CHANDRA AND XMM-NEWTON OBSERVATIONS OF THE MERGING CLUSTER OF GALAXIES PLCK G036.7+14.9

PLCK G036.7+14.9 was observed by Chandra (ObsID 15098) on 2014 February 5 for 9.6 ks with the Advanced CCD Imaging Spectrometer (ACIS-I). The observation was telemetered in VFAINT mode. Standard Chandra data analysis was performed with CIAO version 4.6.1 and calibration database version 4.6.1. The CIAO tool chandra_repro was applied to perform initial processing and to obtain a new event file. Point sources were detected by running wavdetect and were excluded in further analysis (except for the AGN in the center of the north subcluster, see Sections 3 and 4.4). Light curves in the soft- and hard-band were examined and no background flares were found, so we proceeded with the full exposure.

The imaging analysis was performed in the 0.7–7.0 keV band to maximize the signal-to-noise ratio. The period F blank-sky background with proper scaling according to the exposure time and high-energy flux was used. The exposure map was weighted by the best-fitting thermal model to the spectrum of the central part of the cluster.

In the spectral analysis, the blank-sky background was used as the baseline background model. We also varied the blank-sky background by ±5% and added a soft-band adjustment to test how sensitive the results were to the background (Sections 4.4 and 4.6). All spectral analysis was performed in the 0.7–9.0 keV band, unless otherwise stated.

PLCK G036.7+14.9 was observed by XMM-Newton (ObsID 0692931901) on 2013 March 30 for 10.5 ks (EPIC MOS1), 10.6 ks (EPIC MOS2), and 9.7 ks (EPIC PN). Full frame mode was used for the three cameras with medium filters for the EPIC MOS detectors and thin filters for the EPIC PN. Data reduction was done with ESAS¹¹ version 5.6 (Snowden & Kuntz 2013), which uses SAS version 13.5.0 and calibration files updated to 2014 February 27. The initial data processing was done by running emchain and epchain with the default setting in ESAS. Out-of-time events were also accounted for in the EPIC PN analysis. Background flares were identified and rejected by applying a $1.5\sigma$ clipping method to the high-energy count rate histogram. The resulting "cleaned" exposure times are 6.8 ks (EPIC MOS1), 5.4 ks (EPIC MOS2), and 2.0 ks (EPIC PN), respectively. This shows that the XMM-Newton observation was affected by high-energy particle induced background. Due to the limited statistics, we combined data from the three cameras in our analysis. Point sources were detected in the 0.5–10.0 keV band and were excluded from further analysis (except for the AGN in the center of the north subcluster, see Sections 3 and 4.4).

Imaging analysis was performed in the 0.7–2.0 keV band. The count images, quiescent particle background (QPB) images, residual soft proton (SP) background images (see Section 4.1.2), and exposure maps for the three cameras were generated and combined with the ESAS task comb. The QPB and SP images were then subtracted from the combined count image and the resulting image was exposure corrected with the combined exposure map.

Spectra from the same regions of the three cameras were extracted with ESAS tasks mos-spectra and pn-spectra and grouped to contain a minimum of 25 counts per bin. We modeled the various components of the background (see Section 4.1.2). Spectra from different regions and from the three cameras were fit simultaneously. The spectral analysis was carried out in the 0.7–10.0 keV band for EPIC MOS spectra and in the 0.7–7.0 keV band for EPIC PN spectra.

The XMM-Newton image (Figure 1, left panel) shows that the large scale X-ray emission from PLCK G036.7+14.9 is elongated in a northeast–southwest direction. The central region reveals two close (∼72'' = 193 kpc in projection), yet clearly separated, subclusters (G036N in the north and G036S in the south), which suggests that PLCK G036.7+14.9 may be undergoing a merger. The Chandra image (Figure 1, right panel) reveals a bow shaped gap (with an angle of ∼145°) between G036N and G036S, anther indication of interaction between the two subclusters. Spectral analysis reveals a hotter region between G036N and G036S, confirming that they are interacting (see Section 4.7). Beyond the interaction region, neither G036N nor G036S deviates significantly from spherical symmetry, suggesting that the merger is probably at an early stage.

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Optical images of PLCK G036.7+14.9 were obtained using the MOSaic CAmera (MOSCA) at the 2.56 m Nordic Optical Telescope (NOT). Using MOSCA in 2 × 2 binned mode yielded a pixel scale of $0\buildrel{\prime\prime}\over{.} 217\;{\rm pixe}{{{\rm l}}^{-1}}$, and the field of view (FOV) is $7\buildrel{\,\prime}\over{.} 7\times 7\buildrel{\,\prime}\over{.} 7$. Three individual exposures were made in each of the Sloan Digital Sky Survey (SDSS) g, r, and i bands, adding up to total exposure times of 1800, 600, and 600 s, respectively. The images in the r and i bands were smoothed with Gaussian kernels to match the seeing (full width at half maximum, ${\rm FWHM}=1\buildrel{\prime\prime}\over{.} 45$) of the combined g-band image. Object detection and photometry were performed on the combined image for each filter using the SExtractor software (Bertin & Arnouts 1996) in dual image mode with the g-band chosen for the reference image. Total magnitudes were measured by the MAG_AUTO parameter while colors were measured within a $3\buildrel{\prime\prime}\over{.} 6$ diameter aperture. Photometric zero points were calibrated from SDSS photometry of stars in other fields observed using the same setup, and the derived magnitudes were corrected for Galactic extinction using the Schlafly & Finkbeiner (2011) recalibration of the Schlegel et al. (1998) dust maps. The g–r versus r–i color–color diagram of non-stellar objects in the field of PLCK G036.7+14.9 is shown in the left panel of Figure 2. A significant overdensity, encompassed by the shaded circle, corresponding to the location of PLCK G036.7+14.9, is clearly visible. In order to select the red sequence of PLCK G036.7+14.9, we fit a linear relation to the g–i versus i color–magnitude diagram (right panel of Figure 2) for galaxies within the circle and obtained a best-fitting relation represented by the dashed line in the right panel of Figure 2. The color scatter (1σ) about this relation, illustrated by the dotted lines in the diagram, is 0.072 mag, which is typical of the measured intrinsic scatter around the mean color–magnitude relation for early-type galaxies in rich clusters (e.g., Stanford et al. 1998). Galaxies which fall within twice the value of the scatter from the best-fitting color–magnitude relation, down to ${{i}_{AB}}\sim 21$ mag (at fainter magnitudes the photometric errors become non-negligible compared to the intrinsic scatter around the color–magnitude relation), are considered to be the red sequence of PLCK G036.7+14.9 and are plotted in red in the diagram. The colors of the red sequence are in good agreement with those in Eisenstein et al. (2001) at redshifts close to PLCK G036.7+14.9. The Brightest Cluster Galaxies (BCGs) of G036N and G036S are located on the red sequence and are colored green in particular in both panels of Figure 2. As shown in Figure 3 (left panel), the BCGs of the two subclusters, marked with blue squares ($5^{\prime\prime} \times 5^{\prime\prime}$), are very close to the X-ray centers (defined as the X-ray centroids), suggesting that the merger is at an early stage and it should be largely along the line of sight.

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An X-ray AGN was detected in the 2.0–7.0 keV band at the center of G036N in the Chandra image (Figure 1, right panel), while no point source was detected at the center of G036S. Interestingly, the NRAO VLA Sky Survey (NVSS) image (right panel of Figure 3) also reveals a radio source, NVSS J180431+100323, coincident with the center of G036N. This radio source should be hosted by the BCG of G036N. The extent of the radio source is comparable to the angular resolution of the NVSS (${\rm FWHM}=45^{\prime\prime}$), so it is essentially unresolved. The properties of the AGN and the core regions are discussed in more detail in Section 4.8.

Surface brightness profiles for each subcluster were extracted from the background subtracted¹² and exposure corrected images. We chose a half circular region opposite to the interaction region (see Figure 4) to derive the surface brightness profiles for both G036N and G036S. The azimuthally averaged surface brightness profiles are shown in Figure 5. We first tried to model these with single β models (Cavaliere & Fusco-Femiano 1976),

$$\begin{eqnarray}&&S(r)={{S}_{0}}{{[1+{{(\frac{r}{{{r}_{c}}})}^{2}}]}^{-3\beta +1/2}},\end{eqnarray} \tag{ 1 }$$

where r_c is the core radius. We found excess emission in the central ∼10'' regions for both G036N and G036S, so we excluded the radial bins covering the central ∼10'' regions and refit the surface brightness profiles. The best-fitting β models are plotted in Figure 5, with the best-fitting parameters given in Table 1.

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Table 1.  Best-fitting β Model Parameters of the Surface Brightness Profiles

Region	Facility	β	rc (arcsec)	rc (kpc)	${{\chi }^{2}}/{\rm dof}$
G036N	XMM-Newton	0.6418 ± 0.0060	14.57 ± 1.36	39.08 ± 3.65	118.8/94
	Chandra	0.6635 ± 0.0095	14.65 ± 1.22	39.29 ± 3.27	128.6/54
G036S	XMM-Newton	0.6850 ± 0.0078	23.65 ± 1.34	63.43 ± 3.59	121.3/94
	Chandra	0.7104 ± 0.0134	22.43 ± 1.66	60.16 ± 4.45	123.4/44

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As can be seen, β models describe the surface brightness profiles quite well beyond the central ∼10'' for both G036N and G036S, although the reduced ${{\chi }^{2}}$ for Chandra is larger. The best-fitting core radii are consistent for Chandra and XMM-Newton, while the differences between β values are only $1.9\sigma$ for G036N and $1.6\sigma$ for G036S. In the central ∼10'' regions, both G036N and G036S show excess emission relative to the β models. Note that the X-ray AGN at the center of G036N is not excluded in the surface brightness profiles. Compared to the surface brightness profile of G036S, it can be inferred that the contribution from the X-ray AGN to the total flux from G036N is negligible. We further demonstrate this from the spectral analysis in Section 4.4. Given the quality of the data and the goodness of the β model beyond the central ∼10'' regions, we did not try more complicated models.

We also extracted surface brightness profiles in different wedge-shaped regions, trying to identify surface brightness discontinuities, but the current data do not reveal any unambiguous edges.

4.1.1. Chandra

4.1.2. XMM-Newton

XMM-Newton and Chandra give significantly different N_H values, by almost a factor of two. To investigate the origin of this discrepancy, we refit the spectra with energy cut offs of 0.3, 0.5, 0.7, and 1.5 keV. The best-fitting N_H values are all consistent for each observatory, but still significantly different between the two observatories. We also tried different abundance tables, and found that while N_H changes with different abundance tables, the ratio between the two observatories remains almost unchanged. Therefore, we conclude that the discrepancy is most likely caused by cross-calibration issues (see Section 4.6 on their effects on the total mass determinations).

To examine whether N_H is different between G036N and G036S, and whether N_H changes with radius, we fit all spectra (Section 4.4) of G036N and G036S with N_H free in each annulus. We found that all the N_H values are consistent within the $1\sigma$ errors for Chandra, and consistent within the $2\sigma$ errors for XMM-Newton. Therefore, in our spectral analysis we linked N_H in different regions together.

In addition, we estimated the total N_H with the relation¹³

$$\begin{eqnarray}\begin{array}{ccccccccccccccc} {{N}_{{\rm H},{\rm tot}}} & = & {{N}_{{\rm HI}}}+2{{N}_{{{{\rm H}}_{2}}}} \\ {} & = & {{N}_{{\rm HI}}}+2{{N}_{{{{\rm H}}_{2}},{\rm max} }}{{(1-{{e}^{\frac{{{N}_{{\rm HI}}}E(B-V)}{{{N}_{c}}}}})}^{\alpha }}, \\ \end{array}\end{eqnarray} \tag{ 2 }$$

where ${{N}_{{{{\rm H}}_{2}},{\rm max} }}=7.3\times {{10}^{20}}$ cm⁻², $E(B-V)=0.162$ is the dust extinction, ${{N}_{c}}=3.0\times {{10}^{20}}$ cm⁻², and $\alpha =1.1$ (Willingale et al. 2013). We obtained ${{N}_{{\rm H},{\rm tot}}}=0.136\times {{10}^{22}}$ cm⁻². All the results obtained with N_H fixed at this total value are also included for comparison.

To summarize, we used ${{N}_{{\rm H}}}=0.092\times {{10}^{22}}$ cm⁻² for XMM-Newton, ${{N}_{{\rm H}}}=0.164\times {{10}^{22}}$ cm⁻² for the Chandra baseline background model and the baseline background model varied by ±5%, and ${{N}_{{\rm H}}}=0.195\times {{10}^{22}}$ cm⁻² for the Chandra baseline background model with a soft-band adjustment. We also included ${{N}_{{\rm H}}}=0.136\times {{10}^{22}}$ cm⁻² for both observatories for comparison. See Table 2 for the N_H values used for the two observatories and for the different Chandra background models. We treated the uncertainty in N_H as a systematic uncertainty (see Section 4.6).

Table 2.  Best-fitting Hydrogen Column Density and Redshift

Method	Parametera	G036N	G036S
XMM-Newton	NHb	0.136 ($0.092_{-0.006}^{+0.004}$)	⋯
	z	$0.1415_{-0.0054}^{+0.0025}$ ($0.1406_{-0.0029}^{+0.0039}$)	$0.1535_{-0.0051}^{+0.0058}$ ($0.1554_{-0.0059}^{+0.0043}$)
Chandra baseline +	NHb	0.136 ($0.164_{-0.013}^{+0.012}$)	⋯
back*0.95 + back*1.05c	z	$0.1590_{-0.0034}^{+0.0057}$ ($0.1594_{-0.0066}^{+0.0050}$)	$0.1639_{-0.0029}^{+0.0018}$ ($0.1640_{-0.0015}^{+0.0035}$)
Chandra with softd	NHb	0.136 ($0.195_{-0.007}^{+0.014}$)	⋯
	z	$0.1602_{-0.0054}^{+0.0052}$ ($0.1569_{-0.0050}^{+0.0042}$)	$0.1620_{-0.0047}^{+0.0048}$ ($0.1638_{-0.0049}^{+0.0027}$)

Notes:

^aObtained by global spectral fitting with the regions shown in Figure 4. ^bHydrogen column density, in units of 10²² cm⁻². The value without errors was obtained from the relation given in Willingale et al. (2013), while the values with errors are the best-fitting values from our analysis. N_H for G036S is always linked to that for G036N (see Section 4.2). ^cChandra baseline background model and varying Chandra baseline background model by ±5%. Varying the background level by ±5% only affects regions with faint source emission. Since the regions used for the global spectral fitting cover the bright part of the cluster, we only used the baseline background to obtain the best-fitting N_H and z. In deriving the temperature profiles, we used these N_H and z for the three Chandra background models. ^dChandra baseline background model with a soft-band adjustment.

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The only redshift available for PLCK G036.7+14.9 is from the Cluster in the Zone of Avoidance (CIZA) project, which measured a spectroscopic redshift of z = 0.1525 (Ebeling et al. 2002). However, PLCK G036.7+14.9 was treated as a single cluster in Ebeling et al. (2002), so we decided to use our best-fitting X-ray redshifts for G036N and G036S.

Table 2 lists the redshifts obtained by XMM-Newton and Chandra with different Chandra background models and different N_H values. As can be seen, a different N_H for the same observatory and the same background model (Chandra) only has a minor effect on the derived z. The obtained best-fitting redshifts differ by ≲2% and are consistent. However, XMM-Newton and Chandra give values that differ by ∼13% (∼3σ) and ∼7% (∼2σ) for G036N and G036S, respectively, which are probably caused by cross-calibration issues between the two observatories.

We simply averaged the best-fitting redshifts over XMM-Newton and Chandra (baseline background model), and those obtained with different N_H values, to obtain ${{z}_{n}}=0.1501\pm 0.0022$ and ${{z}_{s}}=0.1592\pm 0.0020$, where (and hereafter) we use the subscripts n and s to distinguish between the north and south subclusters. We assume that the difference, which has a significance of $3\sigma$, between the redshifts of the two subclusters is caused by their relative motion, and the redshift of the cluster is the mean of the two, 0.1547 ± 0.0015, which is very close to the optical redshift of 0.1525. All the distance-relevant quantities are relative to a redshift of 0.1547. In our spectral analysis, the redshift is fixed at the value shown in Table 2 according to the context. The uncertainty in the redshift was treated as a systematic uncertainty (see Section 4.6).

Azimuthally averaged temperature profiles were derived in half circular regions opposite to the interaction region (see Figure 4) for G036N and G036S. Spectra were extracted in the 0–35'' (0–35''), 35''–70'' (35''–70''), 70''–130'' (70''–140''), 130''–260'' (140''–280''), and 260''–600'' (280''–600'') regions for G036N (G036S) for XMM-Newton, and in the 0–35''¹⁴ (0–45''), 35''–80'' (45''-100''), 80''–200'' (100''–300''), and 200''–450'' regions for G036N (G036S) for Chandra. All spectra for each observatory were fit simultaneously. Due to the limited statistics, the abundances in each annulus cannot be constrained, so we fixed them at the global best-fitting values.

The temperature profiles for each subcluster and for each set of {N_H, z} values in Table 2, are displayed in Figure 6. In each panel of Figure 6, the temperature profiles for XMM-Newton and for Chandra with different background models (see Section 4.1.1) are indicated by different symbols. When using the same N_H value, XMM-Newton and Chandra generally give consistent results, although at large radii ($\gt 200^{\prime\prime}$), a direct comparison is not straightforward as they do not probe exactly the same region. For G036N, there is an indication of a temperature drop in the central region, although the uncertainties are large. At large radii, the temperature profile declines, dropping to ∼1/2 (∼1/4) of the "peak" value for Chandra (XMM-Newton). This behavior is qualitatively consistent with large samples of cluster temperature profiles (e.g., Vikhlinin et al. 2005; Pratt et al. 2007; Leccardi & Molendi 2008). For G036S, XMM-Newton exhibits a temperature drop in the innermost bin, and a declining temperature profile at large radii, while Chandra, in the much smaller radial range it covers because the cluster is close to the chip boundary, gives an essentially isothermal temperature profile, but with large uncertainties. Different N_H values and different Chandra background models produce the same trend as previously stated for the temperature profiles for both G036N and G036S.

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The observationally determined temperature profile is the projected 2D profile, which contains emission from different parts of the cluster along the line of sight. We used the functional form

$$\begin{eqnarray}&&{{T}_{3{\rm D}}}(r)={{T}_{0}}\frac{{{(\frac{r}{{{r}_{{\rm cool}}}})}^{{{a}_{{\rm cool}}}}}+\frac{{{T}_{{\rm min} }}}{{{T}_{0}}}}{1+{{(\frac{r}{{{r}_{{\rm cool}}}})}^{{{a}_{{\rm cool}}}}}}\frac{{{(\frac{r}{{{r}_{t}}})}^{-a}}}{{{[1+{{(\frac{r}{{{r}_{t}}})}^{b}}]}^{c/b}}},\end{eqnarray} \tag{ 3 }$$

proposed by Vikhlinin et al. (2006), to model the 3D temperature profile. Assuming spherical symmetry, this 3D temperature profile is then projected along the line of sight, weighted by $n_{e}^{2}/{{T}^{3/4}}$ (Mazzotta et al. 2004), where n_e is the electron density and T is the 3D temperature, and is fit to the observed 2D temperature profile. As this functional form has many free parameters, it can describe the temperature profile very well. The results are shown in the Appendix.

For a surface brightness profile described by a β model, the electron density is given by

$$\begin{eqnarray}&&{{n}_{e}}(r)={{n}_{e,0}}{{[1+{{(\frac{r}{{{r}_{c}}})}^{2}}]}^{-3\beta /2}}.\end{eqnarray} \tag{ 4 }$$

The central density,¹⁵ ${{n}_{e,0}}$, was determined by fitting the spectrum extracted in a 200'' circular region, utilizing the relation between the normalization K of the thermal model and electron number density n_e,

$$\begin{eqnarray}&&K=\frac{{{10}^{-14}}}{4\pi {{[{{D}_{A}}(1+z)]}^{2}}}\int {{n}_{e}}{{n}_{{\rm H}}}dV,\end{eqnarray} \tag{ 5 }$$

where D_A is the angular diameter distance, n_H is the Hydrogen number density, and the integration is over a cylindrical volume. The gas mass within radius r is then

$$\begin{eqnarray}&&{{M}_{g}}(r)=\int _{0}^{r}4\pi {{\mu }_{e}}{{n}_{e,0}}{{m}_{p}}{{[1+{{(\frac{r}{{{r}_{c}}})}^{2}}]}^{-3\beta /2}}{{r}^{2}}dr,\end{eqnarray} \tag{ 6 }$$

where ${{\mu }_{e}}=1.172$ is the mean molecular weight of electrons, and m_p is the mass of a proton.

The total mass within radius r can be derived, under the assumption of hydrostatic equilibrium, from (e.g., Sarazin 1988)

$$\begin{eqnarray}&&M(r)=-\frac{kTr}{G\mu {{m}_{p}}}(\frac{d{\rm ln} {{n}_{e}}}{d{\rm ln} r}+\frac{d{\rm ln} T}{d{\rm ln} r}),\end{eqnarray} \tag{ 7 }$$

where k is the Boltzmann constant, G is the gravitational constant, μ = 0.614 is the mean molecular weight of the total particles, and T is the 3D temperature at radius r. Since PLCK G036.7+14.9 is undergoing a merger (Sections 3.1 and 4.7), we avoided the interaction region and measured the surface brightness and temperature profiles in the outer halves of both subclusters (see Figure 4). The surface brightness profiles from these regions are well described by β models (Figure 5 and Table 1), and the morphologies do not deviate significantly from spherical symmetry (Figure 1), so hydrostatic equilibrium in these regions should be a reasonable approximation.

Uncertainties were estimated from Monte Carlo simulations. The errors of the measured 2D temperature profile, the parameters of the surface brightness profile, and the normalization K of the spectral fit to the 200'' region are assumed to obey Gaussian distributions. For each Monte Carlo simulation, a set of randomly drawn 2D temperature profiles, β model parameters,¹⁶ and normalization K from their respective Gaussian distributions, were used to obtain the gas mass, total mass, and gas mass fraction profiles using the deprojection method in Section 4.4. This process was repeated 1000 times. In practice, too steep temperature profiles often lead to unphysical mass determinations. We only accept physical solutions with ${{\rho }_{{\rm tot}}}\gt {{\rho }_{{\rm gas}}}$, where ${{\rho }_{{\rm tot}}}$ and ${{\rho }_{{\rm gas}}}$ are the total and gas densities, respectively, and that are convectively stable, $d\ {\rm ln} T/d\ {\rm ln} \ {{\rho }_{{\rm gas}}}\lt 2/3$. Finally, we quote the mean of all accepted solutions as the "best-fitting" gas mass, total mass, and gas mass fraction, with the uncertainties as the $1\sigma$ standard deviation of all the accepted solutions.

In particular, we are interested in the gas mass, total mass, and gas mass fraction inside three characteristic radii, ${{r}_{{\Delta }}}$ (${\Delta }=2500,500,200$), where ${{r}_{{\Delta }}}$ is the radius within which the mean matter density of the universe is Δ times the critical density at the cluster redshift. The results are listed in Table 3. Since G036S is located near the chip boundary in the Chandra FOV (Figure 1), and the Chandra temperature profile does not cover the declining region at large radii (Figure 6), we did not measure the mass-related quantities for G036S with Chandra.

Table 3.  Radius, Gas Mass, Total Mass, and Gas Mass Fraction

Region	Method	Parametera	Δ = 2500	Δ = 500	Δ = 200
G036N		${{r}_{{\Delta }}}$	$0.52\pm 0.01(0.55\pm 0.02)$	$0.99\pm 0.03(1.03\pm 0.03)$	$1.38\pm 0.04(1.43\pm 0.04)$
		${{M}_{g,{\Delta }}}$	$1.42\pm 0.28(1.51\pm 0.32)$	$3.00\pm 0.62(3.12\pm 0.70)$	$4.33\pm 0.91(4.49\pm 1.02)$
	XMM-Newton	${{M}_{{\Delta }}}$	$2.25\pm 0.18(2.69\pm 0.29)$	$3.20\pm 0.28(3.60\pm 0.29)$	$3.46\pm 0.32(3.85\pm 0.32)$
		${{f}_{{\Delta }}}$	$6.32\pm 1.41(5.63\pm 1.38)$	$9.42\pm 2.21(8.69\pm 2.16)$	$12.57\pm 3.02(11.71\pm 2.97)$
		${{r}_{{\Delta }}}$	$0.55\pm 0.03(0.53\pm 0.03)$	$1.10\pm 0.06(1.07\pm 0.05)$	$1.56\pm 0.08(1.51\pm 0.07)$
	Chandra	${{M}_{g,{\Delta }}}$	$1.51\pm 0.32(1.48\pm 0.31)$	$3.22\pm 0.69(3.19\pm 0.68)$	$4.65\pm 0.99(4.60\pm 0.99)$
	baselineb	${{M}_{{\Delta }}}$	$2.77\pm 0.46(2.52\pm 0.38)$	$4.44\pm 0.67(4.08\pm 0.59)$	$5.02\pm 0.73(4.61\pm 0.65)$
		${{f}_{{\Delta }}}$	$5.49\pm 1.29(5.92\pm 1.36)$	$7.29\pm 1.78(7.83\pm 1.89)$	$9.31\pm 2.32(10.02\pm 2.49)$
		${{r}_{{\Delta }}}$	$0.54\pm 0.04(0.54\pm 0.03)$	$1.20\pm 0.10(1.15\pm 0.06)$	$1.85\pm 0.23(1.66\pm 0.10)$
	Chandra	${{M}_{g,{\Delta }}}$	$1.45\pm 0.33(1.52\pm 0.35)$	$3.47\pm 0.77(3.46\pm 0.80)$	$5.51\pm 1.33(5.09\pm 1.21)$
	with softc	${{M}_{{\Delta }}}$	$2.59\pm 0.65(2.63\pm 0.41)$	$5.75\pm 1.47(5.04\pm 0.73)$	$8.80\pm 3.55(6.07\pm 1.11)$
		${{f}_{{\Delta }}}$	$5.71\pm 1.53(5.81\pm 1.40)$	$6.21\pm 1.76(6.91\pm 1.75)$	$6.70\pm 2.38(8.49\pm 2.35)$
		${{r}_{{\Delta }}}$	$0.54\pm 0.03(0.52\pm 0.03)$	$1.06\pm 0.06(1.03\pm 0.05)$	$1.50\pm 0.08(1.45\pm 0.07)$
	Chandra	${{M}_{g,{\Delta }}}$	$1.46\pm 0.31(1.42\pm 0.30)$	$3.09\pm 0.66(3.03\pm 0.65)$	$4.46\pm 0.94(4.37\pm 0.93)$
	back*0.95d	${{M}_{{\Delta }}}$	$2.55\pm 0.41(2.30\pm 0.34)$	$3.96\pm 0.64(3.57\pm 0.53)$	$4.43\pm 0.69(4.01\pm 0.58)$
		${{f}_{{\Delta }}}$	$5.77\pm 1.37(6.22\pm 1.43)$	$7.89\pm 1.99(8.50\pm 2.09)$	$10.12\pm 2.61(10.94\pm 2.75)$
		${{r}_{{\Delta }}}$	$0.52\pm 0.02(0.54\pm 0.03)$	$1.10\pm 0.05(1.08\pm 0.07)$	$1.63\pm 0.09(1.55\pm 0.09)$
	Chandra	${{M}_{g,{\Delta }}}$	$1.43\pm 0.31(1.49\pm 0.35)$	$3.21\pm 0.74(3.22\pm 0.77)$	$4.88\pm 1.16(4.70\pm 1.12)$
	back*1.05e	${{M}_{{\Delta }}}$	$2.36\pm 0.27(2.56\pm 0.44)$	$4.37\pm 0.55(4.20\pm 0.75)$	$5.74\pm 0.98(4.92\pm 0.81)$
		${{f}_{{\Delta }}}$	$6.06\pm 1.41(5.87\pm 1.47)$	$7.40\pm 1.81(7.69\pm 2.08)$	$8.60\pm 2.28(9.59\pm 2.62)$
G036Sf		${{r}_{{\Delta }}}$	$0.52\pm 0.02(0.56\pm 0.02)$	$0.98\pm 0.03(1.06\pm 0.04)$	$1.37\pm 0.05(1.48\pm 0.06)$
		${{M}_{g,{\Delta }}}$	$1.68\pm 0.33(1.79\pm 0.31)$	$3.36\pm 0.67(3.56\pm 0.63)$	$4.74\pm 0.94(5.02\pm 0.90)$
	XMM-Newton	${{M}_{{\Delta }}}$	$2.36\pm 0.23(2.95\pm 0.32)$	$3.13\pm 0.31(3.90\pm 0.41)$	$3.38\pm 0.34(4.24\pm 0.47)$
		${{f}_{{\Delta }}}$	$7.10\pm 1.42(6.07\pm 1.13)$	$10.72\pm 2.27(9.12\pm 1.77)$	$14.03\pm 3.04(11.85\pm 2.39)$

Notes:

^a ${{r}_{{\Delta }}}$, ${{M}_{g,{\Delta }}}$, ${{M}_{{\Delta }}}$, and ${{f}_{{\Delta }}}$ are the radius, gas mass, total mass, and gas mass fraction, measured inside a radius where the overdensity within that radius is Δ times the critical density of the Universe at the cluster redshift, while the units are Mpc, ${{10}^{13}}\;{{M}_{\odot }}$, ${{10}^{14}}\;{{M}_{\odot }}$, and %, respectively. The values outside and inside of the parentheses were obtained with N_H fixed at the total and best-fitting values (Table 2), respectively. ^bChandra baseline background model, i.e., the blank-sky background. ^cChandra baseline background model with a soft-band adjustment. ^dChandra baseline background model varied by $+5\%$. ^eChandra baseline background model varied by $-5\%$. ^fAs G036S is close to the chip boundary in the Chandra FOV, we can only measure the temperature profile up to $\sim 0.8\;{{r}_{500}}$. In this relatively small region, Chandra gives an essentially isothermal temperature profile, unlike the obviously declining temperature profile revealed by XMM-Newton at large radii where Chandra does not cover. Thus we did not measure mass-related quantities for G036S with Chandra.

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From previous sections, we see that, due to cross-calibration issues, XMM-Newton and Chandra give results inconsistent within their $1\sigma$ errors for some parameters which affect the mass determinations. We treat the uncertainties in N_H, z, other cross-calibration uncertainties between XMM-Newton and Chandra, and the uncertainties in Chandra background subtraction as systematic uncertainties. For each set of {N_H, z} in Table 2, new temperature profiles for G036N and G036S were derived. The characteristic radii, gas mass, total mass, and gas mass fraction were then calculated following the method given in Section 4.5. We also tried different background subtraction methods for the Chandra data (see Section 4.1.1). The results are presented in Table 3, from which we can draw the following conclusions:

• 1.  
  Comparing N_H fixed at the total value to the best-fitting values, all the quantities differ by less than $1.6\sigma$. The differences between the "best-fitting" values of ${{r}_{{\Delta }}}$, ${{M}_{g,{\Delta }}}$, ${{M}_{{\Delta }}}$, and ${{f}_{{\Delta }}}$ for XMM-Newton are $\lesssim 8$%, $\lesssim 7$%, $\lesssim 25$%, and $\lesssim 16$%, while those for Chandra are $\lesssim 10$%, $\lesssim 8$%, $\lesssim 31$%, and $\lesssim 27$%, respectively. The larger differences for Chandra are caused by the Chandra baseline background model with a soft-band adjustment, without which the differences for all four quantities for Chandra are reduced by a factor of at least 2.
• 2.  
  Comparing XMM-Newton to Chandra, all quantities differ by no more than $2.5\sigma$. Varying the Chandra baseline background by +5% (back*0.95) gives the closest results to XMM-Newton, with $\lesssim 9$%, $\lesssim 6$%, $\lesssim 28$%, and $\lesssim 20$% differences between the "best-fitting" values of ${{r}_{{\Delta }}}$, ${{M}_{g,{\Delta }}}$, ${{M}_{{\Delta }}}$, and ${{f}_{{\Delta }}}$, while adding a soft-band adjustment to the Chandra baseline background gives the largest differences to XMM-Newton, with $\lesssim 34$%, $\lesssim 27$%, $\lesssim 154$%, and $\lesssim 46$% differences for the above four quantities, respectively.
• 3.  
  Comparing Chandra different background models, all the quantities are consistent within their $1\sigma$ errors. The differences (with respect to the baseline background model) of ${{r}_{{\Delta }}}$, ${{M}_{g,{\Delta }}}$, ${{M}_{{\Delta }}}$, and ${{f}_{{\Delta }}}$ when varying the baseline background model by ±5% are $\lesssim 6$%, $\lesssim 5$%, $\lesssim 15$%, and $\lesssim 10$%, while adding a soft-band adjustment to the Chandra baseline background gives much larger differences, $\lesssim 19$%, $\lesssim 19$%, $\lesssim 75$%, and $\lesssim 28$%, respectively.

By comparing the results in the above mentioned cases, we can see that adding a soft-band adjustment to the Chandra baseline background always produces the largest differences of the "best-fitting" values of ${{r}_{{\Delta }}}$, ${{M}_{g,{\Delta }}}$, ${{M}_{{\Delta }}}$, and ${{f}_{{\Delta }}}$. Actually, adding a soft-band adjustment also increases the best-fitting N_H for the global cluster (Table 2), which further affects the temperature measurements. This "soft-band-adjustment–N_H–kT" dependence makes the mass determination much more uncertain, which gives rise to the largest differences of the "best-fitting" values for the mass-related quantities in Table 3. Without accurate N_H determination, we consider this model less constraining and do not include it in our further analysis and final results.

To summarize, uncertainties in N_H, z, other XMM-Newton and Chandra cross-calibration uncertainties, and Chandra background subtraction, do not lead to any significantly different ($\lesssim 2.5\sigma$) mass determinations. XMM-Newton gives a mass ${{M}_{200}}\sim (3.1-4.2)\times {{10}^{14}}\;{{M}_{\odot }}$ for G036N and ${{M}_{200}}\sim (3.0\;-4.7)\times {{10}^{14}}\;{{M}_{\odot }}$ for G036S, while Chandra gives a somewhat higher mass, ${{M}_{200}}\sim (3.4-6.7)\times {{10}^{14}}\;{{M}_{\odot }}$, for G036N.

The X-ray morphology of PLCK G036.7+14.9 suggests that it is undergoing a merger between G036N and G036S (Section 3.1). To confirm this spectroscopically, we extracted spectra from a 130'' × 35'' rectangular region (Region 1, see Figure 7) between G036N and G036S, and from the symmetric regions with respect to their centers (Region 2 for G036N and Region 3 for G036S), and fit them to single thermal models. We found that the temperature in Region 1 is indeed higher (by a factor of ∼2 based on the Chandra data) than those in Regions 2 and 3, which could be interpreted as shock heating during the merger.

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Using the Rankine–Hugoniot jump conditions, the Mach number, $\mathcal{M}$, is related to the temperature jump as (e.g., Sarazin 2002)

$$\begin{eqnarray}&&\frac{1}{C}=\frac{2}{{{\mathcal{M}}^{2}}(\gamma +1)}+\frac{\gamma -1}{\gamma +1},\end{eqnarray} \tag{ 8 }$$

and

$$\begin{eqnarray}\begin{array}{ccccccccccccccc} \frac{1}{C} & = & {{[\frac{1}{4}{{(\frac{\gamma +1}{\gamma -1})}^{2}}{{(\frac{{{T}_{2}}}{{{T}_{1}}}-1)}^{2}}+\frac{{{T}_{2}}}{{{T}_{1}}}]}^{1/2}} \\ {} & {} & -\frac{1}{2}\frac{\gamma +1}{\gamma -1}(\frac{{{T}_{2}}}{{{T}_{1}}}-1), \\ \end{array}\end{eqnarray} \tag{ 9 }$$

where the subscripts 1 and 2 denote the preshock and postshock gas, $C\equiv {{\rho }_{2}}/{{\rho }_{1}}$ is the shock compression, and $\gamma =5/3$ is the adiabatic index. If we simply assume that the temperature of the preshock gas is given by the gas temperature in Region 2 (Region 3) and that of the postshock gas is given by the gas temperature in Region 1, using the above relations, we can estimate the Mach number of the shock propagating in G036N (G036S) both for XMM-Newton and Chandra (see Table 4). Note that due to projection effects, the inferred Mach number is only a lower limit.

Table 4.  Characteristics of the Shock and the Merger

Region	Parametera	XMM-Newton	Chandra Baselineb	Chandra Back*0.95c	Chandra Back*1.05d
	$\mathcal{M}$ e	$1.16\pm 0.21(1.19\pm 0.30)$	$2.01\pm 0.46(1.91\pm 0.38)$	$2.01\pm 0.45(1.90\pm 0.38)$	$2.02\pm 0.46(1.91\pm 0.38)$
G036N	${{c}_{{\rm sound}}}$ f	$1246_{-46}^{+54}$ ($1353_{-54}^{+68}$)	$1323_{-71}^{+91}$ ($1267_{-71}^{+76}$)	$1290_{-74}^{+85}$ ($1232_{-68}^{+77}$)	$1349_{-69}^{+103}$ ($1295_{-69}^{+84}$)
	trg	0.94 ± 0.18 (0.87 ± 0.22)	0.57 ± 0.14 (0.61 ± 0.13)	0.57 ± 0.14(0.61 ± 0.13)	0.59 ± 0.14 (0.61 ± 0.13)
	$\mathcal{M}$ e	$1.25\pm 0.19(1.28\pm 0.28)$	$2.27\pm 0.44(2.15\pm 0.36)$	$2.26\pm 0.43(2.14\pm 0.35)$	2.28 ± 0.44 $(2.17\pm 0.36)$
G036S	${{c}_{{\rm sound}}}$ f	$1224_{-41}^{+54}$ ($1318_{-62}^{+44}$)	$1295_{-61}^{+81}$ ($1244_{-60}^{+64}$)	$1271_{-62}^{+63}$ ($1217_{-53}^{+65}$)	$1317_{-60}^{+98}$ ($1266_{-61}^{+63}$)
	trg	0.88 ± 0.14 (0.86 ± 0.19)	0.52 ± 0.11 (0.57 ± 0.10)	0.51 ± 0.10 (0.56 ± 0.10)	0.53 ± 0.11 (0.57 ± 0.10)
⋯	${{t}_{{\rm merge}}}$ h	0.78 (0.79)	0.80 (0.79)	0.80 (0.80)	0.80 (0.80)
	θi	76 (78)	80 (80)	79 (79)	81 (81)

Notes:

^aValues outside and inside of the parentheses were obtained with N_H fixed at the total and best-fitting values (Table 2), respectively. ^bChandra baseline background model. ^cChandra baseline background model varied by $+5\%$. ^dChandra baseline background model varied by $-5\%$. ^eMach number obtained using the temperatures in Region 1 and Region 2 (Region 3) in Figure 7 as the temperatures of the postshock and preshock gas in G036N (G036S). ^fSound speed, in units of km s⁻¹, with the temperature measured in the $[0.15-0.75]{{r}_{500}}$ region (Table 5). ^gTime for the shock to propagate to the subcluster center in units of Gyr. For G036S, as Chandra does not cover a large enough region to measure the mass, hence r₂₀₀, we assumed that the ratios of r₂₀₀ for G036N and G036S are the same for XMM-Newton and Chandra and that the relative errors are the same for both subclusters for Chandra, to obtain r₂₀₀ of G036S for Chandra. ^hTime in Gyr since the merger began, obtained from the simplified model in Section 5.1. ⁱAngle in degree between the merger axis (assuming zero impact parameter) and the plane of the sky obtained from the simplified model in Section 5.1.

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XMM-Newton suggests a weak shock ($\mathcal{M}\sim 1.0-1.6$), while Chandra indicates a stronger shock ($\mathcal{M}\sim 1.5-2.7$). The difference is caused by, when comparing the same N_H, the lower temperature in the interaction region measured from XMM-Newton (7.65–9.19) keV compared to Chandra (10.52–16.86 keV). Actually, from the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS; Reiprich & Böhringer 2002), Schellenberger et al. (2015) found systematic lower temperatures given by XMM-Newton compared to Chandra for high temperature systems, especially for $\gt 8$ keV clusters. When comparing the Mach number obtained with the best-fitting N_H values, the large difference in Mach number between XMM-Newton and Chandra is then caused by higher temperatures in the preshock regions (Regions 2 and 3) given by XMM-Newton. This is because the best-fitting XMM-Newton N_H is almost a factor of 2 less than that of Chandra (Section 4.2), and a smaller N_H increases the temperature, leading to a smaller temperature difference in the postshock region, and a larger temperature difference in the preshock regions. Thus, cross-calibration issues again manifest themselves in terms of the Mach number discrepancy.

From Section 3.1, we know that G036N has an X-ray AGN in the center. We extracted a spectrum in a circular region with a radius of 3'', and used the surrounding region (4''–8'' annulus) as the background. By fixing the index of the power-law model at 1.7, we acquired a bolometric X-ray luminosity (0.01–100 keV in practice) of (1.45–1.50) × 10⁴² erg s⁻¹.

The surface brightness profiles (Figure 5) and the temperature profiles (Figure 6) suggest that the gas may be cooling in the central regions of both G036N and G036S. The isobaric cooling time was calculated as

$$\begin{eqnarray}&&{{t}_{{\rm cool}}}=\frac{H}{{{L}_{{\rm bol}}}}=\frac{\frac{5}{2}\frac{{{M}_{{\rm gas}}}}{\mu {{m}_{p}}}kT}{{{L}_{{\rm bol}}}},\end{eqnarray} \tag{ 10 }$$

where H is the enthalpy, ${{L}_{{\rm bol}}}$ is the bolometric X-ray luminosity, and ${{M}_{{\rm gas}}}$ is the gas mass. We then compared this to the look-back time to z = 1, which is t_L = 7.7 Gyr, a representative time for a cluster to relax and develop a cool core (e.g., Bîrzan et al. 2004; Hudson et al. 2010). If ${{t}_{{\rm cool}}}\lt {{t}_{L}}$, the gas may be cooling. Due to the much larger PSF of XMM-Newton, we only used the Chandra data to study the cores. From Figure 4, varying the blank-sky background by ±5% has little effect on the temperature in the central bright part of the subclusters, so we only used the baseline background model to study the cores.

For G036N, the cooling time (single thermal model) in the central 3''–10'' (full annulus) region is ${{t}_{{\rm cool}}}$ = 2.64–4.71 Gyr, while that in the outer 10''–35'' (half annulus to avoid the interaction region) region is 6.82–12.15 Gyr, so only the gas in the central ∼10'' (27 kpc) region may be cooling. The abundance obtained with a single thermal model is $0.85-2.44\;{{Z}_{\odot }}$, significantly larger than the global abundance ($0.09-0.47\;{{Z}_{\odot }}$) of G036N, suggesting enrichment from the BCG. A two thermal components model, with the higher temperature component fixed at the cluster temperature and abundance, does not improve the fit and results in essentially zero normalization for the higher temperature component. Adding a cooling flow model to a single thermal model does not improve the fit either, and the mass deposition rate given by the normalization of the cooling flow model is highly uncertain with ${{\dot{M}}_{{\rm spec}}}=2.3-27.6\;{{M}_{\odot }}$ yr⁻¹.

For G036S, the cooling time (single thermal model) in the central 0''–15'' (full annulus) region is ${{t}_{{\rm cool}}}=5.65-10.27$ Gyr, already comparable to or greater than t_L, so cooling should be very weak in this region. Adding a cooling flow model, we obtained a $1\sigma$ upper limit on the mass deposition rate of 14.3 ${{M}_{\odot }}$ yr⁻¹.

Previous ROSAT and optical studies (Ebeling et al. 2002) did not resolve the morphological details of PLCK G036.7+14.9. With our high resolution Chandra and XMM-Newton observations, two close (in projection) subclusters, G036N and G036S, were clearly resolved, and spatially resolved spectroscopy could be performed. Spectral analysis produces very similar redshifts for G036N and G036S (Table 2), and reveals a higher temperature in the region between them compared to the symmetric regions away from their centers which could be due to shock heating during the merger (Section 4.7).

The morphologies of G036N and G036S excluding the interaction region do not deviate significantly from spherical symmetry (see Figure 1) and their surface brightness profiles are well described by single β models beyond the central ∼10'' regions (see Figure 5), suggesting that the merger is probably at an early stage so that perturbations generated by the merger have not yet disturbed the outer regions. Another piece of evidence for an early stage of the merger comes from the good spatial correspondence between the X-ray emission centroids of the two subclusters and their BCGs (see left panel of Figure 3). This also favors a merger close to the line of sight.

Projection effects hamper our knowledge of the geometry of the merger. The only observables are the projected distance, d_p = 193 kpc, and the radial velocity difference, v_r = 2356 km s⁻¹, between the two subclusters. To gain some insight into the merger kinematics, we applied the simplified model in Ricker & Sarazin (2001; see also Sarazin 2002; Sauvageot et al. 2005) to G036N and G036S. This model treats the two subclusters as point masses, and assumes that they initially expand away from each other in the Hubble flow. Due to their gravitational attraction, they collapse after reaching the greatest separation d₀, and finally merge. Let ${{t}_{{\rm coal}}}$ be the age of the universe when core coalesce occurs. The parameters d₀ and ${{t}_{{\rm coal}}}$ are related by Kepler's Third Law as

$$\begin{eqnarray}&&{{d}_{0}}\approx {{[2G({{M}_{n}}+{{M}_{s}})]}^{1/3}}{{(\frac{{{t}_{{\rm coal}}}}{\pi })}^{2/3}},\end{eqnarray} \tag{ 11 }$$

where M is the total mass (assumed to be M₂₀₀, see Table 3). Let d be the 3D distance between the two subclusters. The merger velocity v is then

$$\begin{eqnarray}&&{{v}^{2}}\approx 2G({{M}_{n}}+{{M}_{s}})(\frac{1}{d}-\frac{1}{{{d}_{0}}}){{[1-{{(\frac{b}{{{d}_{0}}})}^{2}}]}^{-1}},\end{eqnarray} \tag{ 12 }$$

where b is the impact parameter as defined in Sarazin (2002), and is assumed to be zero in our case since it is usually very small compared to d₀ (Sarazin 2002). The parameters d and v are related to the observables by

$$\begin{eqnarray}&&d=\frac{{{d}_{p}}}{{\rm cos} \theta },\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&v=\frac{{{v}_{r}}}{{\rm sin} \theta },\end{eqnarray} \tag{ 14 }$$

where θ is the angle between the merger axis and the plane of the sky. On the other hand, since the two subclusters have not attained core coalesce, ${{t}_{{\rm coal}}}$ can be written as

$$\begin{eqnarray}&&{{t}_{{\rm coal}}}\approx {{t}_{{\rm age}}}+\frac{d}{v},\end{eqnarray} \tag{ 15 }$$

where ${{t}_{{\rm age}}}=11.52$ Gyr is the age of the Universe at the cluster redshift in our adopted cosmology. To obtain the time since the merger began, ${{t}_{{\rm merge}}}$, i.e., the time from when the two subclusters started physical contact to the present day, we have to treat the two subclusters as extended sources and ${{t}_{{\rm merge}}}$ can be approximated by

$$\begin{eqnarray}&&{{t}_{{\rm merge}}}\approx \frac{{{r}_{n}}+{{r}_{s}}-d}{v},\end{eqnarray} \tag{ 16 }$$

where r is the virial radius (assumed to be r₂₀₀, see Table 3). Solving Equations (11)–(16), we obtained θ ≈ 80° and ${{t}_{{\rm merge}}}\approx 0.8$ Gyr (see Table 4). Although overly simplified, this model produces consistent results with our expectations, i.e., an early stage of the merger, mostly along the line of sight, that can explain the main observational features outlined in the above two paragraphs. Targeted simulations are required to study in detail the dynamics of this system, which is beyond the scope of this paper.

To summarize, PLCK G036.7+14.9 is undergoing a major merger by two nearly equal mass (∼1 : 1) subclusters. The merger should be at an early stage, and should be happening mostly along the line of sight. A simplified model suggests that the merger probably began ∼0.8 Gyr ago, with an angle between the merger axis and the plane of the sky of ∼80°.

In Sections 4.5 and 4.6, we derived the total masses of G036N and G036S under the assumption of hydrostatic equilibrium of the ICM using the regions not affected by the ongoing merger. Chandra does not cover a large enough region to measure the total mass of G036S. If we assume that Chandra would give the same mass ratio of G036N to G036S as XMM-Newton, and the relative errors are the same for G036N and G036S for Chandra, we can obtain the total mass of G036S that would be "measured" by Chandra. Adding the total X-ray masses of G036N and G036S together, we obtained the total X-ray derived mass (measured inside the X-ray derived r₅₀₀, ${{r}_{X,500}}$; see Table 3) of PLCK G036.7+14.9, which is ${{M}_{X,500}}=(5.91-8.00)\times {{10}^{14}}\;{{M}_{\odot }}$ for XMM-Newton and ${{M}_{X,500}}=(6.66-9.85)\times {{10}^{14}}\;{{M}_{\odot }}$ for Chandra.¹⁷

The integrated SZ signal, Y_SZ, is proportional to the total electron pressure of the cluster,

$$\begin{eqnarray}&&D_{A}^{2}{{Y}_{{\rm SZ}}}=\frac{{{\sigma }_{{\rm T}}}}{{{m}_{e}}{{c}^{2}}}\int {{p}_{e}}dV,\end{eqnarray} \tag{ 17 }$$

where ${{\sigma }_{{\rm T}}}$ is the Thomson cross-section, m_e is the mass of an electron, c is the speed of light, and p_e is the electron pressure. Due to the size-flux degeneracy (Planck Collaboration VIII 2011), additional information is needed to refine the blind Planck SZ flux measurement. Using the X-ray measured cluster position and size can break the degeneracy, and if the redshift of the cluster is known, it may be used to further break the degeneracy (Planck Collaboration XXIX 2014). After obtaining the refined SZ flux, the total SZ mass, M_SZ, can be estimated using the Malmquist-bias corrected scaling relation between Y_SZ and M_SZ (Planck Collaboration XX 2014). With the above method, Planck Collaboration XXIX (2014) published the SZ flux, ${{Y}_{{\rm SZ},500}}$, and SZ mass, ${{M}_{{\rm SZ},500}}$, measured inside the SZ r₅₀₀, ${{r}_{{\rm SZ},500}}$, for 813 confirmed clusters with measured redshifts out of the 1227 all-sky SZ sources using the first 15.5 months of data. For PLCK G036.7+14.9, ${{Y}_{{\rm SZ},500}}=0.00234_{-0.00032}^{+0.00033}$ arcmin² (adopting a redshift of 0.1525) and ${{M}_{{\rm SZ},500}}=5.54_{-0.43}^{+0.42}(5.11-5.96)\times {{10}^{14}}\;{{M}_{\odot }}$.

It is clear that ${{M}_{{\rm SZ},500}}$ is greater than the X-ray mass of either G036N or G036S (see Table 3), which is fully expected since Planck did not resolve the two subclusters, so the derived SZ mass is the mass of the whole cluster. However, compared to the X-ray mass of the whole cluster, ${{M}_{X,500}}$, especially the Chandra "measurement" (note that Chandra actually does not directly measure the total mass of the whole cluster), ${{M}_{{\rm SZ},500}}$ is smaller, although there is a small overlapping range between ${{M}_{{\rm SZ},500}}$ and the XMM-Newton derived mass because of the large uncertainties in the X-ray mass measurements (however, see Footnote ¹⁷).

In the derivation of the SZ mass, Planck Collaboration XXIX (2014) used the best-fitting ${{Y}_{{\rm SZ},500}}$–${{M}_{{\rm SZ},500}}$ relation of Planck Collaboration XX (2014). Even if we accounted for the uncertainties in that relation and chose the parameters that maximize or minimize ${{M}_{{\rm SZ},500}}$, we obtained the most conservative SZ mass estimate, ${{M}_{{\rm SZ},500}}=(4.99-6.06)\;\times {{10}^{14}}\;{{M}_{\odot }}$. This only slightly increases the overlapping range between the SZ and XMM-Newton mass measurements, while the lower SZ mass compared to X-ray mass determinations remains unexplained.

The difference between the X-ray and SZ masses should not be entirely caused by the different extraction regions for the SZ and X-ray mass measurements. In Figure 8, we show ${{r}_{{\rm SZ},500}}$ used by Planck (Ebeling et al. 2002; Piffaretti et al. 2011; Planck Collaboration XXIX 2014) and ${{r}_{X,500}}$ used by XMM-Newton and Chandra. The SZ extraction region is larger (by ∼14%) than the XMM-Newton extraction regions, but the XMM-Newton measured mass is higher. The Chandra extraction regions are close to (∼3% smaller than) the SZ extraction region, but the Chandra measured mass is even higher. Therefore, while different extraction region is a factor affecting the mass determinations from X-ray and SZ measurements, some other factors may be more important to explain the difference.

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As we show in Sections 5.1 and 5.3, the merger is most likely at an early stage. The SZ signal Y_SZ relates to the mass M via a power law, which can be written as ${{Y}_{{\rm SZ}}}=A{{M}^{\eta }}$, where A and η can be considered as constants for our purpose. For an early stage of the merger, the total mass of the whole cluster is ${{M}_{n}}+{{M}_{s}}$. However, if the two subclusters are not resolved, as in the case of the Planck observation, the mass of the whole cluster determined in this way will be ${{(M_{n}^{\eta }+M_{s}^{\eta })}^{1/\eta }}$. From Table 3, ${{M}_{n}}\approx {{M}_{s}}$; $\eta =1.79$ as used by Planck Collaboration XXIX (2014). This gives a total mass a factor of ∼0.74 smaller than ${{M}_{n}}+{{M}_{s}}$, which is about the difference between the SZ derived mass and the X-ray derived mass. This demonstrates that the mass discrepancy between the SZ and X-ray measurements is caused by the fact that Planck does not resolve the two subclusters and interprets the whole system as a single cluster.

Based on simulations, Kravtsov et al. (2006) propose that the X-ray analogue of Y_SZ, ${{Y}_{X}}={{M}_{{\rm gas}}}\times {{T}_{X}}$, where T_X is the emission weighted temperature within a certain region, is a low-scatter mass proxy and is less sensitive to the cluster dynamical state. We computed the total ${{Y}_{X,500}}$ by adding those of G036N and G036S, where T_X is measured in the $[0.15-0.75]{{r}_{500}}$ region and ${{M}_{{\rm gas}}}$ is measured within r₅₀₀ (see Table 5 for details). We list ${{Y}_{X,500}}$ in Table 5. ${{Y}_{X,500}}$ and ${{M}_{X,500}}$ follow the scaling relations presented in Arnaud et al. (2010).

Table 5.  Temperature, ${{Y}_{X,500}}$, and ${{Y}_{{\rm SZ},500}}/{{Y}_{X,500}}$

Region	Parametera	XMM-Newton	Chandra Baselineb	Chandra Back*0.95c	Chandra Back*1.05d
G036N	kTe	$5.97_{-0.44}^{+0.52}(7.04_{-0.56}^{+0.71})$	$6.73_{-0.72}^{+0.93}(6.17_{-0.69}^{+0.74})$	$6.40_{-0.73}^{+0.84}(5.84_{-0.64}^{+0.73})$	$7.00_{-0.72}^{+1.07}(6.45_{-0.69}^{+0.84})$
	${{Y}_{X,500}}$ f	1.82 ± 0.43 (2.13 ± 0.54)	2.17 ± 0.52 (2.02 ± 0.48)	2.06 ± 0.50 (1.91 ± 0.46)	2.26 ± 0.58 (2.11 ± 0.54)
G036S	kTe	$5.76_{-0.39}^{+0.51}(6.68_{-0.45}^{+0.63})$	$6.45_{-0.61}^{+0.81}(5.95_{-0.57}^{+0.61})$	$6.21_{-0.61}^{+0.62}(5.70_{-0.50}^{+0.61})$	$6.67_{-0.61}^{+0.99}$ $(6.16_{-0.59}^{+0.61})$
	${{Y}_{X,500}}$ f	1.97 ± 0.41 (2.24 ± 0.42)	2.11 ± 0.48 (1.95 ± 0.43)	1.99 ± 0.44 (1.86 ± 0.41)	2.15 ± 0.50 (2.02 ± 0.45)
Whole	${{Y}_{{\rm SZ},500}}/{{Y}_{X,500}}$ g	1.11 ± 0.35 (0.96 ± 0.30)	0.98 ± 0.33 (1.06 ± 0.35)	1.04 ± 0.34 (1.12 ± 0.37)	0.96 ± 0.33 (1.02 ± 0.35)

Notes:

^aValues outside and inside of the parentheses were obtained with N_H fixed at the total and best-fitting values (Table 2), respectively. ^bChandra baseline background model. ^cChandra baseline background model varied by $+5\%$. ^dChandra baseline background model varied by $-5\%$. ^eTemperature in keV measured in the $[0.15-0.75]{{r}_{500}}$ region. For G036N, we adopted ${{r}_{500}}=1.0$ (1.1) Mpc for XMM-Newton (Chandra), while for G036S, ${{r}_{500}}=1.0$ (1.0) Mpc for XMM-Newton (Chandra), for simplicity. ^fProduct of temperature and gas mass, where temperature was measured in the $[0.15-0.75]{{r}_{500}}$ region and gas mass is that within r₅₀₀. ${{Y}_{X,500}}$ is in ${{10}^{14}}\;{{M}_{\odot }}$ keV. ^gSee Section 5.2 for the definition of this ratio. ${{Y}_{{\rm SZ},500}}$ has been scaled to a redshift of 0.1547.

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Neglecting gas clumping, Y_X relates to Y_SZ by (e.g., Arnaud et al. 2010; Rozo et al. 2012; Planck Collaboration XXIX 2014)

$$\begin{eqnarray}&&\frac{D_{A}^{2}{{Y}_{{\rm SZ}}}}{{{Y}_{X}}}=\frac{{{\sigma }_{{\rm T}}}}{{{m}_{e}}{{c}^{2}}}\frac{1}{{{\mu }_{e}}{{m}_{p}}}\frac{\lt {{n}_{e}}T\gt }{\lt \;{{n}_{e}}\gt {{T}_{X}}}=C\frac{\lt {{n}_{e}}T\gt }{\lt \;{{n}_{e}}\gt {{T}_{X}}}.\end{eqnarray} \tag{ 18 }$$

Therefore, the ratio $D_{A}^{2}{{Y}_{{\rm SZ}}}/C{{Y}_{X}}$ should be close to 1, although the exact value depends on the structure of the cluster. Hereafter, we will refer ${{Y}_{{\rm SZ}}}/{{Y}_{X}}$ to $D_{A}^{2}{{Y}_{{\rm SZ}}}/C{{Y}_{X}}$ for simplicity. Previous studies show that ${{Y}_{{\rm SZ},500}}/{{Y}_{X,500}}$ is between 0.8 and 1 (e.g., Arnaud et al. 2010; Rozo et al. 2012; Planck Collaboration XXIX 2014). Our results are consistent with these studies, although with large uncertainties (see Table 5).

In summary, the SZ mass given by Planck is higher than the X-ray derived mass by XMM-Newton and Chandra for either subcluster, but is lower than the X-ray mass of the whole cluster, due to the fact that Planck does not resolve the two subclusters and interprets the whole system as a single cluster. The ${{Y}_{{\rm SZ}}}/{{Y}_{X}}$ ratio is consistent with previous studies, although with large errors.

The surface brightness profiles show excess emission in the central ∼10'' regions relative to single β models for both G036N and G036S (see Figure 5), and the temperature profiles show indications of temperature drops toward their centers (see Figure 6). The cooling time of the central 3''–10'' region for G036N is 2.64–4.71 Gyr, and beyond this region, the cooling time is longer than 7.7 Gyr. The cooling time of the 0–15'' region for G036S is 5.65–10.27 Gyr, comparable to or longer than 7.7 Gyr (see Section 4.8 for details). Therefore, G036N has a small (∼10'' = 27 kpc), moderate cool core, while G036S has at most a very weak cool core within the central ∼15'' = 40 kpc region. The spectroscopically derived mass deposition rate (see Section 4.8) confirms this scenario.

It is interesting to ask what causes the difference between the cores of the two subclusters. One possibility is that the ongoing merger has disrupted a pre-existing cool core in G036S (e.g., Sanderson et al. 2006; Burns et al. 2008; Rossetti & Molendi 2010; but see, e.g., Poole et al. 2008). From Table 4, the merger began ∼0.78–0.80 Gyr ago based on the simplified merger model (Section 5.1), while the time for the shock to propagate to the center of G036N (G036S), ${{t}_{r,n}}$ (${{t}_{r,s}}$), ${{t}_{r}}={{r}_{200}}/\mathcal{M}{{c}_{{\rm sound}}}$, is 0.65–1.12 (0.67–1.05) Gyr obtained from XMM-Newton, and is 0.43–0.74 (0.41–0.67) Gyr from Chandra, respectively. Taken at face value, Chandra favors a scenario in which the shock has passed the cores of the two subclusters, while the situation for XMM-Newton is less clear.

To further examine this question, we divided the central 3''–10'' annular region of G036N into two equal area half annular regions, with the symmetry axis perpendicular to the line connecting the centers of the two subclusters. We compared the derived temperatures in the two half annular and full annular regions, finding them to be consistent within their $1\sigma$ errors. We then varied the outer radius, i.e., 3''–8'', 3''–12'', 3''–15'', and 3''–20'' (maximum outer radius avoiding the interaction region, see Figure 7), performed the same analysis, and found that all the temperatures are consistent within their $1\sigma$ errors (although in some cases the temperature in the half annular region near the interaction region was poorly constrained). Two possibilities can explain this: (i) the shock has not reached the central ∼10'' region of G036N; (ii) the shock has passed the central ∼10'' region of G036N, but the core is dense enough not to be destroyed. We now show that possibility (ii) is less likely. We first applied the same method to G036S, but the data quality is poorer and all the temperatures are consistent given the large uncertainties. Notice that M₂₀₀, r₂₀₀, $\mathcal{M}$, ${{c}_{{\rm sound}}}$, and t_r for G036N and G036S are all similar (Tables 3 and 4), so we expect that the shock travels similar distances in G036N and G036S at any given time. As a result, if the shock has reached the core of G036N, it should also have reached the core of G036S. The pressure ratio, ${{p}_{n}}/{{p}_{s}}=0.61-1.16$, where p_n and p_s are the mean pressures in the central 3''–10'' region of G036N and in the central 0–15'' region of G036S, respectively, although with large uncertainty, is consistent with 1. This implies that, if possibility (ii) is correct, the core of G036S should also have survived the merger induced shock, in contradiction with observations. Thus, the consistent temperatures in the two half annular regions and in their parent regions in the core of G036N imply that the shock probably has not reached the core, so the lack of gas cooling in the core of G036S is unlikely caused by the merger disrupting a pre-existing cool core in G036S. This is also consistent with our previous expectation of an early stage of the merger, suggesting that the simplified model in Section 5.1 overestimates the time since the merger began. The actual time since the merger began is probably less than ∼0.4–0.7 Gyr (see Table 4).

For cool core clusters, some heating mechanisms must be taking place to prevent the gas from catactrophic cooling (see Fabian 1994). Interestingly, the BCG of G036N hosts a radio source (Section 3.1), with a flux density of 19.7 mJy and a 1.4 GHz luminosity (${{L}_{1.4\,{\rm GHz}}}$) of $1.32\times {{10}^{24}}$ W Hz⁻¹ after the K-correction (Singal et al. 2011) assuming a radio spectral index of 0.8 (Condon et al. 1998).¹⁸ The extent of the radio source is comparable to the angular resolution of the NVSS (${\rm FWHM}=45^{\prime\prime}$, ∼120 kpc at the cluster redshift, see right panel of Figure 3). If it is an extended source, i.e., with radio lobes filled with relativistic particles and magnetic fields (e.g., Bîrzan et al. 2008), there may be undetected cavities, which are generally thought to play a key role in the "radio mode" feedback (e.g., Bower et al. 2006; Croton et al. 2006; Sijacki et al. 2007) in clusters of galaxies (see McNamara & Nulsen 2007, 2012; Fabian 2012; and references therein). Using the scaling relation in Cavagnolo et al. (2010), we estimated the cavity power, ${{P}_{{\rm cav}}}\sim (0.8-1.4)\times {{10}^{43}}$ erg s⁻¹, based on the 1.4 GHz luminosity. The X-ray luminosity of the cool core is $(3.3-4.9)\times {{10}^{43}}$ erg s⁻¹, 2–6 times larger than ${{P}_{{\rm cav}}}$. Studies of large samples show that although in some cases the cavity power is smaller than the X-ray luminosity, on average it is energetic enough to balance the cooling (e.g., Rafferty et al. 2006; Bîrzan et al. 2008; Dunn & Fabian 2008; Cavagnolo et al. 2010). Higher resolution radio data are required to confirm the extended nature of the radio source, and deeper Chandra observations are also necessary to identify any cavities in the core of G036N. Sun (2009) studied a sample of 161 BCGs and 74 strong radio AGNs (${{L}_{1.4\,{\rm GHz}}}\gt {{10}^{24}}$ W Hz⁻¹) in 152 nearby ($z\lt 0.11$) clusters and groups using Chandra archive data. He found that all BCGs with ${{L}_{1.4\,{\rm GHz}}}\gt 2\times {{10}^{23}}$ W Hz⁻¹ in the sample have cool-cores. Although with a higher redshift, G036N is also consistent with his finding.

To conclude, G036N hosts a small, moderate cool core, while G036S has at most a very weak cool core. This difference is unlikely to be caused by the ongoing merger. G036N also hosts a central radio source, which may be heating the gas if the radio source is extended. Examination of the temperature variations in the core of G036N also suggests that the simplified merger dynamical model presented in Section 5.1 overestimates the time since the merger began, which should be less than ∼0.4–0.7 Gyr.