A SYSTEMATIC SEARCH FOR X-RAY CAVITIES IN GALAXY CLUSTERS, GROUPS, AND ELLIPTICAL GALAXIES

To detect X-ray cavities, we used two methods, the β-modeling and the unsharp masking technique (see Figure 1), as previously used in other studies (e.g., Diehl et al. 2008; Dong et al. 2010). First, for β-modeling, the radial distribution of the surface brightness of diffuse X-ray gas is modeled assuming an isothermal distribution of the hot gas (Cavaliere & Fusco-Femiano 1976). Using the Sherpa package in CIAO, we fitted the surface brightness profile with various parameters, e.g., radius, ellipticity, and power-law index, as free parameters except for the location of the center of X-ray emission. We fixed the peak of the distribution as the center since many targets show asymmetric distribution (e.g., cold front). If we fit the center as a free parameter, the center is almost identical to the peak location within ∼1 pixel for the targets that show symmetric distribution (e.g., Abell 85, NGC 533, Abell 383), while for the targets with asymmetric distribution, the center is significantly off from the location of the peak by up to 60 pixels (e.g., Abell 2146, Ophiuchus cluster). To subtract background, we used constant value as representative of the background. We did not exclude the central bright point source (X-ray AGN) since masking or fitting the point source does not improve the results.

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For the targets with strong and large X-ray cavities (21 objects), the β-model does not provide a good fit since the spatial profile dramatically changes (see Figure 2). Instead, we can directly detect cavities from the raw images, or use the unsharp masked image to identify cavities.

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Second, we applied the unsharp masking technique by utilizing the smoothing task "aconvolve" in CIAO. Adopting 2 pixels (i.e., 0984) for small scales and 10 pixels for large scales, we produced smoothed (small and large) images and divided the large-scale smoothed image by the small-scale smoothed image to obtain the unsharp masked image. A weakness of the unsharp masking technique is that it is difficult to determine the size of X-ray cavities because the size varies with smoothing lengths (see Dong et al. 2010). Also, for extreme cases, X-ray cavities are not detected from the unsharp masked image (e.g., NGC 533), while cavities are clearly detected from the β-modeling analysis (see Figure 3). Therefore, we mainly used the β-model to detect X-ray cavities, and used the unsharp masking technique as a secondary method.

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In the detection process, we also used the normalized images, which were generated by dividing a raw image by the best β-model, in order to conservatively define cavities more. By examining the normalized images as well as residual images, we investigated the spatial extent of relative depression. We require a minimum of 15% depression to confirm the presence of cavities and estimate the size for most targets. However, if the cavity is clearly present in the raw images, we further classified these features as X-ray cavities even though the relative depression is slightly lower than 15%. These exceptions are namely, ZwCl 0104+0048, Abell 383, ZwCl 1021+0426, NGC 4104, and MACS J2046.0-3430 (see Figure 3).

In Figure 1, we present an example of the fitting result of RXJ1532.9+3021. Compared to the raw image (left), the residual image (center), after subtracting the best-fit β-model (center left) shows two cavities very clearly with the green lines representing the ellipse models. The normalized image (center right) confirms the presence of cavities (see Figure 1 for more details). For all 133 targets in the sample, we present the results: directly detected cavities from raw images (Figure 2), cavities detected via β-modeling (Figure 3), and uncertain or non-detections (Figure 4).

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We measured the properties of X-ray cavities, either directly detected from the raw X-ray images (for 21 targets) or detected from the β-model analysis (for 48 targets). Since the shape of X-ray cavities typically looks elliptical, we adopted an ellipse model to describe the morphology of X-ray cavities. Note that we tried to fit the shape of the individual X-ray cavities, but failed mainly due to the low photon counts. Thus, we simply overlapped an ellipse model to the raw and beta-model subtracted images, as similarly performed in the previous studies (Dong et al. 2010). Based on the ellipse model, we determined the size in the semimajor and semiminor axes of the X-ray cavities. Note that the size of the cavities depends on the choice of the best ellipse model, hence the systematic uncertainty of the size can be significant (see Section 5.4 for a more detailed discussion).

We also measured the distance between the cavity center (i.e., center of the ellipse) and the center of the diffuse X-ray emission, which is assumed to be the location of the point source. If a point source is not present, we adopted the peak position of diffuse X-ray emission as the center. We assumed two pixels as the measurement uncertainties of the cavity size and the distance. For three targets (ZwCl 0104+0048, NGC 4104, and MACS J2046.0-3430), the detected X-ray cavities are at the center of the diffuse X-ray emission. Perhaps, the radio jet direction is along the line of sight in these cases (see also Dong et al. 2010. In Table 2, we list the properties of X-ray cavities for individual targets.

In our analysis, we find that asymmetric gas distributions (i.e., cold fronts) can produce false detections of X-ray cavities if we use a symmetric β-model. In Figure 5, we present such a case, Abell 1991, for which Dong et al. (2010) detected the presence of two cavities (see Figure 4 in Dong et al. 2010). The distribution of the diffuse emission is somewhat vertically asymmetric in the raw image with a sharp drop in the north and a shallow decrease in the south. As seen in the residual image after subtracting the β-model, we detected only one cavity in the south (middle right panel). There seems to be one more depression in the north but it may still be caused by the asymmetric X-ray gas distribution since the symmetric β-model can produce a false depression by over-subtracting the diffuse emission, respectively, in the north and south in the image. Thus, we conclude that the depression in the north may not be a real cavity, and that the fitting result may not be reliable for such targets with a strong asymmetric gas distribution. Nevertheless, as shown in the south, some targets show real X-ray cavities in the opposite part of the sharp drop, where the diffuse emission is under-subtracted. Thus, the depression in the south is not likely to be a false detection.

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Point sources (AGNs) in the center of diffuse emission may also lead to false detections. For example, in the presence of a strong point source at the center, the β-model tends to over-subtract diffuse emission around the point source, producing a false depression (see, e.g., Abell 2029 and UGC12491 in Figure 4). For these cases, we did not classify them as real cavities. As presented in Figure 4, most of the targets with no cavity detection present these two features, i.e., asymmetric distribution or over-subtraction around the point source. In these objects, it is not clear whether true cavities are present.

To investigate the effect of the environments on X-ray cavities, we quantified the environments of each target in the sample. Since environments can be represented by various physical parameters, e.g., velocity dispersion of galaxies, X-ray gas temperature, and virial mass, we reviewed literatures for measured velocity dispersions and gas temperatures of each target. However, the reported values are often measured from different methods and are incomplete for our sample.

To perform a uniform analysis and minimize systematic uncertainties, we directly measured the gas temperatures within $0.15\,{R}_{2500}$ based on the X-ray data. Since our targets cover a large redshift range (from 0.001 to 2.7), it is difficult to measure R₂₅₀₀ for all targets since, for example, the R₂₅₀₀ of low-redshift targets is far larger than the field of view (FOV) of Chandra images. After testing with various radii, we determined that $0.15\,{R}_{2500}$ is the optimal radius for the majority of targets in the sample. For several lower redshift targets, for which even $0.15\,{R}_{2500}$ is larger than the FOV, we adopted a smaller radius: $0.10\ {{R}}_{2500}$ for M84 and $0.05\ {{R}}_{2500}$ for NGC 4472, M87, NGC 4552, NGC 4636, and NGC 4649, respectively.

The $0.15\,{R}_{2500}$ was calculated from the temperature-radius relation (Equation (12) of Vikhlinin et al. 2006), using an initial temperature value. Since the R₂₅₀₀ varies depending on gas temperatures, we estimated $0.15\,{R}_{2500}$ by iterating radius determination until the estimated temperature becomes consistent within 10%. Note that the uncertainty of gas temperature is large since we calculate $0.15\,{R}_{2500}$ from gas temperature derived within $0.15\,{R}_{2500}$, while we used the temperature-radius relation derived for R₂₅₀₀.

The gas temperature derived from $0.15\,{R}_{2500}$ differs, on average, by 20% compared to that derived from R₂₅₀₀ (Vikhlinin et al. 2006). The method for gas temperature measurement is the same as that described in Section 2, except for the extraction radius. We estimated the uncertainties by combining 1σ fitting error and 20% systematic error to account for the temperature variation due to the adopted size of the aperture (i.e., $0.15\,{R}_{2500}$ versus R₂₅₀₀). If a smaller radius (i.e., $\lt 0.15\ {R}_{2500}$) was used for gas temperature measurements, we adopted 30% higher uncertainty, which is the maximum temperature difference between $0.05\ {{\rm{R}}}_{2500}$ $0.15\,{R}_{2500}$ (see Vikhlinin et al. 2006). If there is no reliable fitting error when ${\chi }^{2}$ is larger than two, we adopted the maximum fitting error from other targets. Gas temperatures and HI column densities are presented in Table 1. Note that for individual sources, the uncertainty of the estimated temperature can be larger than 20%–30% since R₂₅₀₀ can be underestimated due to the degeneracy between temperature and radius.

Using the raw images and applying the β-model, we detected 148 cavities from 69 targets. Out of the 133 targets in our sample with sufficient X-ray photons, ∼52% shows cavities. Among them, 18, 38, and 13 targets show one, two, and more than two cavities, respectively. In general, two cavities are detected as a pair on opposite sides of the center, except for a few cases. Since X-ray cavities are believed to be formed by a radio jet, two bi-symmetric X-ray cavities are expected. However, the presence of more than two cavities in many targets may imply that there were multiple radio events in the past. In the case of more than two cavities, four targets show one pair and one additional cavity (1, NGC 1316) while the other nine targets show various geometry: collinear two pairs (e.g., NGC 5813), two pairs with different direction (two, e.g., NGC 4636 & Cygnus A), or a complicated structure (six, e.g., Abell 426 & M87).

To investigate relations between cavity properties, we compared the cavity size in the semimajor axis (a), distance from the X-ray center (D), and area as shown in Figure 6, using the "FITEXY" method (Tremaine et al. 2002; Park et al. 2012). To calculate uncertainties, we performed Monte Carlo simulations with 10,000 mock data sets by randomizing the error, and adopted the standard deviation as the uncertainty of the fitting results.

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Over the large dynamic range covered by our sample, we confirm a linear correlation of the cavity size with the distance from the X-ray center,

$$\begin{eqnarray}&&\mathrm{log}\ a=(0.97\pm 0.02)\ \mathrm{log}\ D-0.15\pm 0.02,\end{eqnarray} \tag{ 1 }$$

as previous studies reported (Bîrzan et al. 2004; Dong et al. 2010). There are several explanations to understand this correlation in terms of cavity evolution such as buoyancy or momentum from the AGN jet. By testing various models, Diehl et al. (2008) showed that magnetically dominated cavities can be well explained by current-dominated magnetohydrodynamic jet models (Li et al. 2006; Nakamura et al. 2006, 2007).

Since the cavity shape is generally elliptical, cavity area may better represent the cavity property than the size in the semimajor or semiminor axes. In addition, to estimate the total energy emitted from a radio jet, the volume of cavities is required based on additional assumptions (i.e., cavity shape). Instead, cavity area can be measured from the projected image and compared to the distance. As shown in the right panel of Figure 6, we find a similar correlation between the cavity area and the distance from the center

$$\begin{eqnarray}&&\mathrm{log}\,\mathrm{Area}=(1.94\pm 0.04)\ \mathrm{log}\,D+0.02\pm 0.05.\end{eqnarray} \tag{ 2 }$$

The scatter of the area–distance relation is similar to that of the size–distance relation (0.155 ± 0.010 dex and 0.163 ± 0.011 dex, respectively, in distance units). For the rest of the paper, we will use the area as a representative of the cavity size. In Figure 6, gas temperatures are denoted with different colors. Of interest, it seems that high temperature systems tend to have larger cavities. However, the cavity size correlates with the distance regardless of gas temperature, suggesting that the formation and evolution of the X-ray cavities has little dependence on environment.

To investigate the environmental effects on X-ray cavities, we first checked the fraction of X-ray cavity detection as a function of X-ray gas temperatures in Figure 7. At each temperature bin, the number of total targets and the number of targets with cavity detection are represented, respectively, with the unfilled- and filled-histogram. The detection rate of X-ray cavities is on average 49% while the rate varies slightly in individual temperature bins. We do not find a significant change of the detection rate except for the very high temperature bins that contain small numbers of targets, suggesting that there are no strong environmental effects on the presence of X-ray cavities.

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In contrast, there appears to be a trend between cavity size and environments. By comparing cavity sizes to gas temperatures (Figure 8), we find that the cavity size increases with gas temperatures. Since many targets at given gas temperatures have multiple cavities with various sizes, the relation between the cavity size and gas temperature is not strong. Nonetheless, there is a clear trend between them, suggesting that more massive systems possess larger size cavities. However, to confirm the correlation, we should look at the selection effect carefully, which will be discussed in detail in Section 5.1.

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Previous studies reported that the X-ray cavity detection rate is ∼2/3 for cool-core clusters (14 out of 20; Dunn & Fabian 2006), ∼1/2 for galaxy groups (26 out of 51; Dong et al. 2010), and ∼1/4 for elliptical galaxies (24 out of 104; Nulsen et al. 2009). At face value, these results seem to suggest that the detection rate of  the X-ray cavity increases with galaxy density, indicating environmental effects on the formation of X-ray cavities.

As pointed out in Section 2, however, consistent criteria for sample selection and uniform analysis is required to constrain the detection rate and environment effect. By investigating the targets in the previous studies, we find that many targets, for which X-ray cavities were detected, do not have sufficient X-ray photons. For example, 17 targets of Dong et al. (2010) satisfy our sample selection criteria, while the other 38 targets have insufficient photon counts. Among those 17 targets, we found cavities in 11 targets, while Dong et al. (2010) detected cavities in 14 targets. Comparing with the results of Dunn & Fabian (2006), we used all 20 objects in their sample and detected cavities in 16 objects. While Dunn & Fabian (2006) also detected cavities in 16 targets, they did not find cavities in the same 16 targets we did. We found X-ray cavities in Abell 496, Abell 2204, PKS 0745-191, and AWM7, however, Dunn & Fabian (2006) did not. It may be partly due to the fact that Dunn & Fabian (2006) used single exposures per target, without combining all available exposures and that they did not perform β-modeling and unsharp masking analysis. On the other hand, Dunn & Fabian (2006) reported X-ray cavities in Abell 1795, Abell 2029, Abell 4059, and MKW 3s, while we classified these target as non-detections since they show over-subtraction in our analysis. These examples demonstrate the difficulties of direct comparison among various studies in the literature. We provide a more detailed comparison of our work to others in Section 5.4.

In contrast, our results suggest that the cavity detection rate does not show significant dependence on gas temperatures (see Figure 7), indicating that the formation and evolution of the X-ray cavities may be driven by the central engine (i.e., AGN) and affected by the physical conditions at the center (i.e., gas density) rather than the global properties (i.e., environments).

We showed that larger X-ray cavities tend to be detected in the higher gas temperature systems. Since the cavity grows in size and moves away from the center, as indicated by the size–distance relationship, we expect to see small cavities close to the center even in high gas temperature systems. The lack of small cavities in high gas temperature systems may reflect selection effects. To investigate the effect, we compared the cavity size and gas temperature as a function of redshift (Figure 9), finding that systems with high gas temperature tend to be more distant since more massive and more luminous systems with high gas temperature are rarer. Also, we tend to detect larger cavities at higher redshift as shown in Figure 9. This trend can be due to the limited spatial resolution of the Chandra data. Since it is difficult to identify a cavity with a size smaller than ∼1'' with the Chandra PSF, we could not detect small size cavities at high redshift. To illustrate this, we denoted the detection limit for a cavity with a 1'' radius size as a function of redshift with a solid line in Figure 9. The distribution of the detected cavities over the redshift range is consistent with the detection limit, indicating that the lack of small cavities at high redshift is due to the fixed spatial resolution in Chandra images.

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On the other hand, we tend to detect no large cavities in the systems with lower gas temperature since the size of the diffuse X-ray emitting region is intrinsically small. Since the cavities are detected as a form of depression as embedded in the diffuse X-ray gas, the size of X-ray emitting region is the maximum limit of the cavity size. In Figure 10, we present the size of the X-ray halo with a gray line, which represents R₂₅₀₀ as a function of gas temperature, while the thickness represents the range of R₂₅₀₀ at the redshift range of $0.001\lt z\lt 0.7$, which is relevant for all targets in the sample except for one target, MS 1512-cB58 at z = 2.723. This figure demonstrates the growth limit of X-ray cavities. For example, 3C 444 ($\mathrm{log}(D/1\,\mathrm{kpc})\sim 1.8$) and MS 0735.6+7421 ($\mathrm{log}(D/1\,\mathrm{kpc})\sim 2.2$) contain relatively large cavities, which are close to the growth limit and detected at the edge of the X-ray distribution. There are other cavities detected at the edge of the X-ray distribution (e.g., M84 and NGC 4636). However, these targets have much shallower X-ray images, hence, the size of the observed X-ray distribution is much smaller than R₂₅₀₀.

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In Figure 11, we demonstrate the two forbidden areas in the size–temperature plane with the growth limit and the spatial resolution limit. Intrinsically, the cavity size cannot be larger than the X-ray emitting region of individual targets, confining the detected cavities below the growth limit, while Chandra image resolution does not allow us to observationally detect small cavities below the spatial resolution limit.

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While we detected X-ray cavities from 69 out of 133 targets, we did not find any clear evidence for X-ray cavities in the other 64 targets (see Section 4). Since the majority of non-detected targets have asymmetric distributions or over-subtraction issues, it is difficult to confirm the presence of cavities in these objects. This is the limitation of this work since we relied on symmetric β-modeling. The results from the β-modeling often present over-subtraction regions, which were classified as non-detections. For these targets, additional data such as radio can be an aid to reveal the true nature of diffuse X-ray emission. For example, Hodges-Kluck et al. (2010a, 2010b) confirmed the presence of cavities by combining X-ray and radio data.

Another possible reason for non-detection is relatively weak X-ray depression. Previous work reported that cavity detectability strongly depends on the size and distance from the center, suggesting that large cavities with smaller distance can be detected easily (Enßlin & Heinz 2002; Brüggen et al. 2009; Dong et al. 2010). In other words, we tend to not detect small cavities far from the central region. In addition, Enßlin & Heinz (2002) showed that detectability also relies on the inclination angle of a cavity with respect to the plane of sky, showing that cavity depression is maximized when the inclination angle is zero. For these reasons, it is likely that we may have missed some cavities. These effects act as selection effects for our cavity detection and the observed size–distance relation presented in Figure 6.

We consider two additional scenarios for systems with no cavity detections. One scenario is that no X-ray cavity is present due to the lack of AGNs or jets. If there are no radio jets or the radio jets are too weak to push the hot X-ray gas, cavities may not form. As a possible AGN indicator, we investigate the presence of an X-ray point source at the center of each object. We found a central X-ray point source for 33 out of 69 cavity-detected targets (48%) and 33 out of 64 targets with no cavity detection (52%), respectively, suggesting that the X-ray AGN fraction is similar between targets with/without cavities. In the case of the cavity-detected targets without X-ray AGNs, it is possible that the AGN is currently very weak or inactive while the black hole was active in the past. In the case of no cavity targets with X-ray AGNs, the AGN may not have strong jets to form cavities, or cavities are present, but not detected due to the detection issues (i.e., asymmetric distribution or over-subtraction). A detailed investigation of the relationship between AGNs and the presence of cavities is beyond the scope of our current work.

Another possibility is that the radio jet was just launched or launched a long time ago. If the radio jet is just launched, cavities may be too small to resolve in the X-ray images. If the radio jet launched a long time ago, the X-ray cavities may have already moved beyond the edge of the diffuse X-ray emission (see Section 5.1)

To check this scenario, one can use multi-frequency radio data. In detecting X-ray cavities directly, high-frequency data with high resolution could reveal small X-ray cavities. However, due to the energy loss through synchrotron emission, there could be no emission at high-frequency if the jet was launched a long time ago. In that case, low-frequency observations might reveal extended features (e.g., Gitti et al. 2010; Giacintucci et al. 2011). With the combination of multi-frequency radio data, one can check for the presence of radio jets at small and large scales. If there is no radio jet, it could mean there was no AGN activity and thus no cavities as well. On the other hand, if there is evidence of radio jets at small or large scales, it could be good evidence to confirm the second scenario. Furthermore, if the radio image shows multiple jets, it enables us to investigate the duty cycle of AGN activity (e.g., Randall et al. 2011; Chon et al. 2012), which means that we can study in detail the period of AGN feedback duty cycle. However, the current lack of multi-frequency radio data for our targets makes such a study not possible in the current paper.

We note that a scaling relation between jet power derived from the cavities and radio luminosity has been found (Bîrzan et al. 2004, 2008; Cavagnolo et al. 2010; O'Sullivan et al. 2011a). In other words, the jet power can be estimated based on radio luminosity and used to predict the presence of X-ray cavities. Thus, this may be another way to infer the existence of cavities when they cannot be directly detected in X-ray images.

In Figure 12, we present a distribution of the orientation angle of the cavities with respect to the center (or jet direction). We define the orientation angle 0° if the cavity is radially elongated (along with the jet direction; e.g., Cygnus A and Hydra A), while 90° means that the cavity is elongated perpendicular to the jet direction (e.g., NGC 4552 and HCG 62). Here, we only take the targets with a/b ratios over 1.1 or under 0.9 to avoid a systematic uncertainty from a circular shape cavity. We find a bimodal distribution that cavities are elongated either parallel to the jet direction or perpendicular to the jet direction, suggesting no significant trend with respect to the jet direction. Note that since we did not fit the cavity with an ellipse model, and determined a representative model by visual inspection, the uncertainty of the direction of the elongation is relatively large.

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While various simulation results showed different orientations (Sijacki & Springel 2006; Brüggen et al. 2007; Sijacki et al. 2007; Dubois et al. 2010; Gaspari et al. 2011; Li & Bryan 2014), a recent study by Guo (2015) investigated the orientation of cavities with various input physical parameters, suggesting that radial elongation increases with jet density, velocity, and duration, while it decreases with jet energy density and radius, implying that the morphology of the cavities is closely related to the jet properties.

In this section, we compare our cavity detections with previous studies. First, we used the initial sample of ∼800 targets, for which we obtained evidence for diffuse X-ray emission and performed a detailed X-ray count analysis (see Section 2), to find whether X-ray cavities were previously detected by other studies. By searching a number of papers cited for each target, we find that 116 out of ∼800 targets were reported to possess X-ray cavities in the literature.

Among these 116 targets, 69 targets have Chandra images with sufficient X-ray photons (i.e., larger than four counts per pixel at the six to seven pixel annulus; see Section 2), while the X-ray image of the other 47 targets does not have sufficient photons, hence we did not perform the detailed analysis for these targets. The X-ray cavities of these 69 targets were identified by a number of works (e.g., Bîrzan et al. 2004; Dunn et al. 2005; Dunn & Fabian 2006; Rafferty et al. 2006; Diehl et al. 2008; Cavagnolo et al. 2010; Giacintucci et al. 2011; Bîrzan et al. 2012; Hlavacek-Larrondo et al. 2012; Russell et al. 2013; Panagoulia et al. 2014). When we compare them with our work, we find that we independently detected cavities from 47 of these targets. We did not detect X-ray cavities in 22 other targets that were previously claimed to contain X-ray cavities. Since over-subtraction is shown in these targets, we classified them as no-cavity detections (see Figure 4). For these more complex objects, additional information such as radio flux and morphology may help to confirm the existence of the cavities. Note that the presence of X-ray cavities have been confirmed using radio data (e.g., IRAS 09104+4109, O'Sullivan et al. 2012; NGC 4261, O'Sullivan et al. 2011b; Abell 2029, Clarke et al. 2004; and Hercules A, Nulsen et al. 2005a). However, to be consistent with other over-subtraction targets, we left them as no-cavity detections based on X-ray data only.

For the other 47 targets out of the 116 objects, X-ray cavities were also reported in the literature (e.g., Rafferty et al. 2006; Cavagnolo et al. 2010; Dong et al. 2010; Hodges-Kluck et al. 2010a, 2010b; Lal et al. 2010; Machacek et al. 2010; O'Sullivan et al. 2010; Bîrzan et al. 2012; Panagoulia et al. 2014; Hlavacek-Larrondo et al. 2015). In our analysis, however, these targets were excluded from the detailed β-modeling and further analysis since the X-ray images did not satisfy the criterion of having sufficient photons. For example, Panagoulia et al. (2014) investigated a sample of 49 objects, finding X-ray cavities from 30 targets, while only 28 targets among their 49 objects were included in our analysis based on the photon count criterion. As described in Section 2, we note that photon count is the most important parameter for detecting X-ray cavities in our analysis, thus deeper X-ray images are required for confirming cavities in these targets.

In our analysis of the total sample of 133 targets with sufficient X-ray photons, we detected X-ray cavities for 69 objects. While 47 objects among them were previously reported to have X-ray cavities, we found new X-ray cavities for 22 additional objects for the first time. In particular, 5 targets out of these 22 objects were studied by previous works; however, no X-ray cavities were identified. They are namely, AWM 7 (Dunn & Fabian 2006; Bîrzan et al. 2012), EXO 0423.4-0840, RXC J1504.1-0248 (Bîrzan et al. 2012), and Abell 2626 (Panagoulia et al. 2014). One of the reasons why we were able to detect cavities in these objects is that we used deeper X-ray images by combining individual exposures, which is the case for four targets. For the other object, RXCJ 1504.1-0248, though the same X-ray data were used for both our and previous works, we used the β-modeling while the previous works used raw images and an unsharp masking method (except for Dong et al. 2010). Thus, the difference of the depth of the X-ray images and the analysis method seems to explain the discrepancy.

We find that the number of detected cavities for a given target is sometimes different from that of previous studies, presumably due to the use of different analysis methods. For example, we detected three cavities in NGC 5044 and NGC 1316, respectively, while David et al. (2009) detected four cavities in NGC 5044 and Lanz et al. (2010) found only one cavity in NGC 1316. Forman et al. (2007) and Wise et al. (2007) also detected cavities from Hydra A and M87, respectively, but the number of detected cavities in their studies is different from that of this work. In those studies, radio data were additionally used to confirm the presence of cavities, that were not classified as cavities with the X-ray data alone in our study, suggesting that our analysis and measurements of cavity properties are limited. A more statistical investigation of the various X-ray studies for cavities is beyond the scope of this paper.

We have compared the properties of the cavities detected in our study with those in the literature for a consistency check. For this exercise, we used three studies (Dong et al. 2010; Hlavacek-Larrondo et al. 2012; Panagoulia et al. 2014) since they provide cavity size as well as X-ray images, enabling us to cross-match the cavities detected in our study. We found 44 cavities in 24 targets that are common to these other studies. Among these targets, 9 cavities are detected by both Dong et al. (2010) and Panagoulia et al. (2014). By comparing the size of these 44 cavities in Figure 13, we find that the cavity size is similar to that of previous works within 0.07 dex. Compared to the scatter (0.17 dex), our measurements show a good agreement with those in the previous work. When we divided the cavities into two categories: cavities detected from raw images (open) and based on the β-modeling (filled), we do not find any significant difference in comparison. The solid vertical lines between black and red symbols show the nine overlappng cavities between Dong et al. (2010) and Panagoulia et al. (2014). The mean difference of this subsample between two previous works is 0.06 dex, implying negligible difference. Note that the sample of Hlavacek-Larrondo et al. (2012) seems to show the largest offset (0.15 dex) among the three works, while the difference is still smaller than the overall scatter (0.17 dex), suggesting that cavity size measurements are relatively consistent among various works.

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