A Cool Core Disturbed: Observational Evidence for the Coexistence of Subsonic Sloshing Gas and Stripped Shock-heated Gas around the Core of RX J1347.5–1145

Figure 1 shows the X-ray surface brightness (left) and the SZE image (right) of RX J1347.5–1145, both of which clearly exhibit a substructure in the southeast direction. First, we computed the mean X-ray surface brightness over an ellipse, excluding the southeast quadrant (i.e., the substructure), following Ueda et al. (2017). To accurately model the mean surface brightness profile, we searched for the ellipse that minimizes the variance of the X-ray surface brightness relative to its mean in a $15^{\prime\prime} \lt \bar{r}\lt 35^{\prime\prime}$ annulus, where $\bar{r}$ is the geometrical mean of the semimajor and semiminor axis lengths around the X-ray peak. The range of $\bar{r}$ was chosen to match the position of the excess emission in the excluded southeast quadrant and to eliminate the impact of the bright core ($\bar{r}\lt 10^{\prime\prime}$) of this cluster on the overall shape. We found that the axis ratio of the ellipse is 0.66 and its position angle is −87.¹⁹ The resultant annulus is shown in the left panel of Figure 1. We then calculated the mean X-ray brightness over the ellipse at each $\bar{r}$, excluding the southeast quadrant, and subtracted it from the entire brightness. The left panel of Figure 2 shows an X-ray residual image of RX J1347.5–1145.

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We also applied the same procedure for the SZE image. The obtained SZE residual image is shown in the right panel of Figure 2. Note that we used the unsmoothed SZE image with a synthesized beam size of 41 × 25 FWHM (Kitayama et al. 2016). The smoothed images are shown only for display purposes.

Figure 2 clearly shows an excess signal in the southeast quadrant both in the X-ray and SZE images. Thanks to the high-resolution data, we find that the excess SZE signal has an average FWHM of ∼28'' (113 h⁻¹ kpc), which is significantly more extended than that of ∼17'' (69 h⁻¹ kpc) in the X-ray residual image. This indicates that a high-temperature region has a larger extent than seen in X-rays. We will present more detailed analyses and results on this region using two independent methods in Sections 3.2 and 3.3.

A dipolar pattern around the central AGN is apparent only in the X-ray residual image (left panel of Figure 2). The dipolar pattern consists of a northern positive excess and a southern negative excess. The fraction of each component against the mean brightness is roughly 20%. The dipolar pattern is clearly distinct from the excess in the southeast quadrant and extends over a spatial scale of ∼100 h⁻¹ kpc. We will present more detailed results in Section 3.4.

We assessed the uncertainty in subtracting the mean profile of the X-ray and SZE images by the following two methods. One is the same as described above, except that the subtraction of the mean profile is done after smoothing the X-ray image to the same angular resolution as the ALMA image. The other is that we assumed circular symmetry for the mean profile of X-rays and SZE instead of an ellipse. In this check, we do not use any smoothed images. We then find that (1) a difference of angular resolution between Chandra and ALMA does not affect the residual images, and (2) the geometry of the mean profile does not affect the substructure in the southeast quadrant, while it slightly modifies the shape of the dipolar pattern in the core.

To understand the origin and thermodynamic properties of the ICM in the southeast substructure, we performed X-ray spectral analysis. We defined nine regions covering the excess and its surroundings along the ellipse as in Section 3.1 (i.e., regions 1a, 1b, 1c, 2a, ..., 3b, and 3c) and three regions covering the remaining parts of the ellipse (i.e., regions 1d, 2d, and 3d) as illustrated in Figure 3. First, we assumed, for simplicity, that the ICM in each region consists only of a single component 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 photon counts in 0.4–7.0 keV and the best-fit parameters are summarized in Table 1.

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Table 1.  Best-fit Parameters to the X-Ray Spectra in Each Region Shown in Figure 3

Region	1a	1b	1c	1d
Photon counts in 0.4–7.0 keV	4566	8023	10917	21083
kTsingle (keV)	${18.5}_{-2.1}^{+2.2}$	${18.2}_{-1.6}^{+1.9}$	${19.5}_{-1.6}^{+1.6}$	${15.7}_{-0.7}^{+0.7}$
kTexcess (keV)	${21.8}_{-4.9}^{+8.6}$	${20.3}_{-3.1}^{+4.7}$	${24.2}_{-3.8}^{+6.1}$	⋯
nexcess (${10}^{-2}$ cm−3 ${({L}_{\mathrm{excess}}/150\mathrm{kpc})}^{-1/2}$)	${2.53}_{-0.04}^{+0.06}$	${3.71}_{-0.04}^{+0.04}$	${2.97}_{-0.04}^{+0.04}$	⋯
pexcess (keV cm−3 ${({L}_{\mathrm{excess}}/150\mathrm{kpc})}^{-1/2}$)	${0.552}_{-0.124}^{+0.218}$	${0.753}_{-0.115}^{+0.175}$	${0.719}_{-0.113}^{+0.181}$	⋯
Region	2a	2b	2c	2d
Photon counts in 0.4–7.0 keV	3208	4824	5996	12623
kTsingle (keV)	${17.8}_{-1.8}^{+3.1}$	${24.6}_{-3.6}^{+4.3}$	${14.8}_{-1.5}^{+1.5}$	${19.5}_{-1.6}^{+1.6}$
kTexcess (keV)	${17.2}_{-2.9}^{+4.8}$	${29.1}_{-6.9}^{+9.4}$	${11.7}_{-1.5}^{+2.0}$	⋯
nexcess (${10}^{-2}$ cm−3 ${({L}_{\mathrm{excess}}/150\mathrm{kpc})}^{-1/2}$)	${1.93}_{-0.05}^{+0.06}$	${2.55}_{-0.06}^{+0.06}$	${1.77}_{-0.03}^{+0.03}$	⋯
pexcess (keV cm−3 ${({L}_{\mathrm{excess}}/150\mathrm{kpc})}^{-1/2}$)	${0.332}_{-0.057}^{+0.093}$	${0.742}_{-0.177}^{+0.240}$	${0.207}_{-0.027}^{+0.036}$	⋯
Region	3a	3b	3c	3d
Photon counts in 0.4–7.0 keV	3337	3682	4281	9987
kTsingle (keV)	${17.9}_{-2.5}^{+3.1}$	${21.3}_{-3.1}^{+4.0}$	${17.2}_{-1.1}^{+2.2}$	${20.2}_{-1.7}^{+1.9}$
kTexcess (keV)	${16.5}_{-3.2}^{+4.9}$	${22.1}_{-5.2}^{+8.9}$	${14.9}_{-3.6}^{+4.8}$	⋯
nexcess (${10}^{-2}$ cm−3 ${({L}_{\mathrm{excess}}/150\mathrm{kpc})}^{-1/2}$)	${1.40}_{-0.04}^{+0.04}$	${1.34}_{-0.04}^{+0.05}$	${0.88}_{-0.02}^{+0.03}$	⋯
pexcess (keV cm−3 ${({L}_{\mathrm{excess}}/150\mathrm{kpc})}^{-1/2}$)	${0.231}_{-0.045}^{+0.069}$	${0.296}_{-0.070}^{+0.120}$	${0.131}_{-0.032}^{+0.042}$	⋯

Note. The metal abundance is fixed at each 0.38 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 at the best-fit values for the same annulus region (i.e., kT_single of regions 1d, 2d, and 3d). We show the statistical errors alone.

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Second, we adopted a two-component model in which an excess component is embedded in an ambient component in the nine regions. The ambient component was assumed to have the same temperature as the gas temperature in an annulus at the same $\bar{r}$ (i.e., kT_single of regions 1d, 2d, and 3d). We then measured the temperature of the excess component (kT_excess) by using the two-apec model, fixing the temperature of the ambient component at the best-fit value of kT_single in regions 1d, 2d, and 3d. The spectral normalization of the ambient component was scaled by each sky area of interest. The best-fit parameters of the excess component are shown in Table 1. We also estimated the electron density of the excess component (n_excess) assuming that it is uniform over a line-of-sight extent of L_excess = 150 kpc, which is similar to the projected size of the substructure on the sky. For different values of L_excess, the electron density scales as ${L}_{\mathrm{excess}}^{-1/2}$. In addition, we calculated the thermal pressure of the excess electrons (p_excess), i.e., n_excess × kT_excess. In above analyses, we fixed the metal abundance of the ICM at 0.38 solar based on previous X-ray measurements (Ota et al. 2008).

Figures 4–6 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 the excess component in region 1b is the highest among the nine regions, which agrees with the peak position in the X-ray residual image. On the other hand, while the statistical error is large, the temperature of the excess component in region 2b is estimated to be ∼30 keV, which is the highest among the nine regions. The highest temperature region is located at ∼27'' 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 is prominent. This means that the ALMA SZE data play a crucial role in identifying such excess hot gas. The thermal pressure of the excess electrons (p_excess) is nearly constant among regions 1b, 2b, and 1c, as presented in Table 1. This is in good agreement with the excess SZE signal shown in the right panel of Figure 3. The thermal energy of the excess electrons in regions 1b, 2b, and 1c is estimated to be ∼1.1 × 10⁶¹ h⁻² erg, ∼1.6 × 10⁶¹ h⁻² erg, and ∼2.0 × 10⁶¹ h⁻² erg, respectively.

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We estimated the Mach number ${ \mathcal M }$ from the Rankine–Hugoniot jump condition, assuming the ratio of specific heats to be γ = 5/3,

$$\begin{eqnarray}&&\displaystyle \frac{{T}_{2}}{{T}_{1}}=\displaystyle \frac{5{{ \mathcal M }}^{4}+14{{ \mathcal M }}^{2}-3}{16{{ \mathcal M }}^{2}},\end{eqnarray} \tag{ 1 }$$

where T₁ is the pre-shock temperature and T₂ is the post-shock temperature. Using the observed temperature jump between regions 2a and 2b and propagating the statistical errors, we obtain ${ \mathcal M }={1.68}_{-0.47}^{+0.69}$. The adiabatic sound speed of the gas in region 2a is estimated to be ${2140}_{-180}^{+300}$ km s⁻¹, implying a shock speed of the gas in region 2b as ${3590}_{-1050}^{+1560}$ km s⁻¹.

As an alternative measure of the gas temperature and electron density, we combined the SZE and X-ray images. We used SPEX version 3.04.00 for the X-ray data analysis and CASA version 5.1.1 for the SZE data analysis. Note that the analysis in this section does not rely on X-ray spectra and is fully independent of that presented in Section 3.2.

We measured the intensities of X-ray (ΔI_X) and SZE (ΔI_SZ) of the X-ray and SZE residual images shown in Figure 2. Both images were binned so that the angular resolutions of Chandra and ALMA have a common pixel size of 5'' × 5''. The two intensities are then described as

$$\begin{eqnarray}&&{\rm{\Delta }}{I}_{{\rm{X}}}\propto {n}_{\mathrm{excess}}^{2}\times {\rm{\Lambda }}({T}_{\mathrm{excess}})\times {L}_{\mathrm{excess}},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{I}_{\mathrm{SZ}}\propto {n}_{\mathrm{excess}}\times {{kT}}_{\mathrm{excess}}\times {L}_{\mathrm{excess}}\times {f}_{r}({T}_{\mathrm{excess}})\times {f}_{c},\end{eqnarray} \tag{ 3 }$$

where Λ is the X-ray emissivity over the energy range 0.4–7.0 keV, f_r is the relativistic correction to the SZE intensity (Itoh & Nozawa 2004), and f_c is a correction factor for the missing flux in the ALMA data. We set f_c to be equal to the parameter c₁ = 0.88 in Equation (2) of Kitayama et al. (2016) derived from detailed imaging simulations for RX J1347.5–1145.²⁰ We then solved Equations (2) and (3) for n_excess and kT_excess, respectively, assuming L_excess = 150 kpc as in Section 3.2. For different values of L_excess, they approximately scale as ${{kT}}_{\mathrm{excess}}\propto {L}_{\mathrm{excess}}^{-1/2}$ and ${n}_{\mathrm{excess}}\propto {L}_{\mathrm{excess}}^{-1/2}$, if weak dependences of Λ and f_r on temperature are neglected. We focused on the high-significance pixels for which the signal-to-noise ratios (S/Ns) of ΔI_X and ΔI_SZ are both over 4σ. Figure 7 shows the measured temperature of the excess component (left) and its statistical error (right). Figure 8 is the same as Figure 7 but for the electron density of the excess component. The typical errors of temperature and electron density are about 4 keV and 0.05 × 10⁻² cm⁻³, respectively.

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We find that the highest temperature region is located in region 2b. This result is consistent with that measured with an independent method using the X-ray spectra (Section 3.2). We also find that the highest electron density region is in region 1b. In addition, we estimate the thermal energy of the excess electrons to be (1.9 ± 0.1(stat.) ± 0.7(sys.)) × 10⁶¹ h⁻² erg from the SZE residual image directly, within a radius of 50 h⁻¹ kpc around the peak of the SZE residual signal. Further details of the systematic uncertainty are mentioned in Section 3.5. The angular resolution and sensitivity of the previous SZE observations did not match those of the X-ray data. The ALMA SZE data allow us, for the first time, a detailed comparison with the X-ray data with comparable resolution and sensitivity.

The spatial scale of the dipolar pattern is estimated to be 40 h⁻¹ kpc by applying the definition of the size described in Ueda et al. (2017). We analyzed the X-ray spectra of the ICM in the region of the dipolar pattern to examine its thermodynamic properties. The temperature toward the positive and the negative excess is estimated as ${8.8}_{-0.2}^{+0.2}$ keV and ${10.6}_{-0.3}^{+0.4}$ keV, respectively. The metal abundances are ${0.47}_{-0.03}^{+0.03}$ ${Z}_{\odot }$ for the positive excess and ${0.37}_{-0.05}^{+0.05}$ ${Z}_{\odot }$ for the negative excess. These properties are as expected for gas sloshing, i.e., metal-rich, cool, and dense gas is moving around the central galaxy. On the other hand, we find an absence of excess SZE signal in the core, which provides the first direct evidence that the disturbed gas is nearly in pressure equilibrium. This indicates that the gas sloshing motion is subsonic.

Here, we introduce the "equation of state" of the perturbation in gas, w ≡ Δp/Δρ. For similar analyses, see Churazov et al. (2016), Khatri & Gaspari (2016), and references therein. If the perturbation is adiabatic, then w is equal to the sound speed squared, i.e., $w={c}_{s}^{2}$. If the perturbation is isobaric, we should find $w\ll {c}_{s}^{2}$. The SZE residual image gives an estimate of the pressure perturbation Δp, whereas the X-ray residual image gives an estimate of the density perturbation Δρ as

$$\begin{eqnarray}&&\displaystyle \frac{| {\rm{\Delta }}{I}_{{\rm{X}}}| }{\langle {I}_{{\rm{X}}}\rangle }\simeq \displaystyle \frac{{\rm{\Delta }}\langle {n}^{2}\rangle }{\langle {n}^{2}\rangle }\simeq \displaystyle \frac{2{\rm{\Delta }}\rho }{\sqrt{\langle {\rho }^{2}\rangle }}\end{eqnarray} \tag{ 4 }$$

because $| {\rm{\Delta }}{I}_{{\rm{X}}}| \ll \langle {I}_{{\rm{X}}}\rangle$, where $\langle {I}_{{\rm{X}}}\rangle$ is the mean X-ray surface brightness, $\langle {n}^{2}\rangle$ is the mean square electron number density, and $\langle {\rho }^{2}\rangle$ is the mean square gas mass density. First, to cover the dipolar pattern in the X-ray residual image, we used the ellipse with the same geometry as mentioned in Section 3.1, with a semimajor axis length of 22'', excluding the southeast quadrant. We extracted the X-ray spectrum for this elliptical sector and carried out the X-ray spectral analysis. Assuming a line-of-sight depth of 100 kpc, the mean ICM temperature and mean electron number density, $\sqrt{\langle {n}^{2}\rangle }$, in this region are 9.8 ±0.2 keV and (8.24 ± 0.02) × 10⁻² cm⁻³, respectively. Next, using the X-ray and SZE residual images and assuming a line-of-sight depth of 100 kpc, we measured Δρ, Δp, and their statistical errors within the same elliptical sector. We then found that the velocity inferred from the equation of state is $\sqrt{w}\,={420}_{-420}^{+310}$ km s⁻¹. This inferred velocity is much lower than the adiabatic sound speed of the 10 keV ICM, ∼1630 km s⁻¹. The motion of gas sloshing is therefore consistent with being subsonic and isobaric.

The systematic uncertainty of the ICM temperature measured with the ACIS is estimated to be ∼20% for galaxy clusters with high-temperature (over 10 keV) ICM like RX J1347.5–1145 (e.g., Nevalainen et al. 2010; Reese et al. 2010; Schellenberger et al. 2015). Note that the statistical uncertainty of the temperature of the excess component is 20% ∼ 30% in the nine regions. We evaluated the impact of the systematic uncertainty on the X-ray and the SZE data for the combined analysis. We applied the 4% uncertainty of the ACIS effective area,²¹ the 6% uncertainty of the ALMA flux calibration (see Section 2 of Kitayama et al. 2016), and 1.3 μJy arcsec⁻² for the ALMA missing flux correction (see Section 4.2 of Kitayama et al. 2016) to the data. The error of the ICM temperature and density including the systematic uncertainty is about twice as large as that shown in the right panels of Figures 7 and 8; for example, the error for the highest temperature region (23.2 keV) changes from ±3.9 keV to ±8.1 keV. Note that these systematic uncertainties are only relevant to the absolute values of derived parameters but not their relative trends, in which we are mainly interested.

To reveal the geometry of mergers in RX J1347.5–1145, we analyzed the central mass distribution derived by SL. We used the GLAFIC software package (Oguri 2010) for our mass modeling. GLAFIC adopts a parameterized mass model and derives the best-fit mass map that reproduces the observed positions of SL multiple images. The software has been used for SL mass modeling of many massive clusters (e.g., Oguri et al. 2012; Kawamata et al. 2016) and has also been shown to recover central mass distributions of simulated clusters remarkably well (Meneghetti et al. 2017).

We followed the standard procedure to model massive clusters in which we adopted a few dark halo components, cluster member galaxies, and external perturbations on the lens potential (see e.g., Kawamata et al. 2016). For dark halo components, we assumed an elliptical extension of the Navarro–Frenk–White model (Navarro et al. 1997). Each dark halo component is characterized by a set of model parameters including the virial mass, the concentration parameter, positions, eccentricity of the ellipse, and its position angle. For member galaxies, we used the scaling relations to reduce the number of model parameters. We constructed a cluster member galaxy catalog by selecting galaxies near the red sequence in the HST F475W–F814W color–magnitude diagram, where the magnitudes are MAG_APER of SExtractor (Bertin & Arnouts 1996) with 1'' diameter aperture. The mass distribution of the member galaxies was assumed to follow pseudo-Jaffe ellipsoids whose velocity dispersions and truncation radii scale with galaxy luminosity L_gal as $\sigma \propto {L}_{\mathrm{gal}}^{1/4}$ and ${r}_{\mathrm{trunc}}\propto {L}_{\mathrm{gal}}^{1/2}$, respectively. The normalizations of these two scaling relations were treated as model parameters. In addition, to improve the fit, we included external perturbations described by a multipole Taylor expansion of the form $\phi \propto {r}^{2}\cos m(\theta -{\theta }_{* })$. We included terms with m = 2 (external shear), 3, and 4. Each term is specified by its amplitude and position angle as model parameters.

For observational constraints, we used the positions of 21 multiple images from six multiple image sets of the lensed galaxies. These multiple images are identified in previous work on this cluster (Halkola et al. 2008; Köhlinger & Schmidt 2014; Zitrin et al. 2015). In this paper, we re-examined the validity of the previous multiple image identifications in the course of our own mass modeling, and adopted only secure multiple images for our analysis. The redshift of one multiple image set was fixed as the spectroscopic value, whereas for those of four multiple image sets, we included Gaussian priors based on their photometric redshifts. We assumed a positional error of 05 for all the multiple images, which is a standard value in SL mass modeling (e.g., Kawamata et al. 2016). Table 2 summarizes the data of multiple images for our SL analyses.

Our fiducial model contains two dark halo components, which are supposed to model mass distributions near the brightest cluster galaxy (BCG) of the main cluster and the second BCG, which is considered to be the BCG of the subcluster, respectively. This model contains 37 model parameters, which are constrained by 46 observational data points. We also considered another model which contains three dark halo components, as this model may reveal a mass component which does not correspond to either the BCG or the second BCG. In this model, the number of parameters increases to 43. We evaluated statistical errors of model parameters, such as masses of dark halo, concentration parameters, and mass peaks with Markov chain Monte Carlo methods.

The surface mass density map obtained from the two dark halo components is shown in the left panel of Figure 9. The best-fit parameters are summarized in Table 3. The locations of the two mass peaks are treated as free parameters, and we find that the peaks are in good agreement with the positions of the BCG and the second BCG. The estimated virial masses are ${7.2}_{-1.9}^{+2.1}\,\times {10}^{14}$ h⁻¹ ${M}_{\odot }$ for the main cluster and ${2.8}_{-1.1}^{+2.4}\times {10}^{14}$ h⁻¹ ${M}_{\odot }$ for the subcluster. Their concentration parameters are estimated to be $c={6.6}_{-0.9}^{+1.0}$ and $c={4.8}_{-1.6}^{+2.2}$, respectively. The obtained mass and concentration parameter are correlated strongly, therefore the systematic 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 the subcluster has been previously estimated using the excess X-ray flux and applying the luminosity–mass relation to be (3.4 ± 1.7) × 10¹⁴ h⁻¹ ${M}_{\odot }$ (Johnson et al. 2012) and ∼2.3 × 10¹⁴ h⁻¹ ${M}_{\odot }$ (Kreisch et al. 2016), consistent with that by our SL analysis.²² The entire mass distribution of RX J1347.5–1145 is slightly elongated along the northeast direction.

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Table 3.  Best-fit Parameters of Mass Distributions of the Main Cluster and the Subcluster Measured by SL

	Main Cluster	Subcluster
Mass (${10}^{14}\,{h}^{-1}$ ${M}_{\odot }$)	${7.2}_{-1.9}^{+2.1}$	${2.8}_{-1.1}^{+2.4}$
Concentration parameter	${6.6}_{-0.9}^{+1.0}$	${4.8}_{-1.6}^{+2.2}$
Offset of mass peak relative to each BCG (arcsec)a	(${0.2}_{-0.8}^{+0.8}$, ${0.1}_{-0.8}^{+1.0}$)	(${0.5}_{-2.3}^{+1.8}$, ${3.7}_{-3.9}^{+2.9}$)
Semiminor to semimajor axis ratio	${0.62}_{-0.05}^{+0.04}$	${0.31}_{-0.06}^{+0.06}$
Position angle (degree)	${1.1}_{-5.0}^{+4.6}$	${31.7}_{-2.2}^{+2.0}$

Note.

^aThe positions of the BCG and the second BCG are (R.A., decl.) =(13^h47^m30639, −11^d45^m09589) and (R.A., decl.) = (13^h47^m31870, −11^d45^m1120), respectively.

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The right panel of Figure 9 shows the surface mass density map obtained from the three dark halo components. The mass of the third component is weakly constrained to be 1.4 × 10¹⁴ h⁻¹ ${M}_{\odot }$ (95% CL). Its location is also poorly determined, but it lies to the northeast of the BCG. These indicate that the mass distribution of dark matter (DM) near the 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 in the rest of this paper.

We find a clear offset between the mass peak of the subcluster and the position of the substructure in X-rays and the SZE (bottom panels of Figure 10). The second mass peak is away from the peak position of the X-ray substructure with statistical significance of 5.5σ. The second DM component is most likely associated with the infalling subcluster, suggesting that the gas that was originally in the subcluster is stripped by ram pressure of the main cluster.

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The top left panel of Figure 10 shows that the X-ray centroid coincides with the mass peak of the main cluster even though the ICM in the cool core is sloshing. The mass peak of the main cluster is located at the interface between the positive and the negative excesses of the dipolar pattern (see the bottom left panel of Figure 10). These features indicate that part of the gas in the cool core is moving around the BCG, but the DM distribution is not disturbed.

The presence of very hot ICM in excess of 20 keV is inferred in RX J1347.5–1145 for the earlier SZE and X-ray observations (Kitayama et al. 2004; Ota et al. 2008). Combining the X-ray data of Chandra with the SZE data of ALMA, we have confirmed the temperature of the excess hot ICM by two independent methods and have improved the precision of its position. The excess hot ICM is located at a distance of 27'' (or ∼109 h⁻¹ kpc) to the southeast from the cluster center.

Following Section 3.4, we also measure the equation of state of the excess hot ICM. We compute Δp and Δρ for an elliptical region with semimajor and semiminor axis lengths of 14'' and 12'', respectively, and a position angle of −70° around the centroid of the excess SZE signal. We assume a line-of-sight depth of 150 kpc. Given that ${\rm{\Delta }}{I}_{{\rm{X}}}\gt \langle {I}_{{\rm{X}}}\rangle$ in this region, we adopt n_excess given in Equation (2) as a better proxy for Δρ than Equation (4). On the other hand, Δp is directly computed from the SZE residual signal, ΔI_SZ. We analyze the X-ray spectrum in this region using the same procedure as described in Section 3.2. The electron number density and temperature of the excess hot ICM are (3.29 ± 0.02) × 10⁻² cm⁻³ and ${20.2}_{-1.8}^{+2.1}$ keV, respectively. We then find that the velocity inferred from the equation of state of the excess hot ICM is 1970 ± 150 km s⁻¹, which matches ∼85% of the adiabatic sound speed of the 20 keV ICM, ∼2310 km s⁻¹. This supports the picture that the pressure perturbation in the southeast quadrant is induced by shock.

The excess hot ICM in the southeast quadrant is most likely associated with a major merger. The result of SL analysis indicates that the mass peak of the subcluster is offset from the location of the southeast substructure. Our results imply that the gas that was originally in the subcluster is stripped by ram pressure of the main cluster. As mentioned above, the pressure perturbation of the southeast substructure in the SZE residual image is consistent with that created by shock, so it is plausible that this stripped gas has been heated during the major merger. Details of shock-heating processes in RX J1347.5–1145 using numerical simulations will be presented elsewhere.

We have also found a dipolar pattern in the core of RX J1347.5–1145 in its X-ray residual image. This is direct evidence that the core is experiencing gas sloshing, whose presence was suggested by Johnson et al. (2012) and Kreisch et al. (2016). We find that the ICM properties of the disturbed gas obtained by the X-ray spectral analysis are consistent with those expected by gas sloshing. In addition, we find that the equation of state of disturbed gas is consistent with being isobaric, i.e., the motion of gas sloshing is in pressure equilibrium. The morphology of this dipolar patter seems to be a spiral. If so, the direction of the sloshing motion is in the plane of the sky. Such dipolar spiral patterns 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 feature of a major merger. This indicates that their gas sloshing is induced by a minor merger. RX J1347.5–1145, however, has a subcluster and an excess hot ICM in its central 150 h⁻¹ kpc. RX J1347.5–1145 is therefore the first cluster ever known to host both a major merger and gas sloshing in the cool core.

The size of the dipolar pattern is a factor of 2 ∼ 3 smaller than that often found in local cool core clusters (e.g., Ueda et al. 2017). Since the size tends to evolve with time after the passage of a subcluster (e.g., ZuHone et al. 2010), gas sloshing in this cluster is expected to have occurred recently. The dipolar spiral pattern indicates that the orbit of the major merger is in the plane of the sky. This is in accord with the fact that the redshift difference of the second BCG from the BCG is less than 100 km s⁻¹ by optical observations (Lu et al. 2010). The stripped gas is located behind the subcluster, which indicates the infalling subcluster is in the first passage. It is unclear, however, whether or not the infalling subcluster is the origin of gas sloshing. If the direction of the passage is from southwest to northeast, it seems to be hard to disturb and create a rotational motion of the gravitational potential well of the main cluster. A possibility that the subcluster is in the first passage and gas sloshing is induced by another earlier merger was suggested by Kreisch et al. (2016). In this paper, we cannot constrain their scenario.

As discussed above, it seems that the merger in RX J1347.5–1145 is in the plane of the sky. Following Markevitch et al. (2004), an offset in the positions of galaxies, DM halos, and the ICM allows us to constrain the self-interaction cross section of DM. We estimated the surface mass density of DM (Σ_s) in the subcluster using its mass distribution, shown in the left panel of Figure 9. We measured the mean Σ_s within a radius of 25 h⁻¹ kpc from the second mass peak. We also subtracted the contribution of the main cluster based on the parameters listed in Table 3. Assuming the scattering depth of τ_s = Σ_s × σ_DM/m < 1 for DM, we obtained the upper limit of the self-interaction cross section for DM to be σ_DM/m <2.1 h⁻¹ cm² g⁻¹, where σ_DM is the DM collision cross section and m is the mass of a DM particle. To derive more conservative upper limit, we further considered the uncertainty of the surface mass density map of RX J1347.5–1145. We subtracted the 2σ value of the rms noise obtained in Section 4 from the original surface mass density map and re-estimated the cross section in the same manner as mentioned above. The 2σ (95% CL) upper limit of the cross section is then ${\sigma }_{\mathrm{DM}}/m\lt 3.7\,{h}^{-1}$ cm² g⁻¹. The derived upper limits are comparable to those reported in the studies of other clusters (e.g., Markevitch et al. 2004; Harvey et al. 2015).