Cool core disturbed: Observational evidence for coexistence of sub-sonic sloshing gas and stripped shock-heated gas around the core of RX J1347.5-1145
Shutaro Ueda, Tetsu Kitayama, Masamune Oguri, Eiichiro Komatsu, Takuya Akahori, Daisuke Iono, Takumi Izumi, Ryohei Kawabe, Kotaro Kohno, Hiroshi Matsuo, Naomi Ota, Yasushi Suto, Shigehisa Takakuwa, Motokazu Takizawa, Takahiro Tsutsumi, Kohji Yoshikawa
aa r X i v : . [ a s t r o - ph . H E ] A ug Draft version August 29, 2018
Typeset using L A TEX twocolumn style in AASTeX62
Cool core disturbed: Observational evidence for coexistence of sub-sonic sloshing gas and stripped shock-heated gasaround the core of RX J1347.5–1145
Shutaro Ueda,
1, 2
Tetsu Kitayama, Masamune Oguri,
Eiichiro Komatsu,
Takuya Akahori, Daisuke Iono,
Takumi Izumi, Ryohei Kawabe,
9, 10,11
Kotaro Kohno,
4, 12
Hiroshi Matsuo,
9, 10
Naomi Ota, Yasushi Suto,
4, 5
Shigehisa Takakuwa,
Motokazu Takizawa, Takahiro Tsutsumi, and Kohji Yoshikawa Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), 3-1-1 Yoshinodai, Chuo,Sagamihara, Kanagawa 252-5210, Japan Department of Physics, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan Research Center for the Early Universe, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa,Chiba 277-8583, Japan Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild Str. 1, D-85741 Garching, Germany Mizusawa VLBI observatory, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Institute of Astronomy, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan Department of Physics, Nara Women’s University, Kitauoyanishi-machi, Nara, Nara 630-8506, Japan Department of Physics and Astronomy, Graduate School of Science and Engineering, Kagoshima University, 1-21-35 Korimoto,Kagoshima, Kagoshima 890-0065, Japan Department of Physics, Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata, Yamagata 990-8560, Japan National Radio Astronomy Observatory, P.O. Box O, Socorro, NM, 87801, USA Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan (Received; Revised; Accepted)
Submitted to ApJABSTRACTRX J1347.5–1145 ( z = 0 . direct observationalevidence for sub-sonic nature of sloshing motion of the cool core. We find that a residual X-ray imagefrom the Chandra X-ray Observatory after removing the global emission shows a clear dipolar patterncharacteristic of gas sloshing, whereas we find no significant residual in the Sunyaev-Zel’dovich effect(SZE) image from the Atacama Large Millimeter/submillimeter Array (ALMA). We estimate theequation of state of perturbations in the gas from the X-ray and SZE residual images. The inferredvelocity is 420 +310 − km s − , which is much lower than the adiabatic sound speed of the intraclustermedium in the core. We thus conclude that the perturbation is nearly isobaric, and gas sloshingmotion is consistent with being in pressure equilibrium. Next, we report evidence for gas stripping ofan infalling subcluster, which likely shock-heats gas to high temperature well in excess of 20 keV. Usingmass distribution inferred from strong lensing images of the Hubble Space Telescope ( HST ), we findthat the mass peak is located away from the peak position of stripped gas with statistical significanceof > σ . Unlike for the gas sloshing, the velocity inferred from the equation of state of the excess hotgas is comparable to the adiabatic sound speed expected for the 20 keV intracluster medium. All ofthe results support that the southeast substructure is created by a merger. On the other hand, the Corresponding author: Shutaro [email protected]
Ueda et al. positional offset between the mass and the gas limits the self-interaction cross section of dark matterto be less than 3 . h − cm g − (95% CL). Keywords: galaxies: clusters: individual: (RX J1347.5–1145) — X-rays: galaxies: clusters — galaxies:clusters: general — radio continuum: general — gravitational lensing: strong INTRODUCTIONGalaxy clusters are the largest gravitationally-boundand virialized objects in the universe. They are lo-cated at the knots of filaments in the large-scale struc-ture and provide us with unique cosmological informa-tion. Galaxy clusters are also dynamically young and arecontinuously growing through mergers between smallerclusters. Such merger activities induce various high-energy phenomena in the hot and optically thin plasma,i.e., the intracluster medium (ICM), in the gravitationalpotential well of clusters.A large amount of observational and numerical stud-ies have suggested that mergers lead to shock-heating ofthe gas (e.g., Ricker & Sarazin 2001; Markevitch et al.2002; Takizawa 2005, 2006; Bourdin et al. 2013), pro-duction of cold fronts (e.g., Markevitch et al. 2001;Ascasibar & Markevitch 2006; ZuHone et al. 2010;Roediger et al. 2011; Blanton et al. 2011; Ueda et al.2017; Hitomi Collaboration et al. 2018), ram-pressurestripping of the gas from infalling galaxies (e.g.,David & Kempner 2004; Roediger & Br¨uggen 2007;Sasaki et al. 2016), non-equilibrium ionization of theICM (e.g., Akahori & Yoshikawa 2008, 2010, 2012;Inoue et al. 2016), and (re-) acceleration of relativisticparticles (e.g., Feretti et al. 2012; Akamatsu & Kawahara2013; Brunetti & Jones 2014; van Weeren et al. 2017).The entire picture of merging processes is however stillfar from clear; for example, heating mechanisms anddynamics of the ICM are under debate. Observationalstudies in multi-wavelength are therefore crucial forunderstanding the physics of galaxy cluster mergers.RX J1347.5–1145 is one of the most luminous X-ray galaxy clusters and is located at the redshift of z = 0 . ROSAT all sky survey(Schindler et al. 1997). Komatsu et al. (1999) madethe first measurements of the Sunyaev-Zel’dovich effect(SZE: Sunyaev & Zeldovich 1972) toward this clusterwith the James Clerk Maxwell Telescope (JCMT) at350 GHz as well as with the 45 m Nobeyama Radio Tele-scope at 21 and 43 GHz. A higher angular resolution ob-servation of the SZE was performed by Komatsu et al.(2001) using the Nobeyama Bolometer Array (NOBA)and they found a prominent substructure which hasno counterpart in the soft X-ray image by
ROSAT .The presence of the substructure has been confirmed by
Chandra and
XMM-Newton (e.g., Allen et al. 2002;Gitti & Schindler 2004) as well as by more recent SZEmeasurements (Mason et al. 2010; Korngut et al. 2011;Plagge et al. 2013; Adam et al. 2014; Kitayama et al.2016). Allen et al. (2002) measured the mean temper-ature of the ICM to be over 10 keV, which is relativelyhigh compared to other typical clusters. Kitayama et al.(2004) and Ota et al. (2008) found a very hot ( >
20 keV)component of the ICM in this cluster. In addition,the radial profile and spatial distribution of the ICMtemperature indicate that the temperature drops to ∼ r is estimated tobe ∼ . × h − M ⊙ by using the weak-lensing anal-ysis, where r , the radius within which the mean massdensity is 200 times the critical density of the universe,is 1 . h − Mpc (Lu et al. 2010) for this galaxy cluster .It is considered that the hot component is mostlikely associated with a past major merger event (e.g.,Johnson et al. 2012; Kreisch et al. 2016), although itsspecific nature, such as geometry and dynamics of thecollision, is still unclear. Recently, Kitayama et al.(2016) presented the SZE image observed by AtacamaLarge Millimeter/submillimeter Array (ALMA) withangular resolution of 5 ′′ . Such high angular resolutionenables us to remove the emission of the central activegalactic nucleus (AGN) and to reconstruct an accu-rate SZE map. Kitayama et al. (2016) found that theshape of the SZE is elongated toward the southeast andthe peak position of the SZE is located at 11 ′′ south-east from the central AGN. The ALMA high-resolutionSZE image motivates us to directly compare it withhigh-quality data in other wavelengths by Chandra and
Hubble Space Telescope ( HST ). In this paper, we in-vestigate the merger phenomena and merger history inRX J1347.5–1145 by combining the data of
Chandra ,ALMA, and
HST . They adopted the Hubble constant of 70 km s − Mpc − . ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas m = 0 . Λ = 0 .
7. We use the dimen-sionless Hubble constant ( h ≡ H /
100 km s − Mpc − );given controversial results on the value of h (e.g.,Planck Collaboration et al. 2016; Riess et al. 2016), wedo not fix it unless stated otherwise. In this cosmology,an angular size of 1 ′′ corresponds to a physical scale of4.04 h − kpc at the redshift z = 0 . σ . OBSERVATIONS AND DATA REDUCTIONSWe used the X-ray data of RX J1347.5–1145 takenwith the Advanced CCD Imaging Spectrometer (ACIS;Garmire et al. 2003) on board
Chandra . Two out of sixdatasets we used were taken by ACIS-S (ObsID: 506and 507) and the others were by ACIS-I (ObsID: 3592,13516, 13999, and 14407). All the datasets are the sameas used in our previous study (Kitayama et al. 2016).The data reduction is also the same as in Kitayama et al.(2016), except that we used the updated versions, 4.9and 4.7.5.1, of
Chandra
Interactive Analysis of Obser-vations (CIAO; Fruscione et al. 2006) and the calibra-tion database (CALDB), respectively. The backgrounddata were extracted from the region between 2 . ′ and3 . ′ from the peak position of the cluster. Unless statedotherwise, we used XSPEC version 12.9.1 l (Arnaud 1996)and the atomic database for plasma emission modeling(AtomDB) version 3.0.9 in the X-ray spectral analysis,assuming that the ICM is in a collisional ionization equi-librium. The Galactic absorption was fixed at N H =4 . × cm − (Kalberla et al. 2005). We adopted theabundance table of Anders & Grevesse (1989) in the X-ray spectral analysis.The ALMA SZE data used in this paper are thesame as those in Kitayama et al. (2016), except thatan updated version, 5.1.1, of the Common AstronomySoftware Applications ( CASA : McMullin et al. 2007) wasadopted in the imaging analysis.We also used the data of
HST observations ofRX J1347.5–1145 obtained with the Advanced Camerafor Surveys (ACS) to study the central mass distributionfrom strong lensing (SL). These data were provided bythe Space Telescope Science Institute (STScI) and noadditional data reduction was applied in this study. Thedata consisted of F475W, F814W, and F850LP imagesfrom the ACS, which were used in Halkola et al. (2008),K¨ohlinger & Schmidt (2014), and Zitrin et al. (2015). X-RAY AND SZE ANALYSES3.1.
X-ray and SZE imaging analysis
Figure 1 shows the X-ray surface brightness ( left )and the SZE image ( right ) of RX J1347.5–1145, respec-tively, both of which clearly exhibits a substructure in the southeast direction. First, we computed the meanX-ray surface brightness over an ellipse, excluding thesoutheast quadrant (i.e., the substructure), followingUeda et al. (2017). To accurately model the mean sur-face brightness profile, we searched for the ellipse thatminimizes the variance of the X-ray surface brightnessrelative to its mean in a 15 ′′ < ¯ r < ′′ annulus, where¯ r is the geometrical mean of the semi-major and semi-minor axis lengths around the X-ray peak. The range of¯ r was chosen to match the position of the excess emissionin the excluded southeast quadrant and to eliminate theimpact of the bright core (¯ r < ′′ ) of this cluster on theoverall shape. We find that the axis ratio of the ellipseis 0.66 and its position angle is − . ◦ . The resultantannulus is shown in the left panel of Figure 1. We thencalculated the mean X-ray brightness over the ellipseat each ¯ r , excluding the southeast quadrant, and sub-tracted it from the entire brightness. The left panel ofFigure 2 shows an X-ray residual image of RX J1347.5–1145.We also applied the same procedure for the SZE im-age. The obtained SZE residual image is shown in theright panel of Figure 2. Note that we used the un-smoothed SZE image with the synthesized beam size of4 . ′′ × . ′′ FWHM (Kitayama et al. 2016) in the SZEimaging analysis. The smoothed images are shown onlyfor display purposes.Figure 2 clearly shows an excess signal in the southeastquadrant both in the X-ray and SZE images. Thanksto the high-resolution data, we find that the excess SZEsignal has the average FWHM of ∼ ′′ (113 h − kpc),which is significantly more extended than that of ∼ ′′ (69 h − kpc) in the X-ray residual image. This indicatesthat a high temperature region has a larger extent thanseen in X-rays. We will present more detailed analysesand results on this region using two independent meth-ods in Section 3.2 and Section 3.3.A dipolar pattern around the central AGN is appar-ent only in the X-ray residual image (the left panel ofFigure 2). The dipolar pattern consists of a northernpositive excess and a southern negative excess. The frac-tion of each component against the mean brightness isroughly 20 %. The dipolar pattern is clearly distinctfrom the excess in the southeast quadrant and extendsover a spatial scale of ∼ h − kpc. We will describemore detailed results in Section 3.4.We assessed the uncertainty in subtracting the meanprofile of the X-ray and SZE images by the following twomethods. One is the same method as described above, Throughout this paper, the position angle is measured for themajor axis of an ellipse from north (0 deg) through east (90 deg).
Ueda et al. except that the subtraction of the mean profile is doneafter smoothing the X-ray image to the same angularresolution as the ALMA image. The other is that we as-sumed circular symmetry for the mean profile of X-raysand SZE instead of the ellipse. In this check, we do notuse any smoothed images. We then find that 1) a differ-ence of angular resolution between
Chandra and ALMAdoes not affect the residual images, and 2) the geome-try of the mean profile does not affect the substructurein the southeast quadrant, while it slightly modifies theshape of the dipolar pattern in the core.3.2.
X-ray spectral analyses of the southeastsubstructure
To understand the origin and thermodynamic proper-ties of the ICM in the southeast substructure, we per-formed X-ray spectral analyses. We defined nine regionscovering the excess and its surrounding along the el-lipse as in Section 3.1 (i.e., Region 1a, 1b, 1c, 2a, · · · ,3b, and 3c) and three regions covering the remainingparts of the ellipse (i.e., Region 1d, 2d, and 3d) as il-lustrated in Figure 3. First, we assumed, for simplicity,that the ICM in each region consists only of a singlecomponent over the entire line-of-sight. Its temperature( kT single ) was measured using a model phabs * apec in XSPEC , where phabs represents the Galactic absorption(Balucinska-Church & McCammon 1992). The photoncounts in 0 . − . r (i.e., kT single ofRegion 1d, 2d, and 3d). We then measured the temper-ature of the excess component ( kT excess ) by using thetwo apec model, fixing the temperature of the ambi-ent component at the best-fit value of kT single in Re-gion 1d, 2d, and 3d, respectively. The spectral normal-ization of the ambient component was scaled by eachinterested sky area. The best-fit parameters of the ex-cess component are shown in Table 1. We also es-timated the electron density of the excess component( n excess ) assuming that it is uniform over a line-of-sightextent of L excess = 150 kpc, which is similar to the pro-jected size of the substructure on the sky. For dif-ferent values of L excess , the electron density scales as L − / . In addition, we calculated the thermal pressureof the excess electrons ( p excess ), i.e., n excess × kT excess .In above analyses, we fixed the metal abundance ofthe ICM at 0.38 solar based on previous X-ray measure-ments (Ota et al. 2008). Figures 4, 5, and 6 show the spatial maps of kT excess , n excess , and p excess (left panels are their best-fits and right panels are corresponding statistical error),respectively. We find that the electron density of excesscomponent in Region 1b is the highest among the nineregions, which agrees with the peak position in the X-rayresidual image. On the other hand, while the statisticalerror is large, the temperature of the excess componentin Region 2b is estimated to be ∼
30 keV, which is thehighest among the nine regions. The highest tempera-ture region is located at ∼ ′′ away from the center,which is well outside the cool core. Note that the X-ray emission in Region 2b is faint but the SZE signal isprominent. This means that the ALMA SZE data play acrucial role in identifying such excess hot gas. The ther-mal pressure of the excess electrons ( p excess ) is nearlyconstant among Regions 1b, 2b, and 1c, as presented inTable 1. This is in good agreement with the excess SZEsignal shown in the right panel of Figure 3. The thermalenergy of the excess electrons in Region 1b, 2b, and 1c isestimated to be ∼ . × h − erg, ∼ . × h − erg,and ∼ . × h − erg, respectively.We estimated the Mach number M from the Rankine-Hugoniot jump condition, assuming the ratio of specificheats as γ = 5 / T T = 5 M + 14 M − M , (1)where T is the pre-shock temperature and T is thepost-shock temperature. Using the observed tempera-ture jump between Region 2a and 2b and propagatingthe statistical errors, we obtain M = 1 . +0 . − . . Theadiabatic sound speed of the gas in Region 2a is esti-mated to be 2140 +300 − km s − , implying a shock speed ofthe gas in Region 2b as 3590 +1560 − km s − .3.3. Combined analysis of SZE and X-ray imagingdata for the excess component
As an alternative measure of the gas temperature andelectron density, we combined the SZE and X-ray im-ages. We used
SPEX version 3.04.00 for the X-ray dataanalysis and
CASA version 5.1.1 for the SZE data analy-sis. Note that the analysis in this section does not relyon X-ray spectra and is fully independent of that pre-sented in Section 3.2.We measured the intensities of X-ray (∆ I X ) and SZE(∆ I SZ ) of the X-ray and SZE residual images shown inFigure 2. Both images were binned so that the angularresolutions of Chandra and ALMA have a common pixelsize of 5 ′′ × ′′ . The two intensities are then described ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas -8 -7.5 -7 -6.5 -6 -5.532.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on
100 kpc/h log I X (photon/s/arcsec /cm ) -0.2 -0.1 0 0.1 0.232.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on beam
100 kpc/h I SZ (mJy/beam) Figure 1.
Surface brightnesses of the X-ray ( left ) and the SZE ( right ) of RX J1347.5–1145. The green cross corresponds to theposition of the central AGN identified by ALMA at 92 GHz.
Left:
The X-ray surface brightness in the 0 . − . − arcsec − cm − . This image is smoothed by the Gaussian kernel with 2 . ′′ FWHM. Overlaid is a white elliptical annulus within which variation of this surface brightness is minimized at the mean radiusbetween 15 ′′ and 35 ′′ , excluding the southeast quadrant. Right:
The SZE surface brightness overlaid with the contours of theX-ray surface brightness, corresponding to 64, 32, 18, 8, 4, and 2 % of the peak value, after being smoothed by the Gaussiankernel with 2 . ′′ FWHM. Colors indicate the ALMA SZE map in mJy beam − smoothed to a beam size of 5 ′′ FWHM. Thebeam size is presented as a black circle out of the map. -6E-07 -4E-07 -2E-07 0 2E-07 4E-07 6E-0732.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on
100 kpc/h Δ I X (photon/s/arcsec /cm ) -0.1 -0.05 0 0.05 0.132.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on beam
100 kpc/h Δ I SZ (mJy/beam) Figure 2.
Residual images of the X-ray and SZE surface brightness.
Left:
The residual image of
Chandra
X-ray surfacebrightness after subtracting the mean profile, excluding the southeast quadrant. The original surface brightness is the same asthe left panel of Figure 1. For reference, the position of the central AGN is marked by a cross.
Right:
Same as the left panelbut for the ALMA 92 GHz brightness in mJy beam − with the effective beam size of 5 ′′ FWHM. The original surface brightnessis shown in the right panel of Figure 1.
Ueda et al. -6E-07 -4E-07 -2E-07 0 2E-07 4E-07 6E-0734.0 32.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on
100 kpc/h Δ I X (photon/s/arcsec /cm )
1d 2d 3d1a2a
3a 1b2b3b 1c2c3c -0.1 -0.05 0 0.05 0.134.0 32.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on Δ I SZ (mJy/beam)
100 kpc/h
1d 2d 3d
Figure 3.
Same as Figure 2, except that elliptical annuli used in the X-ray spectral analysis are overlaid.
Table 1.
Best-fit parameters to the X-ray spectra in each region shown in Figure 3. The metal abundance is fixed at each of0.38 Z ⊙ . The photon counts are background-subtracted. kT single is obtained by a single component model in the 12 regions. kT excess and n excess are obtained by a two-component fit in each region, fixing the temperature of the ambient component atthe best-fit values for the same annulus region (i.e., kT single of Region 1d, 2d, and 3d). We show the statistical errors alone.Region 1a 1b 1c 1dPhoton counts in 0 . − . kT single (keV) 18 . +2 . − . . +1 . − . . +1 . − . . +0 . − . kT excess (keV) 21 . +8 . − . . +4 . − . . +6 . − . – n excess (10 − cm − ( L excess /
150 kpc) − / ) 2 . +0 . − . . +0 . − . . +0 . − . – p excess (keV cm − ( L excess /
150 kpc) − / ) 0 . +0 . − . . +0 . − . . +0 . − . –Region 2a 2b 2c 2dPhoton counts in 0 . − . kT single (keV) 17 . +3 . − . . +4 . − . . +1 . − . . +1 . − . kT excess (keV) 17 . +4 . − . . +9 . − . . +2 . − . – n excess (10 − cm − ( L excess /
150 kpc) − / ) 1 . +0 . − . . +0 . − . . +0 . − . – p excess (keV cm − ( L excess /
150 kpc) − / ) 0 . +0 . − . . +0 . − . . +0 . − . –Region 3a 3b 3c 3dPhoton counts in 0 . − . kT single (keV) 17 . +3 . − . . +4 . − . . +2 . − . . +1 . − . kT excess (keV) 16 . +4 . − . . +8 . − . . +4 . − . – n excess (10 − cm − ( L excess /
150 kpc) − / ) 1 . +0 . − . . +0 . − . . +0 . − . – p excess (keV cm − ( L excess /
150 kpc) − / ) 0 . +0 . − . . +0 . − . . +0 . − . – ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas kT excess Error kT excess (keV) Figure 4.
Temperature ( left ) and average of its statistical error ( right ) maps of the excess component ( kT excess ) in nine regionsin units of keV. All the best-fit values are the same as shown in Table 1, while the error values are the average of upper andlower statistical errors of each region. -3.5 -3 -2.5 -2 . log n excess Error log n excess (cm -3 ) Figure 5.
Same as Figure 4 but for the logarithm of electron density of the excess component (log n excess ) in units of log cm − .The values are approximately proportional to ( L excess /
150 kpc) − / . Ueda et al. P excess Error P excess (keV cm -3 ) Figure 6.
Same as Figure 4 but for the thermal pressure of the excess electrons ( p excess ) in units of keV cm − . The values arealso approximately proportional to ( L excess /
150 kpc) − / . ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas I X ∝ n × Λ( T excess ) × L excess , (2)∆ I SZ ∝ n excess × kT excess × L excess × f r ( T excess ) × f c , (3)respectively, where Λ is the X-ray emissivity over theenergy range 0 . − . f r is the relativistic correc-tion to the SZE intensity (Itoh & Nozawa 2004), and f c is a correction factor for the missing flux in theALMA data. We set f c to be equal to the parameter c = 0 .
88 in Equation (2) of Kitayama et al. (2016) de-rived from detailed imaging simulations for RX J1347.5–1145 . We then solved Equations (2) and (3) for n excess and kT excess , respectively, assuming L excess = 150 kpcas in Section 3.2. For different values of L excess , theyapproximately scale as kT excess ∝ L − / and n excess ∝ L − / , if weak dependences of Λ and f r on temperatureis neglected. We focused on the high significance pixelsfor which the signal-to-noise ratios (S/N) of ∆ I X and∆ I SZ are both over 4 σ . Figure 7 shows the measuredtemperature of the excess component ( left ) and its sta-tistical error ( right ). Figure 8 is the same as Figure 7but for the electron density of the excess component.The typical errors of temperature and electron densityare about 4 keV and 0 . × − cm − , respectively.We find that the highest temperature region is locatedin Region 2b. This result is consistent with that mea-sured with an independent method using the X-ray spec-tra (Section 3.2). We also find that the highest electrondensity region is in Region 1b. In addition, we esti-mate the thermal energy of the excess electrons to be(1 . ± . . ) ± . . )) × h − erg from the SZEresidual image directly, within a radius of 50 h − kpcaround the peak of the SZE residual signal. Furtherdetails of the systematic uncertainty are mentioned inSection 3.5. The angular resolution and sensitivity ofthe previous SZE observations did not match those ofthe X-ray data. The ALMA SZE data allow us, for thefirst time, the detailed comparison with the X-ray datawith comparable resolution and sensitivity.3.4. Nature of gas sloshing in the core
The spatial scale of the dipolar pattern is estimatedto be 40 h − kpc by applying the definition of the sizedescribed in Ueda et al. (2017). We analyzed the X-rayspectra of the ICM in the region of the dipolar pattern to The bulk of the missing flux in the ALMA data resides in aconstant offset in the brightness, represented by another parame-ter c in Equation (2) of Kitayama et al. (2016). Such an offset,however, is fully removed in the residual image and does not affectthe analysis of the present paper. examine its thermodynamic property. The temperaturetoward the positive and the negative excess is estimatedas 8 . +0 . − . keV and 10 . +0 . − . keV, respectively. The metalabundances are 0 . +0 . − . Z ⊙ for the positive excess and0 . +0 . − . Z ⊙ for the negative excess. These propertiesare as expected for gas sloshing, i.e., metal rich, cool,and dense gas is moving around the central galaxy. Onthe other hand, we find the absence of excess SZE signalin the core, which provides the first direct evidence thatthe disturbed gas is nearly in pressure equilibrium. Thisindicates that the gas sloshing motion is sub-sonic.Here, we shall introduce the “equation of state” ofthe perturbation in gas, w ≡ ∆ p/ ∆ ρ . For similaranalyses, see Churazov et al. (2016), Khatri & Gaspari(2016), and references therein. If the perturbation is adi-abatic, then w is equal to the sound speed squared, i.e., w = c s . If the perturbation is isobaric, we should find w ≪ c s . The SZE residual image gives an estimate ofthe pressure perturbation ∆ p , whereas the X-ray resid-ual image gives an estimate of the density perturbation∆ ρ as | ∆ I X |h I X i ≃ ∆ h n ih n i ≃ ρ p h ρ i (4)because | ∆ I X | ≪ h I X i , where h I X i is the mean X-raysurface brightness, h n i is the mean square electronnumber density, and h ρ i is the mean square gas massdensity. First, to cover the dipolar pattern in the X-ray residual image, we used the ellipse with the samegeometry as mentioned in Section 3.1, with a semi-major axis length of 22 ′′ , excluding the southeast quad-rant. We extracted the X-ray spectrum for this ellip-tical sector and carried out the X-ray spectral analy-sis. Assuming the line-of-sight depth of 100 kpc, themean ICM temperature and the mean electron num-ber density, p h n i , in this region are 9 . ± . . ± . × − cm − , respectively. Next, using theX-ray and SZE residual images and assuming the line-of-sight depth of 100 kpc, we measured ∆ ρ , ∆ p , and theirstatistical errors within the same elliptical sector. Wethen find that the velocity inferred from the equationof state is √ w = 420 +310 − km s − . This inferred veloc-ity is much lower than the adiabatic sound speed of the10 keV ICM, ∼ − . The motion of gas sloshingis therefore consistent with being sub-sonic and isobaric.3.5. Systematic uncertainty of the ICM properties
The systematic uncertainty of the ICM temperaturemeasured with the ACIS is estimated to be ∼
20 % forgalaxy clusters with high temperature (over 10 keV)ICM like RX J1347.5–1145 (e.g., Reese et al. 2010;Nevalainen et al. 2010; Schellenberger et al. 2015).Note that the statistical uncertainty of the tempera-0
Ueda et al. . - : : . Right ascension D ec li n a ti on . - : : . Right ascension D ec li n a ti on kT excess Error kT excess (keV) Figure 7.
Temperature of the excess component in units of keV ( left ) and its statistical error ( right ) inferred from the ALMASZE and
Chandra
X-ray images, assuming a constant line-of-sight length of L excess = 150 kpc. The values are approximatelyproportional to ( L excess /
150 kpc) − / . Regions for which S/N of either data are less than 4 σ are left blank (black colored). Forreference, the elliptical annuli shown in Figure 3 are overlaid. Note that X-ray spectra are not used in computing the quantitiesplotted in this figure. -3.5 -3 -2.5 -2 -1.532.4 13:47:31.2 . - : : . Right ascension D ec li n a ti on . - : : . Right ascension D ec li n a ti on log n excess Error log n excess (cm -3 ) Figure 8.
Same as Figure 7, but for the logarithm of electron density ( left ) and its statistical error ( right ) in units of cm − .The values are also approximately proportional to ( L excess /
150 kpc) − / . ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas ∼
30 % in the nineregions. We evaluated the impact of the systematicuncertainty on the X-ray and the SZE data for the com-bined analysis. We applied the 4 % uncertainty of theACIS effective area , the 6 % uncertainty of the ALMAflux calibration (see Section 2 of Kitayama et al. 2016),and 1.3 µ Jy arcsec − for the ALMA missing flux cor-rection (see Section 4.2 of Kitayama et al. 2016) to thedata. The error of the ICM temperature and density in-cluding the systematic uncertainty is about twice largerthan that shown in the right panels of Figure 7 and 8; forexample, the error for the highest temperature region(23.2 keV) changes from ± . ± . HST
STRONG-LENSING ANALYSIS4.1.
Central mass distribution
To reveal the geometry of mergers in RX J1347.5–1145, we analyzed the central mass distribution de-rived by SL. We used the
GLAFIC software package(Oguri 2010) for our mass modeling.
GLAFIC adopts aparametrized mass model and derives the best-fit massmap that reproduces the observed positions of SL mul-tiple images. The software has been used for SL massmodeling of many massive clusters (e.g., Oguri et al.2012; Kawamata et al. 2016) and has also been shown torecover central mass distributions of simulated clustersremarkably well (Meneghetti et al. 2017).We followed the standard procedure to model massiveclusters in which we adopted a few dark halo compo-nents, cluster member galaxies, and the external pertur-bations on the lens potential (see e.g., Kawamata et al.2016). For dark halo components, we assumed an el-liptical extension of the Navarro-Frenk-White (NFW)model (Navarro et al. 1997). Each dark halo compo-nent is characterized by a set of parameters includ-ing the virial mass, the concentration parameter, po-sitions, the eccentricity of ellipse, and its position an-gle as model parameters. For member galaxies, weused the scaling relations to reduce the number ofmodel parameters. We constructed a cluster mem-ber galaxy catalog by selecting galaxies near the red-sequence in the
HST
F475W-F814W color-magnitudediagram, where the magnitudes are MAG APER of
SExtractor (Bertin & Arnouts 1996) with 1 ′′ diameteraperture. The mass distribution of the member galaxieswas assumed to follow pseudo-Jaffe ellipsoids whose ve- http://cxc.harvard.edu/cal/summary/Calibration Status Report.html locity dispersions and truncation radii scale with galaxyluminosity L gal as σ ∝ L / and r trunc ∝ L / , respec-tively. The normalizations of these two scaling rela-tions were treated as model parameters. In addition,to improve the fit, we included external perturbationsdescribed by a multipole Taylor expansion of the form φ ∝ r cos m ( θ − θ ∗ ). We included terms with m = 2(external shear), 3, and 4. Each term is specified by itsamplitude and position angle as model parameters.For observational constraints, we used the positions of21 multiple images from six multiple image sets of thelensed galaxies. These multiple images are identifiedin previous work on this cluster (Halkola et al. 2008;K¨ohlinger & Schmidt 2014; Zitrin et al. 2015). In thispaper, we reexamined the validity of the previous mul-tiple image identifications in the course of our own massmodeling, and adopted only secure multiple images forour analysis. The redshift of one multiple image set wasfixed as the spectroscopic value, whereas for those of fourmultiple image sets, we included Gaussian priors basedon their photometric redshifts. We assumed a positionalerror of 0 . ′′ . +2 . − . × h − M ⊙ for the main cluster and 2 . +2 . − . × h − M ⊙ for the subcluster. Their concentration pa-rameters are estimated to be c = 6 . +1 . − . and c = 4 . +2 . − . ,respectively. The obtained mass and concentration pa-rameter are correlated strongly, therefore the system-2 Ueda et al.
Table 2.
Data of 21 multiple images from six multiple image sets of the lensed galaxies used for our SL analyses.ID R.A. (deg) Dec. (deg) z obsa Reference b . ± . .
75 1, 22.2 206.871675 -11.7607222.3 206.872312 -11.7612553.1 206.874179 -11.745133 4 . ± . . ± . . ± . az obs without an error bar indicates a spectroscopic redshift which is fixed during mass modeling, whereas those with errorbars are photometric redshifts. In the mass modeling, we regarded source redshifts of the five multiple image sets without thespectroscopic redshifts as model parameters, but included Gaussian priors for those with photometric redshifts. b References: 1 – Halkola et al. (2008) (see also Bradaˇc et al. 2008); 2 – K¨ohlinger & Schmidt (2014); 3 – Zitrin et al. (2015). atic uncertainty of the mass estimates might be large.Nevertheless their mass ratio indicates that RX J1347.5–1145 is a major merging cluster. The total mass of thesubcluster has been previously estimated using the ex-cess X-ray flux and applying the luminosity - mass re-lation to be (3 . ± . × h − M ⊙ (Johnson et al.2012) and ∼ . × h − M ⊙ (Kreisch et al. 2016),which are consistent with that by our SL analysis . Theentire mass distribution of RX J1347.5–1145 is slightlyelongated along the northeast direction.The right panel of Figure 9 shows the surface massdensity map obtained from the three dark halo com-ponents. The mass of the third component is weaklyconstrained to be 1 . × h − M ⊙ (95% CL). The lo-cation of the third component is also poorly determined,but it lies to the northeast of the BCG. These indicate Both masses were originally estimated based on the Hubbleconstant of 70 km s − Mpc − , while we re-calculated them usingour h to adjust to this paper. that the mass distribution of dark matter (DM) nearthe center and in the southeast quadrant of RX J1347.5–1145 is well modeled by the two dark halo components.We therefore neglect the third dark halo component inthe rest of this paper.4.2. Gas stripping and sloshing
We find a clear offset between the mass peak of thesubcluster and the position of the substructure in X-rays and the SZE (the bottom panels of Figure 10).The second mass peak is away from the peak positionof the X-ray substructure with statistical significance of5 . σ . The second DM component is most likely associ-ated with the infalling subcluster, suggesting that thegas that was originally in the subcluster is stripped byram-pressure of the main cluster.The top left panel of Figure 10 shows that the X-raycentroid coincides with the mass peak of the main clus-ter even though the ICM in the cool core is sloshing.The mass peak of the main cluster is located at the in-terface between the positive and the negative excesses ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas Table 3.
Best-fit parameters of mass distributions of the main cluster and the subcluster measured by SLMain cluster SubclusterMass (10 h − M ⊙ ) 7 . +2 . − . . +2 . − . Concentration parameter 6 . +1 . − . . +2 . − . Offset of mass peak relative to each BCG (arcsec) a (0 . +0 . − . , 0 . +1 . − . ) (0 . +1 . − . , 3 . +2 . − . )Semi-minor to semi-major axis ratio 0 . +0 . − . . +0 . − . Position angle (deg) 1 . +4 . − . . +2 . − . a The positions of the BCG and the 2nd BCG are (RA, Dec.) = (13h47m30.639s, -11d45m09.589s) and (RA, Dec.) =(13h47m31.870s, -11d45m11.20s), respectively. : . - : : . Right ascension D ec li n a ti on (10 h M (cid:4330) /Mpc ) : . - : : . Right ascension D ec li n a ti on (10 h M (cid:4330) /Mpc ) Figure 9.
Surface mass density map of RX J1347.5–1145 measured with SL assuming two dark halo components ( left ) or threeones ( right ) in units of 10 h M ⊙ Mpc − . The entire morphology is nearly unchanged by an addition of the third dark mattercomponent. of the dipolar pattern (see the bottom left panel of Fig-ure 10). These features indicate that part of the gas inthe cool core is moving around the BCG, but the DMdistribution is not disturbed. DISCUSSION5.1.
Origin of the excess hot ICM
The presence of very hot ICM in excess of 20 keV is in-ferred in RX J1347.5–1145 for the earlier SZE and X-rayobservations (Kitayama et al. 2004; Ota et al. 2008).Combining the X-ray data of
Chandra with the SZEdata of ALMA, we have confirmed the temperature ofthe excess hot ICM by two independent methods andhave improved precision of its position. The excess hotICM is located at a distance of 27 ′′ (or ∼ h − kpc)to the southeast from the cluster center. Following Section 3.4, we also measure the equationof state of the excess hot ICM. We compute ∆ p and ∆ ρ for an elliptical region with semi-major and semi-minoraxis lengths of 14 ′′ and 12 ′′ , respectively, and a positionangle of − ◦ around the centroid of the excess SZEsignal. We assume the line-of-sight depth of 150 kpc.Given that ∆ I X > h I X i in this region, we adopt n excess given in Equation (2) as a better proxy for ∆ ρ thanEquation (4). On the other hand, ∆ p is directly com-puted from the SZE residual signal, ∆ I SZ . We analyzethe X-ray spectrum in this region using the same pro-cedure as described in Section 3.2. The electron num-ber density and temperature of the excess hot ICM is(3 . ± . × − cm − and 20 . +2 . − . keV, respectively.We then find that the velocity inferred from the equa-tion of state of the excess hot ICM is 1970 ±
150 km s − ,which matches ∼
85 % of the adiabatic sound speed of4
Ueda et al. -8 -7.5 -7 -6.5 -6 -5.532.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on
100 kpc/h a) X-ray & SL mass map log I X (photon/s/arcsec /cm ) -0.2 -0.1 0 0.1 0.232.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on b) SZE & SL mass map I SZ (mJy/beam)
100 kpc/h -6E-07 -4E-07 -2E-07 0 2E-07 4E-07 6E-0732.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on
100 kpc/h c) X-ray res. & SL mass map Δ I X (photon/s/arcsec /cm ) -0.1 -0.05 0 0.05 0.132.0 13:47:30.0 28.0 : . - : : . Right ascension D ec li n a ti on d) SZE res. & SL mass map
100 kpc/h Δ I SZ (mJy/beam) Figure 10.
Comparison of morphology between the surface mass density map derived from two dark halo components andother wavelength images.
Top left:
White contours of the surface mass density map are overlaid on the X-ray surface brightnessimage. The contours indicate levels of 2.0, 3.0, 4.0, · · · , 9.0, 10 . × h M ⊙ Mpc − , respectively. This X-ray image is the sameas the left panel of Figure 1. The mass peak of the main cluster coincides with the X-ray centroid, while no X-ray counterpartsare found at the mass peak of the subcluster. Top right:
Same as the top left panel but for the SZE image. This SZE image isthe same as the right panel of Figure 1. No SZE counterparts are found at the mass peak of the subcluster.
Bottom left:
Sameas the top left panel but for the X-ray residual image. This X-ray residual image is the same as the left panel of Figure 2. Theclear offset between the mass peak of the subcluster and the X-ray substructure is found.
Bottom right:
Same as the top leftpanel but for the SZE residual image. This SZE residual image is the same as the right panel of Figure 2. As shown in this topright panel, the offset between the SZE substructure and the mass peak of the subcluster is found. ool core disturbed: sub-sonic sloshing gas and stripped shock-heated gas ∼ − . This supports picturethat the pressure perturbation in the southeast quadrantis induced by shock.The excess hot ICM in the southeast quadrant is mostlikely associated with a major merger. The result of SLanalysis indicates that the mass peak of the subclusteris offset from the location of the southeast substructure.Our results imply that the gas that was originally inthe subcluster is stripped by ram-pressure of the maincluster. As mentioned above, the pressure perturbationof the southeast substructure in the SZE residual im-age is consistent with that created by shock, so it isplausible that this stripped gas has been heated duringthe major merger. Details of shock-heating processesin RX J1347.5–1145 using numerical simulations will bepresented elsewhere.5.2. Major merger and sloshing cool core
We have also found a dipolar pattern in the core ofRX J1347.5–1145 in its X-ray residual image. This is di-rect evidence that the core is experiencing gas sloshing,whose presence was suggested before by Johnson et al.(2012) and Kreisch et al. (2016). We find that the ICMproperties of the disturbed gas obtained by the X-rayspectral analysis are consistent with those expected bygas sloshing. In addition, we find that the equation ofstate of disturbed gas is consistent with being isobaric,i.e., the motion of gas sloshing is in pressure equilib-rium. The morphology of this dipolar patter seems tobe a spiral. If so, the direction of the sloshing motionis in the plane of the sky. Such dipolar spiral pat-terns are often found in local cool core clusters (e.g.,Churazov et al. 2003; Clarke et al. 2004; Sanders et al.2014; Ueda et al. 2017), which show no apparent featureof a major merger. Those indicate that their gas slosh-ing is induced by a minor merger. RX J1347.5–1145,however, has a subcluster and the excess hot ICM in itscentral 150 h − kpc. RX J1347.5–1145 is therefore thefirst cluster ever known to host both a major mergerand gas sloshing in the cool core.The size of the dipolar pattern is a factor of 2 ∼ − by optical observations (Lu et al.2010). The stripped gas locates behind the subcluster,which indicates the infalling subcluster is in the first pas- sage. It is unclear, however, whether or not the infallingsubcluster is the origin of gas sloshing. If the directionof the passage is from southwest to northeast, it seemsto be hard to disturb and create a rotational motion ofthe gravitational potential well of the main cluster. Apossibility that the subcluster is in the first passage andgas sloshing is induced by another earlier merger, wassuggested by Kreisch et al. (2016). In this paper, we cannot constrain their scenario.5.3. Self-interaction cross section for dark matter
As discussed above, it seems that the merger inRX J1347.5–1145 is in the plane of the sky. FollowingMarkevitch et al. (2004), an offset in the positions ofgalaxies, DM halos, and the ICM allows us to constrainthe self-interaction cross section of DM. We estimatedthe surface mass density of DM (Σ s ) in the subclusterusing its mass distribution shown in the left panel ofFigure 9. We measured the mean Σ s within a radiusof 25 h − kpc from the second mass peak. We also sub-tracted the contribution of the main cluster based onthe parameters listed in Table 3. Assuming the scatter-ing depth of τ s = Σ s × σ DM /m < σ DM /m < . h − cm g − , where σ DM is theDM collision cross section and m is the mass of a DMparticle. To derive more conservative upper limit, wefurther considered the uncertainty of the surface massdensity map of RX J1347.5–1145. We subtracted the 2 σ value of the rms noise obtained in Section 4 from theoriginal surface mass density map and re-estimated thecross section in the same manner as mentioned above.The 2 σ (95% CL) upper limit of the cross section is then σ DM /m < . h − cm g − . The derived upper limits arecomparable to those reported in the studies of other clus-ters (e.g., Markevitch et al. 2004; Harvey et al. 2015). CONCLUSIONSWe have studied RX J1347.5–1145, one of the well-known major merging clusters, combining the high an-gular resolution, multi-wavelength data taken by
Chan-dra , ALMA, and
HST . The conclusions of this paper aresummarized as follows. • The residual image of the X-ray surface bright-ness shows a clear dipolar pattern in the clustercenter, whereas, we find no excess SZE signal inthe central region in the SZE residual image. Thedipolar pattern indicates that a fraction of the gasin the cool core is disturbed by gas sloshing. Wehave estimated the equation of state of the per-turbation in gas using the X-ray and SZE resid-ual images. We find that the inferred velocity is6
Ueda et al. +310 − km s − , which is much lower than the adi-abatic sound speed of the 10 keV ICM inside thecore; thus, the perturbation is consistent with be-ing isobaric. This is the first direct evidence ofsub-sonic nature of gas sloshing motion. • Both X-ray and SZE residual images show anexcess component in the southeast substructure.We find that the peak of excess hot ( ∼
30 keV)ICM is located at 27 ′′ (109 h − kpc) to the south-east from the cluster center. This region is faintin X-rays but bright in the SZE. The X-ray in-ferred thermal pressure of the excess componentis nearly constant among the regions where theSZE signal is prominent. The velocity inferredfrom the equation of state of the excess hot ICMis 1970 ±
150 km s − , which is comparable to theadiabatic sound speed of the 20 keV ICM. This re-sult supports a picture that the perturbation inthe southeast is generated by shock. • The mass distribution of RX J1347.5–1145 ob-tained with SL is reproduced well by the two darkhalo components. Their mass peaks are in goodagreement with the positions of the BCG and the2nd BCG. The mass peak of the main clustermatches the X-ray centroid, while the mass peakof infalling subcluster is offset from the substruc-ture in X-rays and the SZE. This indicates thatthe gas originated in the subcluster is stripped byram-pressure of the main cluster and shock heatedduring an on-going major merger. • In our scenario, this major merger is likely in thefirst passage. RX J1347.5–1145 is therefore an ex-ceptional cluster in which the excess hot gas, on- going major merger, and the sloshing cool corecoexist within the central 150 h − kpc. • We have also constrained the self-interaction crosssection of DM. The resulting upper limit of thecross section is σ DM /m < . h − cm g − (95%CL).We are grateful to the anonymous referee for helpfulsuggestions and comments. This paper makes use of thefollowing ALMA data: ADS/JAO.ALMA Facilities:
CXO, ALMA, HSTREFERENCES