Radio multifrequency observations of galaxy clusters. The Abell 399-401 pair
C. D. Nunhokee, G. Bernardi, S. Manti, F. Govoni, A. Bonafede, T. Venturi, D. Dallacasa, M. Murgia, E. Orrú, R. F. Pizzo, O. M. Smirnov, V. Vacca
MMNRAS , 1–10 (2020) Preprint 8 February 2021 Compiled using MNRAS L A TEX style file v3.0
Radio multifrequency observations of galaxy clusters. The Abell 399 − C. D. Nunhokee ★ , G. Bernardi , , , S. Manti , F. Govoni , A. Bonafede , , T. Venturi ,D. Dallacasa , , M. Murgia , E. Orrú , R.F. Pizzo , O.M. Smirnov , and V. Vacca Department of Astronomy, University of California, Berkeley, CA INAF - Istituto di Radioastronomia, via Gobetti 101, 40129 Bologna, Italy Department of Physics and Electronics, Rhodes University, PO Box 94, Grahamstown, 6140, South Africa South African Radio Astronomy Observatory, Black River Park, 2 Fir Street, Observatory, Cape Town, 7925, South Africa Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy INAF - Osservatorio Astronomico di Cagliari Via della Scienza 5, I-09047 Selargius (CA), Italy Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy ASTRON, Netherlands Institute for Radio Astronomy, PO Box 2, 7990 AA Dwingeloo, The Netherlan
ABSTRACT
Galaxy clusters are assembled via merging of smaller structures, in a process that generates shocks and turbulence in the intracluster medium and produces radio emission in the form of halos and relics. The cluster pair A 399 − A 401 represents a specialcase: both clusters host a radio halo and recent LOFAR observations at 140 MHz revealed the presence of a radio bridgeconnecting the two clusters and two candidate relics, one South of A 399 and the other in between the two clusters in proximityof a shock front detected in X-ray observations. In this paper we present Westerbork observations at 1.7, 1.4 and 1.2 GHz and346 MHz of the A 399 − A 401 cluster pair. We detected the radio halo in the A 399 cluster at 346 MHz, extending up to ∼
650 kpcand with a 125 ± 𝛼 = . ± .
05, and 𝛼 = . ± .
14 respectively. The two candidate relics are also seen at 346 MHz and we determinedtheir spectral index to be 𝛼 = . ± .
14 and 𝛼 = . ± .
14. The low surface brightness bridge connecting the two clusters isbelow the noise level at 346 MHz, therefore we constrained the bridge average spectral to be steep, i.e. 𝛼 > . 𝜎 confidencelevel. This result favours the scenario where dynamically-induced turbulence is a viable mechanism to reaccelerate a populationof mildly relativistic particles and amplify magnetic fields even in cluster bridges, i.e. on scales of a few Mpcs. Key words: galaxies: clusters: general - galaxies: clusters: individual: Abell 399 - radio continuum: general
Clusters of galaxies are located at the nodes of the cosmic web andformed by subsequent merging of smaller structures. These mergerevents are likely accelerating particles and amplifying magnetic fieldsin the intra-cluster medium, generating diffuse radio sources observedin clusters like radio halos and relics (see Brunetti & Jones 2014; vanWeeren et al. 2019, for recent reviews on the topic). Although it islargely accepted that radio halos are generated by merger-induced tur-bulence (e.g., Cassano & Brunetti 2005; Brunetti & Lazarian 2016;Pinzke et al. 2017) and radio relics by shocks (e.g., Hoeft & Brüggen2007; Kang & Ryu 2016), several questions on the acceleration ef-ficiency and, therefore, the details of the re-acceleration mechanismremain still open (e.g., Brunetti 2016; Wittor et al. 2017).The A 399 − A 401 pair holds a special position in the cluster land-scape. It is a local pair ( 𝑧 = . 𝑧 = . ∼ . × M (cid:12) and 9 . × M (cid:12) respectively, with ★ email: [email protected] similar gas temperatures, 𝑘𝑇 ≈ . × − cm − gas density (Bonjean et al. 2018).At radio wavelengths, both clusters host a radio halo whose inte-grated flux density at 1.4 GHz is 𝑆 = . 𝑆 = . ∼
570 kpc,whereas the A 401 halo has a more irregular morphology and extendsup to ∼
350 kpc. This pair was the target of recent, deep LOFARobservations at 140 MHz (Govoni et al. 2019) that detected bothradio halos, extending up to 970 kpc and 800 kpc respectively. Theseobservations also revealed a series of diffuse emission features notvisible at GHz frequencies, in particular, they revealed a bridge ofradio emission connecting the two radio halos, providing the firstevidence of relativistic particles and magnetic fields on a few Mpc © a r X i v : . [ a s t r o - ph . C O ] F e b C. D. Nunhokee et al.
Figure 1.
Monochromatic 𝑢𝑣 coverage at 346 MHz, including all the sixconfigurations. The two gaps are due to antenna 5 that was missing acrossall the observations. The low declination of the cluster pair results in a fairlyellipsoidal 𝑢𝑣 coverage, which, in turns, results in a limited resolution alongdeclination (Table 1). scales, at distances greater than the cluster virial radius (together withthe A 1758 double system; Botteon et al. 2018, 2020).Radio emission on such large scales may be due to a distribu-tion of weak shocks that fill the bridge volume and reaccelerate apreexisting population of mildly relativistic particles (Govoni et al.2019). Conversely, Brunetti & Vazza (2020) propose an alternativescenario where acceleration happens via second order Fermi mecha-nisms: relativistic particles scatter with magnetic field lines diffusingin super-Alfvenic turbulence which also amplifies magnetic fields. Inthis case, steep-spectrum synchrotron emission can be generated inthe entire intra-cluster bridge region. Spectral index measurements ofthe bridge emission are therefore necessary to understand the particleacceleration mechanism in action here.In this paper we present observations at 1.7, 1.4, 1.2 GHz and346 MHz (18, 21, 25 and 92 cm respectively) of the A 399-A 401cluster pair, aimed to characterize the spectral properties of their dif-fuse radio emission. The paper is organized as follows: observationsand data reduction are described in Section 2, the spectral analysisis presented in Section 3 and conclusions are offered in Section 4.Throughout the paper we used the Planck cosmology (Planck Col-laboration et al. 2020), where 1 (cid:48)(cid:48) = .
345 kpc at the distance of thecluster pair.
Observations were carried out with the Westerbork Synthesis RadioTelescope (WSRT) at four frequencies centred at 1.7, 1.4, 1.2 GHzand 346 MHz. The WSRT is an aperture synthesis array composedof 14 dishes with a diameter of 25 m, arranged on an east-west track,that uses the Earth rotation to fill the 𝑢𝑣 plane in a 12 hour synthesisobservation. Ten telescopes have a fixed location, and are spaced bya distance of 144 m whereas the four remaining dishes (identifiedwith the A, B, C and D letters respectively) can be moved along tworail tracks to provide different array configurations.Observations were conducted during night time in December 2010 for the 1.7 and 1.4 GHz bands and in November 2011 for the 1.2 GHzand 346 MHz bands. The so called Maxi-Short configuration wasused for both the 1.7 and 1.4 GHz observations with the aim to pro-vide good sensitivity to extended structures with dense 𝑢𝑣 coveragebetween 36 and 2760 m baselines. Four different configurations wereused at 1200 MHz where the four movable telescopes were movedby 18 m increments, from 36 to 90 m, therefore pushing the gratinglobe out to a radius of ∼ ◦ . Six configurations were used for the346 MHz observations, with the four movable telescopes stepped at12 m increments and the shortest spacing ran from 36 to 96 m. Thisprovided continuous 𝑢𝑣 coverage with baselines ranging from 36 to2760 m (Figure 1). Table 1 presents the details of the observing setup.Each observing run included a ∼
20 minute observation of a cal-ibration source. The absolute flux calibration was set to the Scaife& Heald (2012) scale using observations of 3C48 at 1.7, 1.4 and1.2 GHz and 3C295 at 346 MHz. The observed polarization calibra-tor was DA240. Data were initially tapered using a Hanning window;the edges of each sub-band were discarded and Radio FrequencyInterference (RFI) were identified and flagged using the AOFlaggerpackage (Offringa et al. 2010). Data were further reduced using theCASA software and integrated with routines specifically developedfor calibration of WSRT data (Bernardi et al. 2009, 2010).The reduction of the 1.7 GHz data can be summarized by thefollowing steps. An initial bandpass calibration was derived fromobservations of 3C48 and applied to the target field. A dirty imagewas generated by Fourier transforming the visibilities. All the subbands were combined together using the multifrequency synthesisalgorithm with uniform weights. The dirty image was then decon-volved using the Cotton–Schwab algorithm down to a threshold of0.1 mJy beam − , corresponding to the first negative model compo-nent. Such model was used for self–calibration where antenna basedphase solutions were computed every minute. Self–calibration solu-tions were applied to the data and further flagging was performed onthe residual visibilities. A new dirty image was then generated anddeconvolved down to a final threshold of 80 𝜇 Jy beam − .The reduction of the 1.4 GHz and the 1.2 GHz band data wascarried out in a similar fashion. At 1.4 GHz, the deconvolution andself–calibration followed the same path as the 1.7 GHz band reduc-tion, with phase solutions computed every minute. The final imagewas deconvolved down to a 0.15 mJy beam − threshold. At 1.2 GHz,all the four configurations and the eight sub bands were combinedsimultaneously using the multifrequency synthesis algorithm. Thedeconvolution and self–calibration then followed the same path asthe 1.7 GHz band reduction, with phase solutions computed everyminute. The final image was obtained after deconvolution down to a2 mJy beam − threshold.At 346 MHz the initial bandpass calibration was derived fromobservations of 3C295 for each night and applied to the data. All thesix configurations and eight sub bands were imaged jointly using themultifrequency synthesis algorithm. The subsequent deconvolutionand self–calibration followed the same path as the 1.7 GHz bandreduction but with phase solutions computed every 10 seconds. Thefinal image was obtained after deconvolution down to a 3 mJy beam − threshold.The system noise between the calibrator and the target field can http://casa.nrao.eduMNRAS000
20 minute observation of a cal-ibration source. The absolute flux calibration was set to the Scaife& Heald (2012) scale using observations of 3C48 at 1.7, 1.4 and1.2 GHz and 3C295 at 346 MHz. The observed polarization calibra-tor was DA240. Data were initially tapered using a Hanning window;the edges of each sub-band were discarded and Radio FrequencyInterference (RFI) were identified and flagged using the AOFlaggerpackage (Offringa et al. 2010). Data were further reduced using theCASA software and integrated with routines specifically developedfor calibration of WSRT data (Bernardi et al. 2009, 2010).The reduction of the 1.7 GHz data can be summarized by thefollowing steps. An initial bandpass calibration was derived fromobservations of 3C48 and applied to the target field. A dirty imagewas generated by Fourier transforming the visibilities. All the subbands were combined together using the multifrequency synthesisalgorithm with uniform weights. The dirty image was then decon-volved using the Cotton–Schwab algorithm down to a threshold of0.1 mJy beam − , corresponding to the first negative model compo-nent. Such model was used for self–calibration where antenna basedphase solutions were computed every minute. Self–calibration solu-tions were applied to the data and further flagging was performed onthe residual visibilities. A new dirty image was then generated anddeconvolved down to a final threshold of 80 𝜇 Jy beam − .The reduction of the 1.4 GHz and the 1.2 GHz band data wascarried out in a similar fashion. At 1.4 GHz, the deconvolution andself–calibration followed the same path as the 1.7 GHz band reduc-tion, with phase solutions computed every minute. The final imagewas deconvolved down to a 0.15 mJy beam − threshold. At 1.2 GHz,all the four configurations and the eight sub bands were combinedsimultaneously using the multifrequency synthesis algorithm. Thedeconvolution and self–calibration then followed the same path asthe 1.7 GHz band reduction, with phase solutions computed everyminute. The final image was obtained after deconvolution down to a2 mJy beam − threshold.At 346 MHz the initial bandpass calibration was derived fromobservations of 3C295 for each night and applied to the data. All thesix configurations and eight sub bands were imaged jointly using themultifrequency synthesis algorithm. The subsequent deconvolutionand self–calibration followed the same path as the 1.7 GHz bandreduction but with phase solutions computed every 10 seconds. Thefinal image was obtained after deconvolution down to a 3 mJy beam − threshold.The system noise between the calibrator and the target field can http://casa.nrao.eduMNRAS000 , 1–10 (2020) he Abell 399-401 pair Figure 2.
346 MHz WSRT contours overlaid on the 1.4 GHz VLA image (Murgia et al. 2010) of the A 399 − A 401 complex. Neither image was corrected forthe primary beam. The 1.4 GHz image original resolution 45 (cid:48)(cid:48) × (cid:48)(cid:48) was smoothed down to the WSRT resolution of 205 (cid:48)(cid:48) × (cid:48)(cid:48) . Contours are drawn at -4 𝜎 (dashed, where 𝜎 is the noise rms reported in Table 1), 4 𝜎 and spaced by √ 𝜎 , after which they are spaced by 2. The A 399 radio halo is clearlyvisible. Other than the two clusters, labels indicate diffuse sources 𝑑 and 𝑓 , identified at 140 MHz (Govoni et al. 2019). Yellow dashed circles indicates the1.5 Mpc virial radius, similar for both clusters (Sakelliou & Ponman 2004). vary significantly at low frequencies and cannot be safely calibratedusing the WSRT online loop gain system due to the RFI contami-nation. We estimated these variations by calculating the total powerratio between 3C295 and the target field in clean areas of the spec-trum (e.g., Brentjens 2008; Pizzo & de Bruyn 2009; Bernardi et al.2009). We found the ratio to be ∼
5% averaged over the 346 MHzband and the visibility data were corrected accordingly.Polarization calibration was carried out in the same way regardlessof the observing frequency. Leakage corrections were determinedusing the unpolarized calibrator for every sub band at each observingfrequency. The unknown phase offset between the two orthogonalpolarizations was determined from the polarized calibrator. Since3C286 and DA240 have rotation measures RM = 0 (Perley & Butler 2013) and 3.3 rad m − (Brentjens 2008) respectively, we correctedthe phase difference by rotating the polarization vector in the planedefined by the Stokes 𝑈 − 𝑉 parameters in order to minimize theStokes 𝑉 flux density, where the direction of the rotation needs to beconsistent with the source RM (e.g, Brentjens 2008; Bernardi et al.2010). In this paper we focus on the total intensity results and leavethe polarization analysis for the future. The 346 MHz image is shown in Figure 2 overlaid on the Murgiaet al. (2010) 1.4 GHz VLA image. The WSRT observation wascentred on the A 399 cluster, whereas the VLA observation was the
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Table 1.
Observational details. Each observing band is divided into 8 contiguous sub bands. Noise levels are calculated at the edge of the field of view wherethe primary beam attenuates the intrinsic sky emission.Reference wavelength Frequency range Channel width Integration time Synthesized beam Noise rms(cm) (GHz) (MHz) (hours) (arcsec) (mJy beam − )18 1 . − .
79 1.17 12 53 × . − .
46 1.17 12 53 ×
11 0.05925 1 . − .
29 1.17 4 ×
12 58 ×
12 0.06392 0 . − .
38 0.156 6 ×
12 205 ×
43 1.2
Figure 3.
Zoom into the A 399 radio halo (from Figure 2). Contours at346 MHz are drawn at 4.8 (4 𝜎 ), 9.6, 13, 18 and 20 mJy beam − respectivelyand overlaid on the 1.4 GHz VLA image (Murgia et al. 2010). combination of two pointings centred on each cluster respectively.Sources away from the A 399 cluster, which is detected with highsignificance (see also Figure 3), are therefore attenuated by the WSRTprimary beam. The central ∼
10 arcmin WSRT images at 1.2, 1.4and 1.7 GHz are shown in Figures 4 and 5 respectively. Our 1 . − . ∼
650 kpc, somewhat more extended than at 1.4 GHz ( ∼
570 kpc). Murgia et al. (2010) identified three compact sources withinthe halo, named A (RA
J2000 = h m s , DEC J2000 = ◦ (cid:48) (cid:48)(cid:48) ), B(RA J2000 = h m s , DEC J2000 = ◦ (cid:48) (cid:48)(cid:48) ) and C (RA J2000 = h m s , DEC J2000 = ◦ (cid:48) (cid:48)(cid:48) ) respectively. After the 1.4 GHzVLA image was convolved to match the coarser WSRT resolution,sources A and B remain visible whereas source C, the faintest, isnot. At 346 MHz, however, source B completely disappears whereassource A is clearly detected with an emission tail extending for ∼ 𝜎 contour) is 125 ± J2000 = h m s , DEC J2000 = ◦ (cid:48) (cid:48)(cid:48) ) and (RA J2000 = h m s , DEC J2000 = ◦ (cid:48) (cid:48)(cid:48) ) respectively,whereas there is no clear emission where the 1.4 GHz halo is detected- likely due to the sensitivity drop away from the pointing centre. Figure 7 shows the 140 MHz observations (Govoni et al. 2019)overlaid on our 346 MHz image, with a zoom into the A 399 radiohalo in Figure 8. The halo appears more extended at 140 MHz andits morphology more regular. Discrete sources embedded in the haloand visible at 1.4 GHz do not appear visible in the 140 MHz imageand the peak of the halo brightness distribution is offset by ∼ 𝑢𝑣 -coverage up to 1 ◦ scales, a spectral index map of the A 399 radiohalo was derived between 1.4 GHz, 346 MHz and 140 MHz. For thispurpose, the 346 MHz and 140 MHz images were convolved at thesame resolution of 205 (cid:48)(cid:48) × (cid:48)(cid:48) .We calculated spectral index uncertainty maps Δ 𝛼 as: Δ 𝛼 ( 𝑥, 𝑦 ) = √︄(cid:18) 𝜎 𝜈 𝑆 𝜈 ( 𝑥, 𝑦 ) (cid:19) + (cid:18) 𝜎 𝜈 𝑆 𝜈 ( 𝑥, 𝑦 ) (cid:19) ln 𝜈 𝜈 (1)where ( 𝑥, 𝑦 ) indicate the pixel of the map, 𝜈 = ( , ) MHzand 𝜈 = ( , ) MHz respectively, and 𝜎 is the uncertaintycalculated as the quadrature sum of the image noise map and theabsolute flux density calibration uncertainty, assumed to be 1%, 5%and 15% at 1.4 GHz, 346 MHz and 140 MHz respectively. Thespectral index distributions and their relative uncertainties are shownin Figure 9 and Figure 10.Spectral index distributions appear somewhat different between thetwo frequencies. Between 140 MHz and 346 MHz, the spectral indexappears in the 1 . < 𝛼 < < 𝛼 < 𝛼 = . ± .
04 between 346 MHz and 1.4 GHz and 𝛼 = . ± . 𝛼 ∼ . − . 𝛼 ∼ . − . We used the notation 𝑆 𝜈 ∝ 𝜈 − 𝛼 , where 𝑆 𝜈 is the flux density at thefrequency 𝜈 .MNRAS000
04 between 346 MHz and 1.4 GHz and 𝛼 = . ± . 𝛼 ∼ . − . 𝛼 ∼ . − . We used the notation 𝑆 𝜈 ∝ 𝜈 − 𝛼 , where 𝑆 𝜈 is the flux density at thefrequency 𝜈 .MNRAS000 , 1–10 (2020) he Abell 399-401 pair Figure 4.
346 MHz WSRT contours at an angular resolution of 205 (cid:48)(cid:48) × (cid:48)(cid:48) overlaid on the 1.7 GHz (left) and 1.4 GHz (right) WSRT images centred on theA 399 cluster and with a synthesized beam of 53 (cid:48)(cid:48) × (cid:48)(cid:48) and 53 (cid:48)(cid:48) × (cid:48)(cid:48) respectively. Contours are the same as Figure 2. No evident emission corresponding tothe 346 MHz radio halo contours is visible. Figure 5.
Same as Figure 4, but for the 1.2 GHz WSRT image.
As mentioned in the introduction, Govoni et al. (2019) detecteda bridge of radio emission connecting A 339 and A 401 with a ∼ . average surface brightness at 140 MHz. The pres-ence of radio emission produces by relativistic particles on scales ofa few Mpc poses a question on their acceleration mechanism. Dueto synchrotron and inverse Compton losses, the particle life time at Figure 6.
346 MHz (black) and 1.4 GHz (white) VLA contours overlaid on theA 401 X–ray image. 346 MHz contours are drawn at 4.8 and 9.6 mJy beam − and 1.4 GHz contours are drawn at 240 and 960 𝜇 Jy beam − respectively.The 1.4 GHz image was smoothed down to 346 MHz angular resolution205 (cid:48)(cid:48) × (cid:48)(cid:48) .
140 MHz is of the order of 10 years (Govoni et al. 2019), thereforeparticles can only travel one tenth of the bridge extension in their lifetime, requiring a mechanism of in situ particle acceleration. Gov-oni et al. (2019) investigated diffuse shock acceleration, normallyconsidered responsible for radio emission from cluster relics. Theyfound that shock acceleration of thermal electrons would not be suf-ficiently efficient to achieve the observed emissivity levels, however,re-acceleration of a pre-existing population of mildly relativistic elec-trons by a population of weak shocks (Mach number of the order of2 −
3) that fills the bridge volume may be able to produce the observedradio emission. In this case, the spectral index of the bridge wouldbe 𝛼 ∼ . − .
3, similar to that observed in relics. Our 346 MHz
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C. D. Nunhokee et al. (f)(d)
A 399A 401
Figure 7.
140 MHz contours (Govoni et al. 2019) overlaid on the 346 MHz WSRT image. The resolution of the 140 MHz image is 72 (cid:48)(cid:48) × (cid:48)(cid:48) . The first contouris drawn at 1 mJy beam − , increasing by a factor of 2. Labels are same as Figure 2. Arrows indicate the synchrotron bridge connecting both clusters. observations offer the opportunity to constrain the bridge spectralindex and, potentially, discriminate between particle re-accelerationmechanisms.The comparison between the 140 MHz and the 346 MHz images(Figure 7), shows no evidence of the bridge emission at 346 MHz. Asthe bridge is an extended, low surface brightness region, the simpleimage rms does not represent a reliable estimate of the upper limit onits flux density as it would be for point sources. We therefore adopteda procedure similar to the one used to quantify upper limits on theradio halo flux density in cluster observations (e.g., Venturi et al.2007; Kale et al. 2015; Bernardi et al. 2016) in order to set an upperlimit on the bridge flux density at 346 MHz, which, conversely, turnsinto a lower limit on its spectral index: • we first selected the model image of the bridge emission fromthe LOFAR image at 𝜈 =
140 MHz. It consists of the emissionabove the 3 𝜎 contour in a 2 × • the bridge model image was extrapolated to 𝜈 = [ , , , , , , ] MHz, corresponding to the cen-tral frequencies of the WSRT spectral windows, using a single spec-tral index: 𝑆 𝑚,𝜈 ( 𝑥, 𝑦, 𝛼 ) = 𝑆 𝑚,𝜈 ( 𝑥, 𝑦 ) (cid:18) 𝜈 𝜈 (cid:19) − 𝛼 , (2)where 𝑆 𝑚,𝜈 is the flux density of the model image at the frequency 𝜈 and position ( 𝑥, 𝑦 ) . The extrapolated model images were attenuatedusing the WSRT primary beam model (e.g., Bernardi et al. 2010); MNRAS000
140 MHz. It consists of the emissionabove the 3 𝜎 contour in a 2 × • the bridge model image was extrapolated to 𝜈 = [ , , , , , , ] MHz, corresponding to the cen-tral frequencies of the WSRT spectral windows, using a single spec-tral index: 𝑆 𝑚,𝜈 ( 𝑥, 𝑦, 𝛼 ) = 𝑆 𝑚,𝜈 ( 𝑥, 𝑦 ) (cid:18) 𝜈 𝜈 (cid:19) − 𝛼 , (2)where 𝑆 𝑚,𝜈 is the flux density of the model image at the frequency 𝜈 and position ( 𝑥, 𝑦 ) . The extrapolated model images were attenuatedusing the WSRT primary beam model (e.g., Bernardi et al. 2010); MNRAS000 , 1–10 (2020) he Abell 399-401 pair Figure 8.
140 MHz contours of the A 399 radio halo (Govoni et al. 2019)overlaid on the 346 MHz image (Figure 2). The first contour is drawn at1.5 mJy beam − , with other contours spaced by a factor of 2. The halo at140 MHz extends further than at 346 MHz, and has a more round morphology. • The primary beam-attenuated model images were Fourier trans-formed into visibilities, added to the calibrated visibilities, then im-aged and deconvolved following the same procedure described inSection 2. This procedure takes care of the proper sampling of thebridge emission by the WSRT 𝑢𝑣 -coverage. We introduced the ratio 𝑅 ( 𝛼 ) : 𝑅 ( 𝛼 ) = (cid:205) 𝑁𝑥,𝑦 = 𝑆 𝑤 ( 𝑥, 𝑦 ) (cid:205) 𝑁𝑥,𝑦 = 𝑆 𝑤 ( 𝑥, 𝑦 ) + 𝑆 𝑚,𝜈 ( 𝑥, 𝑦, 𝛼 ) , (3)where 𝑆 𝑤 is the 346 MHz image (Figure 4) and 𝑁 is the total num-ber of pixels of the model image. The numerator of equation 3 isessentially the flux density calculated over the bridge area from the346 MHz image and the denominator is flux density of the 346 MHzimage after the bridge model was added to (“injected" into) the visi-bilities. We notice that 𝑅 ( 𝛼 ) is a monotonically decreasing functionof 𝛼 : lim 𝛼 →∞ 𝑅 ( 𝛼 ) =
1, i.e. in the limit of no bridge emission “in-jected", the ratio is unity. Conversely, for lim 𝛼 →−∞ 𝑅 ( 𝛼 ) = +∞ , i.e.the ratio diverges when the bridge is much brighter than the imageemission. This means that there must exist a spectral index value 𝛼 𝑟 for which 𝑅 ( 𝛼 𝑟 ) is significantly greater than one, i.e. the injectedhalo is detectable above the noise of the 346 MHz observations.Spectral indices greater than 𝛼 𝑟 are all consistent with the 346 MHzobservations, i.e. 𝛼 𝑟 represents a spectral index lower limit; • we determined the spectral index lower limit by calculating 𝑅 ( 𝛼 ) for 0 < 𝛼 <
5, with Δ 𝛼 = .
25 steps, and constructing itscumulative distribution function 𝑃 ( 𝑅 < 𝑟 ) normalized to unit areaover the chosen interval. For 𝑟 =
15, corresponding to 𝛼 𝑟 = . 𝑃 ( 𝑅 < ) = 𝛼 𝑟 < .
5. Inother words, if the spectral index were flatter 𝛼 𝑟 < .
5, we wouldexpect to measure an flux density excess in the 346 MHz image witha 95% (or greater) significance. Given no detection at 346 MHz, thisresult sets a lower limit on the spectral index of the bridge 𝛼 > . 𝜎 confidence level.Govoni et al. (2019) also detected two diffuse sources with no obviousoptical counterpart - sources 𝑑 and 𝑓 in Figure 7 -, suggesting thatthey could either be relics or faint radio galaxies with switched- off tails. The presence of an X-ray shock (Akamatsu et al. 2017)in the proximity of source 𝑑 , would support the relic hypothesis- at least for that source. Both sources are visible at 346 MHz,with a similar morphology compared to the 140 MHz (Figure 12and 13). Source 𝑑 is somewhat resolved in two brightness peaks at346 MHz, and the interconnecting region appears to be at the noiselevel. We integrated the brightness distribution at 346 MHz above the5 𝜎 contour at 140 MHz and obtained flux densities 𝑆 = ± 𝑆 = ± d and f respectively, yielding steepspectral indices 𝛼 = . ± .
14 (source d ) and 𝛼 = . ± . f ). We presented radio observations of the A 399–A 401 cluster pair at1.7, 1.4, 1.2 GHz and 346 MHz with the WSRT telescope, focusedon the analysis of the diffuse radio emission. This cluster pair is asomewhat unique case in the literature: it appears to be a system in itsearly merging state, connected by a 3 Mpc-long mass filament witha 4 . × − cm − density. Both clusters host a radio halo, detectedat 1.4 GHz (Murgia et al. 2010) and 140 MHz (Govoni et al. 2019).Observations at 140 MHz also reveal the presence of a low surfacebrightness radio bridge connecting both clusters as well as other twodiffuse features that may be either switched-off tail radio galaxies orrelics.Our observations at GHz frequencies are not sufficiently deep toimprove the existing radio halo images at 1.4 GHz. At 346 MHzwe detected the A 399 radio halo at high significance, with a 125 ± ∼ 𝛼 = . ± .
04 and 𝛼 = . ± . 𝛼 = . ± .
14 (source d ) and 𝛼 = . ± . f ). We found some evidence of spectral index steepeningin the direction parallel to the sources rather than transversal, moreindicative of a dying galaxy rather than a relic. Any more conclusivestudy will require higher resolution observations.The bridge is not visible in the 346 MHz data and we used them,together with the 140 MHz observations, to set a constraints on theaverage spectral index of the bridge through the “injection" method.We found a lower limit on the spectral index to be 𝛼 > . 𝜎 confidence level. Such steep spectral index values cannot be easilyexplained by diffusive shock acceleration even if an initial popula-tion of mildly relativistic electrons is assumed (Govoni et al. 2019),and, instead, is more aligned with the expectations of second or-der Fermi mechanisms where particles are accelerated and magneticfields amplified by turbulence (Brunetti & Vazza 2020). MNRAS , 1–10 (2020)
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Figure 9.
Left: 1.4 GHz contours (Murgia et al. 2010) overlaid on the radio spectral index map. Right: Same as left panel, but overlaid on the radio spectralindex error map. In both panels contours are drawn at 240, 480, 960 and 1920 𝜇 Jy beam − . Figure 10.
Left: 140 MHz contours (Govoni et al. 2019) overlaid on the radio spectral index map evaluated using the 140 MHz LOFAR and 346 MHz observationssmoothed to the same angular resolution of 205 (cid:48)(cid:48) × (cid:48)(cid:48) . Right: Same as left panel, but overlaid on the radio spectral index error map. In both panels the firstcontours are drawn at 5 mJy beam − and the remaining are spaced by a factor of 2. ACKNOWLEDGEMENTS
This work is based on research supported by the National ResearchFoundation under grant 92725. Any opinion, finding and conclusionor recommendation expressed in this material is that of the author(s)and the NRF does not accept any liability in this regard. We ac-knowledge the use of the Wright (2006) cosmology calculator. This research is supported by the South African Research Chairs Initiativeof the Department of Science and Technology and National ResearchFoundation. GB acknowledges helpful discussions with GianfrancoBrunetti and Franco Vazza on particle acceleration mechanisms.
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Figure 11.
Example of 346 MHz images where the simulated bridge was “injected" into visibilities. Discrete sources were subtracted before visibilities areimaged. The bridge spectral index is 𝛼 = . 𝛼 = Figure 12.
Left: 140 MHz contours of the diffuse source 𝑑 (Govoni et al. 2019) overlaid on the 346 MHz image. Both images were smoothed to the same angularresolution of 205 (cid:48)(cid:48) × (cid:48)(cid:48) (same as Figure 7). The first contour is drawn at 4 mJy beam − (3 𝜎 , with an rms noise of 1.3 mJy beam − ), and the following onesare spaced by a factor of two. The surface brightness peaks match very well between the two observing frequencies, although the interconnecting region is notvery visible at 346 MHz. Right: Same contours as left, but overlaid on the radio spectral index map of sources 𝑑 between 140 MHz and 346 MHz. We note asteepening of the spectral index across the source. Blank regions correspond to pixels fainter than 5 𝜎 at either 140 MHz or 346 MHz. REFERENCES
Akamatsu H., et al., 2017, A&A, 606, A1Bernardi G., et al., 2009, A&A, 500, 965Bernardi G., et al., 2010, A&A, 522, A67Bernardi G., et al., 2016, MNRAS, 456, 1259Bonafede A., et al., 2012, MNRAS, 426, 40Bonjean V., Aghanim N., Salomé P., Douspis M., Beelen A., 2018, A&A,609, A49Botteon A., et al., 2018, MNRAS, 478, 885Botteon A., et al., 2020, MNRAS, 499, L11Brentjens M. A., 2008, A&A, 489, 69Brunetti G., 2016, Plasma Physics and Controlled Fusion, 58, 014011 Brunetti G., Jones T. W., 2014, International Journal of Modern Physics D,23, 1430007Brunetti G., Lazarian A., 2016, MNRAS, 458, 2584Brunetti G., Vazza F., 2020, Phys. Rev. Lett., 124, 051101Brunetti G., et al., 2008, Nature, 455, 944Cassano R., Brunetti G., 2005, MNRAS, 357, 1313Cassano R., et al., 2013, ApJ, 777, 141Cuciti V., Cassano R., Brunetti G., Dallacasa D., Kale R., Ettori S., VenturiT., 2015, A&A, 580, A97Fabian A. C., Peres C. B., White D. A., 1997, MNRAS, 285, L35Fujita Y., Koyama K., Tsuru T., Matsumoto H., 1996, PASJ, 48, 191Govoni F., et al., 2019, Science, 364, 981Hoeft M., Brüggen M., 2007, MNRAS, 375, 77 MNRAS , 1–10 (2020) C. D. Nunhokee et al.
Figure 13.
Same as Figure 12 but for source f . As for source d , the spectral index is steeper in low surface brightness regions.Kale R., et al., 2015, A&A, 579, A92Kang H., Ryu D., 2016, ApJ, 823, 13Macario G., et al., 2013, A&A, 551, A141Markevitch M., Forman W. R., Sarazin C. L., Vikhlinin A., 1998, ApJ, 503,77Murgia M., Govoni F., Feretti L., Giovannini G., 2010, A&A, 509, A86Oegerle W. R., Hill J. M., 2001, AJ, 122, 2858Offringa A. R., de Bruyn A. G., Biehl M., Zaroubi S., Bernardi G., PandeyV. N., 2010, MNRAS, 405, 155Perley R. A., Butler B. J., 2013, ApJS, 206, 16Pinzke A., Oh S. P., Pfrommer C., 2017, MNRAS, 465, 4800Pizzo R. F., de Bruyn A. G., 2009, A&A, 507, 639Planck Collaboration et al., 2020, A&A, 641, A6Sakelliou I., Ponman T. J., 2004, MNRAS, 351, 1439Scaife A. M. M., Heald G. H., 2012, MNRAS, 423, L30Venturi T., Giacintucci S., Brunetti G., Cassano R., Bardelli S., Dallacasa D.,Setti G., 2007, A&A, 463, 937Venturi T., Giacintucci S., Dallacasa D., Cassano R., Brunetti G., MacarioG., Athreya R., 2013, A&A, 551, A24Wilber A., et al., 2018, MNRAS, 473, 3536Wittor D., Vazza F., Brüggen M., 2017, MNRAS, 464, 4448Wright E. L., 2006, PASP, 118, 1711van Weeren R. J., de Gasperin F., Akamatsu H., Brüggen M., Feretti L., KangH., Stroe A., Zandanel F., 2019, Space Sci. Rev., 215, 16This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000