TWO-PHASE ICM IN THE CENTRAL REGION OF THE RICH CLUSTER OF GALAXIES A1795: A JOINT CHANDRA, XMM-NEWTON, AND SUZAKU VIEW

In Table 1, we list 11 Chandra data sets of A1795 obtained with the Advanced CCD Imaging Spectrometer (ACIS), which are all used in the analysis. Among the 11 observations, 5 ACIS-S3 exposures focused on the cluster center, and 6 ACIS-I exposures covered off-center regions up to r ∼ 1.5 Mpc. All data were telemetered in VFAINT mode, except for the one with ObsID 494 in FAINT mode. Using CIAO v4.4 and CALDB v4.4.7, we removed bad pixels and columns, as well as events with ASCA grades 1, 5, and 7. We then executed the gain, charge transfer inefficiency, and astrometry corrections. The cumulative exposure time was reduced from ≈170 ks to ≈163 ks after removing intervals contaminated by occasional background flares with count rate >20% of mean value, which were detected by examining 0.3–10.0 keV light curves extracted from source-free regions near the CCD edges (e.g., Gu et al. 2009). When available, ACIS-S1 data were also used to cross-check the determination of the contaminated intervals. The obtained clean exposure time for each observation is listed in Table 1. In Figure 1(a) we show the combined ACIS image, which has been corrected for exposure but not for background.

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XMM-Newton was used to observe the central and the south periphery regions of A1795 on 2000 June 26 and 2003 January 13, respectively, both with the EPIC operated in the full window mode with thin filter, and with the RGS in the spectroscopy mode (Table 1). Data reduction and calibration were carried out with SAS v11.0.1. In the screening process we set FLAG = 0 and kept events with PATTERNs 0–12 for MOS cameras and events with PATTERNs 0–4 for the pn camera. By examining light curves extracted in 10.0–14.0 keV and 1.0–5.0 keV from source-free regions, we rejected time intervals affected by hard- and soft-band flares, respectively, in which the count rate exceeds a 2σ limit above the quiescent mean value (e.g., Katayama et al. 2004; Nevalainen et al. 2005). The cleaned MOS1, MOS2, and pn data sets of the central pointing have exposure times of 43.6 ks, 40.3 ks, and 30.2 ks, respectively (Table 1). The RGS data were screened using the method described in Tamura et al. (2001).

As listed in Table 1, A1795 was also observed by Suzaku on 2005 December 10, with five pointings aimed at its central region, near south and north regions (offset ≈12'), and far south and north regions (offset ≈24'). The onboard X-ray Imaging Spectrometer (XIS; Koyama et al. 2007) and the Hard X-ray Detector (HXD; Takahashi et al. 2007) were both operated in normal modes. The same XIS data sets were already utilized by Bautz et al. (2009). In analyzing the obtained data, we used the software HEASoft 6.11.1 and latest CALDB (20111109 for the XIS and 20110913 for the HXD). We started with version 2.0 processing data and removed the data obtained either near South Atlantic Anomaly or at low elevation angles from the Earth rim (<5° and <20° for night and day, respectively). Cutoff rigidity criteria of >8 GV for HXD-PIN data were also applied. For the XIS instrument, we further examined 0.3–10.0 keV light curves of a source-free region in each CCD and filtered off anomalous time bins with count rate above the 2σ limit of the quiescent mean value. The combined XIS image is shown in Figure 1(b). The data obtained in the far north field are contaminated seriously by solar wind charge exchange emission (Fujimoto et al. 2007) and thus are not included in the following data analysis. The obtained clean exposure times are listed in Table 1. We do not consider HXD-GSO data in this paper.

We extracted the ACIS and EPIC spectra from eight thin annuli, i.e., 0–30 h⁻¹₇₁ kpc (0'–04), 30–51 h⁻¹₇₁ kpc (04–07), 51–80 h⁻¹₇₁ kpc (07–11), 80–116 h⁻¹₇₁ kpc (11–16), 116–238 h⁻¹₇₁ kpc (16–33), 238–354 h⁻¹₇₁ kpc (33–49), 354–707 h⁻¹₇₁ kpc (49–98), and 707–1335 h⁻¹₇₁ kpc (98–185), and the XIS spectra from four thick annuli, i.e., 0–144 h⁻¹₇₁ kpc (0'–20), 144–320 h⁻¹₇₁ kpc (20–44), 320–700 h⁻¹₇₁ kpc (44–97), and 700–1444 h⁻¹₇₁ kpc (97–200). When fitting these spectra, the lower energy cut was set at 0.7 keV, 0.7 keV, and 0.6 keV for the ACIS, EPIC, and XIS, respectively, while the upper cut was fixed at 8.0 keV for all three detectors. Also, the Si K edge (1.8–1.9 keV) was excluded from all the XIS spectra. Independent fittings were carried out for the Chandra (ACIS-S and ACIS-I), XMM-Newton (MOS and pn), and Suzaku (BI and FI) spectrum sets, by applying a common absorbed APEC model and linking all annuli with XSPEC model PROJCT, which performs projection of three-dimensional (3D) shells onto two-dimensional (2D) annuli to evaluate the projected emission of outer shells on inner ones. For each shell, the gas temperature, metal abundance, and column density of the neutral absorber were set free. The best-fit model yielded χ²/ν = 1750/1496, 1040/881, and 845/775 for the ACIS, EPIC, and XIS spectra, respectively. Figures 2(b) and (c) show the best-fit deprojected 1P fittings to the spectra extracted from 320–700 h⁻¹₇₁ kpc and core regions (0–80 h⁻¹₇₁ kpc for the ACIS and EPIC, and 0–144 h⁻¹₇₁ kpc for the XIS), respectively.

As shown in Figure 3(a), the best-fit deprojected 1P temperature drops inward from ≈6.0 keV at ≈100–350 h⁻¹₇₁ kpc to ≈3.0 keV in the central 30 h⁻¹₇₁ kpc, which shows apparent diagnostic of a cool core (e.g., Sanderson et al. 2006). On the other hand, in the cluster's outskirt (≈350–1100 h⁻¹₇₁ kpc), the temperature declines outward steeply down to ≈3.0 keV. Generally, our 1P temperature profiles are consistent with previous reports (e.g., Ettori et al. 2002; Vikhlinin et al. 2006; Snowden et al. 2008; Bautz et al. 2009). Incidentally, in ≈150–300 h⁻¹₇₁ kpc, the temperature obtained with the ACIS spectra is higher by about 1.0 keV than those measured with the EPIC and XIS spectra. This discrepancy can be ascribed to a local temperature structure (see Section 3.2.2), which is smoothed to some extent in the XMM-Newton and Suzaku data.

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Although the best-fit 1P model can reproduce the three data groups with reasonable goodness, i.e., χ²/ν ≈ 1.09 ∼ 1.18, the fitting residuals become drastically significant in the central 80 h⁻¹₇₁ kpc regions, where the averaged gas temperature is measured to be ≃ 4.5 keV (Figure 3(a)). As shown in Figure 2(c), the 1P model significantly underestimates the Fe-L blend and the continuum in >5.0 keV. This indicates that these annular spectra exhibit stronger multi-temperature nature than is predicted by foreground and background contributions from different radii that are accounted for by the PROJCT model. To further examine the issues with the 1P ICM model for these regions, following, e.g., Cavagnolo et al. (2008), we fitted the ACIS spectra in 0.7–4.0 keV and 4.0–8.0 keV with the 1P model, both extracted from the central 80 h⁻¹₇₁ kpc and corrected for projection effects. The 1P gas temperature obtained in 0.7–4.0 keV (T_{0.7–4.0 keV} = 3.5 ± 0.2 keV) became lower than its counterpart in 4.0–8.0 keV (T_{4.0–8.0 keV} = 5.7 ± 0.7 keV) at the 99% confidence level. The bandpass dependence cannot be ascribed to the calibration problem of Chandra at soft band, because a similar dependence can be obtained using the XMM-Newton data, with T_{0.7–4.0 keV} = 3.3 ± 0.1 keV and T_{4.0–8.0 keV} = 4.7 ± 0.5 keV. Thus, the 1P modeling of the ICM is considered inadequate, and a 2P ICM spectral model is hence invoked.

Next we investigate whether or not the 2P ICM model, as inferred in the above 1P analysis, is applicable to the spectra extracted in the inner 80 h⁻¹₇₁ kpc region, after the projection effects are taken into account. Here, the 2P ICM components were both represented by thermal APEC models, which were constrained to have the same metallicity and absorption. Both the cool and hot phase ICM temperatures (T_c and T_h, respectively) were tied among all the thin shells in the central 80 h⁻¹₇₁ kpc, while the 1P ICM model (Section 3.1.1) was retained for the outer parts. This fitting yielded overall χ²/ν = 1608/1494 and 929/879 for the ACIS and EPIC spectrum sets, respectively. The fitting goodness was compared to the 1P one (Section 3.1.1) using an F-test, which yielded F-statistics of 66.0 and 52.5 for the ACIS and EPIC data, respectively, indicating that the 2P model gives a better fit than the 1P model at >99% confidence level. As shown in Figure 2(c), the 2P ICM model apparently better reproduces the Fe-L blend and the continuum in >5.0 keV than its 1P counterpart. This shows that the 2P ICM model is strongly and consistently required for the inner 80 h⁻¹₇₁ kpc region even after removing (via PROJCT) foreground and background contributions from the outer shells. The 2P temperatures (T_c, T_h) were determined as (2.2 ± 0.2, 5.7 ± 0.4) keV and (2.0 ± 0.2, 5.0 ± 0.3) keV by using the ACIS and EPIC data, respectively. For the regions with r > 80 h⁻¹₇₁ kpc, the 2P model does not significantly improve the fitting over the 1P model.

The same 2P ICM model was also applied to the thick shell spectra obtained with the XIS. Compared to the 1P case (Section 3.1.1; χ²/ν ≈ 845/775), the 2P ICM model again gave a significantly better fit to the XIS spectra within the central 320 h⁻¹₇₁ kpc region, with reduced chi-squared improved to χ²/ν = 802/773. Since the PSF of the XIS is much wider than those of the ACIS and EPIC, with the XIS alone we cannot constrain the boundary between the 1P and 2P regions to a small radius, as we did with the ACIS and EPIC data. To examine the PSF effect on the spectral fitting of the innermost thick shell (0–144 h⁻¹₇₁ kpc), we performed a ray-tracing simulation (e.g., Ishisaki et al. 2007; Reiprich et al. 2009) based on the ACIS image and found that the 0.5–8.0 keV counts in this shell are mostly (≈75%) from the emission originated in 0–80 h⁻¹₇₁ kpc; only a small fraction (≈5%) come from the 116–238 h⁻¹₇₁ kpc region, where a hotter component (T_X ≈ 6.5 keV; Figure 3(a)) is detected with the ACIS data. Hence, this hot component cannot bias the 2P result significantly. In fact, the best-fit 2P temperatures for this region, T_c = 2.1 ± 0.5 keV and T_h = 5.5 ± 0.4 keV, are consistent with those obtained in the thin shell analysis. Thus, the PSF of the XIS little affects the 2P results obtained for the innermost thick shell.

As the most consistent form of our 2P analysis, we simultaneously fitted the thin shell spectra (the ACIS and EPIC) and those from the thick shell (the XIS), by allowing to vary independently the pair of 2P temperatures of each inner shell, i.e., ⩽80 h⁻¹₇₁ kpc and ⩽320 h⁻¹₇₁ kpc for the ACIS/EPIC and XIS cases, respectively. Nearly the same fit goodness was achieved (Table 2), and the best-fit T_c and T_h, as shown in Figure 4(a) and Table 2, exhibit nearly insignificant spatial variations across the inner shells. The values of T_c and T_h are consistent among the three instruments and broadly consistent with the ASCA result, (T_c, T_h) = (1.7 ± 0.3, 6.5 ± 0.6) keV, reported in Xu et al. (1998). In short, the ICM in the cool core of this cluster can be described by two discrete temperatures, T_c ≈ 2.0–2.2 keV and T_h ≈ 5.0–5.7 keV, which are both consistent with being spatially constant. This makes the simple 2P ICM picture (Makishima et al. 2001) a natural and reasonable description.

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Employing the 1P formalism, Fabian et al. (2001) reported a filamentary structure in the inner 50 h⁻¹₇₁ kpc region of A1795, with a possible temperature of ∼1 keV, apparently lower than the value of T_c obtained in our 2P analysis. To look for such a component, we added a third APEC component to the 2P ICM model describing the XIS data from the central 144 h⁻¹₇₁ kpc region. Indeed, we obtained a significantly better fit (χ²/ν = 791/771) by adding a third APEC component, whose temperature is kT₃ = 0.8 ± 0.4 keV, while its metal abundance, absorption, and redshift were tied to those of the 2P ICM components. An F-test indicates that the probability of this improvement being caused by chance is <5 × 10⁻³. The 0.3–10.0 keV luminosity of this 0.8 keV component is 3.6^+1.2 _{− 2.6} × 10⁴² erg s⁻¹, which is consistent with the luminosity of the filamentary structure measured with the ACIS in Fabian et al. (2001; ∼4 × 10⁴² erg s⁻¹). As shown in Table 2, the values of T_c and T_h, as well as the ICM abundances, remain nearly the same by adding this 0.8 keV component because it contributes only ≈0.7% of the total 0.3–10.0 keV luminosity of the central 144 h⁻¹₇₁ kpc region (≈5.0 × 10⁴⁴ erg s⁻¹).

In order to cross-check the XIS result, we analyzed the XMM-Newton RGS and deprojected EPIC spectra extracted from the central 80 h⁻¹₇₁ kpc region by fitting them with a three-component spectral model, i.e., 2P ICM plus a third APEC component. Since the RGS is not so sensitive to hot gas components, we fixed T_c and T_h at the best-fit EPIC results, i.e., 2.0 keV and 5.0 keV, respectively. By fitting the RGS1 and RGS2 spectra simultaneously in 6–23 Å, a weak 0.8 keV component was again detected, with a probability of 6 × 10⁻² for the detection to be caused by chance. The fitting of the EPIC spectra was improved to χ²/ν = 923/878 by including the 0.8 keV component, significantly better than previous 2P fitting in terms of F-test (>98% confidence level). The 0.3–10.0 keV luminosities of this component determined with the RGS and the EPIC are (2.7 ± 2.3) × 10⁴² erg s⁻¹ and (2.6 ± 1.7) × 10⁴² erg s⁻¹, respectively, nicely consistent with the XIS value and the ACIS result in Fabian et al. (2001).

Using the high-resolution Chandra, XMM-Newton, and Suzaku data, we have demonstrated that the 2P ICM model gives a significantly better description of the ICM thermal condition in the central 80 h⁻¹₇₁ kpc of A1795 than the 1P counterpart. The cool and hot phase ICM components have 0.3–10.0 keV luminosities of about 1.4 × 10⁴⁴ erg s⁻¹ and 2.5 × 10⁴⁴ erg s⁻¹, respectively. Also a weak 0.8 keV component has been detected in the same region, which has a 0.3–10.0 keV luminosity of about 3.6 × 10⁴² erg s⁻¹.

The 2P ICM picture implicitly assumes that these phases with different temperatures coexist, each occupying a certain fraction of the total volume under study in the cluster center, which can be described as the volume filling factor (e.g., Ikebe et al. 1999; Makishima et al. 2001; Takahashi et al. 2009). To quantify this quantity, we followed the method described in Ikebe et al. (1999) and calculated the filling factor of the cool phase gas, η_c(R), where R denotes 3D radius. With η_c, the specific emission measures of the two phases, Q_c(R) and Q_h(R), are described as

$$\begin{equation} Q_{\rm c}(R) = n_{\rm c}(R)^{2}\eta _{\rm c}(R), \mbox{ } Q_{\rm h}(R) = n_{\rm h}(R)^{2}(1-\eta _{\rm c}(R)), \end{equation} \tag{ 1 }$$

where n_c(R) and n_h(R) are the density distributions of the cool and hot phases, respectively. Assuming a pressure balance between the two phases

$$\begin{equation} n_{\rm c}(R)T_{\rm c}(R) = n_{\rm h}(R)T_{\rm h}(R), \end{equation} \tag{ 2 }$$

we have

$$\begin{equation} \eta _{\rm c}(R) = \left[ 1+\left(\frac{T_{\rm h}(R)}{T_{\rm c}(R)}\right)^{2} \left(\frac{Q_{\rm h}(R)}{Q_{\rm c}(R)}\right) \right] ^{-1}. \end{equation} \tag{ 3 }$$

Figure 4(b) shows radial profiles of η_c(R), calculated with the best-fit deprojected ACIS, EPIC, and XIS model parameters as listed in Table 2. Thus, the ACIS and EPIC data sets consistently indicate that the hot component dominates in volume over its cool counterpart not only in outer regions but also in the core region (<80 h⁻¹₇₁ kpc). The cool phase gas occupies up to η_c ≈ 0.2 of the volume in the central 30 h⁻¹₇₁ kpc, whereas η_c declines steeply to below 0.05 outside the central 80 h⁻¹₇₁ kpc region. The XIS result for the inner 144 h⁻¹₇₁ kpc is consistent with those of the ACIS and EPIC, whereas the relatively large value of η_c indicated by the outer 144–320 h⁻¹₇₁ kpc XIS bin can be attributed to the broad PSF of the XIS. In fact, by performing a ray-tracing simulation (see Section 3.1.2 for more details), the outer XIS bin at 144–320 h⁻¹₇₁ kpc was found to be contaminated by photons scattered from the inner regions, in such a way that ≈37% of the emission in this region actually comes from the central 144 h⁻¹₇₁ kpc. In this case, a weighted mean of η_c ≈ 0.08 measured with the XIS over the inner 144 h⁻¹₇₁ kpc and η_c ≈ 0.01 measured with the other two missions at the 144–320 h⁻¹₇₁ kpc region becomes ≈0.04, in agreement with the outer XIS point. Hence, after correcting for the PSF effect, all data indicate the same 2P configuration in the central region.

The ICM in the central 144 h⁻¹₇₁ kpc may alternatively be in a multi-phase condition (e.g., Kaastra et al. 2004), to be described by a more complicated emission measure distribution in a wide temperature range than that used in Section 3.1.2. To examine this possibility, we analyzed the deprojected XIS spectra from the inner 144 h⁻¹₇₁ kpc region with the same multi-temperature fitting approach as used in Tamura et al. (2001) and Takahashi et al. (2009). That is, the spectra were modeled as a cumulative contribution of seven APEC components, whose temperatures are given as T₀, 1.5T₀, (1.5)²T₀,..., and (1.5)⁶T₀, where T₀ is a base temperature and left free in the fitting. The seven components were constrained to have the same metal abundance and suffer the same absorption. The fit has been acceptable, and the goodness of fitting (χ²/ν = 786/769) is as good as that of the 2P ICM plus a 0.8 keV component model (Table 2). The base temperature was constrained as T₀ = 0.7 ± 0.2 keV. As shown in Figure 5, in the multi-phase model, only one weak component at ≈0.7 keV and two strong components at 2.4 keV and 5.3 keV remain significant (68% confidence level), while the rest components cannot be constrained. This is essentially identical to the 2P ICM plus 0.8 keV modeling. Our result is consistent with the multi-phase fitting with the EPIC data in Kaastra et al. (2004), which also shows a two-temperature structure (2.5 keV and 4.9 keV, see their Table 6) in the cluster center. Hence, the XIS data prefer the discrete 2P model, to a continuous temperature distribution, although the latter cannot be ruled out based on available data.

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As shown in Figure 3(b), the deprojected metal abundance profiles appear roughly consistent between the 1P and 2P ICM modelings (Sections 3.1.1 and 3.1.2, respectively). Both profiles show a peak in the shell of 30–51 h⁻¹₇₁ kpc and a mild decline outward. This abundance profile, however, should be regarded as an average among those of different elements, because we have so far assumed the solar abundance ratios. To examine the ICM for possible deviation from the solar ratios, we employed two VAPEC models and reran the deprojected 2P fittings of the Suzaku XIS spectra extracted from the central 320 h⁻¹₇₁ kpc region. Specifically, we left the abundances of O, Mg, Si, and Fe free, fixed the abundances of He, C, and N at the solar value (Anders & Grevesse 1989), and tied the abundance of Ni to that of Fe and those of other elements (Ne, Al, S, Ar, and Ca) to that of Si. This model gave nearly the same set of temperatures for the 2P ICM and a fit goodness (χ²/ν = 787/761) slightly better than that of the best-fit APEC model (χ²/ν = 802/773). As shown in Table 3, the best-fit Fe and Si abundances increase significantly toward the center, while the O and Mg abundances are nearly constant throughout the cluster. This confirms the previous ACIS result reported in Ettori et al. (2002; see also Matsushita et al. 2007). We also added another APEC model (A = 0.5 Z_☉; see Table 2) in the central 144 h⁻¹₇₁ kpc to account for the 0.8 keV component, while the model gave nearly the same best-fit abundance profiles for the 2P ICM components.

To examine the possible existence of any intrinsic absorption, we compared the absorption obtained in the spectral analysis with the Galactic value. Regardless of the 1P or 2P modeling, the ACIS and XIS fitting results revealed a significant excess absorption by (1–2) × 10²⁰ cm⁻² (Table 3) beyond the Galactic value of 1.2 × 10²⁰ cm⁻², at least in the central 30 h⁻¹₇₁ kpc region. The excess absorption could not be mitigated by varying the abundances of specific elements (e.g., oxygen) whose emission lines couple with the absorption feature. This result is in good agreement with the ACIS result of Ettori et al. (2002; ≈2.5 × 10²⁰ cm⁻²). On the contrary, our best-fit EPIC result (≈1.1 × 10²⁰ cm⁻²), as shown in Table 3, implies lack of excess absorption, in agreement with Nevalainen et al. (2007), who used the same XMM-Newton MOS data. The discordance among the three detectors may be caused by a temporal solar wind charge exchange emission, which biased the EPIC absorption low. As shown in Wargelin et al. (2004), the brightness of charge exchange can reach ∼2 × 10⁻⁶ photon s⁻¹ arcmin⁻²cm⁻² in 0.5–0.9 keV, which is sufficient to undermine the absorption by (0.5–1.0) × 10²⁰ cm⁻². The origin of the central excess absorption detected with the ACIS and XIS, on the other hand, still remains unclear.

Combining five Chandra ACIS-S pointings onto the central region together, we have collected sufficient photons for a high-resolution 2D spectral analysis. Following the procedure described in detail in Gu et al. (2009), a set of >10,000 discrete points (r_i, i = 1, 2, 3, ...), or "knots," were chosen in the central 240 h⁻¹₇₁ kpc, which are randomly distributed with a separation of <6 h⁻¹₇₁ kpc between any two adjacent knots. To each knot we assigned a circular region, which is centered on the knot and has an adaptive radius of 15–80 h⁻¹₇₁ kpc, ensuring that it encloses >10,000 photons in 0.5–8.0 keV after all detected point sources (Section 2.2) were excluded. The spectrum extracted from each circular region was fitted with the 1P and 2P APEC models, both subjected to an absorption that was set free. In the 2P spectral fitting, the temperatures of the cool and hot components were fixed at 2.2 keV and 5.7 keV (i.e., best-fit ACIS results; Section 3.1.2), respectively, and the two components were assumed to have the same abundance and absorption. For each knot r_i, we obtained the best-fit 1P gas temperature, 1P/2P abundance, and specific emission measure ratio between the cool and hot components (Q_c/Q_h), as well as their 1σ errors.

Then, following Gu et al. (2009), we calculated continuous maps based on the obtained knots. For any position r within the map region, we defined a scale s(r), so that there are >10, 000 net photons in a circular region centered at r, whose radius is s(r). The 1P temperature at r was then calculated by a weighted mean of all the knots r_i in the circular region,

$$\begin{eqnarray} T({\bf r}) &=& \sum _{{\bf r}_{i}} (G_{{\bf r}_{i}}(R_{{\bf r},{{\bf r}_i}})T_{\rm c}({\bf r}_{i}))\big/\sum _{{\bf r}_{i}} G_{{\bf r}_{i}}(R_{{\bf r},{\bf r}_{i}}), \mbox{ }\nonumber\\ &&\rm when \mbox{ } \it R_{{\bf r},{\bf r}_{i}} < s({\bf r}), \end{eqnarray} \tag{ 4 }$$

where $R_{{\bf r},{\bf r}_{i}}$ is the distance from r to r_i, and $G_{{\bf r}_i}$ is the Gaussian kernel whose scale parameter σ is fixed at s(r_i). The use of a compact Gaussian kernel guarantees an angular resolution of ∼15 h⁻¹₇₁ kpc within the central 100 h⁻¹₇₁ kpc region. The abundance and Q_c/Q_h maps, along with their 1σ error maps, are calculated in the same way. The resulting 1P temperature and abundance maps are shown in Figure 6, and the 2P abundance (hereafter A_2P) and Q_c/Q_h maps are presented in Figure 7. The 0.8 keV component (Section 3.1.3) was not considered in the above 2D analysis, because it will introduce negligible effects, i.e., uncertainties of about 0.05 keV and 0.02 Z_☉, to the temperature and abundance measurements, respectively.

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The primary purpose of 2D spectral analysis is to assess the validity of the spherically symmetric temperature distribution that we assumed in the radial 1P/2P analysis. To do this, we examined the obtained 1P temperature map for any significant anisotropic distribution. As shown in Figure 6(a), the 1P temperature distribution in the cluster central region exhibits an approximate elliptical symmetry; the temperature variation in the azimuthal direction is about 0.5 keV, 1.0 keV, and 1.0 keV at r = 20 h⁻¹₇₁ kpc, 40 h⁻¹₇₁ kpc, and 80 h⁻¹₇₁ kpc, respectively, which is insufficient, at least by a factor of three, to imitate the obtained 2P ICM condition. Similar morphology is seen in the Q_c/Q_h map of the core region as shown in Figure 7(b). This confirms that the 2P view is not an artifact caused by a 1P ICM with large azimuthal asymmetry. It also indicates that the two phases, in terms of the 2P view, must be separated on scales smaller than the spatial resolution allowed by the present analysis (≈15 h⁻¹₇₁ kpc).

The most prominent feature on the 1P temperature map (Figure 6(a)) is a high-temperature arc (≈7.5 keV according to the 1P model) located at ≈100–180 h⁻¹₇₁ kpc southeast (SE) of the cluster's center, with an open angle of >120°. Given the temperature difference of about 2 keV, the hot structure is significant over the ambient on the 90% confidence level. This feature agrees with a high-temperature bin (116–238 h⁻¹₇₁ kpc) on the deprojected ACIS temperature profile shown in Figure 3(a). The same high-temperature structure was found by Markevitch et al. (2001), who carried out a 1P azimuthal spectral analysis for the southern part of the cluster. Markevitch et al. (2001) also reported a density jump by a factor of 1.3–1.5 near the inner edge (≈85 h⁻¹₇₁ kpc from the cluster center) of the high-temperature arc and ascribed the density jump to a cold front. Since both the high-temperature component and the cold front locate outsides of the 2P region (i.e., r < 80 h⁻¹₇₁ kpc), they are unable to affect the obtained 2P result significantly, even for the XIS thick shell as indicated by the ray-tracing simulation shown in Section 3.1.2.

A comparison of the A_2P map (Figure 7(a)) with the Q_c/Q_h map (Figure 7(b)) suggests a spatial correlation on a scale of 50–100 h⁻¹₇₁ kpc between the two quantities. Both maps reveal strongly inhomogeneous distributions outside the relaxed core region, with substructures protruding toward southwest, northeast, and northwest of the cluster center by ≈80–100 h⁻¹₇₁ kpc. Most of these substructures show both higher metal abundances, typically by a factor of 2–3, and larger cool phase fractions than their neighborhoods. The best-fit A_2P and Q_c/Q_h values for all the knot-centered circular regions in 50–100 h⁻¹₇₁ kpc, obtained in our 2D spectral analysis (Section 3.2.1), were compared directly in Figure 7(c). Indeed, it reveals a positive linear correlation, which is represented by an analytic form as A_2P = 0.38^+0.11 _{− 0.12} × Q_c/Q_h + 0.48^+0.08 _{− 0.07} Z_☉. The linear correlation coefficient was obtained as 0.97.

To quantify the suggested correlation, following, e.g., Shibata et al. (2001), we calculated a 2D cross-correlation function as

$$\begin{eqnarray} &&\xi (R) = \left< \frac{\left\lbrace A_{\rm 2P}({\bf r}_{1}) - \overline{A_{\rm 2P}} \right\rbrace \left\lbrace Q_{\rm c}({\bf r}_{2})/Q_{\rm h}({\bf r}_{2}) - \overline{Q_{\rm c}/Q_{\rm h}} \right\rbrace }{\overline{A_{\rm 2P}}\overline{Q_{\rm c}/Q_{\rm h}}} \right>_{\rm r_{12} = R},\nonumber\\ \end{eqnarray} \tag{ 5 }$$

where $\overline{A_{\rm 2P}}$ and $\overline{Q_{\rm c}/Q_{\rm h}}$ are averages of A_2P and Q_c/Q_h maps, respectively, r₁₂ = |r₁ − r₂| is the distance between r₁ and r₂, and the bracket is ensemble average. The obtained correlation function is shown in Figure 7(d). A reference profile (ξ_ref(R)) was also calculated, based on a series of random maps, A_{2P, ran} and Q_{c, ran}/Q_{h, ran}, which were obtained by randomizing the maps within the same data range and smoothing to the same spatial resolution as the original A_2P and Q_c/Q_h maps. The error bars shown in Figure 7(d) were calculated from the variances of ξ(R) when scattering the A_2P and Q_c/Q_h maps by their 1σ error maps. Comparing to the ξ_ref(R), the ξ(R) profile shows a significant excess within 100 h⁻¹₇₁ kpc, reconfirming the result that cool phase ICM is indeed more metal-rich.

Given the detected correlation, the assumption made in Sections 3.1.2 and 3.1.6 that the two phases of the ICM have approximately the same abundances may not stand now. Therefore, we refitted the deprojected XIS spectra of the central 144 h⁻¹₇₁ kpc region with the 2P ICM (VAPEC + VAPEC) + 0.8 keV component (APEC; 0.5 Z_☉) model, the same as the one in Section 3.1.6, except that the iron abundances of the cool and hot phases were let float separately. The absorption column densities of the three components were again tied together in the fitting as a free parameter. We found that the abundance of cool phase ICM (A_{Fe, c}) does appear higher than that of the hot one (A_{Fe, h}), i.e., (A_{Fe, c}, A_{Fe, h}) = (0.80 ± 0.25, 0.36 ± 0.06) Z_☉. Compared to the model presented in Section 3.1.6 (Table 3), the current model improves fit goodness to χ²/ν = 779/759 from 787/761, with a probability of 2 × 10⁻² for the improvement to be caused by chance.

Following, e.g., Simionescu et al. (2008), the iron abundance to be obtained with a 2P model assuming a single common metallicity can be estimated by

$$\begin{equation} A_{\rm Fe}^{\prime } \approx \frac{Q_{\rm c}A_{\rm Fe, c}+Q_{\rm h}A_{\rm Fe, h}}{Q_{\rm c}+Q_{\rm h}}. \end{equation} \tag{ 6 }$$

Eliminating Q_c and Q_h with Equation (1), we have

$$\begin{equation} A_{\rm Fe}^{\prime } \approx \frac{T_{\rm h}^2 \eta _{\rm c} A_{\rm Fe, c} + T_{\rm c}^2 (1-\eta _{\rm c}) A_{\rm Fe, h}}{T_{\rm h}^2 \eta _{\rm c} + T_{\rm c}^2 (1-\eta _{\rm c})}. \end{equation} \tag{ 7 }$$

Adopting η_c = 0.08 (Figure 4(b)) and (A_{Fe, c}, A_{Fe, h}) obtained above, A'_Fe is then calculated as 0.51 Z_☉, which agrees with that derived with the XIS spectra (0.48 ± 0.03 Z_☉, Table 3). Thus, all the ACIS and XIS results obtained so far can be interpreted as evidence for the relatively high metal abundance of the cool phase ICM.

In many cool-core clusters, the X-ray surface brightness exhibits a central excess over a β model that well fits the outer region. Makishima et al. (2001) argued that the central excess is a combined result of two major effects: the presence of a cool phase component and the existence of hierarchical potential structure. According to their definition, the hierarchical potential is specified as a halo-in-halo structure, i.e., a smaller potential component is nested on a larger one, so that the overall potential shows a central deepening relative to a simple King profile. Here we examined the surface brightness profile of A1795 for such a central excess. In order to measure the surface brightness profile precisely by taking advantage of both high spatial resolution of the Chandra ACIS and stable low background of the Suzaku XIS, we calculated exposure-corrected surface brightness profiles from the inner 1000 h⁻¹₇₁ kpc ACIS and 1200–1800 h⁻¹₇₁ kpc XIS data, i.e., S_ACIS(r) and S_XIS(r), respectively, where r is projected radius. The method described in, e.g., Markevitch et al. (1998) was employed to compensate discrepancies on calibration and instrumental background between the two instruments. First, we performed simulations using the xissim tool (Ishisaki et al. 2007) to smooth the Chandra images with the Suzaku PSF and extracted the simulated surface brightness profile in the central 1000 h⁻¹₇₁ kpc, i.e., S'_ACIS(r). Then, S'_ACIS(r) was scaled to S_XIS(r) by solving aS'_ACIS(r) − b = S_XIS(r), where a and b represent the differences in normalization and NXB, respectively. A modified S_ACIS(r) with the original ACIS resolution was obtained by applying a and b to S_ACIS(r) in the same way as we normalized S'_ACIS(r).

Then, the modified S_ACIS(r) and S_XIS(r), shown in Figure 8, were fitted jointly with the β model, S(r) = S(0){1 + (r/r_c)²}^{−3β + 1/2} + S_BG, where S(0) is the central brightness, r_c is the core radius, and S_BG is the background. To represent the possible halo-in-halo structure, a double-β model was also tested as $S(r) = S_1(0) \lbrace 1+(r/r_{\rm c1})^2\rbrace ^{-3\beta _1 + 1/2} + S_2(0) \lbrace 1+(r/r_{\rm c2})^2\rbrace ^{-3\beta _2 + 1/2}+ S_{\rm BG}$, where subscripts 1 and 2 denote compact and extended components, respectively. As shown in Table 4, the fit with the β model can be rejected on the 95% confidence level because it significantly underestimates the surface brightness in the central ∼100 h⁻¹₇₁ kpc, while the double-β model gives an acceptable fit to the data. The successful fits in Figure 8 are based on a still more sophisticated model, a β+double-β gas density model, to be explained later. The properties of the central excess brightness, represented by the compact β component (β₁ ≈ 0.75, r_c1 ≈ 53 h⁻¹₇₁ kpc), are consistent within errors between the 0.5–3.0 keV and 3.0–8.0 keV bands. Such an energy-independent central excess is likely to be caused by an intrinsic hierarchical potential shape, rather than the presence of a cool phase component. This result agrees with the earlier ASCA result reported in Xu et al. (1998).

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To further quantify the central emission excess, we corrected the surface brightness profile for the projection effect using the best-fit deprojected 2P gas temperature and abundance profiles (Table 2; Section 3.1.2). The observed surface brightness profile was modeled as

$$\begin{eqnarray} S(r)&=& \int ^{\infty }_{r}\Lambda (T_{\rm c},A_{\rm c})Q_{\rm c}(R)\frac{RdR}{\sqrt{R^{2}-r^{2}}}\nonumber\\ &&+ \int ^{\infty }_{r}\Lambda (T_{\rm h},A_{\rm h})Q_{\rm h}(R)\frac{RdR}{\sqrt{R^{2}-r^{2}}} + S_{\rm BG}, \end{eqnarray} \tag{ 8 }$$

where Λ is the cooling function, Q_c and Q_h are the same as in Equation (1), and S_BG is the averaged background value. Following Ikebe et al. (1999), we represented the specific emission measure profiles by a 2P β+double-β model, which consists of a β component for the cool phase ICM,

$$\begin{equation} Q_{\rm c}(R) = \left\lbrace \begin{array}{@{}c}Q_{\rm 0,c} \left[ 1 + \left(\frac{R}{R_{\rm c,c}}\right)^{2} \right] ^{-3\beta _{\rm c}} \mbox{ } \mbox{ } \mbox{ } \mbox{ } R \le 80\ h_{71}^{-1}\mbox{ } {\rm kpc},\\ \ms 0 \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } \mbox{ } R > 80\ h_{71}^{-1}\mbox{ } {\rm kpc}, \end{array} \right. \end{equation} \tag{ 9 }$$

and a double-β component for the hot phase ICM,

$$\begin{eqnarray} Q_{\rm h}(R) &=& Q_{\rm 0,h1} \left[ 1 + \left(\frac{R}{R_{\rm c,h1}}\right)^{2} \right] ^{-3\beta _{\rm h1}}\nonumber\\ && + Q_{\rm 0,h2} \left[ 1 + \left(\frac{R}{R_{\rm c,h2}}\right)^{2} \right] ^{-3\beta _{\rm h2}}, \end{eqnarray} \tag{ 10 }$$

where Q_{0, c}, Q_{0, h1}, and Q_{0, h2} are the model normalizations of the cool phase, the compact hot phase, and the extended hot phase components, respectively. The filling factor η_c is renormalized into these parameters.

With these preparations, we fitted the 0.5–8.0 keV ACIS + XIS surface brightness profiles using Equation (8), where Λ was calculated from the best-fit 2P spectral parameters. The fit has been successful with χ²/ν = 161/151. The best-fit values of R_{c, c}, R_{c, h1}, R_{c, h2}, β_c, β_h1, and β_h2 are given in Table 4. The fittings with surface brightness profiles extracted in different energies (i.e., 0.5–3.0 keV and 3.0–8.0 keV bands) are shown in Figure 8. As presented in Table 4, all the fittings yielded consistent parameters for the 2P β+double-β model.

In some clusters, the central excess can be alternatively explained by a cuspy dark matter distribution proposed in Navarro et al. (1996; hereafter NFW model). The NFW model predicts potential structure with a single spatial scale, instead of the dual structure assumed by the β+double-β model. Given the NFW dark matter density profile,

$$\begin{equation} \rho _{\rm DM}(R) = \rho _{\rm c} \delta _{\rm c} \left(\frac{R}{R_{\rm s}}\right)^{-1} \left(1 + \frac{R}{R_{\rm s}}\right)^{-2}, \end{equation} \tag{ 11 }$$

where ρ_c is the critical density, δ_c is characteristic density, and R_s is scale radius, the ICM density profile is expressed as

$$\begin{equation} n_{\rm NFW} (R) = n_{\rm 0,NFW} \frac{\left(1+ \frac{R}{R_{\rm s}}\right)^{\frac{\alpha R_{\rm s}}{R}}-1}{e^{\frac{R}{R_{\rm s}}}-1}, \end{equation} \tag{ 12 }$$

where n_{0, NFW} is model normalization and α is a parameter related to the ICM temperature. Then the projected ICM surface brightness profile was modeled as a single component,

$$\begin{equation} S(r)= \int ^{\infty }_{r}\Lambda (T_{\rm 1P},A_{\rm 1P})n_{\rm NFW}^{2}(R)\frac{RdR}{\sqrt{R^{2}-r^{2}}} + S_{\rm BG}. \end{equation} \tag{ 13 }$$

We found that this NFW model cannot give acceptable fits to the 0.5–8.0 keV surface brightness profile for the entire cluster, with a minimum χ²/ν = 307/155. As shown in Figure 8, the central excess emission is too strong to be explained by the NFW model that best fits the >100 h⁻¹₇₁ kpc region. Hence, we reconfirmed the ASCA result reported in Xu et al. (1998) that the halo-in-halo hierarchical model is preferred to the single-halo NFW model in A1795.

Next we calculated the total gravitating mass profile M(R) based on the best-fit 2P temperatures (Section 3.1.2) and the emission measure profiles obtained with the β+double-β model (Section 3.3.1). With the help of Equations (1)– (3), the best-fit emission measure profiles, Q_c(R) and Q_h(R), were converted to gas density profiles of the cool and hot phases, n_c(R) and n_h(R), respectively. Then, under the assumptions of spherical symmetry and hydrostatic equilibrium, the gravitating mass profile M(R) was calculated as

$$\begin{equation} M (R) = - \frac{R^2}{G \rho _{\rm g}(R)} \frac{{\rm d}P (R)}{{\rm d}R}, \end{equation} \tag{ 14 }$$

where P(R) = n_c(R)k_BT_c(R) = n_h(R)k_BT_h(R) is the gas pressure, ρ_g(R) = μm_p{η_c(R)n_c(R) + [1 − η_c(R)]n_h(R)} is the averaged gas mass density, μ = 0.609 is the approximated mean molecular weight, and m_p is the proton mass. As shown in Figure 9, the obtained mass profile exhibits a significant shoulder-like feature at R_x ≈ 120 h⁻¹₇₁ kpc, enclosing an excess mass (M_excess) of about 1.5 × 10¹³ M_☉ above a flat core mass distribution calculated with the extended hot phase component alone. Our result agrees with the ASCA result, R_x ≈ 110 h⁻¹₇₁ kpc and M_excess ≈ 2.1 × 10¹³ M_☉, as reported in Xu et al. (1998).

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To examine systematic errors of the mass profile due to different modelings of the ICM temperature distribution, we also calculated the gravitating mass profile using the best-fit deprojected 1P spectral parameters (Section 3.1.1). The projected X-ray surface brightness profile was modeled with a single ICM component as

$$\begin{equation} S(r)= \int ^{\infty }_{r}\Lambda (T_{\rm 1P},A_{\rm 1P})Q_{\rm 1P}(R)\frac{RdR}{\sqrt{R^{2}-r^{2}}} + S_{\rm BG}, \end{equation} \tag{ 15 }$$

where the specific emission measure is given by a double-β model,

$$\begin{eqnarray} Q_{\rm 1P}(R) = n^{2}_{\rm 1P}(R) &=& Q_{\rm 0,1} \left[ 1 + \left(\frac{R}{R_{\rm c,1}}\right)^{2} \right] ^{-3\beta _{\rm 1}}\nonumber\\ && + Q_{\rm 0,2} \left[ 1 + \left(\frac{R}{R_{\rm c,2}}\right)^{2} \right] ^{-3\beta _{\rm 2}}. \end{eqnarray} \tag{ 16 }$$

The fit is as good as the 2P case, with χ²/ν = 165/154. The resulting mass profile, derived by substituting P(R) = n_1P(R)k_BT_1P(R) and ρ_g(R) = μm_pn_1P(R) into Equation (14), is shown in Figure 9 by a red curve. Thus, the shoulder-like potential structure is again found, although the 1P model systematically underestimates the gravitating mass within 80 h⁻¹₇₁ kpc by ≈30%. This bias is negligible in >80 kpc.

Another concern is that the assumption of hydrostatic equilibrium may not hold for the ICM near the cold front located southeast of the cluster center (Section 3.2.2), casting doubt on the validity of the mass profile obtained in the related region (Markevitch et al. 2001). To investigate this, we excluded the southern half of the cluster and recalculated the mass profile for the northern half using the best-fit 2P spectral results and surface brightness profile with the ACIS data. The 2P temperatures, T_{c, north} = 2.0 keV and T_{h, north} = 5.9 keV, are consistent with previous ACIS results. The same applies for the obtained n_{h, north}(R) profile, except for the annulus of the cold front (i.e., R = 100–180 h⁻¹₇₁ kpc), where n_{h, north}(R) is lower than n_h(R) by 5%–20% in 100–180 h⁻¹₇₁ kpc. After comparing M_north(R) to M(R) in Figure 9, we found that the shoulder-like structure, though diminished by ≈10%, still remains significant after the high-temperature arc is excluded. Hence, we conclude that the existence of the central hierarchical structure is unambiguously confirmed in A1795.