TRACING MULTIPLE GENERATIONS OF ACTIVE GALACTIC NUCLEUS FEEDBACK IN THE CORE OF ABELL 262

VLA radio observations of B2 0149+35 were taken at frequencies around 1400 and 330 MHz with the VLA in A configuration. At 330 MHz these observations (obtained 2003 July 27) provide a resolution of ∼6'', while at 1400 MHz (obtained 2000 December 19) the resolutions is ∼15. The source 3C48 was observed as a calibrator for the 330 MHz observations and was used for bandpass, flux, and phase calibration of the target. The 330 MHz data were obtained in spectral line mode to permit excision of radio frequency interference (RFI) and avoid problems of bandwidth smearing. The 1400 MHz A configuration data were taken in the continuum mode and used 3C147 as a flux calibrator and 0201+365 as a phase calibrator. These observations were supplemented by VLA archival observations at 1400 MHz from B and C configurations (taken in 2005 April 16 and 1997 September 18, respectively) to provide sensitivity to extended low surface brightness emission. The B configuration 1400 MHz data was taken in the spectral line mode and used 3C48 as bandpass, flux, and phase calibrator. The C configuration observations were obtained in the continuum mode and used 3C48 as a flux calibrator and 0119+321 as a phase calibrator. Observations at 4500 MHz in the VLA D configuration on 2000 October 1 were also reduced in order to obtain total flux information for the integrated spectrum of the source. These observations were taken in the continuum mode and had 3C286 as a flux calibrator and used 0145+386 as a phase calibrator.

The data were calibrated and reduced with the NRAO Astronomical Image Processing System (AIPS). Images were produced through the standard Fourier transform deconvolution method. All data sets were processed through several loops of imaging and self-calibration to reduce the effects of phase and amplitude errors in the data. Frequencies near 1400 MHz and below were reduced using the wide-field imaging capabilities within the AIPS task IMAGR. The two frequencies near 330 MHz were combined together to make the final image. Similarly all frequencies and configurations for the 1400 MHz data were combined into the final image.

Abell 262 was observed with the GMRT on 2004 July 24. The observations were taken in the dual frequency mode providing two single polarization (Stokes RR) frequencies near 610 MHz and one single polarization (Stokes LL) frequency near 235 MHz. The 610 MHz observations had a bandwidth of 16 MHz for each frequency resulting in a total bandwidth of 32 MHz and a resolution of ∼6''. The total bandwidth of the 235 MHz data was 8 MHz and the resolution was ∼13''. All data were taken in the spectral line mode to allow RFI excision and reduce problems of bandwidth smearing. At both frequencies we used 3C48 as bandpass, flux, and phase calibrator.

The GMRT data reductions were carried out with AIPS. The GMRT data near 610 MHz were fairly clear of interference while the 235 MHz data required a significant effort to flag the RFI. The calibration followed standard wide-field imaging techniques and both data sets were self-calibrated through several loops of phase and amplitude calibration. The two frequencies near 610 MHz were calibrated and imaged separately and the final combined image was made using the image plane deconvolution task APCLN within AIPS.

Abell 262 was observed by Chandra on 2006 November 20 (ObsID 7921) and 2001 August 3 (ObsID 2215) for 111,934 s and 30,305 s, respectively. For each observation, the center of the cluster was positioned on the back-illuminated ACIS-S3 detector with the events telemetered in very faint (VF) mode and an energy filter of 0.1–13 keV. The cluster centroid was positioned with a 1' offset from the nominal pointing to avoid node boundaries. The "level 1" event files were processed with CIAO version 3.4 following the standard procedure for the VF mode. Only events with ASCA grades 0, 2, 3, 4, and 6 were included. By analyzing light curves of the two back-illuminated detectors (ACIS-S1 and ACIS-S3) throughout the observation period, it was determined that no background flares occurred to contaminate the data. The data were corrected for hot pixels and cosmic-ray afterglows using standard techniques. The resulting cleaned exposure times were 110,674 s and 28,744 s.

A merged image of both pointings (chips ACIS-S2, ACIS-S3, and ACIS-S4) was created by reprojecting the event files of the older ObsID 2215 to the WCS reference frame of our new deeper observations (ObsID 7921). This resulted in a total combined exposure time of 139,418 s. Energy was restricted within the range of 0.3–10.0 keV. Background files were taken from the blank sky observations of M. Markevitch included in the CIAO calibration database (CALDB) and reprojected to match both observations of A262. The background files for both pointings were then merged using ObsID 7921 as a reference. Matching exposure maps were created for each observation and merged in a similar manner.

In Figure 2, we show the VLA B configuration 1400 MHz image of B2 0149+35. The central radio emission contains a compact core connected to a western extension, which may trace the western radio jet. A bright region to the east of the core may be associated with the counterjet, which would suggest an initial position angle of ∼65° (from north to the east) for the jet axis. Beyond the bright central regions the radio emission extends into the western and eastern radio lobes. The outer lobes lie at a different position angle through the core as compared to the bright jet and counterjet. This variation in the source position angle may indicate bulk rotation of the surrounding ICM such as suggested by Gopal-Krishna & Saripalli (1984) for Centaurus A. Numerical simulations of the impact of bulk ICM motions on embedded radio galaxies reveal that such motions can reproduce observed radio galaxy morphologies (Heinz et al. 2006). An alternative explanation for the structure of B2 0149+35 is that the position angle of the radio jets has precessed over time as suggested for clusters such as Perseus (Dunn et al. 2006), RBS797 (Gitti et al. 2006), and Abell 2626 (Wong et al. 2008).

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Blanton et al. (2004) showed that the eastern radio lobe is coincident with the inner eastern cavity seen in the Chandra data. Figure 2 shows that in addition to the S-shaped radio source, there is a compact radio source located ∼17 kpc east of the core of B2 0149+35. This source has no X-ray counterpart and no known optical identification but seems to be located near the eastern edge of a faint optical source on the Second Generation Digitized Sky Survey (DSSII) images. The total radio flux of the compact source at 1400 MHz is 0.67 ± 0.17 mJy. Although the low signal to noise on this source makes the calculation of the spectral index uncertain, we note that it is consistent with that of typical extragalactic sources.

Combining the A, B, and C configuration 1400 MHz data allows us to trace more extended radio emission from B2 1049+35 since these data are sensitive to lower surface brightness emission. Figure 3(a) shows the combined three configuration data set as contours overlaid on the central region of the residual Chandra image. We note the presence of bright X-ray clumps to the northeast and southwest of the radio core at roughly the projected location where the radio jets change position angle. Higher resolution radio data of the jets would help determine if there is a connection between the X-ray clumps and the jet deflection. The entire radio source appears to be fully confined by the bright X-ray rims seen in the residual Chandra image.

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The radio emission shown in Figure 3(a) extends further to the west and northwest of the radio core than is seen by Parma et al. (1986). Beyond the northwest emission there is a further radio extension to the southwest, along the X-ray tunnel. The radio emission appears to be continuous from the core toward the northwest to a distance of ∼34'' (∼11 kpc) at which point it appears to break up into two connected clumps to the southwest within the tunnel. Both clumps reveal extended structure and do not have any optical identifications; thus they are most likely tracing radio plasma ejected from the central AGN in NGC 708. At the lowest contour level (3σ) the western emission does not reveal an obvious sharp edge to the source suggesting that we may not be tracing the full extent of the emission at this frequency. The emission to the east, beyond the counterjet location, fills the inner eastern X-ray cavity and appears to have a relatively well-defined edge.

Lower frequency full-resolution radio observations at 610 MHz from the GMRT highlight again the close confinement of the synchrotron emission by the bright X-ray rims seen in the Chandra image (Figure 3(b)). These new radio data also confirm the presence of extended radio emission tracing the southwest X-ray tunnel and show that the emission extends further down the tunnel at this frequency. They also reveal diffuse emission running from the eastern radio lobe to the region south of the compact radio source. This eastern emission is coincident with the location of the faint ghost cavity mentioned in Blanton et al. (2004) and thus supports the interpretation of this region as an X-ray cavity. The total flux in the eastern extension (excluding the compact source) is 5.3 ± 0.5 mJy.

We have also analyzed the 610 MHz data applying a suitable taper to the uv distribution to produce a map sensitive to the large-scale diffuse emission. The taper was chosen to allow us to match the 131 beam of our lowest frequency observation at 235 MHz. The tapered 610 MHz image (Figure 4(a)) reveals radio emission extending the full length of the tunnel and shows a series of connected clumps of emission running ∼22 kpc eastward (in projection) from the eastern X-ray cavity. These previously unknown radio clumps are coincident with the newly detected extended outer eastern cavity discussed in Section 3. An inspection of the DSS images shows that there are no apparent optical counterparts to the eastern emission regions. The total (projected) linear extent of the radio emission at 610 MHz is ∼60 kpc, more than three times larger than previously reported by Parma et al. (1986). Similar evidence of larger source sizes at low frequencies has been seen in other cluster-center radio sources such as M87 (Owen et al. 2000), Perseus (Fabian et al. 2002), and Hydra A (Lane et al. 2004) where the large outer structures have been interpreted as signatures of one or more past AGN outbursts. The clumpy morphology of the eastern emission and total extent of the radio emission in Abell 262 is also seen in Figure 4(b) where we show the VLA 330 MHz data convolved to the same resolution as the tapered 610 MHz data.

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Our lowest frequency observations at 235 MHz are shown in Figure 4(c). These data also trace the western radio emission over the full length of the X-ray tunnel. On the eastern side of the source, the 235 MHz observations reveal radio emission located well beyond the eastern compact source out to the edge of the 610 MHz extensions seen in Figure 4(a). At the 3σ contour level this emission does not show a continuous connection to B2 0149+35 but this is likely due to the lower sensitivity of the 235 MHz data.

We have made a spectral index map of the central radio source using the 235 and 610 MHz GMRT data. The uv-coverage of both data sets was matched and both frequencies were imaged with a circular 131 × 131 beam. We show this spectral index map in Figure 5 where we have blanked the spectral index map at the 3σ level on each of the input maps. The color bar at the top shows the (linear) spectral index scale running from α = −3.0 to α = −0.4, where S_ν ∝ ν^α. We have overlaid the 610 MHz tapered contours in white in Figure 5 to provide a reference for the source morphology in the locations where we have measured the spectral index. Typical uncertainties in the flux measurements due to calibration and systematic errors at the GMRT are of the order of 5% at 235 and 610 MHz (Lal & Rao 2007), resulting in a typical error on the spectral index of σ_α = 0.2.

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The spectral index in the area of the radio core is fairly flat (α = −0.5) which is typical of recently injected particles. The spectral index toward the western part of the source steepens away from the core reaching a value of α = −1.7 in the region of the X-ray tunnel. The integrated spectral index of the radio emission in the tunnel is α⁶¹⁰₂₃₅ = −1.3 ± 0.2. The origin of the apparent spectral flattening of the emission on the western edge of the tunnel is uncertain and may be a result of low signal to noise at the edge of the 235 MHz image since the apparent steepening is within roughly the 3σ errors on the spectral index map. Toward the eastern edge of the source the spectral index steepens less dramatically away from the core reaching α⁶¹⁰₂₃₅ = −0.9. The region of the eastern radio clumps shows an even steeper spectral index of roughly α⁶¹⁰₂₃₅ = −1.8. Although we cannot use the current data to trace small spectral index variations accurately across the source, we note that the spectral steeping observed from the core toward the outer source edges is significant above the 3σ level and likely traces spectral aging of the relativistic particles as they travel further from the core. We have also made spectral index maps using the 330 MHz and 1400 MHz images and find similar evidence of spectral steepening away from the core in those maps.

The spectral index determined for the full source measured from our observations between 235 and 4535 MHz is α = −0.90 ± 0.16, where we have assumed an uncertainty of 5% on the GMRT 235 MHz flux, and 1% on the VLA 4535 MHz flux. Assuming a similar flux uncertainty of 5% on the GMRT 610 MHz observations we find an integrated low-frequency spectral index of α = −0.71 ± 0.17 between 235 and 610 MHz. These observations suggest a possible flattening of the radio spectrum to low frequencies but we note that this cannot be confirmed from these data due to the relatively large errors on the GMRT flux estimates. We have searched the literature for total flux measurements of B2 1049+35 in order to determine the overall spectral shape of the radio emission. We list the available flux measurements in Table 2 and plot the radio spectrum including both our new measurements and the data from the literature in Figure 6. Several of the measurements from the literature were obtained with sufficiently large beams that the measured flux is contaminated by sources surrounding B2 0149+35. These measurements are marked with triangles in the figure.

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The shape of the radio spectrum can be used to estimate the age of the source by using models to fit the balance of energy injection and losses. Although the available flux measurements for B2 0149+35 cover roughly a factor of 65 in frequency, they still do not sample a large portion of the radio spectrum. We have fit all measurements in Table 2 to several particle injection models to determine the break frequency⁶ of the emission of the full source. The fits were done for both the full sample of flux measurements and also the subset of uncontaminated flux measurements. The three models used to fit the data were the Jaffe–Perola (JP), Kardashev–Pacholczyk (KP), and continuous injection (CI) spectral models. The JP and KP models both assume a single "one-shot" injection of a power-law distribution of electrons with no further acceleration (Jaffe & Perola 1973; Kardashev 1962; Pacholczyk 1970). The JP model allows for pitch-angle scattering, resulting in an exponential cutoff in the emission spectrum, while the KP model does not allow pitch-angle scattering and thus has an emission spectrum consisting of two power laws. The CI model assumes a continual injection of a power-law distribution of relativistic particles resulting in a spectral break that changes by −0.5 in α. All three models produce similar fits to the data and predict the break frequency lies in the range of 1400–9600 MHz. We find similar spectral break frequencies if we include or exclude the contaminated flux measurements from the literature. We have also separately fit the break frequency for the bright emission filling the eastern cavity as well as the fainter emission in the tunnel and to the east of the X-ray cavity. These regions were fit using only the data presented in this paper as the individual regions needed to be isolated to determine the fluxes. The break frequency in the bright regions is between 2200 and 12000 MHz, while in the fainter extended emission it is between 1900 and 7400 MHz. For all models we assume an initial injection spectrum of α = −0.6 which is the measured spectral index of the source between 330 and 610 MHz.

The average radiative age of the synchrotron emission is given by Miley (1980) as

$$\begin{equation} \tau =0.82 \frac{B^{0.5}}{B^2 + B_{\rm IC}^2} [(1+z)\nu _{b}]^{-0.5}\ \ {\rm yr,} \end{equation} \tag{ 1 }$$

where B is the magnetic field strength in the source in Gauss, B_IC is the equivalent magnetic field strength of the microwave background (4 × 10⁻⁶(1 + z)² Gauss), and ν_b is the break frequency in GHz. Assuming a break frequency at the low end of the model predictions of 1400 MHz and that the source field strength is $B=B_{\rm IC}/\sqrt{3}$ to give the maximum radiative lifetime (van der Laan & Perola 1969), we estimate the age of B2 0149+35 as ∼47 Myr. If the break frequency is near the high end from the spectral fits (9600 MHz), we then obtain a younger age of ∼18 Myr.

The western extension along the X-ray tunnel is fairly faint at 1400 MHz and thus the spectral index of the extension is not well constrained at high frequencies. In Section 4.2, we estimate the low-frequency spectral index of the emission in the tunnel to be α⁶¹⁰₂₃₅ = −1.3 ± 0.2. We use this spectral index measurement together with the flux measurement at 610 MHz to estimate the minimum energy properties of the western radio extension. We follow the notation of Miley (1980) and assume that the emission from the western extension comes from a uniform prolate cylinder with a filling factor (f) of unity and that there is equal energy in relativistic ions and electrons (κ = 1). We use a source size of ∼16.5 × 6.0 kpc and a model where the magnetic field is perpendicular to the line of sight and the spectral index is constant between the lower cutoff frequency of 10 MHz and the upper frequency cutoff of 100 GHz. Using these parameters for the tunnel, we calculate a minimum energy magnetic field strength of B_me = 5.0 μG, a nonthermal pressure of P_me = 1.4 × 10⁻¹² dyn cm⁻² and a synchrotron lifetime at 1400 MHz of τ_me = 37 Myr. Note that adiabatic expansion reduces the loss rate of the relativistic electrons, and as a result the synchrotron lifetime may be shorter than derived from the observed radio properties.

The X-ray gas pressure in the region surrounding the tunnel is estimated from the Chandra observations to be P_X = 6.4 × 10⁻¹¹ dyn cm⁻². This X-ray pressure is more than 25 times larger than our estimated minimum energy synchrotron pressure. This discrepancy between the synchrotron and X-ray pressure is typical of many cooling core systems as shown by Dunn et al. (2005). Similar pressure discrepancies are found in the case of lobes associated with several more powerful FRII sources as well (e.g., Hardcastle & Worrall 2000). Such a pressure difference cannot be physical since it would result in a rapid collapse of the radio lobes. This may suggest that the assumptions used in our minimum energy calculations are wrong. Equipartition between the synchrotron plasma and thermal gas would require κ/f = 260, which would suggest that the lobes are fed by heavy jets. An alternative solution to the pressure discrepancy is that there is an additional form of pressure support in the lobes (e.g., a very hot diffuse thermal gas).

The synchrotron emission coincident with the outer eastern X-ray cavity has a spectral index ranging from α = −1.0 to as steep as α = −1.5 between 235 and 610 MHz. Using the flatter spectral index and the minimum energy assumptions above, we estimate a minimum energy magnetic field strength of B_me = 2.6 μG, a nonthermal pressure of P_me = 4.1 × 10⁻¹³ dyn cm⁻² and a synchrotron lifetime (neglecting adiabatic expansion) at 1400 MHz of τ_me = 46 Myr. We estimate an average X-ray pressure of P_X = 5 × 10⁻¹¹ dyn cm⁻² in the same region as the synchrotron emission. As discussed above, this pressure difference cannot be physical and likely indicates either incorrect minimum energy assumptions or the presence of an additional form of pressure support within these regions.

If the western radio extension represents a buoyant lobe from a previous outburst then we can estimate the buoyancy rise time for the lobe to reach the end of the tunnel. The sound speed in the thermal gas is $c_s=\sqrt{\frac{\gamma kT}{\mu m_{H}}}$ where γ = 5/3 is the adiabatic index of the gas, T is the X-ray temperature of the gas, μ is the mean molecular weight of the gas, and m_H is the mass of the proton. Using T = 1 keV from Blanton et al. (2004), the sound speed in the central cluster region is c_s = 475 km s⁻¹. As the lobe rises it will approach a terminal velocity that is determined by the balance of buoyancy and drag forces. Based on the terminal velocity approach of Churazov et al. (2001), McNamara & Nulsen (2007) give the terminal velocity in terms of the Kepler speed (v_K) as v_b ∝ (4v_k/3)(2r/R)^0.5, where r is the bubble radius, R is the bubble distance from the cluster center and the Kepler speed is given by v_K = (gR)^0.5. The local gravitational acceleration, g, can be estimated from the local stellar velocity dispersion assuming the galaxy is an isothermal sphere, g ≃ 2σ²/R. The stellar velocity dispersion for NGC 708 is given by Bernardi et al. (2002) as 235 km s⁻¹, which results in a terminal velocity of v_b= 245 km s⁻¹ for the outer bubble.

Based on the above terminal velocity, we find a buoyant lobe would reach the observed (projected) location at the end of the tunnel on a timescale τ_buoy ≳ 80 Myr. Note that the lower limit on the buoyancy timescale is due to projection since the radio structure may not be in the plane of the sky. On the other hand, if the tunnel remains evacuated of thermal ICM between successive outbursts then the rise time calculated above overestimates the timescale for the synchrotron emitting plasma to reach the end of the tunnel. We cannot make a firm statement regarding the need for particle re-acceleration in the tunnel due to the uncertainties in the estimates of the synchrotron lifetime of the particles in the tunnel (Section 5.1) as well as the uncertainties in the buoyancy rise time.

The radio emission on the eastern side of the core (beyond the eastern lobe) likely represents emission from one or more previous outburst episodes from the central AGN. We measure projected distances from the center of the eastern cavity of ∼10, 17, and 21 kpc for the three eastern structures. Assuming that each of these represents a buoyant lobe from a past AGN outburst and using the calculated terminal velocity of the buoyant bubbles (v_b= 245 km s⁻¹), we can estimate the outburst repetition rate in this system to be τ_rep ∼ 28 Myr.⁷ This outburst timescale is similar to the estimate for Perseus using the observed spacing of the X-ray ripples (Fabian et al. 2003) and to the estimate for Abell 2052 using the X-ray shock separation or the rise time of the X-ray cavities (Blanton et al. 2009). Such a short repetition timescale would suggest that multiple outbursts may be responsible for creating the emission seen in the tunnel. We note that it seems unlikely that the repetition rate is as long as the typically assumed 10⁸ yr since buoyancy arguments would require the bubbles to be aligned at an inclination of less than 20° from the line of sight. An alternative interpretation for the new radio morphology is that the three eastern clumps may represent a much larger fragmented bubble from a single outburst that occurred prior to the current activity powering the inner lobes. In this case (even without considering projection effects), our repetition timescale would be an underestimate of the true repetition timescale.

Our new radio observations of B2 0149+35 show significant structure in the radio source to the east of the X-ray cavity. Interpreting the synchrotron emission as a series of buoyantly rising bubbles from past radio outbursts allows us to obtain a lower limit on the total energy input into the ICM over at least four outburst episodes in this source. We assume that the bubbles rise buoyantly and undergo adiabatic expansion in pressure equilibrium with the surrounding thermal gas. Following the notation of Churazov et al. (2002), the initial energy input from the outburst is related to the final bubble properties by

$$\begin{equation} E_o=\frac{\gamma }{\gamma -1}p_fV_f \left(\frac{p_o}{p_f}\right) ^\frac{\gamma -1}{\gamma }, \end{equation} \tag{ 2 }$$

where γ is the adiabatic index of the plasma in the lobes, p_o is the initial ambient pressure where the lobe was originally inflated, p_f is the surrounding pressure at the current location of the buoyant lobe, and V_f is the volume of the bubble at the current location. Due to sensitivity limitations, X-ray depressions are difficult to isolate for all radio features of B2 0149+35 and thus the cavity volumes are estimated based on the observed synchrotron emission seen at 610 MHz. The radio emission is less sensitive to projection effects than X-ray depressions (as also noted by Bîrzan et al. 2008).

The A262 cavity system provides us with the opportunity to estimate variations in outburst energies over several episodes for the same AGN. We have separated the radio source into seven components (four east of the core and three west of the core; Figure 7) and calculated the initial input energy from the AGN required to create these regions. The inner (spherical) eastern cavity was defined based on the X-ray cavity size and morphology. We use the same bubble shape and volume to match the inner western cavity while the remainder of the western X-ray tunnel is represented by a prolate cylinder. At the end of the western tunnel we define a small prolate cylinder based on the radio morphology. The outer eastern components were defined based on the radio morphology visible above the 5σ level. The first component is spherical while the outer two components are represented by prolate cylinders. The bubbles were assumed to be initially inflated at a radius consistent with that of the active eastern radio lobe and associated X-ray cavity. Using the location of the active eastern cavity rather than the cluster center as the inflation and detachment point avoids complications from likely supersonic or transonic jets closer to the cluster core. The X-ray pressure surrounding each region was determined from the radial profile obtained from the Chandra observations.

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In Table 3, we present a summary of the sizes and initial input energies calculated for each component. The lower limit on the initial energy input varies from ∼5 × 10⁵⁶ erg up to ∼8 × 10⁵⁷ erg, while the total energy summed over all seven radio components is 2.2 × 10⁵⁸ erg. This total energy input is similar to the average energy calculated for typical "single" outburst systems (Bîrzan et al. 2004). From the results in Table 3 we find that the current epoch of activity from B2 0149+35 is the most energetic if our underlying assumptions on the origin of the radio morphology hold. In fact, the distribution of the outburst energy for each of the components of the source shows that the energy appears to be roughly consistent with a continual increase to the current epoch. Such an increase in outburst energy may be the signature of a system where the cooling luminosity continues to dominate over the AGN energy injected into the ICM leading to an increase in the fueling of the AGN with time and thus more energetic outbursts. The observed trend in outburst energy for B2 0149+35 is different from that seen for the multicavity system in Hydra A (Wise et al. 2007). In that case, Wise et al. (2007) found that the energy required to create the outer cavities is nearly an order of magnitude larger than that for the inner cavities. We also note that the cavity size trend for B2 0149+35 seen in Table 3 does not follow the bubble size versus radius trend seen in the cavity sample of Diehl et al. (2008).

Based on the radio morphology, we suggest that the source components are the result of four outburst episodes that have a repetition time of ∼28 Myr. The total AGN kinetic luminosity over these outbursts is L_AGN = 6.2 × 10⁴² erg s⁻¹. Blanton et al. (2004) estimated the cooling luminosity in A262 to be L_cool = 1.3 × 10⁴³ erg s⁻¹, which is roughly a factor of 2 higher than the estimated AGN kinetic luminosity. Although Blanton et al. showed that the current radio outburst is apparently too weak to offset cooling assuming τ_rep = 10⁸ yr, our new data suggest that the AGN in NGC 708 can offset cooling on average with our shorter repetition timescale over the observed multiple outburst episodes. If the eastern radio morphology is instead the result of fragmentation from a single outburst episode it is likely that the energy output estimate above would underestimate the true AGN output.

The presence of the ICM confining the radio lobes allows us to compare estimates of the kinetic energy of the radio jets to the observed bolometric radio luminosity of the system. The radiative efficiency determined from embedded AGNs provides important insights into the impact of AGN outbursts on the evolution of the host galaxy and the ICM as well as information relating to AGN accretion and jet formation models. Theoretical estimates of the radiative efficiency fall in the range of 5%–10% (De Young 1993; Bicknell 1995). An observational estimate of the radiative efficiency of 10% was obtained by Wold et al. (2007) using a sample of FRI and FRII sources from the 3CRR catalog of Laing et al. (1983). Using a sample of radio sources associated with cluster-center cavities, Bîrzan et al. (2004) found that the radiative efficiencies fall in the range of a few tenths of a percent to a few percent.

The total radio luminosity of B2 0149+35 was calculated by integrating the flux between 10 MHz and 10 GHz assuming a constant spectral index of α = −0.90 and the total flux as measured from our 235 MHz observations. We find the bolometric radiative power to be L_radio = 3.9 × 10³⁹ erg s⁻¹, roughly 50% higher than the bolometric luminosity calculated in Bîrzan et al. (2008). A lower limit on the total AGN energy output is obtained from the mechanical power deposited into the ICM from this radio source (pV work) divided by the timescale for the energy input. From Section 5.4, we estimate the total AGN kinetic luminosity to be L_AGN = 6.2 × 10⁴² erg s⁻¹, giving a radiative efficiency similar to Bîrzan et al. (2004) of ∼0.1%, reinforcing the view that this source appears to be a very inefficient radiator.

The inferred black hole mass for B2 0149+35 can be calculated using the velocity dispersion versus black hole mass relation of Tremaine et al. (2002). The stellar velocity dispersion of 235 km s⁻¹ for NGC 708 (Bernardi et al. 2002) corresponds to a black hole mass of 2.6 × 10⁸ M_☉. The total energy output estimated for the four outburst episodes traced by the radio emission implies an average accretion rate of 0.001 M_☉ yr⁻¹ assuming = 0.1 as the efficiency of converting accreted mass to kinetic energy outflow. This mass accretion estimate is similar to that determined by Rafferty et al. (2006) from the analysis of only the inner X-ray cavities in Abell 262.