SEARCHING FOR BULK MOTIONS IN THE INTRACLUSTER MEDIUM OF MASSIVE, MERGING CLUSTERS WITH CHANDRA CCD DATA

The Chandra observations used in this work are listed in Tables 1 and 2. All of the observations were taken in VFAINT mode with ACIS-I, except in the case of A2142 which was observed with ACIS-S. The data are reduced using the ciao software (version 4.7) with CALDB 4.6.8. The detailed data reduction procedure has been described in Liu et al. (2015). The area of the clusters used in this analysis is defined as the circular region which provides the maximum S/N in the 0.5–10 keV band once the unresolved sources are removed. Point sources are detected by running the wavdetect task and are then visually inspected, in particular, to remove those deeply embedded in the strong ICM emission. The background files are extracted from a series of circular regions as far as possible from the cluster area, but still on the solid angle defined by the overlap of all of the ObsIDs. To define the cluster subregions, we apply the contour binning technique (Sanders 2006) within the maximum S/N circle. Regions are identified simply on the basis of the surface brightness contours in the 0.5–10 keV band image. To make sure that each region can be used to constrain the X-ray redshift with comparable accuracy, we set a criterion in terms of S/N in the 0.5–10 keV band in each region. Clearly, this criterion does not take into account the expected gradient in the iron abundance, which significantly affects the visibility of the iron emission line complex. We set this threshold to S/N > 140, except in the case of Abell 2146 where we choose a weaker constraint of S/N > 100 due to the relatively lower number of counts. The S/N threshold and the number of regions selected in each cluster are listed in Table 3. For each region, the spectrum is extracted from the merged event file after the removal of unresolved sources, while the calibration files (response matrix files, RMF, and ancillary response files, ARF) are generated independently for each ObsID and then combined by weighting them by the corresponding exposure times. In this way, we keep track of all the differences in the ACIS effective area among the different regions in the detector and among the ObsIDs taken at different epochs.

In this work, we use the same analysis strategy presented in Liu et al. (2015) to measure the projected X-ray redshift z_X in each region and estimate the total (statistical and systematic) uncertainty. Our analysis is optimized on the basis of the spectral simulations shown in Liu et al. (2015). Here, we simply recall the relevant aspects of the adopted spectral analysis.

The spectra are analyzed using Xspec v12.8.2 (Arnaud 1996). To successfully model the X-ray emission, we use two mekal plasma emission models (Mewe et al. 1985, 1986; Liedahl et al. 1995) that include thermal bremsstrahlung and line emission, with abundances measured relative to the solar values of Asplund et al. (2005) in which Fe/H = 3.6 × 10⁻⁵. During the fit, the redshift parameters of the two thermal components are always linked together, while the two temperatures and abundances are left as free parameters.

The main advantage in using a double-temperature thermal spectrum is reducing the possible bias in the measurement of the iron line centroid due to the presence of unnoticed thermal structure along the line of sight. As a matter of fact, different temperature components above 3 keV are not detectable, and a single-temperature thermal component would return an excellent fit even in the presence of widely different temperatures (see Mazzotta et al. 2004). However, in Liu et al. (2015), using spectral simulations we showed that the use of two components provides better results for the measurement of the actual redshift of the ICM, while the temperature structure, which is not our main interest here, is essentially left unconstrained. Clearly, this also introduces a larger systematic uncertainty associated with the temperature structure, which is carefully evaluated during our analysis, as explained below.

Galactic absorption is described by the model tbabs (Wilms et al. 2000). The central values of the Galactic HI column density NH_Gal are based on Kalberla et al. (2005). We conservatively allow ${\mathrm{NH}}_{\mathrm{Gal}}$ to vary by an interval of ∼10% around the central value. This has a small effects since our best-fit z_X are obtained from spectral fits in the hard (2–10 keV) band, which is only marginally affected by Galactic absorption. Cash statistics (Cash 1979) are applied to the unbinned source and background spectra in order to exploit the full spectral resolution of the ACIS-I and ACIS-S CCD. Cash statistics are preferred for faint spectra with respect to the canonical χ² analysis of binned data (Nousek & Shue 1989). To avoid local minima, we repeat the fit several times before and after running the steppar command on all of the free parameters, particularly on the redshift, with a step of δz = 10⁻⁴. Finally, the plots of ΔC_stat versus redshift are visually inspected to investigate whether or not there are other possible minima around the best-fit values (see also Yu et al. 2011), which could indicate a noisy spectrum and therefore an unreliable best-fit value for z_X. We decide to conservatively exclude all of the results with a secondary minimum closer than ΔC = 6.6, which corresponds to a formal 99% confidence level for one free parameter.

Our reference spectral analysis consists of two steps. As the first step, we fit the spectra in the 2–10 keV energy range to obtain the best-fit redshift.We choose to use only the 2–10 keV energy range to minimize the effects of the presence of low-temperature components on the centroid of the iron line emission complex. This conservative choice is also supported by the spectral simulations we presented in Liu et al. (2015). For each region, we produce a plot showing the ΔC_stat value versus the redshift, obtained by varying the redshift parameter and marginalizing the fit with respect to the other parameters. The minimum is generally well defined and roughly symmetric, and therefore provides a robust estimate of the statistical uncertainty.

As a second step, we carefully take into account the systematic uncertainties on redshift due to the unknown thermal structure of the ICM. We conservatively consider all of the possible temperature distributions of the ICM by setting a four-dimensional grid of spectral parameters, namely, temperature and abundance of the two thermal components T₁, T₂, Z₁, and Z₂. The steps of the grid are typically 0.5 keV for the temperature and 0.05 for the metal abundance. Clearly, only a subgrid of temperature and abundance values should be taken into account, since some combination of them provides an unacceptable fit. To efficiently select the subgrid, we make use of the full 0.5–10 keV energy range in order to exploit the complete information on the thermal structure and the chemical composition. Therefore, for each region, we measure the best-fit redshift in the full, 0.5–10 keV band leaving all of the parameters free, and collect the absolute minimum C_min. Then, we select all of the sets of values on the grid that provide a best fit close enough to the absolute best fit. The criterion we adopt is given by ${\rm{\Delta }}{C}_{{\rm{stat}}}\equiv {C}_{{\rm{stat}}}-{C}_{{\rm{min}}}\lt 4.72$, which corresponds to a 1σ confidence level for four free parameters. By applying the criterion ΔC_stat < 4.72 for the fits performed in the full 0.5–10 keV band, we select a subgrid of T₁, T₂, Z₁, and Z₂ values statistically compatible within 1σ with the spectrum observed in each region. Then, we run the spectral fit on the subgrid, but focusing again in the 2–10 keV band only, and measure a set of best-fit z_X values corresponding to the subgrid parameters. The distribution of z_X obtained in this manner is used to derive a redshift range defined by the upper and lower 90% percentiles of the z_X distribution on the grid, and thus the systematic uncertainties on redshift. Since the systematic uncertainty σ_syst is due to the degeneracy of the temperature values, we assume that it is uncorrelated to the statistical error σ_stat. Therefore, we compute the total 1σ uncertainty as ${\sigma }_{{\rm{tot}}}=\sqrt{{\sigma }_{{\rm{stat}}}^{2}+{\sigma }_{{\rm{syst}}}^{2}}$. We do not consider other relevant sources of systematic errors. Systematics related to calibration issues or the time dependence of the gain are kept under control with a direct check on the fluorescent lines of Au Lα and Ni Kα, which are prominent in the ACIS-I background spectrum at 7.5 and 9.7 keV, respectively. Typically, uncertainties introduced by calibration variation (as a function of position on the CCD or as a function of the observation period) on the merged spectrum of each region correspond to errors ∼5 times smaller than the typical total uncertainty on z_X (see Liu et al. 2015). Having assessed that gain-calibration does not significantly affect our conclusions, we do not perform a full treatment of the gain-calibration uncertainties in ACIS-I data.

The complete spectral results for each clusters are presented, where the best-fit redshifts and the corresponding lower and upper statistic and systematic error bars are listed for each region of each cluster (values are rounded to the fourth decimal digit). Results are presented in the form of redshift maps and significance maps. In particular, in the significance maps, we combine the information included in the best-fit redshift and the corresponding total error by showing $({z}_{{\rm{X}}}-\langle {z}_{{\rm{X}}}\rangle )/{\sigma }_{{\rm{tot}}}$, where $\langle {z}_{{\rm{X}}}\rangle$ is the average z_X found across the analyzed regions for which we have realiable a spectral fit. Significant (larger than 2σ) deviations in the redshift map are thus visible as bright blue and bright red regions.

In this section, we describe how we use the results of the spatially resolved spectral analysis to investigate and possibly characterize the presence of bulk motions in the ICM of each cluster. The first check, analogous to what we did in Liu et al. (2015), is to perform a simple χ² test on the distribution of z_X under the assumption of a unique value for the ICM redshift. Therefore, we compute ${\chi }^{2}\equiv {\rm{\Sigma }}{({z}_{{\rm{X}}}-\langle {z}_{{\rm{X}}}\rangle )}^{2}/{\sigma }_{{\rm{tot}}}^{2}$ and, assuming N_reg − 1 degrees of freedom (dof), where N_reg is the number of selected regions, we evaluate the probability of being inconsistent with the constant redshift hypothesis. To account for the small differences in the lower and upper error bars, we use the corresponding total error for z_X values lower or higher than $\langle {z}_{{\rm{X}}}\rangle$.

We also compute the typical bulk motion velocity as the excess of the redshift fluctuations with respect to the statistical and systematic noise. To do that, we simply compute the total root mean square deviation of z_X with respect to the mean, defined as ${\sigma }_{{\rm{rms}}}^{2}\equiv {\rm{\Sigma }}{({z}_{{\rm{X}}}-\langle {z}_{{\rm{X}}}\rangle )}^{2}$, and compare it to the average uncertainty $\langle {\sigma }_{{\rm{tot}}}\rangle ={\rm{\Sigma }}{\sigma }_{{\rm{tot}}}/{N}_{{\rm{reg}}}$ (where we use the average value of the lower and upper error bars when they differ). The average excess, which can be ascribed to bulk motions, is computed as ${\sigma }_{{\rm{BM}}}^{2}={\sigma }_{{\rm{rms}}}^{2}-\langle {\sigma }_{{\rm{tot}}}^{2}\rangle$. Therefore, the bulk motion velocity averaged over the region included in the maximum S/N radius is finally estimated as ${v}_{{\rm{BM}}}=c\times {\sigma }_{{\rm{BM}}}/(1+\langle z\rangle )$. The error on v_BM is estimated as $\sqrt{2}$ times the total error on the mean. Moreover, in those cases where there is some evidence of bulk motions in the ICM, we also provide the value of the maximum velocity difference Δv_max found across all of the regions with a reliable spectral fit.

We visually inspect the histogram distribution of z_X and the redshift and significance maps to infer information on the dynamical status of the ICM. This was done in Liu et al. (2015) for the Bullet cluster, where the two regions with a maximally different redshift are found to be aligned along the bullet trail. We tentatively interpreted them as two regions pushed in opposite directions and perpendicularly to the direction of the bullet at velocities ∼5−6 × 10³ km s⁻¹ with respect to the average cluster redshift. Clearly, it is not always possible to draw simple pictures like this one. However, we try to achieve a simple qualitative classification as pre-merger, ongoing, or post-merger according to whether we can clearly identify two well-defined halos with distinct redshift or a few scattered regions with different redshift. Along this same line, clusters with disturbed surface brightness but no signs of bulk motion may be described as post-merger, a phase in which the bulk motions created by the merger already evolved toward a turbulent velocity field with velocity values below the sensitivity achievable in our data. As previously discussed, the regime of evolved merger, when most of the initial kinetic energy due to the merger evolved into a turbulent velocity field of a few ×100 km s⁻¹, can be probed only with the much higher spectral resolution of X-ray bolometers.

Abell 2142 has already been identified as a merger cluster on the basis of ROSAT observations (Henry & Briel 1996), and more recently has been classified as "non-relaxed" on the basis of the X-ray morphology obtained with Chandra data by Parekh et al. (2015). The two cold fronts, identified in the northwest and southeast regions, clearly separate cooler gas (kT ∼ 7–9 keV) from hotter (kT > 12 keV; Markevitch et al. 2000), making it a promising target to investigate the onset of Kelvin–Helmholtz instabilities at the cold fronts. Evidence of dynamical substructure was also found with optical spectroscopy of the member galaxies (Oegerle et al. 1995). Interestingly, the presence of a narrow-angle tailed radio galaxy may be explained by significant bulk motions in the ICM, as suggested by the statistical analysis of Bliton et al. (1998). Finally, Cuciti et al. (2015) reported A2142 to have a radio halo.

We use the three most recent observation with Chandra ACIS-S for a total of 155.1 ks, as listed in Table 1, while we discard two older observations with ACIS-I (ObsID 5005 and 7692). This choice will minimize the difference in calibration between ObsID. The total number of net counts in the 0.5–10 keV band within a circle of 3 arcmin is about 10⁶. This makes A2142 an ideal target for our analysis, with 52 potentially useful regions for spatially resolved spectral analysis. The best-fit redshift obtained by fitting the total X-ray emission within 3 arcmin is ${z}_{{\rm{Xtot}}}={0.0852}_{-0.0009}^{+0.0012}$. To evaluate the systematic uncertainty on z_X, we consider a temperature range from 3 to 16 keV to explore the temperature structure of the ICM, despite the fact that the projected temperature shows only a moderate range from 8 to 12 keV. Metal abundances are mildly scattered around Z = 0.45 Z_⊙ in the units provided by Asplund et al. (2005), nevertheless we consider a wide range $0.15\lt Z/{Z}_{\odot }\lt 1.5$ in order to account for possible large fluctuations. In 5 regions, we find that the X-ray spectral analysis does not provide a reliable value of z_X, and therefore we use only 47 regions. The best-fit z_X of the regions used in our analysis with the corresponding statistical and systematic errors are listed in Table 5. The average redshift is $\langle {z}_{{\rm{X}}}\rangle =0.0855$, which is almost coincident with the global, emission-weighted redshift z_Xtot.

The hypothesis of a constant redshift is rejected at more than 3σ, with a χ² = 88.02 for 46 dof, as listed in Table 4. However, the histogram distribution of z_X (see Figure 1) clearly shows that the evidence of bulk motions comes from three regions (region 2, 8, and 50) maximally distant from the average redshift. The rest of the z_X values are distributed according to a Gaussian slightly narrower than the Gaussian whose variance is the average σ_tot². This is expected since we assumed a very conservative estimate for σ_tot. The projected X-ray redshift map and significance map are shown in Figure 2. We measure v_BM = 1400 ± 300 km s⁻¹ for the average bulk motion velocity in the ICM of A2142 within a radius of 3 arcmin. Excluding the three extreme z_X regions, we are able to establish a hard upper limit of v_BM < 1450 km s⁻¹. This result is consistent with the Suzaku X-ray spectral analysis by Ota & Yoshida (2015), which provided Δv < 4200 km s⁻¹. However, thanks to the Chandra angular resolution, we find that region 50 is redshifted with respect to the average velocity by 5000 ± 1500 km s⁻¹, while the contiguous regions 2 and 8 are blueshifted by 7400 ± 2200 km s⁻¹. In particular, we can interpret region 50 as being dominated by a significant amount of ICM mass pushed at high velocity as a result of the ongoing merger. The two blueshifted regions can be tentatively associated with some rotation of the ICM. We note that, given the small field of view of the ACIS-S detector, we repeated the spectral analysis with a different choice of background, finding the same statistical results. Therefore, our conclusions are not affected by uncertainties in the background, despite the fact that the cluster emission covers almost the entire ACIS-S field of view.

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Table 4.  The Results of the χ² Test on the Distribution of Redshift of the Clusters, and Corresponding Constraints on v_BM and Δv_max in km s⁻¹

Cluster Name	zXtot	$\langle {z}_{{\rm{X}}}\rangle$	Degrees of Freedom	χ2	Prob of BM	vBM	Δvmax	Classification
			(Nreg − 1)			(km s−1)	(km s−1)
A2142	${0.0852}_{-0.0009}^{+0.0012}$	0.0855	46	88.02	99.98%	1400 ± 300	7400 ± 2200	post-merger
A2034	${0.1124}_{-0.0044}^{+0.0039}$	0.1122	10	12.70	76%	1700 ± 840	6200 ± 3300	pre/ongoing merger
A115	${0.1892}_{-0.0040}^{+0.0030}$	0.1979	11	30.4	99.9%	4600 ± 1100	8600 ± 3000	pre/ongoing merger
A520	${0.2082}_{-0.0049}^{+0.0046}$	0.2083	17	23.4	86%	1800 ± 900	5900 ± 4000	post-merger
1RXS J0603.3+4214	${0.2316}_{-0.0033}^{+0.0029}$	0.2303	7	8.6	72%	$\lt 2100$	7200 ± 2800	pre-merger
A2146	${0.2310}_{-0.0010}^{+0.0022}$	0.2338	16	19.68	77%	480 ± 490	8200 ± 3600	pre/ongoing merger
A1689	${0.1814}_{-0.0008}^{+0.0028}$	0.1814	9	9.3	59%	<1600	4600 ± 3000	relaxed
A1835	${0.2478}_{-0.0012}^{+0.0021}$	0.2483	10	11.5	38%	<1350	4200 ± 2600	relaxed

Note. This information is combined with visual inspection of the redshift maps to obtain the qualitative classification listed in the last column.

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Table 5.  Spectral Analysis Results of Abell 2142

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.0839	−0.0030	0.0033	−0.0009	0.0002	−0.0031	0.0034
1	0.0847	−0.0021	0.0026	−0.0007	0.0013	−0.0022	0.0029
2	0.0674	−0.0048	0.0050	−0.0014	0.0005	−0.0051	0.0050
3	0.0881	−0.0013	0.0029	−0.0001	0.0018	−0.0014	0.0034
4	0.0762	−0.0064	0.0061	−0.0040	0.0001	−0.0076	0.0061
5	0.0863	−0.0065	0.0058	−0.0054	0.0026	−0.0084	0.0063
6	0.0917	−0.0022	0.0024	−0.0001	0.0013	−0.0022	0.0027
7	0.0866	−0.0031	0.0032	−0.0001	0.0015	−0.0031	0.0035
8	0.0612	−0.0064	0.0075	−0.0001	0.0455	−0.0064	0.0461
10	0.0808	−0.0039	0.0039	−0.0001	0.0040	−0.0039	0.0055
11	0.0843	−0.0030	0.0032	−0.0001	0.0020	−0.0030	0.0038
12	0.0885	−0.0042	0.0098	−0.0001	0.0010	−0.0042	0.0099
13	0.0946	−0.0034	0.0036	−0.0001	0.0014	−0.0034	0.0039
14	0.0787	−0.0043	0.0036	−0.0007	0.0013	−0.0044	0.0039
15	0.0874	−0.0043	0.0036	−0.0001	0.0016	−0.0043	0.0040
16	0.0860	−0.0036	0.0038	−0.0001	0.0030	−0.0036	0.0049
17	0.0888	−0.0029	0.0031	−0.0020	0.0001	−0.0035	0.0031
18	0.0908	−0.0032	0.0024	−0.0001	0.0013	−0.0032	0.0027
20	0.0844	−0.0029	0.0028	−0.0004	0.0015	−0.0030	0.0031
21	0.0885	−0.0061	0.0083	−0.0015	0.0025	−0.0063	0.0087
22	0.0852	−0.0033	0.0033	−0.0012	0.0020	−0.0036	0.0039
23	0.0841	−0.0037	0.0038	−0.0001	0.0020	−0.0037	0.0043
25	0.0848	−0.0028	0.0027	−0.0001	0.0022	−0.0028	0.0034
26	0.0811	−0.0027	0.0029	−0.0010	0.0010	−0.0028	0.0031
27	0.0882	−0.0040	0.0038	−0.0010	0.0001	−0.0041	0.0038
28	0.0831	−0.0029	0.0024	−0.0010	0.0001	−0.0031	0.0024
29	0.0777	−0.0044	0.0045	−0.0017	0.0043	−0.0047	0.0062
31	0.0914	−0.0036	0.0040	−0.0001	0.0025	−0.0036	0.0047
32	0.0869	−0.0023	0.0022	−0.0010	0.0010	−0.0025	0.0024
33	0.0878	−0.0071	0.0100	−0.0028	0.0132	−0.0076	0.0166
34	0.0847	−0.0027	0.0027	−0.0007	0.0007	−0.0028	0.0028
35	0.0966	−0.0083	0.0058	−0.0087	0.0043	−0.0120	0.0072
36	0.0846	−0.0027	0.0026	−0.0006	0.0024	−0.0028	0.0035
37	0.0821	−0.0053	0.0050	−0.0010	0.0060	−0.0054	0.0078
38	0.0808	−0.0045	0.0046	−0.0013	0.0032	−0.0047	0.0056
39	0.0853	−0.0034	0.0035	−0.0001	0.0016	−0.0034	0.0038
40	0.0832	−0.0033	0.0035	−0.0007	0.0023	−0.0034	0.0042
41	0.0826	−0.0055	0.0041	−0.0001	0.0034	−0.0055	0.0053
42	0.0876	−0.0024	0.0027	−0.0001	0.0030	−0.0024	0.0040
43	0.0820	−0.0049	0.0053	−0.0001	0.0050	−0.0049	0.0073
44	0.0848	−0.0027	0.0023	−0.0008	0.0012	−0.0028	0.0026
45	0.0884	−0.0054	0.0051	−0.0024	0.0036	−0.0059	0.0062
47	0.0823	−0.0037	0.0036	−0.0001	0.0010	−0.0037	0.0037
48	0.0885	−0.0029	0.0031	−0.0001	0.0010	−0.0029	0.0033
49	0.0866	−0.0028	0.0030	−0.0001	0.0014	−0.0028	0.0033
50	0.1124	−0.0052	0.0063	−0.0025	0.0045	−0.0057	0.0077
51	0.0881	−0.0049	0.0044	−0.0001	0.0052	−0.0049	0.0068

Note. Column 1: region number; Column 2: best-fit redshift z_X obtained fitting the 2.0–10 keV energy range; Columns 3 and 4: lower and upper 1σ error bars from fit statistics; Columns 5 and 6: lower and upper 1σ error bars from systematics associated to the ICM temperature structure; Columns 7 and 8: total lower and upper 1σ error bars computed as ${\sigma }_{{\rm{tot}}}=\sqrt{{\sigma }_{{\rm{stat}}}^{2}+{\sigma }_{{\rm{syst}}}^{2}}.$

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To summarize, as in the case of the Bullet cluster (Liu et al. 2015), the evidence of bulk motions is coming from a few regions with an extreme redshift difference with respect to the mean after a very conservative selection of reliable spectra and an accurate estimate of the total uncertainty on z_X. This may suggest that the cluster is a post-merger or caught in a stage where the shocks have developed since ∼1 dynamical time or more and the velocity field of the ICM still shows a few regions with large velocities with respect to the velocity of the center of mass. The interpretation in terms of ICM dynamics is nevertheless still very hard, and a significantly higher spectral resolution with the same angular resolution is needed before the actual velocity field of the ICM can be accurately measured.

Abell 2034, at redshift z_opt = 0.113 (Muriel & Coenda 2014), shows many signatures typically associated with merging clusters, from a radio relic near the position of a discontinuity in the X-ray surface brightness, to significant heating of the ICM above its equilibrium temperature, and a significant offset of the cD galaxy from the centroid of the X-ray emission (Kempner & Sarazin 2001; Kempner et al. 2003; Giovannini et al. 2009; Van Weeren et al. 2011). In a recent detailed study by Owers et al. (2014) using a deep Chandra observation of 250 ks, a shock with a Mach number of 1.59 ± 0.06, corresponding to a shock velocity of ∼2000 km s⁻¹, was clearly observed. Combining Chandra data with spectroscopic observations for 328 spectroscopically confirmed member galaxies, they show the presence of a substructure located at the front edge of the shock and that the merger is proceeding along a north–south direction with an inclination angle of ∼23° with respect to the plane of the sky. The cluster is included in the sample of the Merging Cluster Collaboration.⁵

We use Chandra ACIS-I observations for a total of 254.5 ks. The total number of net counts in the 0.5–10 keV band is 2.66 × 10⁵ within a circle of 3 arcmin in the merged image. We select 14 ICM regions for redshift analysis, but we obtained reliable spectral fits only in 11 out of 14. We find ${z}_{{\rm{Xtot}}}={0.1124}_{-0.0044}^{+0.0039}$, which is in very good agreement with z_opt and $\langle {z}_{{\rm{X}}}\rangle =0.1122$. To evaluate the systematic uncertainties on z_X, we consider a temperature and abundance range of 6–12 keV and 0.2–0.8 Z_⊙, respectively. The best-fit z_X of the 11 regions used in our analysis with corresponding errors are listed in Table 6. The histogram distribution of z_X shows that most of the best-fit z_X values are approximately distributed as a Gaussian, with the exception of two high-redshift values (see Figure 3). However, due to the estimated uncertainties, the probability of a uniform redshift distribution across the ICM is still high at the 24% level (χ² = 12.70 for 10 dof), which implies no significant detection (less than 2σ) of global bulk motions. Formally, we measure an average bulk motion of v_BM = 1700 ± 840 km s⁻¹. In addition, the projected redshift map shows that the two high-redshift regions 4 and 9 are contiguous (see Figure 4, lower panels), which can be interpreted as an enhanced likelihood of a redshift difference between the diffuse emission in the north and the main halo. The average redshift of regions 4 and 9 is 0.1310, while that of the other regions is 0.1081. This implies a velocity difference of Δv_max = 6200 ± 3300 km s⁻¹. The presence of two distinct halos with different redshift may suggest a classification as a pre-merger. Due to the presence of a well-developed shock, this cluster may be caught in the early stages of the merger process, in agreement with the conclusion of Owers et al. (2014), who estimate that the merger is observed only ∼0.3 Gyr after core-passage.

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Table 6.  Spectral Analysis Results of Abell 2034

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.1056	−0.0057	0.0056	−0.0001	0.0033	−0.0057	0.0065
1	0.1085	−0.006	0.0068	−0.0016	0.0014	−0.0062	0.0069
2	0.1004	−0.0062	0.0088	−0.0001	0.0054	−0.0062	0.0103
3	0.1089	−0.0074	0.008	−0.0017	0.0053	−0.0075	0.0095
4	0.1318	−0.0093	0.0076	−0.0035	0.0001	−0.0099	0.0076
6	0.1116	−0.0038	0.0055	−0.0001	0.0018	−0.0038	0.0057
9	0.1301	−0.0067	0.0058	−0.0049	0.0001	−0.0083	0.0058
10	0.1124	−0.0055	0.0059	−0.0018	0.0001	−0.0057	0.0059
11	0.1099	−0.0077	0.0061	−0.0051	0.0001	−0.0092	0.0061
12	0.1142	−0.0075	0.0102	−0.0035	0.0018	−0.0082	0.0103
13	0.1011	−0.0068	0.0095	−0.0001	0.0040	−0.0068	0.0103

Note. The columns are the same as in Table 5.

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Abell 115 has been classified as a merger on the basis of its double X-ray morphology (Forman et al. 1981). The ICM thermal structure is best described by two halos that host a cool core with significantly hotter gas between and around them, suggesting that the system is in an advanced stage of merging, despite the fact that no shock front has been found in this region (Shibata et al. 1999; Gutierrez & Krawczynski 2005). A dynamical analysis based on 88 cluster member spectra (Barrena et al. 2007) shows a line-of-sight velocity difference of 1646 km s⁻¹ between the northern and southern subclusters at a projected separation of 0.89 Mpc. In addition, Barrena et al. (2007) interpret the system as a pre-merger based on the location of the BCGs being consistent with the peaks in the X-ray surface brightness distribution. Diffuse radio emission north of the cluster has been found by Govoni et al. (2001) with a 1.4 GHz VLA observation and interpreted as a radio relic that may be associated with the ongoing merger. Abell 115 is also included in the Merging Cluster Collaboration sample.

We used 4 ACIS-I contiguous-in-time observations for a total of 310.6 ks. The total number of counts in the 0.5–10 keV band within a circle of 5.2 arcmin in the merged image is 2.88 × 10⁵. This allows us to obtain 18 useful regions for spectral analysis. Our spatially resolved spectroscopic analysis provides us with reliable z_X only in 12 regions out of 18. The average redshift $\langle {z}_{{\rm{X}}}\rangle =0.1979$ is in good agreement with z_opt = 0.197 (Hiroi et al. 2013) while the global redshift ${z}_{{\rm{Xtot}}}={0.1892}_{-0.004}^{+0.003}$ is significantly lower. To evaluate systematic uncertainties on z_X, we consider temperature and abundance ranges of 2–12 keV and 0.2–0.9 Z_⊙, respectively. The best-fit z_X of the 12 regions used in our analysis with corresponding errors are listed in Table 7.

Table 7.  Spectral Analysis Results of Abell 115

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.1980	−0.0019	0.0036	−0.0000	0.0025	−0.0019	0.0044
1	0.1998	−0.0027	0.0028	−0.0000	0.0002	−0.0027	0.0028
2	0.2026	−0.0036	0.0039	−0.0000	0.0037	−0.0036	0.0053
4	0.1988	−0.0051	0.0042	−0.0000	0.0061	−0.0051	0.0074
6	0.1922	−0.0067	0.0083	−0.0032	0.0018	−0.0074	0.0085
8	0.1897	−0.0124	0.0123	−0.0037	0.0053	−0.0129	0.0134
10	0.2090	−0.0082	0.0086	−0.0040	0.0040	−0.0091	0.0095
11	0.2367	−0.0060	0.0048	−0.0087	0.0000	−0.0106	0.0048
12	0.1679	−0.0094	0.0113	−0.0049	0.0020	−0.0106	0.0115
14	0.1591	−0.0064	0.0094	−0.0000	0.0210	−0.0064	0.0230
15	0.2263	−0.0177	0.0107	−0.0000	0.0000	−0.0177	0.0107
17	0.1943	−0.0069	0.0074	−0.0038	0.0107	−0.0079	0.0130

Note. The columns are the same as in Table 5.

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The hypothesis of a constant redshift across the 12 regions is rejected at more than 3σ (χ² = 30.4 for 11 dof). The histogram distribution of z_X (see Figure 5) shows the presence of two regions significantly above and below the central value. We measure an average bulk motion velocity of v_BM = 4600 ± 1100 km s⁻¹.

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Visual inspection of the redshift and significance maps (see Figure 6, lower panels) allows us to identify three main regions with compatible redshift. We first isolate regions belonging to the northern (regions 0, 1, 2, 4, and 10) and southern (3, 6, 11, 17, and 15) clumps. We find a redshift difference that corresponds to about 1σ, and is therefore consistent with having the same redshift. Formally, translated into a velocity difference, this would imply a relative velocity of 3300 ± 3200 km s⁻¹. If we consider instead regions 12 and 14, then we find an average redshift of 0.1634, corresponding to a velocity difference of 8600 ± 3000 km s⁻¹ with respect to the bulk of the ICM. We note that this is also the gas that is found to be significantly hotter (at least by a factor of two, as verified in the projected temperature map not discussed here), and therefore it is likely to be heated and violently displaced by the ongoing merger. This is consistent with a substantial amount of the shocked gas being compressed between the two halos and pushed toward the observer, with the two halos having a minimum in the velocity difference. Therefore, we conclude that A115 is caught in the early phase of the merging process, with the two ICM halos still well separated.

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Abell 520, at z_opt = 0.203 (Cassano et al. 2013), was found to host a radio halo elongated in the NE-SW direction, corresponding to the apparent merger axis (Giovannini et al. 1999; Govoni et al. 2001). Its X-ray morphology and the optical spectroscopy suggest a disturbed dynamical state (Proust et al. 2000; Govoni et al. 2001, respectively). Despite recent in-depth studies (Mahdavi et al. 2007; Girardi et al. 2008), the detailed structure of the merger of Abell 520 is still unclear. However, a prominent bow shock with $M={2.1}_{-0.3}^{+0.4}$ has been identified thanks to Chandra data analysis (Markevitch et al. 2005). Abell 115 is also included in the Merging Cluster Collaboration sample.

A520 has the longest Chandra ACIS-I exposure for a total of 516.4 ks. The number of net counts in the 0.5–10 keV band in the merged image is 3.36 × 10⁵ in a circle of 3.2 arcmin radius. The best-fit redshift from the global emission is ${z}_{{\rm{Xtot}}}={0.2082}_{-0.0049}^{+0.0046}$. To estimate the systematic uncertainty on z_X, we consider ranges of 3–15 keV and 0.2–1 Z_⊙ for temperature and abundance, respectively.

We discard only two regions that do not provide reliable redshifts. Therefore, we base our analysis on 18 regions, whose best-fit z_X and associated errors are listed in Table 8. The average redshift among those regions is $\langle {z}_{{\rm{X}}}\rangle =0.2083$, in good agreement with z_Xtot and z_opt. The hypothesis of a constant redshift is rejected at an ∼87% confidence level (χ² = 23.4 for 17 dof), which is therefore less than 2σ. We find v_BM ∼ 1800 ± 900 km s⁻¹. This is mostly contributed by the presence of blueshifted regions, mostly in the central 1 arcmin, and the surrounding higher-redshift regions, as can be seen by comparing the histogram distribution (see Figure 7) with the redshift and significance maps (see Figure 8). If we compute the difference between the two sets of regions with comparable redshifts, then we find Δv_max = 5900 ± 4000 km s⁻¹. The overall redshift map suggests a merger with a halo moving toward the observer that was caught shortly after the first pericentric passage.

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Table 8.  Spectral Analysis Results of Abell 520

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.2102	−0.0037	0.0065	−0.0001	0.0021	−0.0037	0.0068
1	0.2069	−0.0047	0.0043	−0.0001	0.0027	−0.0047	0.0050
2	0.1933	−0.0085	0.0096	−0.0001	0.0074	−0.0085	0.0121
3	0.1962	−0.0075	0.0076	−0.0001	0.0024	−0.0075	0.0079
5	0.2276	−0.0155	0.0147	−0.0025	0.0049	−0.0157	0.0154
6	0.2207	−0.0146	0.0079	−0.0122	0.0001	−0.0190	0.0079
8	0.1937	−0.0128	0.0133	−0.0018	0.0056	−0.0129	0.0144
9	0.2048	−0.0087	0.0075	−0.0006	0.0027	−0.0087	0.0079
10	0.2271	−0.0164	0.0138	−0.0039	0.0001	−0.0168	0.0138
11	0.2152	−0.0106	0.0096	−0.0012	0.0058	−0.0106	0.0112
12	0.2138	−0.0046	0.0053	−0.0001	0.0044	−0.0046	0.0068
13	0.2282	−0.0149	0.0126	−0.0175	0.0006	−0.0229	0.0126
14	0.2217	−0.0153	0.0166	−0.0066	0.0001	−0.0166	0.0166
15	0.1921	−0.0088	0.0085	−0.0083	0.0001	−0.0120	0.0085
16	0.195	−0.0124	0.0131	−0.0081	0.0001	−0.0148	0.0131
17	0.1837	−0.0085	0.0086	−0.0001	0.0038	−0.0085	0.0094
18	0.208	−0.0102	0.0068	−0.0057	0.0005	−0.0116	0.0068
19	0.2104	−0.0099	0.0093	−0.0001	0.0114	−0.0099	0.0147

Note. The columns are the same as in Table 5.

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At redshift z_opt = 0.225 (Van Weeren et al. 2012), 1RXS J0603.3+4214 (the "Toothbrush" cluster) was discovered in the radio band thanks to its prominent linear radio relic and radio halo plus several additional features which suggest that this is a complex merger. Simulations also show that the merger might be a triple process: in addition to northern and southern subclusters with similar mass, there might be another smaller subcluster infalling in the south (Brüggen et al. 2012). Measurement of the radio spectral index allowed Van Weeren et al. (2012) to constrain the merger Mach number to be in the range 3.3–4.6. However, X-ray observation by XMM-Newton returned a Mach number of <2 (Ogrean et al. 2013), which is inconsistent with the radio constraints. 1RXS J0603.3+4214 is also included in the Merging Cluster Collaboration sample.

We use three Chandra ACIS-I observations for a total of 235.9 ks. The total number of counts in the 0.5–10 keV band within a circle of 3.5 arcmin is 1.74 × 10⁵ in the merged image. To evaluate the systematic uncertainty on z_X, we consider ranges of 8–16 keV and 0.3–0.8 Z_⊙ for the temperature and abundance, respectively. We are able to obtain reliable spectral fits in 8 out of the 9 regions originally considered for analysis. The best-fit z_X and corresponding errors are listed in Table 9. The average redshift across the regions is $\langle z\rangle =0.2303$, which is in good agreement with ${z}_{{\rm{Xtot}}}={0.2316}_{-0.0033}^{+0.0029}$ and in reasonable agreement with z_opt. The hypothesis of a constant redshift is acceptable (χ² = 8.7 for 7 dof), as also shown in Figure 9 by the histogram distribution of the best-fit z_X values. The upper limit to the average bulk motion velocity is v_BM < 2100 km s⁻¹. However, there is a significant uniform gradient in the best-fit redshift from the northern clump (high-z) to the southern clump (low-z; see Figure 10), which corresponds to a maximum difference of ∼0.0295 ± 0.0115 or a maximum velocity difference of Δv_max ∼ 7200 ± 2800 km s⁻¹. On the basis of these results, this cluster can be classified as a pre-merger.

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Table 9.  Spectral Analysis Results of 1RXS J0603.3+4214

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.2317	−0.0062	0.0065	−0.0030	0.0004	−0.0068	0.0065
1	0.2206	−0.0069	0.0072	−0.0021	0.0065	−0.0072	0.0097
2	0.2347	−0.0075	0.0119	−0.0008	0.0071	−0.0075	0.0138
4	0.2493	−0.0067	0.0091	−0.0069	0.0001	−0.0096	0.0091
5	0.2198	−0.0070	0.0063	−0.0045	0.0001	−0.0083	0.0063
6	0.2254	−0.0108	0.0078	−0.0055	0.0001	−0.0121	0.0078
7	0.2294	−0.0094	0.0066	−0.0044	0.0021	−0.0103	0.0069
8	0.2316	−0.0091	0.0075	−0.0001	0.0042	−0.0091	0.0085

Note. The columns are the same as in Table 5.

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Despite the lack of diffuse radio emission, A2146 is classified as an extreme binary, head-on cluster merger in Mann & Ebeling (2012). A deep Chandra study reveled the presence of two shock fronts with Mach numbers of M = 2.2 ± 0.8 and M ∼ 1.7 ± 0.3 (Russell et al. 2010). Using the radial velocity of BCGs in the subcluster and the main cluster, Canning et al. (2012) find that the merger axis has an angle of 17° with respect to the plane of the sky. Based on these properties and its appearance in the X-ray, Abell 2146 is often compared to the Bullet cluster.

We use observations with Chandra ACIS-I for a total of 375.3 ks, as listed in Table 1. For simplicity, we do not consider observations with ACIS-S for a total of 45 ks in order to retain uniform calibration throughout our analysis, given the smaller amount of observing time contributed by the ACIS-S exposures. The total number of net counts in the 0.5–10 keV band within a circle of 3.6 arcmin is about 1.99 × 10⁵. The best-fit redshift obtained by fitting the total X-ray emission is ${z}_{\mathrm{Xtot}}={0.2310}_{-0.0010}^{+0.0022}$. Measured temperatures range from the inner ∼3 keV to the outer ∼8 keV in our analysis of the temperature structure (not reported in this work). To evaluate the systematic uncertainty on z_X, we consider ranges from 1 to 12 keV and 0.15 to 1.5 Z/Z_⊙ to explore the temperature and metal abundance throughout the ICM, respectively.

We are able to obtain a reliable spectral fit in 17 out of the 19 regions originally selected in the X-ray image. The best-fit z_X of the regions used in our analysis, along with their corresponding statistical and systematic errors, are listed in Table 10. The average redshift across the region is $\langle {z}_{{\rm{X}}}\rangle =0.2338$, which is consistent with z_Xtot within 1σ. We find χ² = 19.68 for 16 dof, as listed in Table 4, which is pretty much consistent with a constant redshift across the ICM. The histogram distribution of z_X, shown in Figure 11, is consistent with a Gaussian dominated by noise and shows no clear evidence of bulk motions. The average bulk motion is formally v_BM = 480 ± 490 km s⁻¹. The projected X-ray redshift map and significance map are shown in Figure 12. The maximum redshift difference is Δv_max = 8200 ± 3600 km s⁻¹ and is obtained between two distinct regions with homogeneous redshift: the "bullet" and its trail, along the direction of the merger, which are blueshifted with respect to the average redshift, and all of the surrounding ICM emission, which is redshifted. Despite the low S/N, the redshift map depicts a clear dynamical situation where the central ICM is dominated by a halo moving toward the observer, while the larger scale emission has, on average, a larger redshift. This provides support for the presence of bulk motions that are still dominated by the infall velocity of the merging halos.

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Table 10.  Spectral Analysis Results of Abell 2146

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.2292	−0.0045	0.00312787	−0.0000	0.0000	−0.0045	0.0031
1	0.2282	−0.0035	0.00311993	−0.0017	0.0018	−0.0039	0.0036
2	0.2277	−0.0038	0.00571345	−0.0000	0.0083	−0.0038	0.0100
3	0.2282	−0.0051	0.0026654	−0.0027	0.0000	−0.0057	0.0027
4	0.2294	−0.0037	0.00436681	−0.0000	0.0036	−0.0037	0.0057
5	0.2276	−0.0065	0.00615287	−0.0001	0.0044	−0.0065	0.0076
6	0.2325	−0.0074	0.00676923	−0.0055	0.0000	−0.0092	0.0068
7	0.2354	−0.0060	0.00619396	−0.0114	0.0000	−0.0129	0.0062
8	0.2473	−0.0125	0.0069235	−0.0223	0.0000	−0.0255	0.0069
9	0.2436	−0.0072	0.0066689	−0.0036	0.0000	−0.0080	0.0067
10	0.2277	−0.0083	0.00881529	−0.0000	0.0140	−0.0083	0.0165
12	0.2372	−0.0062	0.00682796	−0.0010	0.0010	−0.0063	0.0069
13	0.2326	−0.0088	0.00909447	−0.0025	0.0074	−0.0091	0.0117
14	0.2256	−0.0077	0.00950732	−0.0025	0.0086	−0.0081	0.0128
15	0.2495	−0.0089	0.00691656	−0.0015	0.0000	−0.0090	0.0069
16	0.2226	−0.0114	0.0110643	−0.0060	0.0000	−0.0129	0.0110
18	0.2505	−0.0075	0.00798135	−0.0080	0.0000	−0.0110	0.0080

Note. The columns are the same as in Table 5.

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Abell 1689 is a typical relaxed cluster at z ∼ 0.183 (Hiroi et al. 2013). We reduced and analyzed four ACIS-I observations for a total of 151.3 ks (see Table 2). The total number of net counts in the 0.5–10 keV band within a circle of 1 arcmin is about 1.86 × 10⁵ in the ACIS-I merged image. The best-fit redshift obtained fitting the total X-ray emission is ${z}_{{\rm{Xtot}}}={0.1814}_{-0.0008}^{+0.0028}$. To evaluate the systematic uncertainty on z_X, we consider ranges from 5 to 15 keV and 0.3 to 0.9 Z/Z_⊙ to explore the temperature and metal abundance throughout the ICM, respectively.

We are able to obtain a reliable spectral fit in all 10 of the regions originally selected in the X-ray image. The best-fit z_X of the regions used in our analysis with the corresponding statistical and systematic errors are listed in Table 11. The average redshift across the region is $\langle {z}_{{\rm{X}}}\rangle =0.1814$. The histogram distribution of z_X, shown in Figure 13, is consistent with a Gaussian distribution whose σ is the average statistical error on z_X. We find χ² = 9.31 for 9 dof, as listed in Table 4. Therefore, we do not find any hint of bulk motion, as expected, and find a hard upper limit of v_BM < 1600 km s⁻¹.

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Table 11.  Spectral Analysis Results of Abell 1689

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.1767	−0.0061	0.0048	−0.0001	0.0037	−0.0061	0.0060
1	0.1774	−0.0047	0.0061	−0.0014	0.0001	−0.0049	0.0061
2	0.1864	−0.0103	0.0109	−0.0001	0.0066	−0.0103	0.0127
3	0.1774	−0.0065	0.0049	−0.0019	0.002	−0.0067	0.0052
4	0.1675	−0.0074	0.0066	−0.0019	0.0001	−0.0076	0.0066
5	0.1859	−0.0045	0.0038	−0.0001	0.0016	−0.0045	0.0041
6	0.1895	−0.0084	0.0087	−0.0001	0.0385	−0.0084	0.0394
7	0.1859	−0.006	0.0078	−0.0001	0.0041	−0.0060	0.0088
8	0.1826	−0.0087	0.0073	−0.0001	0.005	−0.0087	0.0088
9	0.1847	−0.0047	0.0071	−0.0001	0.0031	−0.0047	0.0077

Note. The columns are the same as in Table 5.

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Abell 1835 is a relaxed cluster at z ∼ 0.234 (Girardi et al. 2014). We reduced and analyzed three ACIS-I observations for a total of 193.7 ks (see Table 2). The total number of net counts in the 0.5–10 keV band within a circle of 1 arcmin is about 2.33 × 10⁵ in the ACIS-I merged data. The best-fit redshift obtained while fitting the total X-ray emission is ${z}_{{\rm{Xtot}}}={0.2478}_{-0.0012}^{+0.0021}$, which is significantly larger than the optical value. To evaluate the systematic uncertainty on z_X, we consider ranges from 4 to 14 keV and 0.2 to 0.8 Z/Z_⊙ to explore the temperature and metal abundance throughout the ICM, respectively.

We are able to obtain a reliable spectral fit in all 11 of the regions originally selected in the X-ray image. The best-fit z_X of the regions used in our analysis with the corresponding statistical and systematic errors are listed in Table 12. The average redshift across the region is $\langle {z}_{{\rm{X}}}\rangle =0.2483$. The histogram distribution of z_X, shown in Figure 15, is consistent with a Gaussian distribution whose σ is the average statistical error on z_X. We find χ² = 11.5 for 10 dof, as listed in Table 4. Therefore, we do not find any hint of bulk motion, as expected, and find a hard upper limit of v_BM < 1350 km s⁻¹.

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Table 12.  Spectral Analysis Results of Abell 1835

Region	z	${\sigma }_{{\mathrm{stat}}_{b}}$	${\sigma }_{{\mathrm{stat}}_{u}}$	${\sigma }_{{\mathrm{syst}}_{b}}$	${\sigma }_{{\mathrm{syst}}_{u}}$	${\sigma }_{{\mathrm{tot}}_{b}}$	${\sigma }_{{\mathrm{tot}}_{u}}$
0	0.2524	−0.0031	0.0041	−0.0024	0.0001	−0.0039	0.0041
1	0.2547	−0.0024	0.003	−0.0001	0.0025	−0.0024	0.0039
2	0.2478	−0.003	0.0052	−0.0001	0.0021	−0.0030	0.0056
3	0.2474	−0.003	0.0027	−0.002	0.0003	−0.0036	0.0027
4	0.2472	−0.0048	0.006	−0.002	0.0018	−0.0052	0.0062
5	0.2408	−0.0028	0.0045	−0.0001	0.0052	−0.0028	0.0068
6	0.2538	−0.01	0.0065	−0.0057	0.0016	−0.0115	0.0066
7	0.2519	−0.0046	0.0064	−0.0028	0.0001	−0.0053	0.0064
8	0.2486	−0.006	0.0052	−0.0001	0.0046	−0.0060	0.0069
9	0.2372	−0.0065	0.0073	−0.0002	0.007	−0.0065	0.0101
10	0.2496	−0.0068	0.0078	−0.0019	0.0023	−0.0070	0.0081

Note. The columns are the same as in Table 5.

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