . = (0 . ± . ff usive shock acceleration we interpretthe measurements of the northern relic with a continuous injec-tion model, represented by a broken power-law. This gave usan injection spectral index α inj = . ± . α = . ± .
1, resulting in a Mach number M = . ± .
9, consistentwith the recent X-ray estimates. No significant steepening of therelic radio emission beyond 2.5 GHz is seen in the data up to8.35 GHz. By fitting with a simple power-law spectrum (S ν ∝ ν − α )the measurements of the southern relic, we obtained a spectral in-dex α = . ± .
7, corresponding to a Mach number M = . ± . + ± + ± + ′ we also found thegalaxy 2MASX J22445565 + ∼ − ∼ − ff in the integratedspectrum and on the relaxed morphology. This finding confirmsthe tendency for these rare radio sources to be preferentially foundin the dense environment of galaxy clusters (Murgia et al. 2011).We notice that the dying source is close to an arc-like featurewhich appears to be a secondary shock or a possible extensionof the northern relic, although a discontinuity between these twostructures is present. The remnant lobes could be a source of seedelectrons for the relic shock-wave, a possibility that has alreadybeen suggested in the case of other galaxy clusters (Bonafede et al.2014; van Weeren et al. 2017).Finally, we evaluated the rotation measure of the northernrelic by applying the RM Synthesis technique at the 6.6 GHz data.The Faraday depth image shows negative values with a gradientalong the relic length from about −
150 at the east end to about − / m at the west end. At the polarization peak we foundRM = ( − ± / m . Our Faraday depth image is in goodagreement with that obtained by Kierdorf et al. (2016). We derivethe presence of a RM gradient of ∼ / m over an angularscale of 10 ′ , a factor of 2 larger than the gradient inferred in thatwork. These results provide insights on the magnetic field structureof the ICM surrounding the relic, but further observations areneeded to clarify the nature of the observed Faraday rotation.In conclusion, this study demonstrates that single dish obser-vations can be helpful to properly study the di ff use emission ingalaxy clusters, especially when used in combination with inter-ferometric observation at higher resolution. Future observations atfrequencies higher than 10 GHz could be obtained with the newSRT 7-feed K-band receiver, and could play a decisive role to con-straining the physics of relic sources, and helping to distinguishbetween the di ff erent acceleration models proposed to explain theorigin of the relativistic electrons. ACKNOWLEDGEMENTS
We thank an anonymous referee for her / his comments and sugges-tions which helped us to improve this paper. The Sardinia RadioTelescope (Bolli et al. 2015; Prandoni et al. 2017) is funded by theMinistry of Education, University and Research (MIUR), ItalianSpace Agency (ASI), the Autonomous Region of Sardinia (RAS)and INAF itself and is operated as National Facility by the Na-tional Institute for Astrophysics (INAF). The development of theSARDARA back-end has been funded by the Autonomous Regionof Sardinia (RAS) using resources from the Regional Law 7 / MNRAS , 1–20 (2017) F. Loi et al. ity l.3.1.). This research was partially supported by PRIN-INAF2014. The National Radio Astronomy Observatory (NRAO) is afacility of the National Science Foundation, operated under coop-erative agreement by Associated Universities, Inc. This researchmade use of the NASA / IPAC Extragalactic Database (NED) whichis operated by the Jet Propulsion Laboratory, California Instituteof Technology, under contract with the National Aeronautics andSpace Administration. Basic research in radio astronomy at theNaval Research Laboratory is funded by 6.1 Base funding. Thisresearch was supported by the DFG Forschengruppe 1254 Mag-netisation of Interstellar and Intergalactic Media: The Prospects ofLow-Frequency Radio Observations. F. Vazza acknowledges fund-ing from the European Union’s Horizon 2020 research and inno-vation programme under the Marie-Sklodowska-Curie grant agree-ment No 664931. This publication makes use of data products fromthe Two Micron All Sky Survey, which is a joint project of the Uni-versity of Massachusetts and the Infrared Processing and AnalysisCenter / California Institute of Technology, funded by the NationalAeronautics and Space Administration and the National ScienceFoundation.
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