Suzaku and Chandra observations of the galaxy cluster RXC J1053.7+5453 with a radio relic
Madoka Itahana, Motokazu Takizawa, Hiroki Akamatsu, Reinout J. van Weeren, Hajime Kawahara, Yasushi Fukazawa, Jelle S. Kaastra, Kazuhiro Nakazawa, Takaya Ohashi, Naomi Ota, Huub J. A. Röttgering, Jacco Vink, Fabio Zandanel
aa r X i v : . [ a s t r o - ph . H E ] A ug Publ. Astron. Soc. Japan (2014) 00(0), 1–13doi: 10.1093/pasj/xxx000 Suzaku and Chandra observations of the galaxycluster RXC J1053.7+5453 with a radio relic
Madoka I
TAHANA , Motokazu T AKIZAWA , Hiroki A KAMATSU , Reinout J. VAN W EEREN , Hajime K AWAHARA , Yasushi F
UKAZAWA , Jelle S.K AASTRA , Kazuhiro N
AKAZAWA , Takaya O HASHI , Naomi O TA , HuubJ. A. R ¨ OTTGERING , Jacco V INK and Fabio Z ANDANEL School of Science and Engineering, Yamagata University, Kojirakawa-machi 1-4-12,Yamagata 990-8560, Japan Department of Physics, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata 990-8560,Japan SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, TheNetherlands Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138,USA Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo,Bunkyo-ku, Tokyo 133-0033, Japan Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo113-0033, Japan Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 133-0033,Japan Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo192-0397, Japan Department of Physics, Nara Women’s University, Kitauoyanishi-machi, Nara 630-8506,Japan Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands Anton Pannekoek InstituteGRAPPA, University of Amsterdam, PO Box 94249, NL-1090 GEAmsterdam, the Netherlands GRAPPA Institute, University of Amsterdam, 1098 XH Amsterd am, The Netherlands ∗ E-mail: [email protected], [email protected]
Received ; Accepted
Abstract
We present the results of Suzaku and Chandra observations of the galaxy cluster RXCJ1053.7+5453 ( z = 0 . ), which contains a radio relic. The radio relic is located at thedistance of ∼ kpc from the X-ray peak toward the west. We measured the temperatureof this cluster for the first time. The resultant temperature in the center is ∼ . keV, which islower than the value expected from the X-ray luminosity - temperature and the velocity disper-sion - temperature relation. Though we did not find a significant temperature jump at the outeredge of the relic, our results suggest that the temperature decreases outward across the relic.Assuming the existence of the shock at the relic, its Mach number becomes M ≃ . . A possi-ble spatial variation of Mach number along the relic is suggested. Additionally, a sharp surface c (cid:13) Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 brightness edge is found at the distance of ∼ kpc from the X-ray peak toward the westin the Chandra image. We performed X-ray spectral and surface brightness analyses aroundthe edge with Suzaku and Chandra data, respectively. The obtained surface brightness andtemperature profiles suggest that this edge is not a shock but likely a cold front. Alternatively,it cannot be ruled out that thermal pressure is really discontinuous across the edge. In thiscase, if the pressure across the surface brightness edge is in equilibrium, other forms of pres-sure sources, such as cosmic-rays, are necessary. We searched for the non-thermal inverseCompton component in the relic region. Assuming the photon index Γ = 2 . , the resultant up-per limit of the flux is . × − erg s − cm − for . × − deg area in the 0.3-10 keV band,which implies that the lower limit of magnetic field strength becomes . µ G . Key words: galaxies: clusters: individual (RXC J1053.7+5453) — X-rays: galaxies: clusters — acceler-ation of particles — shock waves — magnetic fields
According to the standard theory of structure formation in theuniverse, galaxy clusters are built up through mergers and ab-sorption of smaller galaxy clusters and groups. Cluster majormergers are the most energetic phenomena ( ∼ erg) in theuniverse. Edge-like features are found in X-ray images obtainedby Chandra and XMM-Newton for some clusters. Such struc-tures are believed to be a shock or cold front. Temperature, den-sity and pressure profiles show a discontinuity across a shockfront. Similarly, the temperature and density are discontinuous,but the pressure is continuous across a cold front. It is believedthat these are the evidences of a cluster merger. Numerical sim-ulations show that shocks and contact discontinuities appear inthe intracluster medium (ICM) during cluster major mergers(Ricker & Sarazin 2001; Takizawa 2005; Akahori & Yoshikawa2010; Takizawa et al. 2010). The features of a contact discon-tinuity agree with those of cold fronts. While a large part ofthe kinetic energy is converted into the thermal ICM duringcluster mergers, some part of it will be converted into a non-thermal form such as magnetic fields and cosmic-rays (Ohnoet al. 2002; Takizawa 2008; Zuhone et al. 2011; Donnert et al.2013). Some merging clusters host diffuse non-thermal radiosources (Feretti et al. 2012; Brunetti & Jones 2014). This ra-dio emission is from synchrotron radiation by the interactionof relativistic electrons whose energy is ∼ GeV , and magneticfield of ∼ µ G in the ICM, which are classified into three cate-gories by their size, morphology and location. Radio halos arein the central part of the cluster and have similar morphologyto the ICM X-ray emission (Feretti et al. 1997; Govoni et al.2004; van Weeren et al. 2011; Scaife et al. 2015). Mini halos arealso located in the cluster center, but their typical size is muchsmaller than halos (Feretti et al. 2012; Giacintucci et al. 2014).On the other hand, radio relics are usually in cluster outskirtsand show an arc-like shape (R¨ottgering et al. 1997; Bonafede etal. 2009; van Weeren et al. 2010; van Weeren et al. 2016).Owing to their locations and morphology, it is believed that radio relics should have a close connection with shock frontscaused by cluster mergers. Thus, radio relics can be good trac-ers of merger shocks in clusters and the shocks are expected tobe located at the outer edge of the relics. Recently, in fact, tem-perature and density jumps are found across the relic outer edgein some clusters by the X-ray observations (Finoguenov et al.2010; Akamatsu et al. 2012a; Akamatsu et al. 2013; Ogrean etal. 2013; Eckert et al. 2016; Akamatsu et al. 2017). This is directevidence of the relationship between relics and shocks. Machnumbers of shocks can be estimated from radio and X-ray ob-servations independently. From radio observations, we can ob-tain radio spectral index at the outer edge of relics. Assuminga simple diffusive shock acceleration (DSA) theory (Drury1983; Blandford & Erichler 1987), this spectral index can berelated with the shock Mach numbers (Rybicki & Lightman1979) . From X-ray observations, we can obtain the temper-ature and density distribution around relics. We can estimatethe Mach number with Rankine-Hugoniot conditions from thetemperature and density jump at shock front (Landau & Lifshitz1959; Shu 1992). If the simple DSA model is true, consistentresults will be obtained through both methods.The high energy electrons in synchrotron radiation regions(radio relics and halos) emit non-thermal X-rays via the inverseCompton scattering of cosmic microwave background (CMB)photons (Bartels et al. 2015). By comparing synchrotron ra-dio and non-thermal X-ray fluxes , we are able to estimate themagnetic field strength in the non-thermal radio emission re-gions. Even if we obtained only the upper limit of non-thermalX-ray flux, we can estimate the lower limit of the magnetic fieldstrength. Though a lot of attempts to search for the non-thermalX-ray components have been done, no firm detections are re-ported (Ajello et al. 2009; Nakazawa et al. 2009; Sugawara etal. 2009; Itahana et al. 2015; Akamatsu et al. 2017).The galaxy cluster RXC J1053.7+5453 ( z = 0 . ) isknown to host a radio relic. The radio relic is located at the dis-tance of kpc from the X-ray peak toward the west. Its X-ray ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 luminosity with ROSAT is L X[0 . − . = 0 . × erg / s (Popesso et al. 2004). Ebeling et al. (1998) estimated the tem-perature kT ∼ from L X − kT relation. This value israther low for clusters with radio relics. However, there is no di-rect temperature measurement for this cluster. According to theSloan Digital Sky Survey (SDSS) data, the velocity dispersionof the member galaxies is +51 − km / s and the virial radius is r = 1 .
52 Mpc (Aguerri et al. 2007), which is defined as theradius within which the mean density becomes 200 times of thecritical density of the universe. From the radio observation, vanWeeren et al. (2011) reported that the relic length and the radioflux density are
600 kpc and S = 15 ± , respec-tively. There is no observational information about the radiospectra of this relic.We observed a field around a radio relic in the galaxy clus-ter RXC J1053.7+5453 with Suzaku. Suzaku is more suitablefor spectral analysis of the ICM in the outer parts of the cluster,because the mounted X-ray Imaging Spectrometer (XIS) has agood sensitivity for low surface brightness diffuse sources andlow and stable background (Mitsuda et al. 2007). Additionally,we used Chandra archive data for the surface brightness anal-ysis and the point sources removal, because the AdvancedCCD Imaging Spectrometer (ACIS) has high spatial resolution.Figure 1 shows a ROSAT image of RXC J1053.7+5453 in the0.1-2.4 keV band. The yellow and light blue boxes show thefield of views (FOVs) in the Chandra ACIS and Suzaku XISobservations, respectively. The white dashed circle shows thevirial radius of RXC J1053.7+5453 ( r = 18 . ′ ).In this paper, we present the Suzaku and Chandra X-ray ob-servations of the galaxy cluster RXC J1053.7+5453. The out-line of the paper is organized as follows. We describe the ob-servation and data reduction in section 2. Data analysis andour results are presented in section 3. We discuss the resultsin section 4. We summarize the results in section 5. We usedcanonical cosmological parameters of H = 70km s − Mpc − , Ω = 0 . , and Λ = 0 . . At the redshift of the cluster, ′ corresponds to kpc. The solar abundances are normalizedto Asplund et al. (2009). Unless otherwise stated, the errorscorrespond to 90% confidence level. We observed a field around the radio relic in galaxy cluster RXCJ1053.7+5453 with Suzaku on 2014 November 01 - 03. Thisobservation is one of the Suzaku AO9 Key projects. In orderto estimate the background components, we used the Suzakuarchive data of the Lockman Hole. We used the data observedon 2009 June 12 - 14 (ID:104002010) because this is the data ofthe field nearest to this cluster on the sky plain among LockmanHole observations of Suzaku. Table 1 shows an observationallog of RXC J1053.7+5453 and the Lockman Hole. RXJ1053 : . : : . : . : . : : . Right ascension D e c li na t i on XIS
Chandra W ESTChandra Suzaku
Fig. 1.
A ROSAT image of RXC J1053.7+5453 in the 0.1-2.4 keV band. Theimage intensity is arbitrary unit and rms value of the image fluctuation is σ = 0 . . The yellow and light blue boxes show the FOVs of the ChandraACIS and Suzaku XIS observations. The white dashed circle shows the virialradius of RXC J1053.7+5453 ( r = 18 . ′ ). and Lockman Hole data were processed with Suzaku pipelineprocessing, version 2.8.20.37 and 2.4.12.26, respectively. Weused HEAsoft version 6.19 for the Suzaku data. The 20150312calibration data files were adopted.The XIS data were processed through default screening cri-teria. In addition, data obtained in the periods with geomagneticcomic-ray cut-off rigidity ( COR ) > . GV were excluded. Asa results, the effective exposure times became 71.6 ks and 63.8ks for the cluster and Lockman Hole regions, respectively. Inorder to reduce the non-X-ray background (NXB) level, whichincreased after changing the amount of charge injection, we ap-plied additional processing for XIS1 following the processes de-scriptions in the Suzaku XIS analysis topics . We did not usethe XIS0 segment A which is damaged because of a microme-teorite accident . NXB spectra and images of XIS were gener-ated using the ftool “xisnxbgen” (Tawa et al. 2008). Top panelof figure 2 shows a 0.5-8.0 keV XIS1 image with the 1382 MHzradio contours (van Weeren et al. 2011). The X-ray image wascorrected for exposure and vignetting effects after subtractingNXB, and smoothed by a Gaussian kernel with σ = 0 . ′ .RXC J1053.7+5453 was also observed with Chandra on2013 June 22 (ObsID:15322). In addition, we observed afield around the radio relic with Chandra on 2016 February 09(ObsID:17207), to search for point sources. We used CIAO ver-sion 4.8 with the calibration files of CALDB version 4.7.0. Theevent files were reprocessed using the task “chandra repro”. Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0
The “lc clean” algorithm was used to filter the soft proton flares,and the light curves were visually inspected to check for anyresidual flaring. As a results, the effective exposure times be-came 24.5 ks and 6 ks for the central and west field, respec-tively. A Chandra image in the 0.5-2.0 keV band is shown inthe bottom panel of figure 2.
We used Suzaku data for the spectral analysis. For the spec-tral analysis of the XIS data, we generated redistribution matrixfiles (RMFs) and ancillary response files (ARFs) with the ftool“xisrmfgen” and “xissimarfgen” (Ishisaki et al. 2007), respec-tively. Uniform emission over a circular region with ′ radiuswas used as an input image to generate an ARF. We estimate the background components using the data of theLockman Hole field. We assume that the background compo-nents are composed of the Local Hot Bubble (LHB), the hot gasof the Milky Way Halo (MWH) and the Cosmic X-ray back-ground (CXB). Then, we fit the spectrum of the backgroundfield using the following model: apec
LHB + phabs ∗ ( apec MWH + powerlaw CXB ) , (1)where apec LHB , apec MWH and powerlaw
CXB represent theLHB, MWH and CXB, respectively. We fix the temperatureof LHB to 0.08 keV, and the redshift and abundance of boththe LHB and MWH to zero and solar, respectively. We assume N H = 6 . × cm − for the Galactic absorption (Willingaleet al. 2013). The photon index of the CXB is fixed to Γ = 1 . (Kushino et al. 2002). For the spectral fitting of the backgroundcomponents, we used energy bands of 0.7 - 7.0 keV (XIS0, 3)and 0.6 - 7.0 keV (XIS1). However, the energy band of 1.7 -1.8 keV was ignored, because the response matrix around Si-Kedge had residual uncertainties.Figure 3 shows the spectra of the background field fittedwith the above-mentioned model, where black, red, and greencrosses show the spectra of XIS0, XIS1, and XIS3, respectively.The each component and total of the best-fit model spectra arealso shown with solid histograms. Table 2 shows the detailedresults of the best-fit model. The obtained temperature of theMWH component ( kT = 0 . +0 . − . keV) is consistent with thetypical value ( kT ∼ . keV; Yoshino et al. 2009). We investigate the temperature structure across the radio relicwhich is the candidate shock regions. Assuming that a shockis located at the relic outer edge, we chose regions as shown in : . : : . : . : : . : . Right ascension D e c li na t i on : : . : . : . : . : : . Right ascension D e c li na t i on S u z a k u X I S F O V Fig. 2.
Top: An XIS1 image in the 0.5-8.0 keV band (Obs.ID:809120010)with the 1382 MHz radio contours (van Weeren et al. 2011). The X-ray imagewas corrected for exposure and vignetting effects after subtracting NXB andsmoothed by a Gaussian kernel with σ = 0 . ′ . The radio contours aredrawn at [1 , , , , ... ] × . / beam . The green and yellow regionswere used for the spectral analysis, with annular radius of 2’, 4’, 6’, 9’, 15’and 3’, 5’, 7’, 10’, respectively. The light blue circles are excluded regions of apoint source. Bottom: A Chandra image in 0.5-2.0 keV band (Obs.ID:15322).The image was corrected for exposure. The green sector is a region usedfor extracting surface brightness profile (in subsection 3.3). Light blue box isthe Suzaku XIS FOV. ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 Table 1.
The observational log of RXC J1053.7+5453 and Lockman Hole.
Name (Obs.ID) (RA, Dec) Observation Date Exposure (ks) ∗ Suzaku RXC J1053.7+5453(809120010) (163.1807,54.9140) 2014/11/01-03 71.6LOCKMAN HOLE (104002010) (162.9375,57.2667) 2009/6/12-14 63.8Chandra RXC J1053.7+5453(15322) (163.4148,54.8296) 2013/6/22 24.5RXC J1053.7+5453 WEST(17207) (163.2642,54.9077) 2016/2/09 6 ∗ Effective exposure time after data screening as described in the text.
Table 2.
Best-fit background parameters for the XIS spectra
Model Component Parameter ValueLHB kT ∗ N † . +9 . − . × − MWH kT ∗ . +0 . − . N † . +7 . − . × − CXB Γ ‡ N § . +0 . − . × − χ /d.o.f ∗ Temperature of the each component in keV. † Normalization in the apec model for each component scaled with a factor / π . N = π R n e n H dV/ [4 π (1 + z ) D ] × − cm − arcmin − ,where D A is the angular diameter distance to the source. ‡ Photon index of the power-law component. § Normalization in the power-law component in photons keV − cm − s − at 1 keV −4 −3 c oun t/ k e V / s ( da t a − m ode l ) / e rr o r Energy (keV)
Fig. 3.
The XIS spectra of the background field fitted with the backgroundmodel described in the text. The black, red, and green crosses show thespectra of XIS0, XIS1, and XIS3, respectively. The each component andtotal of the best-fit model spectra are also shown with solid histograms. Theblue, light blue, and magenta solid histograms represent the LHB, MWH, andCXB components, respectively. the top panel of figure 2 by green annular. We search for pointsources with Chandra data, whose spatial resolution is betterthan Suzaku. In order to reduce the contamination and CXBsystematic errors, we exclude ′ radius circular regions centeredby the position of a point source (light blue circles in the figure 2top panel) whose flux is more than × − erg / s / cm (2.0-10 keV). We fit the spectrum of each region by the following model; constant ∗ [ apec LHB + phabs ∗ ( apec MWH + powerlaw CXB + apec ICM )] , (2)where, apec ICM represents the emission from the ICM. Wefixed all parameters of the background components ( apec
LHB , apec MWH and powerlaw
CXB ) to the values derived fromthe background field analysis in subsection 3.1. We add powerlaw
AGN in case of the model fitting for the central re-gion, because there is an active galactic nuclei (AGN) whichcan not be excluded. Therefore, we fit the spectrum of the cen-tral region by the following model; constant ∗ [ apec LHB + phabs ∗ ( apec MWH + powerlaw CXB + apec ICM + powerlaw AGN )] . (3)We assume N H = 8 . × cm − for the Galactic absorp-tion (Willingale et al. 2013). The redshift and abundance of theICM components are fixed to 0.0704 and 0.3 solar, respectively.We introduced a parameter constant to correct for slight dif-ferences in normalization among the XIS sensors. It is knownthat there is uncertainty in the gain with negligible energy de-pendence in Suzaku XIS (Koyama et al. 2007; Yamaguchi et al.2008; Bamba et al. 2008). The constant is fixed to be unity forXIS1 and allowed to vary freely for XIS0 and XIS3. For thespectral fitting of the ICM component, we used the energy band Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 of 0.7 - 7.0 keV. However, the energy band of 1.7 - 1.8 keVwere ignored, because the response matrix around Si-K edgehad residual uncertainties. Systematic errors of CXB are esti-mated in a way same as in Itahana et al. (2015). We assumethe upper cutoff flux of S c = 5 × − erg / s / cm . From thesize of each region, the calculated CXB fluctuations at the 90 %confidence level are shown in table 3. In addition, it is reportedthat the reproducibility of the NXB was 4.9 % at the 90 % con-fidence level (Tawa et al. 2008). We estimated CXB and NXBsystematic errors taking into account of these uncertainties.Figure 4 shows the spectra of each region fitted with theabove-mentioned model. The ICM components of the outsideregion ( > ′ ) are fainter than the CXB component. The re-sultant best-fit parameters are listed in table 3. The first, sec-ond, and third errors are statistical, CXB systematic, and NXBsystematic at the 90% confidence level, respectively. For theoutside region of the radio relic ( ′ − ′ ), the ICM compo-nent is marginally detected if we consider only statistical er-rors. Taking into account of systematic errors, however, thenormalization of the apec component is consistent with zero.The temperature profile is shown in figure 5, where the hori-zontal axis represents the angular distance from the X-ray peak.In the central region, the best-fit parameters of powerlaw AGN photon index and normalization are
Γ = 2 . +0 . − . and norm =1 . +0 . − . × − photon / keV / s / cm , respectively, and fluxof the AGN becomes × − erg / s / cm (2.0-10 keV). Here,we also measured the temperature in the central region with theChandra data. As a result, the obtained temperature becomes kT = 1 . +0 . − . keV. This value is consistent with the Suzakuresult taking account of statistical errors. Though we did notfind a significant temperature jump at the outer edge of the relic,the temperature decreases outward across the radio relic.If the shock is not located just at the relic outer edge, the tem-perature in the pre- and post-shock regions could be over- andunderestimated, respectively. To check this, we measured thetemperature of the yellow regions in figure 2 top panel, whichare ′ shifted outward compared with green ones. The obtainedtemperatures are shown with light gray crosses in figure 5. Thissuggests that the shock could be located ′ − ′ from the X-raypeak and that the temperature in the ′ − ′ region could be un-derestimated. The Chandra image shows a surface brightness edge at the dis-tance of ∼ ′ from the X-ray peak toward the west. We in-vestigate temperature and density structures of this region withSuzaku and Chandra, respectively. First, we extract the surfacebrightness profile from Chandra data and estimate the densityratio across the surface brightness edge. We exclude compactsources detected in the 0.5-7.0 keV band with the “CIAO” task “wavdetect” using scales of 1, 2, 4, 8, 16 pixels and cuttingat the σ level. We used PROFFIT (Eckert et al. 2011) to ex-tract and fit the profile. The green sector shown in the bottompanel of figure 2 is used to extract the surface brightness pro-file. The instrumental backgrounds are subtracted, and we usedthe energy band of 0.5 - 2.0 keV. We determine the sky back-ground component by fitting a constant model for the outerregion ( . − . arcmin) of the profile. In the following analy-sis, the sky background component was fixed to this value. Weassume the following density model: n ( r ) = n (cid:16) rR f (cid:17) − α , r < R f n C (cid:16) rR f (cid:17) − α , r > R f (4)where n ( r ) is the electron number density at the radius r , n i ( i = 1 , ) is the density, and R f is the radius of the location ofthe discontinuity in arcmin. α i ( i = 1 , ) is powerlaw index, C is the density contrast ( n /n ), and 1 and 2 denote the insideand outside region, respectively. The profile and best-fit model( χ /d.o.f = 4 . / ) are shown in the figure 6. The fittingresults are summarized in table 4. We obtain the density contrastof C = 2 . +2 . − . at the edge ( R f = 2 . ′ +0 . − . ).Secondly, we investigate the temperature structures aroundthe surface brightness edge with Suzaku. Regions used in thisanalysis are displayed with green in figure 7. The radius of an-nulus region are ′ , ′ , ′ , ′ , and ′ , respectively. We fit thespectrum of each region by the model same as in subsection 3.2.The resultant best-fit parameters are listed in table 5, and thetemperature profile is shown in figure 8. We obtained the tem-perature difference T /T = 0 . +0 . − . at the surface brightnessedge, using the results of ′ − ′ and ′ − ′ regions. This indi-cates that the temperature increases outward across the edge. The same electron population attributed to the radio relic areexpected to emit non-thermal X-rays via the inverse Comptonscattering of the CMB photons. We selected the yellow regionin figure 7, whose shape and size are similar to those for theradio flux measurement in van Weeren et al. (2011). First, wedetermine the thermal ICM temperature in this region by fittingthe same spectral model as in subsection 3.2. We obtain theICM temperature of kT = 1 . keV. In the following fit, wefix the temperature of the ICM component to this value becausethe inverse Compton component most-likely to be much weakerthan the thermal ICM one. Second, we fit the extracted spectrafrom the radio relic region by the following model; constant ∗ [ apec LHB + phabs ∗ ( apec MWH + powerlaw CXB + apec ICM + powerlaw IC )] , (5) ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 Table 3.
Fitting results of region across the relic.
Region kT (keV) ∗ normalization ∗ χ /d.o.f ∆ CXB (%) † . +0 . . . − . − . − . . +1 . . . − . − . − . × − . +0 . . . − . − . − . . +0 . . . − . − . − . × − . +0 . . . − . − . − . . +0 . . . − . − . − . × − . +0 . . . − . − . − . . +3 . . . − . − . − . × − . +0 . . . − . − . − . . +1 . . . − . − . − . × − . +0 . . . − . − . − . . +1 . . . − . − . − . × − . +0 . . . − . − . − . . +0 . . . − . − . − . × − . +0 . . . − . − . − . . +2 . . . − . − . − . × − ∗ The first, second, and third errors are statistical, CXB systematic, and NXB systematic, respectively. † CXB fluctuations at the 90 % confidence level estimated. −4 −3 c oun t/ k e V / s ( da t a − m ode l ) / e rr o r Energy (keV) 10 −4 −3 c oun t/ k e V / s ( da t a − m ode l ) / e rr o r Energy (keV)10 −4 −3 c oun t/ k e V / s ( da t a − m ode l ) / e rr o r Energy (keV) 10 −4 −3 c oun t/ k e V / s ( da t a − m ode l ) / e rr o r Energy (keV)10 −4 −3 c oun t/ k e V / s ( da t a − m ode l ) / e rr o r Energy (keV)
Fig. 4.
The XIS spectra of regions across the relic fitted with the model described in the text. The black, red and green crosses show the spectra of XIS0,XIS1,and XIS3, respectively. The blue, light blue, magenta, and orange solid histograms represent the LHB, MWH, CXB, and ICM components, respectively.The Gray solid line in the ′ − ′ region spectra is an AGN component. Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0
Table 4.
Fitting results of the surface brightness profile. α α R f § C S ∗ const † χ /d.o.f . +0 . − . . +1 . − . . +0 . − . . +2 . − . . +0 . − . × − . × − (fixed) . / § The radius of the location of the discontinuity in arcmin. ∗ Normalization of the surface brightness. † The sky background component.
Table 5.
Spectral fitting results of regions across the surface brightness edge.
Region kT (keV) ∗ normalization ∗ χ /d.o.f ∆ CXB (%) † . +0 . . . − . − . − . . +0 . . . − . − . − . × − . +0 . . . − . − . − . . +0 . . . − . − . − . × − . +0 . . . − . − . − . . +0 . . . − . − . − . × − . +1 . . . − . − . − . . +0 . . . − . − . − . × − . +1 . . . − . − . − . . +4 . . . − . − . − . × − ∗ The first, second, and third errors are statistical, CXB systematic, and NXB systematic, respectively. † CXB fluctuations at the 90 % confidence level estimated. . . k T [ k e V ] Distance from the X−ray peak [arcmin]
Fig. 5.
The temperature profile across the radio relic. The horizontal axisrepresents the angular distance from the X-ray peak. Black and light graycrosses shows the results from green and yellow regions of figure 2 toppanel. Only statistical errors are displayed. The positions of the inner andouter edges of the relic are displayed by dark gray dotted lines. where, powerlaw IC represents the inverse Compton compo-nent. We fixed all parameters of the background components( apec LHB , apec MWH and powerlaw
CXB ) to the values derivedfrom the background field in subsection 3.1. We assume twocases for the powerlaw IC photon index ( Γ ); 2.0 or 3.8. Notethat there is no observational information about the radio spec-tra of this relic. Assuming that a simple diffusive shock ac-celeration (DSA) theory with the obtained Mach number ( M X )from our results, the photon index becomes Γ = α + 1 = 3 . (see sec.4.2). However, this implies spectra much steeper thantypical radio relics. On the other hand, a simple DSA dose notseem to hold for some relics. For example, in toothbrush clus-ter, the obtained M X ∼ . from Suzaku data (Itahana et al.2015) is significantly lower than the value estimated from theradio data (van Weeren et al. 2012). If a similar situation occurs, Fig. 6.
The surface brightness profile across the surface brightness edge.The profile was binned to a minimum signal-to-noise ratio of 2 per bin. Thebest fit model described in the text is displayed with the black line. Γ can be significantly smaller than . . Therefore, we assume Γ = 2 . as an extreme case. Systematic errors of CXB and NXBwere taken into account in the same way as in the former anal-ysis. The fitting results are summarized in table 6. Though wedid not detect the inverse Compton component, we obtain anupper limit of the inverse Compton component. The resultantupper limits on the flux are F IC < . × − erg / s / cm and < . × − erg / s / cm for Γ = 2 . and Γ = 3 . , respectively,in 0.3-10 keV considering both the statistical and systematic er-rors for . × − deg area. ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 Table 6.
Spectral fitting results of the spectrum model with inverse Compton components. components kT (keV) or Γ normalization ‡ apec ICM . (fixed) ∗ . +3 . . . − . − . − . × − powerlaw IC . (fixed) † . +1 . × +2 . × +45 . − . − . − . × − ( < . × − § ) χ /d.o.f . / apec ICM . (fixed) ∗ . +3 . . . − . − . − . × − powerlaw IC . (fixed) † . . × +0 . . − . − . − . × − ( < . × − § ) χ /d.o.f . / ∗ The value obtained from spectral fitting of the relic region in figure 7. † Assumed values for the photon index. ‡ Normalizations in the apec code and powerlaw component are written in the same way as in table 2.The errors are represented as in table 3. § Upper limits of normalization. : . : : . : . : : . : . Right ascension D e c li na t i on Fig. 7.
The XIS image and radio contours same as in the top panel of figure2, but overlaid with green regions utilized in the surface brightness edgeanalysis. The radius of annulus region are ′ , ′ , ′ , ′ , and ′ . Yellowregion was used to search for inverse Compton component, whose size is . × − deg . The light blue circles are excluded regions of a pointsource. L X − kT and σ v − kT relations (Wu et al. 1998; Xeu & Wu2000; Novicki et al. 2002; Hilton et al. 2012) are useful to in-vestigate the physical status of galaxy clusters. We compare thetemperature of our results in the cluster central region with theexpected one from L X − kT and σ v − kT relations. First, Hiltonet al. (2012) reported a L X − kT relation as follows, log (cid:18) E − ( z ) L X erg / s (cid:19) = (44 . ± . k T [ k e V ] Distance from the X−ray peak [arcmin]
Fig. 8.
The temperature profile across the surface brightness edge. Theposition of the surface brightness edge is displayed by dark gray dotted line. + (3 . ± .
16) log (cid:16) kT (cid:17) − (1 . ± .
5) log(1 + z ) , (6)where L X is X-ray luminosity in the 0.1-2.4 keV band, z is red-shift and E ( z ) = [Ω (1 + z ) + Λ ] / . Using equation (6), thededuced temperature of this cluster is kT = 3 . ± .
08 keV ( σ confidence level) with L X[0 . − . = 0 . × erg / s (Popesso et al. 2004). We also checked the deduced temperaturefrom another L X − kT relation (Novicki et al. 2002). The ob-tained temperature is kT = 2 . ± .
24 keV and consistent withthe above-mentioned one. Next, Wilson et al. (2016) reported a σ v − kT relation as follows, log (cid:18) σ v / s (cid:19) = (0 . ± . . ± .
14) log (cid:16) kT (cid:17) − (0 . ± .
33) log E ( z ) , (7)where σ v is velocity dispersion. Using equation (7), the de-duced temperature is kT = 2 . ± .
10 keV ( σ confidence Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 level) with σ v = 665 +51 − km / s (Aguerri et al. 2007). Again, wealso checked the deduced temperature from another σ v − kT relation (Wu et al. 1998). The resultant temperature is kT =3 . ± .
28 keV and consistent with the above-mentioned one.The estimated temperatures from both relations are higher thanour result at the center considering both statistical and system-atic errors ( . +0 . − . keV ; σ confidence level ).Cool core components should be removed in the analysiswith L X − kT and σ v − kT relations. If this point is not appro-priately treated, we will have lower temperature than expected.In fact, we see a weak temperature decrease towards the cen-ter. However, the cool core clusters usually have a centrally-peaked distribution of metal abundance. We checked the abun-dance in the central region with the spectral fitting where theabundance is free parameter. As a result, the obtained value( Z = 0 . +0 . − . Z ⊙ ) is not so high and we did not find sucha feature in this cluster. Thus, our result is not likely due toa cool core in this cluster. As another possibility, it is likelythat this cluster is not in dynamical equilibrium. Numericalsimulations of cluster mergers shows that the ICM tempera-ture decreases due to an adiabatic expansion after the collision(Ishizaka 1997; Takizawa 1999).The σ v − kT relation is derived from most of galaxy clusterswhich are regarded as in dynamical equilibrium. If the cluster isin an adiabatic expansion phase after the collision, the velocitydispersion could be high, and the ICM temperature decreases.As a result, the expected temperature from the σ v − kT relationcould be higher than the obtained temperature from observation.In fact, the measured temperature is lower than the expectedone. Thus, the above results also suggest that this cluster mightbe in an adiabatic expansion phase after the collision. Though we did not find a significant temperature jump at theouter edge of the relic, figure 5 shows that the temperature de-creases outward across the relic. This suggests the existence ofthe shocks. We derive the Mach number ( M X ) from the tem-perature difference of the shock candidate region using the aRankine-Hugoniot relation as follows, T post T pre = 5 M + 14 M − M , (8)where T pre and T post are temperature of pre-shock and post-shock regions, respectively, and we assume that the specific heatratio γ ≡ / . We did not find a significant temperature jump atthe relic outer edge where the shock is expected. From figure 5,if shock exists, it could be located in ′ − ′ from the X-ray peak.Considering Suzaku’s spatial resolution, the temperatures of thepost-shock region could be underestimated. Therefore, we usedthe temperatures of regions ′ − ′ and ′ − ′ in figure 2 toppanel for pre- and post-shock, respectively. As a result, we ob- tain the M X = 1 . +0 . . . − . − . − . , where the first, second, andthird errors are statistical, CXB systematic, and NXB system-atic at the 90% confidence level, respectively. Some theoreticalstudies suggest that there are difficulties in particle accelerationat low Mach number shocks. For example, Vink & Yamazaki(2014) reported that shocks of the Mach number less than √ cannot accelerate particles. Our results seem to contradict thisbecause the existence of radio relics is evidence of the acceler-ated particles.Assuming a shock with the above-mentioned Mach num-ber exists at the radio relic, we can calculate the expectedradio spectral index. We can obtain the shock compression( C ≡ ρ /ρ ) from a Mach number. If the electrons are ac-celerated by DSA, the energy spectrum of electrons becomes apower-law with index p ( n ( E ) dE ∝ E − p dE ), which is relatedwith shock compression and given by p = ( C + 2) / ( C − . Forour result, the obtained shock compression is C = 1 . becausethe M X = 1 . . From this value, the power-law index becomes p = 5 . . This means that the spectral index of synchrotron radioat the injection region is α inj = ( p − / . . The integratedradio spectrum is steeper by 0.5 compared to α inj (Pacholczyk1970; Miniati 2002). As a result, α = α inj + 0 . . . Thus,we used the photon index of Γ = α + 1 = 3 . in subsection 3.4.If the Mach number of the shock is estimated from futureradio observations, we might be able to get crucial informationabout the particle acceleration process around the radio relicin this cluster. Unfortunately, because no radio spectral infor-mation has been obtained so far, we cannot compare the Machnumber of the shock from radio observations with our result.Radio observations at other frequency bands are necessary forthis cluster.In the figure 8, the temperature profile south of the relicsuggests that a decrease of the temperature around ′ fromthe X-ray peak. The obtained Mach number is M X =3 . +3 . . . − . − . − . using the temperature difference of the re-gions ′ − ′ and ′ − ′ . This is higher than the aforemen-tioned value around the relic, which suggests that Mach numbervaries along the radio relic, though errors are large. We estimate the pressure profile across the surface brightnessedge. This is important to investigate the physical states of theedge. In figure 8 and 6, we see that the temperature and densityincreases and decreases outward across the surface brightnessedge, respectively. This suggests that this structure is not associ-ated with a shock. We calculate the pressure ratio ( P /P ) at theedge. Using our results about the temperature ratio ( kT /kT =0 . +0 . − . ) and density ratio ( n /n = 2 . +2 . − . ) at the edgefrom Suzaku and Chandra data, we obtain P /P = 1 . +1 . − . .In the X-ray image, cold fronts are seen as an edge-like ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 structure. The temperature and the density are discontinuousbut the pressure is continuous across a cold front. Our resultsshow that the temperature and the density show an increase anda sharp decrease outward across the surface brightness edge,respectively. Additionally, the pressure could be continuousacross the edge. These suggest that the edge could be a coldfront. If the existence of a cold front is true, this could be ev-idence that the galaxy cluster RXC J1053.7+5453 experiencedmerger with other cluster (or group). Considering the overallmorphology of X-ray emission in the Chandra image, the loca-tion of a possible cold front, and the orientation and locationof the relic, it seems that this cluster is in an east-west mergerevent. Alternatively, the thermal pressure ratio at the edge couldbe really more than unity. It cannot be ruled out that the thermalpressure is discontinuous at the edge. In this case, if the pres-sure across the surface brightness edge is in equilibrium, otherforms of pressure sources such as cosmic-rays are necessary. We constrain the magnetic field strength in the relic.Blumenthal & Gould (1970) derived following equations forthe synchrotron and inverse Compton emissions from an elec-tron population with a power-law energy spectrum at frequency ν Synch and ν IC , respectively. dW Synch dν Synch dt = 4 πN e B ( p +1) / m e c (cid:16) e πm e c (cid:17) ( p − / a ( p ) ν − ( p − / , (9) dW IC dν IC dt = 8 π r c h − ( p +3) / N ( kT CMB ) ( p +5) / F ( p ) ν − ( p − / , (10)where N is the normalization, p is the power-law index of theelectron spectrum ( N ( γ ) = N γ − p ; γ is the Lorentz factor ofthe electron), r is the classical electron radius, h is the Planckconstant, and T CMB is CMB temperature ( T CMB = 2 . z ) ).The function a ( p ) and F ( p ) are given as follows (Blumenthal& Gould 1970): a ( p ) = 2 ( p − / √ (cid:0) p − (cid:1) Γ (cid:0) p +1912 (cid:1) Γ (cid:0) p +54 (cid:1) π / ( p + 1)Γ (cid:0) p +74 (cid:1) , (11) F ( p ) = 2 p +3 ( p + 4 p + 11)Γ (cid:0) p +52 (cid:1) ζ (cid:0) p +52 (cid:1) ( p + 3) ( p + 5)( p + 1) . (12)The magnetic field strength in the radio relic can be esti-mated from the comparison of the observed flux density ofthe synchrotron and inverse Compton emissions by the relation S Synch /S IC = dW Synch dν Synch dt / dW IC dν IC dt (Ferrari et al. 2008; Ota et al.2008; Ota et al. 2014; Akamatsu et al. 2017).First, in case of Γ = 2 . , we derive the upper limit of the in-verse Compton flux density as S IC < . × − Jy at 10 keV( ν IC = 2 . × Hz) from the spectral analysis for the non-thermal power-law component (
Γ = 2 . in sec.3.4). Comparingthis limit with the radio flux density of the relic as S Synch = 15 mJy at 1382 MHz (van Weeren et al. 2011), the magnetic fieldstrength becomes
B > . µ G . This value is similar with thoseof other relics ( B > . − µ G ).Secondly, when Γ = 3 . , we obtain B > . µ G using S IC < . × − Jy as well as case of Γ = 2 . . This lowerlimit of magnetic field strength is rather high. Additionally, ifthis is true, the energy density of the magnetic field could behigher than the thermal one. We will discuss this problem in thenext subsection. From our results, we estimate the energy densities of the ther-mal ICM, non-thermal electrons, and magnetic field. These arefundamental and important parameters for radio relic studies.We estimate in the same way as in Itahana et al. (2015). Forsimplicity, we assume that the radio relic region is a cylinderwhose radius and height are 284 kpc and 243 kpc, respectively.The estimated electron number density of the thermal ICM inthe radio relic region becomes n e = 3 . +0 . − . × − cm − from the normalization of the apec ICM model (table 6). Theenergy density of the thermal ICM is U th = 3 n e kT / µ =1 . +1 . − . × − erg / cm with the obtained n e and the tem-perature of this region ( kT = 1 . +0 . − . keV), assuming that themean molecular weight is µ = 0 . .Next, we estimate the energy densities of the magnetic field( U mag = B / π ) and the non-thermal electrons ( U e ) for eachphoton index ( Γ =
Γ = 2 . , the energydensity of the magnetic field is U mag > . × − erg / cm .As a result, U mag /U th > . . This means that the magneticenergy could be more than a ten percent of the thermal one. Theenergy densities of the non-thermal electrons corresponding to0.3-10 keV X-ray band (or, . × < γ < . × ) is U e < . × − erg / cm . Therefore, U e /U th < . × − for Γ =2 . , although we did not included the contribution from lowerenergy electrons in these calculation, which could be dominantin the energy density of the non-thermal electron populations.On the other hands, when Γ = 3 . , we obtain U mag > . × − erg / cm and U e < . × − erg / cm . As a re-sult, U mag /U th > . and U e /U th < . . This means that themagnetic field energy density might be higher than the thermalone. This seems to be quite odd and makes us suspicious ofthe underlying assumptions. For example, DSA does not holdand hence Γ = 3 . , or, the electron spectrum is significantlydeviated from a single power-law form. Another possibility isthat the Mach number derived from our results is seriously un-derestimated owing to projection effects and/or limited spatialresolution. In this case, the actual electron spectrum should beflatter. Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0
We observed the field around the radio relic in the galaxy clus-ter RXC J1053.7+5453 ( z = 0 . ) with Suzaku and Chandra.From the Suzaku XIS analysis, we measured temperature of thiscluster for the first time and the resultant temperature around thecenter is lower than the values expected from both its X-ray lu-minosity and velocity dispersion. Additionally, we found thetemperature decrease outward across the relic and derived theMach number ( M X ∼ . ) assuming that it is due to a shockassociated with the radio relic. Because no radio spectral infor-mation has been obtained, we cannot compare the Mach num-ber of the shock derived from radio observations with our re-sult. We found a surface brightness edge at the distance of ∼ ′ from the X-ray peak toward the west in the Chandra X-ray image. We performed X-ray spectral and surface brightnessanalyses around the edge with the Suzaku and Chandra data,respectively. The obtained surface brightness and temperatureprofiles suggest that the edge is not a shock but a cold front,because the pressure ratio at the edge is consistent with unity.However, it cannot be ruled out that the thermal pressure is dis-continuous across the edge. In this case, to balance the pres-sure across the surface brightness edge, other forms of pressuresource, such as cosmic-rays, are necessary. We searched forthe non-thermal inverse Compton component in the relic region.Though we did not detect the inverse Compton component, weobtained the upper limit on the flux are . × − erg / s / cm and . × − erg / s / cm for Γ = 2 . and Γ = 3 . , respec-tively. The lower limit of magnetic field strength becomes . µ G and . µ G for Γ = 2 . and Γ = 3 . , respectively. Incase of Γ = 3 . , however, odd physical situation occurs, whichseems to be unlikely. Acknowledgments
The authors would like to thank T. Akahori, S. Shibata, and H. Ohno forhelpful comments. We are also grateful to the Suzaku operation team fortheir support in planning and executing this observation. MT is supportedin part by Japan Society for the Promotion of Science (JSPS) KAKENHIGrant Number 26400218. HA and FZ acknowledge the support of NWOvia a Veni grant. SRON is supported financially by NWO, the NetherlandsOrganization for Scientific Research. Support for this work was providedby the National Aeronautics and Space Administration through ChandraAward Number GO5-16140X issued by the Chandra X-ray ObservatoryCenter, which is operated by the Smithsonian Astrophysical Observatoryfor and on behalf of the National Aeronautics Space Administration undercontract NAS8-03060. R.J.W. is supported by a Clay Fellowship awardedby the Harvard-Smithsonian Center for Astrophysics.
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