A perfect power-law spectrum even at highest frequencies: The Toothbrush relic
K. Rajpurohit, F. Vazza, M. Hoeft, F. Loi, R. Beck, V. Vacca, M. Kierdorf, R. J. van Weeren, D. Wittor, F. Govoni, M. Murgia, C. J. Riseley, N. Locatelli, A. Drabent, E. Bonnassieux
AAstronomy & Astrophysics manuscript no. RX42 © ESO 2020September 22, 2020 L etter to the E ditor A perfect power-law spectrum even at highest frequencies: TheToothbrush relic
K. Rajpurohit , , , F. Vazza , , , M. Hoeft , F. Loi , R. Beck , V. Vacca , M. Kierdorf , R. J. van Weeren , D. Wittor ,F. Govoni , M. Murgia , C. J. Riseley , , N. Locatelli , A. Drabent , and E. Bonnassieux Dipartimento di Fisica e Astronomia, Universitát di Bologna, via P. Gobetti 93 /
2, 40129, Bologna, Italye-mail: [email protected] INAF-Istituto di Radio Astronomia, Via Gobetti 101, 40129 Bologna, Italy Thüringer Landessternwarte (TLS), Sternwarte 5, 07778 Tautenburg, Germany Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029, Hamburg, Germany INAF-Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius (CA), Italy Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The NetherlandsSeptember 22, 2020
ABSTRACT
Radio relics trace shock fronts generated in the intracluster medium (ICM) during cluster mergers. The particle acceleration mecha-nism at the shock fronts is not yet completely understood. We observed the Toothbrush relic with the E ff elsberg and Sardinia RadioTelescope at 14.25 GHz and 18.6 GHz, respectively. Unlike previously claimed, the integrated spectrum of the relic closely followsa power law over almost three orders of magnitude in frequency, with a spectral index of α . = − . ± .
03. Our finding isconsistent with a power-law injection spectrum, as predicted by di ff usive shock acceleration theory. The result suggests that there isonly little magnetic field strength evolution downstream to the shock. From the lack of spectral steepening, we find that either theSunyaev-Zeldovich decrement produced by the pressure jump is less extended than ∼
600 kpc along the line of sight or, conversely,that the relic is located far behind in the cluster. For the first time, we detect linearly polarized emission from the “brush” at 18.6 GHz.Compared to 8.3 GHz, the degree of polarization across the brush increases at 18.6 GHz, suggesting a strong Faraday depolarizationtowards lower frequencies. The observed depolarization is consistent with an intervening magnetized screen that arise from the denseICM containing turbulent magnetic fields. The depolarization, corresponding to a standard deviation of the Rotation Measures as highas σ RM = ±
23 rad m − , suggests that the brush is located in or behind the ICM. Our findings indicate that the Toothbrush can beconsistently explained by the standard scenario for relic formation. Key words.
Galaxies: clusters: individual (1RXS J0603.3 + − Galaxies: clusters: intracluster medium − large-scale structuresof universe − Acceleration of particles − Radiation mechanism: non-thermal: magnetic fields
1. Introduction
Radio relics are large, di ff use sources that are associated withpowerful shock fronts originating in the intracluster medium(ICM) during clusters merger (for a review, see e.g. Feretti et al.2012; van Weeren et al. 2019). One striking observational featureof radio relics is their high degree of polarization. The magneticfield vectors are often found to be well aligned with the shocksurface (van Weeren et al. 2010; Bonafede et al. 2012; Owenet al. 2014; de Gasperin et al. 2014; Kierdorf et al. 2017).Despite progress in understanding radio relics, the actual ac-celeration mechanism at the shock fronts is not fully understood.It is generally believed that di ff usive shock acceleration (DSA;Drury 1983) generates the observed cosmic ray electrons (CRe).However, it is currently debated if the acceleration starts fromthe thermal pool (standard scenario; Ensslin et al. 1998; Hoeft &Brüggen 2007) or from a population of mildly relativistic elec-trons (re-acceleration scenario; Kang & Ryu 2011, 2016)The standard scenario has successfully reproduced many ofthe observed properties of relics, however, three major di ffi cul-ties remain: (i) the spectra of some relics are reported to show aspectral break above 10 GHz (Stroe et al. 2016), which is incom- patible with the power-law spectrum predicted by DSA theory,(ii) a power-law energy distribution from the thermal pool CReenergies relevant for the synchrotron emission may require anunphysical acceleration e ffi ciency (van Weeren et al. 2016; Bot-teon et al. 2020), and (iii) the Mach numbers derived from X-ray observations are often significantly lower than derived fromthe overall radio spectrum (Akamatsu et al. 2012; Botteon et al.2020).According to the re-acceleration scenario the shock fronts re-accelerate electrons from a pre-existing fossil population. Thereare a few examples, which seem to show a connection betweenthe relic and active galactic nuclei. (Bonafede et al. 2014; vanWeeren et al. 2017; Di Gennaro et al. 2018; Stuardi et al. 2019).If relics originate according to the re-acceleration scenario, weakshocks may become radio bright, solving issue (ii) and (iii). Abreak in the radio spectrum is expected at high frequency, whenthe shock passes through a finite size cloud of fossil electronpopulation (Kang & Ryu 2016). If the fossil population is homo-geneously distributed, the re-acceleration scenario also predictsa power-law spectrum.The merging galaxy cluster 1RXS J0603.3 + z = . Article number, page 1 of 5 a r X i v : . [ a s t r o - ph . C O ] S e p & A proofs: manuscript no. RX42
B1B2B3F P
Fig. 1.
Total power emission from the Toothbrush relic at 70 (cid:48)(cid:48) resolution.
Left : E ff elsberg 14.25 GHz image. The largest linear size of the relic is ∼ . √ [1 , , , , . . . ] × σ rms , where σ rms , . = . − and σ rms , . = . − . Right : SRT 18.6 GHz image overlaid with the SRT (gray) and E ff elsberg (white) contours. Cyan boxes definethe area used for measuring the integrated spectrum of the relic and its sub-regions. The emission at the top right corner in the SRT image is dueto blending of discrete sources. a spectacular toothbrush-shaped relic (van Weeren et al. 2012,2016; Rajpurohit et al. 2018, 2020; de Gasperin et al. 2020).It consists of three distinct components, namely the brush (B1)and two parts forming the handle (B2 + B3). The relic shows anunusual linear morphology and is quite asymmetric with respectto the merger axis. The handle extends into very low densityICM.Stroe et al. (2016) reported evidence for a spectral steepen-ing above 2.5 GHz in the integrated radio spectrum of the relic.This claim was mainly based on the 16 GHz and 30 GHz ra-dio interferometric observations. It has been suggested that thesteepening in the integrated radio spectrum can be reproducedwith the re-acceleration scenario (Kang 2016). Basu et al. (2016)studied the impact of the Sunyaev-Zeldovich (SZ) e ff ect on theobserved synchrotron flux density. They suggested that SZ con-tamination leads to a high frequency steepening for relics, al-beit not at the level claimed by Stroe et al. (2016). Recently, westudied the integrated spectrum of the relic between 120 MHzto 8 GHz and excluded any steepening up to 8 GHz (Rajpurohitet al. 2020). However, the spectral behavior of the relic remaineduncertain between 10-20 GHz. The Toothbrush is known to behighly polarized (van Weeren et al. 2012). E ff elsberg observa-tions revealed a high fractional polarization at 8.3 GHz and astrong depolarization and Rotation Measure (RM) gradient fromthe brush to the handle (Kierdorf et al. 2017).The main aim of this paper is to answer the question if theoverall spectrum of the Toothbrush steepens in the frequencyrange between 10-20 GHz. If the spectrum steepens at high fre-quency, this would have a tremendous impact on the radio relicformation scenario, since it would clearly be in conflict with thestandard scenario for relic formation, which predicts a powerlaw towards high frequencies. A steepening would be di ffi cultto explain within the standard scenario and would favor the re-acceleration scenario. We adopt a flat Λ CDM cosmology with H =
70 km s − Mpc − , Ω m = .
3, and Ω Λ = .
7. At the clus-ter’s redshift, 1 (cid:48)(cid:48) corresponds to a physical scale of 3.64 kpc.
2. Observations
The radio observation at 14.25 GHz were performed with theE ff elsberg 100-m telescope with the new Ku-band receiver indual polarization mode. The total on-source observation timewas 20 hours with 2500 MHz bandwidth. We obtained 31 cover-ages of a field of 11 × and processed the data with theNOD3 tool (Müller et al. 2017). The data reduction involves Ra-dio Frequency Interference removal and baselevel corrections,like Basket-Weaving of two maps with scanning in orthogonaldirections (RA / DEC).The Sardinia Radio Telescope (SRT) observations were per-formed in a full polarization mode with the 7-feed K-Band re-ceiver centered at 18.6 GHz with a bandwidth of 1200 MHz. Theobservations were carried out between January and February2020, for a total of 24 hours. The data were reduced using theproprietary software package Single-dish Spectral-polarimetrySoftware (SCUBE; Murgia et al. 2016).The uncertainty in the flux density measurements were esti-mated as: ∆ S ν = (cid:113) ( f · S ν ) + N beam ( σ rms ) , (1)where f is the absolute flux density calibration uncertainty, S ν isthe flux density, σ rms is the rms noise and N beams is the number ofbeams. We assume an absolute flux density uncertainty of 10 %for both SRT and E ff elsberg.
3. Results and discussion
In Figure 1, we show the E ff elsberg and the SRT total intensityimages at 70 (cid:48)(cid:48) resolution. The relic is clearly detected at both fre-quencies. The largest linear size of the relic is ∼ . . ± . . ± . S
16 GHz = . ± . ff ects. Interferometric ob-servations underestimate the flux density of extended emission Article number, page 2 of 5ajpurohit et al.: A power-law spectrum from 58 MHz to 18.6 GHz Frequency (MHz) F l u x d e n s i t y ( m J y ) relicB1B2+B3 10 Frequency (MHz) F l u x d e n s i t y ( m J y ) = 3.7 = 1.3 d LOS = 200kpc d LOS = 400kpc d LOS = 600kpc d LOS = 200kpc d LOS = 400kpc d LOS = 600kpc
Fig. 2.
Left : Integrated spectrum of the Toothbrush relic between 58 MHz and 18.6 GHz. Dashed lines show the fitted power laws. The spectrumfollows a close power law with a slope of α = − . ± .
03. The new flux density points are highlighted by the cyan regions, other values areadopted from Rajpurohit et al. (2020).
Right : The possible impact of SZ decrement (shown with horizontal color lines) as a function of line ofsight depth ( d LOS ) on the radio spectra of the relic emission. Blue circles show the observed flux densities. In order to produce an SZ decrementcompatible within the error-bars of the new 14.25 and 18.6 GHz observations, the depth of the shock pressure jump along the line of sight isrequired to be d LOS ≤
600 kpc. when the size of emission region gets close to Largest AngularScale detectable with the interferometer.
To obtain the integrated spectrum of the relic, we combine ournew flux density measurements with those presented in Rajpuro-hit et al. (2020). In addition, we include the flux density mea-surements from the LOFAR LBA observations at 58 MHz (deGasperin et al. 2020). We measure flux densities for the entirerelic as well as for the regions B1 and B2 + B3; see Table 1.The resulting integrated spectra are shown in the left panelof Figure 2. We find that the relic follows a close power lawover almost three orders of magnitude in frequency. The inte-grated spectral index of the relic between 58 MHz and 18.6 GHzis − . ± .
03. The spectral index value is consistent withour previous estimates (Rajpurohit et al. 2018, 2020). Recently,the power-law spectrum results are also found for the relic inCIZA J2242.8 + ff ectin the relic overall spectrum.According to the DSA theory in the test-particle regime andadopting a constant shock strength and CRe cooling in a ho-mogeneous medium, the “integrated” spectrum is related to theMach number according to M = (cid:114) α int − α int + . (2)The radiative lifetime of electrons observed at 58 MHz is about120 Myr when adopting a magnetic field strengths of 1 µ G. If theshock propagates with 1000 km s − this corresponds to lengthof about 160 kpc. The slope of the spectrum down to 58 MHz can only interpreted as a Mach number according to Eq. 2 if thephysical conditions at the shock do not change significantly on ascales of 160 kpc. This condition is likely fulfilled for the Tooth-brush since it is located at a projected distance to the clustercenter of about 1.1 Mpc. The index above therefore correspondsto a Mach number of M = . ± . ∼ . ffi -cient electron acceleration is adopted (see, e.g., Fig. 9 in Botteonet al. 2020). We note, however, that even in this situation a fewpercent of the kinetic energy dissipated at the shock front needsto be transferred by DSA to the supra-thermal accelerated at theshock front. It is conceivable, that the magnetic field strength downstreamof the shock increases, e.g., due to a turbulent dynamo processdriven by the curvature of the shock front, or decreases, e.g.,
Article number, page 3 of 5 & A proofs: manuscript no. RX42 by expansion of the shock compressed material. Depending onfrequency, the observed radio emission probes very di ff erent vol-umes. At the highest frequency, 50 % of the emission are emittedfrom a volume with an extent of about 5 kpc downstream to theshock front. In contrast, the emission at 58 MHz is extended toabout 85 kpc. If the strength of the magnetic field would changesignificantly on these lengths scales, this would a ff ect the inte-grated spectrum of the relic.A non-linear change of the field strength would either sig-nificantly boost the emission at short or at large distances, inboth cases this would result in a curved spectrum, see e.g., Don-nert et al. (2016). Since the integrated spectrum almost perfectlyfollows a power law, only a marginal non-linear increase or de-crease of the magnetic field strength seems to be possible onscales probed by the relic.However, if the field strength changes linearly with distance,the power-law integrated spectrum is preserved but the relationEquation 2 does not hold anymore. An increasing field strengthwould steepen the integrated spectrum while a decreasing onewould flatten it. If the field strength doubles one a scale of85 kpc, the spectrum would steepen by about − . ffi ciency problem. Table 1.
Integrated flux densities
Region S
58 MHz S .
25 GHz S . α . Jy mJy mJyrelic 12 . ± . . ± . . ± . − . ± . . ± . . ± . . ± . − . ± . + B3 2 . ± . . ± . − − . ± . Notes.
The flux densities 14.2 and 18.6 GHz are measured from70 (cid:48)(cid:48) resolution images. Flux density at 58 MHz are measured fromLOFAR LBA image. The relic flux exclude the contribution fromsources F and P.
The SZ e ff ect contributes a negative signal against the cos-mic microwave background for ν ≤
220 GHz. In the case ofrelics, Basu et al. (2016) showed that the SZ e ff ect from theshock downstream also scales proportional to the Mach num-ber squared, producing a contamination within exactly the samespatial scales responsible for the relic emission.At 15 GHz, the SZ e ff ect is expected to reduce the observedsynchrotron flux density by ∼ − must be expected if the shock leading to observedrelic involve thermal gas, a lack of spectral steepening can beused to further constrain the shock parameters.The SZ decrement at a given observation frequency dependson the line-of-sight projection of the pressure jump, d LOS , andtherefore on the (unknown) shock geometry at the location ofthe relic. For a simple plane-parallel geometry and ignoring cur-vature, the total SZ decrement can be obtained by integrating y over the visible relic area: L × W , where L is the shock lengthand W is the width, leading to an angular size of the relic Ω relic ≈ L W / D A steradians (with D A the angular diameter dis- tance). Following Basu et al. (2016), we calculate the maximum total allowed SZ flux decrement from the region sampled by ournew high frequency radio observation of the Toothbrush: | ∆ S SZ ν, relic | ≤ . µ Jy (cid:32) D A
700 Mpc (cid:33) − (cid:32) L (cid:33) (cid:32) d LOS (cid:33) (cid:32) W
100 kpc (cid:33) × (cid:32) n u T u − keV cm − (cid:33) (cid:18) M (cid:19) (cid:18) ν . (cid:19) . (3)We use D A =
751 Mpc, L = .
86 Mpc, W =
422 kpc, andtwo possible shock strengths, either M = . M = . n u and T u are the pre-shock density and temperature that can be derivedby the two Mach numbers, respectively. For each Mach num-ber, the temperature and density are derived from the standardRankine-Hugoniot jump conditions based on the assumed post-shock values, n d = × − cm − and T d = | ∆ S SZ ν, relic | for di ff erent frequen-cies, by fixing the above model parameters and varying the un-known value of d LOS . Our results are given in the right panel ofFigure 2. In order to produce an SZ decrement compatible withinthe error-bars of our 14.25 and 18.6 GHz observations, the depthof the shock pressure jump along the line of sight is required tobe d LOS ≤
600 kpc for a shock of strength M = .
7. For a shockof strength M = .
3, the SZ decrement at d LOS =
600 kpc al-ready produces a spectrum falling below the error bars of our ob-servations. Hence, requiring an even smaller depth of the shockalong the line of sight. We emphasize that the quoted values onlyrefers to the contribution to the SZ decrement from the shock dis-continuity along the line of sight, for the same range of spatialscales responsible for the radio emission.Furthermore, the assumption of a simple planar geometryand the absence of curvature along the line of sight is clearlyan oversimplification, which may indeed explain the surprisinglylow value of d LOS . Incidentally, such a small SZ decrement mayalso be explained if the shock responsible for the relic is at amore peripheral location in the cluster. In this case the densityand temperature values suggested by X-ray observations origi-nate from regions which are denser than the one responsible forthe radio emission. In this case, Equation 3 would significantlyoverestimate the pressure jump at the shock, and the requirementon d LOS would be relaxed.
All of the information on the polarization properties of relics aremainly collected in the frequency range of 1-8.3 GHz. Since theFaraday rotation is expected to be almost negligible at 18.6 GHz,the intrinsic polarization of the relic could be directly mapped byour observations.For the first time, we detect polarized emission from therelic at 18.6 GHz. We detect polarized emission mainly fromthe brush region; see Figure 3. The degree of polarization variesalong the brush and the magnetic field vectors are mainly alignedto the relic orientation. The fractional polarization reaches ∼
66% in some areas, the average being ∼ ± ff ected by beam depolarization.Previous polarization measurements of the toothbrush relichave shown that the fractional polarization of B1 decreases Article number, page 4 of 5ajpurohit et al.: A power-law spectrum from 58 MHz to 18.6 GHz
Fig. 3.
B-vectors distribution across the brush region at 51 (cid:48)(cid:48) resolutionoverlaid with the SRT total power contours at 3 σ . The length of thevectors depict the degree of polarization. The vectors are corrected forFaraday rotation e ff ect. The mean polarization fraction at the brush is(30 ± rapidly towards lower frequencies. B1 is polarized at a level ofabout 15% at 8.3 GHz (Kierdorf et al. 2017) and about 11%at 4.9 GHz. The polarization fraction drops below 1% at fre-quency near 1.4 GHz (van Weeren et al. 2012). The compari-son between 8.3 GHz and our measurement suggests significantdepolarization even between 18.6 and 8.3 GHz. Other than theToothbrush relic, the polarization observations above 4.9 GHzare available only for three relics, namely the Sausage relic, therelic in ZwCl 0008 +
52, and Abell 1612 (Kierdorf et al. 2017;Loi et al. 2017). For the above mentioned relics, the fractionalpolarization remains nearly constant at 4.9 GHz and 8.3 GHz.The standard deviation of the RM, σ RM , is a useful param-eter to characterize Faraday rotation and depolarization causedby an external Faraday screen. The depolarization induced byan external Faraday screen containing turbulent magnetic fields(Burn 1966; Sokolo ff et al. 1998) can be described as p ( λ ) = p e − σ λ , (4)where p is the intrinsic polarization fraction. The maps between4.9 and 18.6 GHz show depolarization of DP . . = . ± . σ RM = ±
23 rad m − . Theobserved σ RM for the brush of Toothbrush is several times higherthan for any other radio relic. This indicates that the brush regionof the relic experiences strong Faraday rotation from the denseICM. The strong depolarization suggests that the emission liesin or behind the ICM, which is very likely causing a low Machnumber shock detected via X-ray observations (Ogrean et al.2013; van Weeren et al. 2016) .
4. Conclusions
We presented high frequency radio observations of the Tooth-brush relic with the SRT and the E ff elsberg telescope. Wefind that the relic follows a close power-law spectrum between58 MHz to 18.6 GHz, with a slope of α = − . ± .
03. Our find-ings indicate that the Toothbrush can be consistently explainedby the standard scenario for relic formation. The slope of thespectrum disfavors that the strength of the magnetic field signifi- cantly changes on scales probed by the radio emission, i.e., about85 kpc.We detected polarized emission at 18.6 GHz. Compared tomeasurements at lower frequencies, the polarization fraction ofthe brush increases at 18.6 GHz. The high value of σ RM is consis-tent with σ RM fluctuations of an ICM screen with tangled mag-netic fields. This suggests that the brush is located in or behindthe ICM.From the lack of steepening in the relic spectra, we find thateither the SZ decrement at the shock along the line of sight is ≤
600 kpc thick, or the pressure jump associated with the relicis located far behind in the cluster. The latter explanation canalso be reconciled with the trends of polarization fraction for thebrush region.
Acknowledgements.
KR and FV acknowledge financial support from the ERCStarting Grant “MAGCOW”, no. 714196. FL acknowledge financial supportfrom the Italian Minister for Research and Education (MIUR), project FARE,project code R16PR59747, project name FORNAX-B. RJvW acknowledgessupport from the VIDI research programme with project number 639.042.729,which is financed by the Netherlands Organisation for Scientific Research(NWO). CJR and EB acknowledges financial support from the ERC StartingGrant “DRANOEL”number 714245. AD acknowledges support by the BMBFVerbundforschung under grant 05A17STA. We thank Sorina Reile for process-ing part of the E ff elsberg data. Based on observations with the 100-m telescopeof the MPIfR (Max-Planck-Institut für Radioastronomie) at E ff elsberg. The Sar-dinia Radio Telescope (Bolli et al. 2015; Prandoni et al. 2017) is funded by theMinistry of Education, University and Research (MIUR), Italian Space Agency(ASI), the Autonomous Region of Sardinia (RAS) and INAF itself and is oper-ated as National Facility by the National Institute for Astrophysics (INAF). Thedevelopment of the SARDARA back-end has been funded by the AutonomousRegion of Sardinia (RAS) using resources from the Regional Law 7 / References
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