A CHANDRA–VLA INVESTIGATION OF THE X-RAY CAVITY SYSTEM AND RADIO MINI-HALO IN THE GALAXY CLUSTER RBS 797

RBS 797 was observed with the Chandra Advanced CCD Imaging Spectrometer I (ACIS-I) on 2000 October 20 (ObsID 2202), for a total exposure of 13.3 ks (Schindler et al. 2001). On 2007 July 9 (ObsID 7902), a new 38.3 ks was acquired with ACIS-S in imaging mode, operating at the focal plane temperature of −120° C. The two Chandra exposures were combined for our analysis, giving a total of 51.6 ks of uncleaned exposure time.

Data were reprocessed with CIAO 4.2, using CALDB 4.2.0 and corrected for known time-dependent gain problems following techniques similar to those described in the Chandra analysis threads.⁸ Screening of the event files was applied to filter out strong background flares. Blank-sky background files, filtered in the same manner as in the RBS 797 image and normalized to the count rate of the source image in the 10–12 keV band, were used for background subtraction. The final exposure time is ∼49.6 ks.

For both chips, point sources have been identified and removed using the CIAO task WAVDETECT. The "holes" left by the discarded point sources are re-filled, for imaging purposes only, by values interpolated from surrounding background regions using the task dmfilth. Images, instrument maps, and exposure maps were created in the 0.5–7.0 keV band. Data with energies above 7.0 keV and below 0.5 keV were excluded in order to prevent background contamination and uncertainties in the ACIS calibration, respectively.

The existing VLA⁹ data for the radio source RBS 797 at 300, 1400, 4800, and 8400 MHz have already been presented and discussed in Gitti et al. (2006), Bîrzan et al. (2008), and Cavagnolo et al. (2011). Here, we present new observations at 1.4 GHz performed in 2006 December with the VLA in C-array, a configuration that was not used in previous observations. The data were acquired in channels centered at 1465 and 1385 MHz, with a 50 MHz bandwidth, for a total integration time of 5 hr. In these observations, the source 3C 48 (0137+331) is used as the primary flux density calibrator, while the source 1044+809 is used as secondary phase calibrator. We have also performed a re-analysis of the archival 1.4 GHz data in A- and B-array, and then have added them together with the new 1.4 GHz data in C-array to produce a total, combined 1.4 GHz image.

Data reduction was done using the NRAO AIPS (Astronomical Image Processing System) package. Accurate editing of the UV data was applied to identify and remove bad data. Images were produced by following the standard procedures: Calibration, Fourier-Transform, Clean, and Restore. Self-calibration was applied to remove residual phase variations. The final images, produced using the AIPS task IMAGR, show the contours of the total intensity.

The pronounced central surface brightness peak (discussed below in this section) and the presence of strong O[II]λ3727 line, and weak, narrow Hβ and O[III]λλ4959/5007 emission lines (Schindler et al. 2001) indicate the presence of a central AGN recognized by Schindler et al. (2001). In order to avoid contamination by the central source, we exclude it in the spectral analysis (Section 4).

The raw ACIS-S image of RBS 797 in the 0.5–7 keV energy band is shown in the left panel of Figure 1. We confirm the presence of two central X-ray deficient lobes already discovered with the existing Chandra observations of RBS 797 (Schindler et al. 2001; Cavagnolo et al. 2011). These two striking features are ∼10 arcsec apart in an NE–SW orientation (Figure 1). The physical properties of the cavities are discussed in Section 6.1. The cavity system in RBS 797 is surrounded by bright rims. One possible explanation for the presence of these strong features is that the expansion of the 1.4 GHz radio lobes displaced the ICM formerly in the cavities, compressing it to form the bright rims that now surround the cavities (as seen in the right panel of Figure 1). In particular, the rims of the SW cavity appear to have a stronger contrast than the NE cavity rims, almost totally enclosing the SW cavity, while the NE rims seem to be more open and less bright. Beyond the cavities and rims, the cluster morphology is elliptical in shape.

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These details are more evident in the Chandra unsharp masked image (Figure 1, right panel), which is created with an image reprocessing technique aimed at emphasizing possible substructures and faint features. We also note in the unsharp masked image that the cavity system appears to be surrounded by two edges, with the inner edge extending ∼8''–10'' from the core. An outer edge is also visible at ∼14''–17''. These features appear as edges in the surface brightness profile at ∼8'' and ∼20'' (see below). Taking into account these peculiarities, RBS 797 appears to be very similar to NGC 5813 (Randall et al. 2011), in which are observed distinct cavity systems due to multiple AGN outbursts. Also in RBS 797, as in NGC 5813, the edges seen in the Chandra X-ray image may be identified as weak shocks (for a further discussion about shocks see Section 3.3.3 in Cavagnolo et al. 2011). These shocks could be produced by distinct AGN outbursts, with the inner edge associated with the NE–SW inner cavities, and the outer edge associated with possible outer cavities.

We also performed a study of the surface brightness profile of RBS 797 by means of the Chandra ACIS-S data. An azimuthally averaged surface brightness profile was computed over the range 0.5–2.0 keV with the task dmextract by subtracting the background from the point-source-removed image and then dividing by the exposure map.

In particular, we considered 360° annular bins of 1'' width, starting from 2'' up to 150''. Since there is clear evidence of ICM/AGN interaction in the central region of RBS 797, we excluded the cavity system and the rims (see Figure 2) in order to get a profile of the so-called "undisturbed" ICM. This surface brightness profile was fitted with a single β-model (Cavaliere & Fusco-Femiano 1976) using the tool SHERPA with the χ² statistics with Gehrels' variance. A fit over the external 25''–110'' interval, which excludes the whole cooling region (green line in Figure 3), shows evidence of a central excess of the observed profile with respect to the β-model (Figure 3). This evident deviation from the fit prediction is a strong indication of the presence of a cool core in RBS 797, as seen in many other cool core clusters (Fabian 1994). We then fitted the surface brightness profile of the undisturbed cluster with a double β-model, finding that it is able to provide a better description of the entire profile (χ²_red ∼ 0.96 for 142 dof). The best-fit values for the double β-model (assuming a common β value) are core radii r_c(1) = 347 ± 028 and r_c(2) = 1289 ± 113, central surface brightness S₀(1) = 1.15 ± 0.06 × 10⁻⁶ and S₀(2) = 2.21 ± 0.50 × 10⁻⁷, and slope parameters β(1) = 0.6044 ± 0.0543 and β(2) = 0.6332 ± 0.0194.

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For a comparison of the surface brightness profile along the cavities with the azimuthally averaged profile, we considered two sectors along the cavity directions, chosen to be tangent to the cavities (Figure 2, in red). Figure 3 also shows the two profiles along the cavities compared separately with the azimuthally averaged profile. We found a clear drop in the radial range between 2'' and 7'' in both the surface brightness profiles along the cavities compared to the azimuthally averaged profile. These distances clearly correspond to the two X-ray deficient lobes, thus giving us a very good indication for the estimate of the cavity dimensions (see Section 6.1).

RBS 797 is known to possess a unique radio source that exhibits large changes in orientation with scale. The subarcsec resolution radio image first presented by Gitti et al. (2006) shows the details of the innermost 4.8 GHz radio jets, which clearly point in a north–south direction. Remarkably, these inner jets are almost perpendicular to the axis of the 1.4 GHz emission detected at ∼1 arcsec resolution (A-array), which is elongated in the northeast–southwest direction, filling the X-ray cavities (see Figure 4 of Gitti et al. 2006). The ∼4 arcsec resolution VLA image at 1.4 GHz (B-array) shows large-scale radio emission with amorphous morphology, slightly extended in the north–south direction (see Figure 2 of Gitti et al. 2006).

Figure 4 (left panel) shows the radio map of RBS 797 observed at 1.4 GHz with the VLA in C-array configuration, with a restoring beam of 183 × 122. At this low resolution, the source is barely resolved, showing an amorphous morphology apparently extending to the north (an unrelated source is present to the east). The source has a total flux density of ≃ 23.0  ±  0.3 mJy. In order to fully exploit the relative advantages in terms of angular resolution and sensitivity of the three VLA configurations used for the observations at 1.4 GHz, we have combined this new set of data taken with the C-array with the archival data from the A- and B-array. The total 1.4 GHz radio map, with a circular restoring beam of 3'', is shown in Figure 4 (right panel). This combined image is able to reveal the morphology of the radio source in the central ∼10 kpc, showing its elongation in the cavity direction, without losing flux at the larger scales. In particular, the radio emission is detected out to ∼90 kpc. The total flux density is ≃ 24.0 ± 0.3 mJy.

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In order to estimate the flux density of the diffuse radio emission, it is necessary to subtract the emission contributed by the central nuclear source. One way is to consider the high-resolution map. The central component imaged by the A-array observations (see Figure 2 of Gitti et al. 2006) is found to consist of a resolved core elongated in the northeast–southwest direction, plus a jet-like feature emanating from the center to the west. The total flux density coming from the central region (inner jets included) was measured by Gitti et al. (2006) as ≃ 12.1  ±  0.1 mJy. Another way is to estimate the contribution of the central emission directly from the new combined image presented here (Figure 4, right panel). In this map, the flux density of the unresolved core is ≃ 12.9 ± 0.1 mJy. The slight difference between the two estimates may be due to the contribution of the short baselines in the combined image with respect to the image in A-array only. To be conservative, we decided to adopt the mean of the two flux densities measured above. We thus estimate that the discrete radio source located at the cluster center has a 1.4 GHz flux density of ≃ 12.5  ±  0.5 mJy, where the errors include the minimum and maximum variation of such an estimate based on our analysis. By subtracting this from the total flux density of the 1.4 GHz emission, we measure a diffuse radio emission of ≃ 11.5 ± 0.6 mJy. The more drastic approach of subtracting the total flux density measured in A-array (17.9 ± 0.2 mJy; Gitti et al. 2006), i.e., the entire radio source filling the X-ray cavities, would still leave a residual ≃ 6.1  ±  0.4 mJy of diffuse radio emission. The variety of methods discussed here demonstrates the difficulty of disentangling the relative contribution of the diffuse emission and of the discrete sources in the total observed radio emission. The nature of the large-scale radio emission, and its possible origin, will be discussed in Section 6.4.

A projected radial profile was computed using 10 concentric annuli centered on the cluster core. The radii were selected in order to obtain sufficient counts to constrain the temperature to at least ∼20% accuracy in each annulus (except the outermost annulus, see Table 1 for details). The only parameters free to vary in this wabs*apec model are the metallicity Z, and the temperature kT. Spectra were fitted in the range 0.5–7.0 keV. The best-fitting parameters and relative errors are listed in Table 1. The measured temperature and metallicity profiles are shown in Figure 5 (upper panels). The temperature values in the outer two annuli are surprisingly high and do not show the decline in the outskirt of the cluster. To test the reliability of these measurements, we adopted as a different background spectrum that extracted in a circular annulus in the outer regions of the two CCDs, finding similar results.

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There is an indication of a discontinuity in the projected temperature profile (upper left panel of Figure 5) between the bins 10''–12'' and 12''–16'', which correspond to the region of the rims just outside the cavities. The limited statistics and the edge of the ACIS-I chip do not allow us to measure the behavior of the temperature profile beyond 125''. Therefore, we are not able to observe the decline of the temperature typically observed at larger radii in relaxed clusters (Vikhlinin et al. 2005).

The metallicity profile of RBS 797 (central panel of Figure 2) shows a hint of gradient, with an average abundance of ∼0.4 Z_☉. A more detailed analysis of the azimuthally averaged metallicity profile is not possible due to the large uncertainties.

Because of the projection effects, the spectral properties at any point in the cluster are the emission-weighted superposition of radiation originating at all points along the line of sight through the cluster. To correct for this effect, we performed a deprojection analysis by adopting the XSPEC projct model. We thus fit the spectra extracted in the same ten 360° concentric annular regions adopted for the projected temperature profile (see Section 4.1) with a projct*wabs*apec model. Temperature, abundance, and normalization values are free to vary, while the density column and the redshift are frozen at the same values adopted for the wabs*apec model.

Results of the deprojection analysis are listed in Table 2. We note that the deprojection analysis increases the error bars without producing significant changes in the global profile shapes. In particular, the metallicity measurement is strongly limited by poor statistics. Therefore, in the following discussion we adopt the projected values of metallicity.

We also derived the density profile by deprojecting the surface brightness profile (see Ettori et al. 2002 for details of the method), obtaining a typical profile of a cool core cluster (Figure 5, lower panel). This is in agreement with the density profile derived from the spectral deprojection analysis (Table 2).

The comparison between the X-ray luminosity of the ICM within the cooling radius and the cavity power provides us with an estimate of the balance between the energy losses of the ICM by the X-ray emission and the cavity heating (Bîrzan et al. 2004; Rafferty et al. 2006). The bolometric X-ray luminosity inside the cooling region is estimated from a spectral deprojection analysis as L_{X, cool} = 1.33 × 10⁴⁵ erg s⁻¹, consistent with the estimate of Rafferty et al. (2006).

The power of the cavities P_cav is given by the ratio of the cavity energy and the cavity age. The energy required to create a cavity with pressure p and volume V is the sum of the pV work done by the jet to displace the X-ray emitting gas while it inflates the radio lobes, and the internal energy E of the cavity system. This quantity is the enthalpy defined as

$$\begin{equation} E_{\rm cav} = H = E + pV = \frac{\gamma }{\gamma - 1} pV, \end{equation} \tag{ 2 }$$

where γ = 4/3 for relativistic plasma. Pressure and volume can be estimated directly by X-ray observations through measurements of the cavity size and of the temperature and density of the surrounding ICM. A potential issue is the uncertainty in determinations of the cavity volumes. The cavity size is usually estimated through a visual inspection of the X-ray images. This method is therefore dependent on the quality of the X-ray data and is also prone to systematic error. Furthermore, projection affects the determination of the actual spatial geometry of the cavity system. The cavity size and geometry measured by different observers may vary significantly depending on the approach adopted, leading to differences between estimates of up to a factor of a few in pV (e.g., Gitti et al. 2010; O'Sullivan et al. 2011; Cavagnolo et al. 2011). Here, we estimate the cavity size from the surface brightness profile of the central region of the cluster. From the decrement of the surface brightness observed within the two X-ray deficient regions containing the lobes (Figure 3), we estimated the extent of the major axis of the two ellipses. The surface brightness in the directions of the cavities clearly falls below that of the undisturbed cluster within the ∼2''–7'' radius.

For the estimate of the ICM pressure (p ≃ 1.92n_ekT) surrounding the cavities, we considered the electron density and temperature within the bin 4''–6'' in the cluster profiles (upper and lower panels of Figure 5). We calculated that the total enthalpy of the cavity system is E_cav = 1.68 × 10⁶⁰ erg. For the estimate of the cavity age, we adopted the sound crossing time, defined as t_sound ≈ R/c_s, where R is the distance of the center of the cavity from the central radio source and c_s is the sound speed. Finally, we find the total cavity power of P_cav = 2.49 × 10⁴⁵ erg s⁻¹. The cavity properties are listed in Table 3.

Although we estimate slightly smaller cavity volumes and we adopt a different assumption for the cavity age (sound crossing time instead of buoyancy time), we find values of energy and power of the cavities consistent with those of the configuration-I in Cavagnolo et al. (2011).

Hydrodynamic simulations (e.g., Brüggen 2002; Roediger et al. 2007; Mathews & Brighenti 2008) predicted that in cool core clusters with a cavity system, the ICM in the core is stirred. Jets from the central source in clusters of galaxies can contribute both to quench the deposition of cold gas and to induce motions affecting the metallicity profile. Moreover, Gaspari et al. (2011a, 2011b) show new detailed models of AGN-injected jets which uplift the metal-enriched gas in the core by feedback cycles. These are split in two phases during the outburst; initially, the gas with higher abundance lies asymmetrically along the jet axis, followed by a phase of turbulence and mixing. Gaspari et al. (2011a, 2011b) estimate that the maximum distance along the cavity axis at which the enriched gas could be spread is ∼40 kpc, and that the contrast of the iron abundance in the cavity directions with that in the rest of the ICM is ∼0.1–0.2.

In RBS 797, we find differences in the iron abundance distribution, depending on direction. We considered four sectors delimited by a variable outer radius starting from the same 15 inner radius (see Figure 7). In our analysis, we consider the N and the S sectors as unperturbed, since they enclose only the regions of the cluster in which the ICM distribution does not show special features such as the cavities. The first analysis is performed in the annulus from 15 to 12'', while the second outer radius was set at 15'' and the last at 30''. As for the study of the azimuthally averaged temperature profile, the temperature, abundance, and normalization were left free to vary, while redshift and gas column density were fixed to the same values previously used in Section 4.1. Spectra were fitted with a single plasma model for a collisionally ionized diffuse gas.

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The results in Table 4 and Figure 8 indicate higher metallicity along the NE and SW cavity directions compared to the unperturbed N sector in all the three annuli (at 1σ error). In the biggest annulus (15–30''), the NE sector shows higher abundance compared to both the unperturbed N and S regions. Combining spectra from the two cavity sectors in a joint fit and comparing to the results of fitting the two unperturbed sectors supports the relationship between metallicity and direction (see the lower section of Table 4 for details).

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Likely, the AGN outburst may have lifted the cooler, metal-rich gas from the central region to larger radii along the directions of the inflating cavities. We found that, taking into account three different outer radii, the cavity sectors have higher abundances than the unperturbed regions, at 1σ confidence. So, this behavior also persists at larger radii and not only nearby the cavity system. This effect has been found in other systems (e.g., M87, Simionescu et al. 2008; Hydra A, Kirkpatrick et al. 2009, Simionescu et al. 2009b; NGC 5813, Randall et al. 2011). In particular, recent work by Kirkpatrick et al. 2011 shows a correlation between jets and metallicity.

In Section 6.2, we described the analysis of the azimuthal variations of the ICM properties. Here, we want to perform a more detailed analysis of the projected temperature in the cavities and in the surrounding gas. We extracted the spectra separately in both the cavities, and in each sector surrounding a single cavity (clearly excluding the cavities). Spectra were then fitted with the model wabs*apec in XSPEC, with the temperature and abundance as free parameters and column density set at the Galactic value. Considering the regions of Figure 9, in the cavities we found projected temperatures (1σ errors) of kT_cavNE = 5.86^+0.91_−0.79 keV for the NE cavity and kT_cavSW = 5.71^+0.92_−0.72 keV for the SW cavity. These have been compared with the kT_gasNE = 4.62^+0.24_−0.23 keV and kT_gasSW = 5.08^+0.25_−0.24 keV, respectively, the values for the gas surrounding the NE and the SW cavities. Since these results do not provide definite constraints due to the low statistics of the selected regions, we tried to combine together the two cavities and compare them to the combined spectra of the external gas. The results of the joint fits give an indication for hotter cavities: kT_gas = 4.84^+0.17_−0.17 keV and in the cavities kT_cav = 5.27^+0.59_−0.40 keV.

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We performed an additional test by means of a "softness ratio" (SR), which is defined as SR = (S − H)/(S + H), where S and H are the count rates in the soft and in the hard band, respectively. After extracting the surface brightness profile in the cavity system and in the external gas, both in the X-ray soft (0.5–2.0 keV) and hard (2.0–7.0 keV) energy band, we compared their SRs. The SR method can be used as an indicator of the temperature, since higher SR values would imply the prevalence of the soft emission, thus lower projected temperatures. We found that the regions surrounding the cavities have an SR slightly higher than that of the cavities: SR_cav = 0.5468  ±  0.0216, SR_gas = 0.5747  ±  0.0093. This means that the relative quantity of soft photons is higher in the outer gas, indicating that the cavities are hotter than the surrounding ICM.

Finally, we made a further attempt to compare the projected temperature within the cavities with that of the gas in the other directions. We considered four sectors, two along the cavity directions and two in the perpendicular unperturbed regions, excluding the cavity rims from the selection. Based on the unsharp masked image (right panel of Figure 1), we divided the NE and the SW sectors in three annuli tangent to the inner and outer edge of the cavities (Figure 10). The first bin goes from the center of the cluster to the beginning of the cavity (0''–27 for the NE and 0''–19 for the SW directions, (a) sectors in Figure 10), the second embodies the whole cavities (27–81 for NE and 19–73 for SW, (b) sectors in Figure 10) and the last includes the rims (81–11'' for NE and 73–11'' for SW, (c) sectors in Figure 10). SRs for these regions are listed in Table 5. In Figure 11, we compare the SR of the unperturbed sectors with the values of the NE cavity sector (left panel) and with the SW cavity region (right panel). Looking at the second bin in both the plots of Figure 11, we find further support for the indication that the gas in the cavities of RBS 797 is hotter than the surrounding ICM, as previously found in other clusters of galaxies such as 2A 0335+096 (Mazzotta et al. 2003), MS 0735+7421 (Gitti et al. 2007a), and M87 (Million et al. 2010).

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Table 5. Softness Ratio

	Bin	$\frac{S-H}{S+H}$
		Cavity NE	Cavity SW
	(a)	0.1522 ± 0.0420	0.3561 ± 0.0628
Cavities	(b)	0.5695 ± 0.0266	0.5349 ± 0.0233
	(c)	0.4915 ± 0.0335	0.5461 ± 0.0232
	(a)	0.4028 ± 0.0297	0.2203 ± 0.0444
No-cavities	(b)	0.5948 ± 0.0141	0.6007 ± 0.0138
	(c)	0.5139 ± 0.0255	0.5242 ± 0.0219

Notes. Values of the softness ratio calculated in each annulus. The considered bins (values (a), (b), (c)) are different for the two cavities and are better visualized in Figure 10.

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Despite our detailed study of the cavities and surroundings temperatures, what we found here may only be a projection effect. The hotter gas along our line of sight through the cavities could have a greater impact on the spectra of the cavities than on those of the brighter gas surrounding them (the rims), making the cavities to appear hotter. Furthermore, the cavities are likely to be regions from which the (cooler) X-ray emitting gas has been pushed out, so a larger fraction of the emission along our line of sight may be coming from the projected hotter gas at larger radii. We performed a further test in order to investigate whether the X-ray emission of the cavities along our line of sight is due exclusively to the outer gas emission, or not. From the surface brightness and density profiles (Figure 3 and the lower panel of Figure 5, respectively), we found an average density of ∼0.075 cm⁻³ and a counts estimate of ∼5.4 counts s⁻¹ arcmin⁻² in the annular region containing the cavities. Therefore, at the ambient density and temperature, we expect to have ∼119 counts s⁻¹ with ACIS-S3 chip in the 0.5–7.0 keV energy band, with the apec normalization (K_apec) set to unity. Considering a spherical volume approximately equal to the volume of the cavities and solving the equation for the apec normalization, we estimated K_apec ≃ 4.78 × 10⁻⁵. From this spherical volume of unperturbed gas located at the cavity position, we would thus measure an emission of ∼1.04 counts s⁻¹ arcmin⁻² that, with the exposure time of the ACIS-S3 observation (t_{exp, S3} ≃ 36 ks), is equivalent to ∼206 counts. We considered several regions outside the cavity directions having the same cavity area and located at the same distance from the center, and we estimated the average number of counts from the 0.5–7.0 keV image. We found that the difference between the average number of counts within these regions (∼1140) and the average number of counts inside the cavities (∼766) exceeds the number of counts originating from the estimated contribution of the unperturbed gas inside the cavities. As a zero-order test, this indicates that there is no emission related to the cavities, so that they can be considered devoid of X-ray emitting gas. Unfortunately, the poor statistics did not allow us to test this hypothesis with some more complicated spectral models, such as deprojection analysis.

The radio properties of RBS 797 presented in Section 3.2 are consistent with a scenario of three distinct outbursts, with the jet axis precessing ∼90° between outbursts, with a period of ∼10⁷ yr. The X-ray observations show features that are consistent with this picture: the northeast–southwest inner cavities and the elliptical inner edge revealed by the Chandra images (Figure 1) could be associated with the intermediate outburst; the outer edge shown by Chandra (Figure 1) could be associated with the oldest outburst. Alternatively, the observed change in the orientation of the radio axis, most evident between the inner 4.8 GHz jets and the 1.4 GHz emission filling the cavities (black and green contours in Figure 12, right panel, see also Figure 4 of Gitti et al. 2006), may be due to jet deflection. Jet deflection is caused either by ICM pressure gradients or by dense regions of cold gas that may have been ionized by massive stars born in a starburst triggered by the CF (e.g., Salomé & Combes 2003). The existing data do not allow us to discriminate between these two possibilities.

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On the other hand, the fact that the total size of the large-scale radio emission is comparable to that of the cooling region suggests a different interpretation, which would be consistent with either jet precession or jet deflection: that RBS 797 hosts a diffuse radio mini-halo. Mini-halos are diffuse radio sources, extended on a smaller scale (up to ∼500 kpc), surrounding a dominant radio galaxy at the cluster center. They are generally only observed in cool core clusters and it has been found that these sources are not connected to ongoing cluster major merger activity. Their radio emission is indicative of the presence of diffuse relativistic particles and magnetic fields in the ICM, since these sources do not appear as extended lobes maintained by an AGN, as in classical radio galaxies (Giovannini & Feretti 2002). In particular, due to the fact that the radiative lifetime of radio-emitting electrons (∼10⁸ yr) is much shorter than any reasonable transport time over the cluster scale, the relativistic electrons responsible for the extended radio emission from mini-halos need to be continuously re-energized by various mechanisms associated with turbulence in the ICM (reaccelerated primary electrons), or freshly injected on a cluster-wide scale (e.g., as a result of the decay of charged pions produced in hadronic collisions, secondary electrons).

Gitti et al. (2002) developed a theoretical model which accounts for the origin of radio mini-halos as related to electron reacceleration by MHD turbulence in CFs. In this model, the necessary energetics to power radio mini-halos is supplied by CFs themselves, through the compressional work done on the ICM and the frozen-in magnetic field. This supports a direct connection between CFs and radio mini-halos. Although secondary electron models have been proposed to explain the presence of their persistent, diffuse radio emission on large scale in the ICM (e.g., Pfrommer & Enßlin 2004; Keshet & Loeb 2010), the observed trend between the radio power of mini-halos and the maximum power of CFs (Figure 13) has given support to a primary origin of the relativistic electrons radiating in radio mini-halos, favored also by the successful, detailed application of the model of Gitti et al. (2002) to two cool core clusters (Perseus and A 2626; Gitti et al. 2004) and by recent statistical studies (Cassano et al. 2008). However, the origin of the turbulence necessary to trigger the electron reacceleration is still debated. The signatures of minor dynamical activity have recently been detected in some mini-halo clusters, thus suggesting that additional or alternative turbulent energy for the reacceleration may be provided by minor mergers (Gitti et al. 2007b; Cassano et al. 2008) and related gas sloshing mechanism in cool core clusters (Mazzotta & Giacintucci 2008; ZuHone et al. 2011). Given the prevalence of mini-halos in clusters with X-ray cavities, another attractive possibility is that the turbulent energy is provided by a small fraction of the energy released by the lobes rising from the central AGN (as suggested by Cassano et al. 2008).

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We can test qualitatively the consistency of the observational X-ray and radio properties of RBS 797, with the trend between the radio power on the mini-halos and the maximum power of the CFs expected by the reacceleration model. This has been observed in a first sample of mini-halos selected by Gitti et al. (2004), who found that the strongest radio mini-halos are associated with the most powerful CFs. In Figure 13, we show with a red triangle the radio power at 1.4 GHz of the diffuse emission (in terms of integrated radio luminosity νP_ν) versus the maximum power of the CF $P_{\rm CF} = \dot{M} k T/\mu m_{\rm p}$ (here, $\dot{M}$ is the mass accretion rate, k is the Boltzmann constant, T is the global ICM temperature, μ ≈ 0.61 is the molecular weight, and m_p is the proton mass) in RBS 797, overlaid onto the values measured for the mini-halo clusters known so far. The monochromatic radio power at the frequency ν is calculated as

$$\begin{equation} P_{\nu }=4 \pi \, D_{\rm L}^2 \, S_{\nu } \, (1+z)^{-(\alpha +1)}, \end{equation} \tag{ 3 }$$

where D_L is the luminosity distance, S_ν is the flux density at the frequency ν, and (1 + z)^{−(α + 1)} is the K-correction term (Petrosian & Dickey 1973), which in the case of RBS 797 is negligible (α ∼ −1; Gitti et al. 2006). The radio spectral index α is defined so that S_ν∝ν^−α. From the flux density measured in Section 3.2, we estimate a radio mini-halo power of P_1.4GHz = (5.2 ± 0.2) × 10²⁴ W Hz⁻¹. From the global cluster temperature derived in Section 4 and the mass accretion rate $\dot{M}$ derived in Section 5, which are measured consistently with the methods adopted for the other objects in Figure 13,¹⁰ we estimate P_CF = 1.55^+2.12_−1.53 × 10⁴⁴ erg s⁻¹ (errors at 90% confidence level). Despite its large error bar, we can say that RBS 797 agrees with the observed trend, thus indicating that its diffuse radio emission can be classified as a radio mini-halo.

On the other hand, we stress that the classification of a radio source as a mini-halo is not trivial: their detection is complicated by the fact that the diffuse, low surface brightness emission needs to be separated from the strong radio emission of the central radio galaxy. Furthermore, the criteria adopted to define mini-halos are somewhat arbitrary (e.g., total size, morphology, presence of cool core) and some identifications are still controversial.