Cycling of the powerful AGN in MS 0735.6+7421 and the duty cycle of radio AGN in Clusters
We present an analysis of deep Chandra X-ray observations of the galaxy cluster MS 0735.6+7421, which hosts the most energetic radio AGN known. Our analysis has revealed two cavities in its hot atmosphere with diameters of . The total cavity enthalpy, mean age, and mean jet power are , , and , respectively. The cavities are surrounded by nearly continuous temperature and surface brightness discontinuities associated with an elliptical shock front of Mach number () and age of . The shock has injected at least into the hot atmosphere at a rate of . A second pair of cavities and possibly a second shock front are located along the radio jets, indicating that the AGN power has declined by a factor of over the past . The multiphase atmosphere surrounding the central galaxy is cooling at a rate of , but does not fuel star formation at an appreciable rate. In addition to heating, entrainment in the radio jet may be depleting the nucleus of fuel and preventing gas from condensing out of the intracluster medium. Finally, we examine the mean time intervals between AGN outbursts in systems with multiple generations of X-ray cavities. We find that, like MS0735, their AGN rejuvenate on a timescale that is approximately of their mean central cooling timescales, indicating that jet heating is outpacing cooling in these systems.
keywords:X-rays: galaxies: clusters – galaxies: clusters: individual (MS 0735.6+7421) – galaxies: clusters: intracluster medium – galaxies: active – galaxies: jets
The hot atmospheres at the centres of cool core clusters are often bright enough to radiate away their energy in X-rays in less than . If uncompensated by heating, the atmospheres will cool and fuel star formation in central cluster galaxies at rates of tens to hundreds of solar masses per year (reviewed by Fabian 1994). However, high resolution spectroscopy with the Chandra and XMM-Newton X-ray Observatories revealed only weak X-ray line-emission below that is inconsistent with gas cooling out of the X-ray band at the expected rates, implying that cooling is compensated by heating (Peterson et al., 2003). The most likely heating mechanism is feedback from the central active galactic nucleus (AGN) (reviewed by McNamara & Nulsen 2007). Outbursts from the central AGN inflate bubbles filled with radio emission that are visible as surface brightness depressions, or cavities, in X-ray imaging. These bubbles heat the ICM in their wake as they rise buoyantly through the cluster atmosphere (Churazov et al., 2001). A study of the Brightest 55 clusters showed that bubbles are present in at least of cool core clusters (Dunn & Fabian, 2006; Bîrzan et al., 2012), though this fraction may actually exceed (Fabian, 2012).
Radio jets launched by central AGN also drive shock fronts into hot atmospheres that have been identified in a growing number of clusters and groups (e.g. M87: Forman et al. 2007, Hydra A: Nulsen et al. 2005, A2052: Blanton et al. 2011, Hercules A: Nulsen et al. 2005, NGC 5813: Randall et al. 2011, and others). Though their total energies can be large, the shocks are usually weak with Mach numbers lying between and . Heating from weak shocks is most effective at small radii, and may be a critical element of a feedback cycle (reviewed by McNamara & Nulsen 2012). Sound waves, such as those detected in Perseus (Fabian et al., 2006), Centaurus (Sanders & Fabian, 2008), and A2052 (Blanton et al., 2011), deposit energy on large scales. Quantifying their contribution to heating is difficult as it depends on uncertain transport coefficients.
Continual AGN activity is required to suppress cooling over the ages of clusters. AGN must rejuvenate on timescales shorter than the central cooling time in order to regulate or prevent star formation in central galaxies. Sequential AGN outbursts are indicated by the radio morphologies of several systems (Schoenmakers et al., 2000; Saripalli et al., 2002). Likewise, deep Chandra observations have revealed multiple generations of cavities from a number of nearby systems, including Perseus (Fabian et al., 2006), M87 (Forman et al., 2007), Hydra A (Wise et al., 2007), HCG 62 (Rafferty et al., 2013), Abell 2199 (Nulsen et al., 2013), Abell 2052 (Blanton et al., 2009, 2011), NGC 5813 (Randall et al., 2011), Abell 3581 (Canning et al., 2013), and NGC 5846 (Machacek et al., 2011).
The cool core cluster MS 0735.6+7421 (hereafter MS0735) hosts unusually large X-ray cavities in an otherwise relaxed system (Gitti et al., 2007). Each cavity has a diamater of roughly and is filled with synchrotron emission from the radio jet. A weak but powerful shock front encompasses the cavities (McNamara et al., 2005). The total energy required to inflate the bubbles and drive the shock front exceeds , making this the most powerful AGN outburst known. The interaction between radio jet and the surrounding hot atmosphere is a key piece of information for the process of AGN feedback. Deep X-ray observations of the most powerful AGN outbursts are crucial in understanding this interaction.
MS0735 is an enigmatic object that challenges our understanding of how galaxies and supermassive black holes coevolve and how AGN are powered. With a mechanical power in excess of , quasar-like power output requires of gas to be accreted onto the central black hole at a rate of . At the same time, far UV imaging has revealed no trace of star formation or emission from a nuclear point source (McNamara et al., 2009). Therefore, a surprisingly large fraction of the molecular gas supply (Salomé & Combes, 2008) would need to be consumed over roughly in order to power the outburst. Unless MS0735 hosts an ultramassive black hole with a mass approaching , it would be difficult to power the AGN by Bondi accretion (McNamara et al., 2009). Tapping the spin energy of the black hole would ease the demands on accretion, although this suggestion has its own problems (McNamara et al., 2011).
Here we present a deep () Chandra X-ray observation of MS 0735.6+7421. In Section 2 we describe the observations and data reduction methods. Projected and deprojected profiles of cluster properties are presented in Section 3. New, more accurate measurements for cavity and shock energetics are presented in Section 4. In Section 5 we present evidence for a rejuvenated AGN outburst and provide estimates of its energetics. In Section 6 we present the first comparison of outburst interval to central cooling time and cavity heating time for the objects that have measured outburst intervals. All results are summarized in Section 7. Throughout this analysis we assume a flat cosmology with , , and . This gives an angular scale of arcsec at the redshift of MS0735, . All errors are unless otherwise stated.
|Obs ID||Date||Exposure Time||Cleaned|
|(ks)||Exposure Time (ks)|
|10468||June 21, 2009||46.0||41.7|
|10469||June 11, 2009||93.3||86.7|
|10470||June 16, 2009||142||134.8|
|10471||June 25, 2009||19.5||18.1|
|10822||June 18, 2009||75.4||71.8|
|10918||June 13, 2009||65.2||61.8|
|10922||June 26, 2009||35.4||32.3|
2 Observations and Data Reduction
This analysis combines seven Chandra observations of MS0735.6+7421 taken on the ACIS-I detector in June 2009. The cumulative exposure time for these observations is . Table 1 summarizes the exposure times for each observation. Each observation was reprocessed with CIAO version 4.5 and CALDB version 4.5.6, which were provided by the Chandra X-ray Center. The level 1 event files were reprocessed to apply the latest gain and charge transfer inefficiency correction and then filtered to remove photons detected with bad grades. The additional data obtained in VFAINT mode were used to improve screening of the particle background. Background light curves were extracted from the level 2 events files of chip 0 on the ACIS-I detector. These background light curves were filtered using the lc_clean script provided by M. Markevitch in order to identify periods affected by flares. None of the observations showed any significant flares. The final cleaned exposure time was .
The cleaned events files were then reprojected to match the position of the observation with obs ID 10468. An image for each observation was produced by summing events in the energy range . These images were then summed to create a single image for identifying features in the X-ray emission. Point sources were identified using wavdetect (Freeman et al., 2002). The identified point sources were inspected visually and excluded from subsequent analysis. The final image, with point sources removed, is shown in Figure 1. The image is not corrected for exposure.
Blank-sky backgrounds were extracted for each observation, processed the same way as the events files, and reprojected to the corresponding position on the sky. Each blank-sky background was normalized to the energy band in the observed data set. This was a correction for all observations. The normalized blank-sky background data sets were compared to source-free regions of the observed data set for consistency, and were found to be a close match to the background of the observed data set.
Spectral data was analyzed by first extracting source spectra and background spectra from each observation independently. All extracted spectra and background spectra were summed and the exposure times were adjusted accordingly. Spectra may be summed because each observation was taken on the same detector over the course of about weeks. The roll angles are similar, so spectral extraction regions are from similar regions of the chip and therefore have similar responses. Auxiliary response files were weighted by the number of counts in the spectrum and summed using the addarf command. The redistribution matrix files were also weighted by the number of counts and summed using addrmf. Finally, the summed spectrum was binned to a minimum of 20 counts per energy bin.
The loss of area resulting from point sources and chip gaps was corrected by creating an exposure map for each observation with the mkexpmap command in ciao, omitting effective area and quantum efficiency. Each exposure map was weighted by exposure time, summed, and then normalized by the total exposure time. The appropriate area correction was obtained from the mean value of this exposure map within the region of interest. The correction was applied to the spectrum and background spectrum by setting the areascal keyword.
3 Cluster X-ray Properties
In this section we present an analysis of the X-ray properties of MS0735, including profiles of surface brightness, temperature, and abundance as well as quantities derived from these profiles. Maps of temperature and abundance are also presented. We find that MS0735 is a relaxed, cool core cluster with no evidence of a recent merger. This system hosts the largest known AGN outbursts, with cavities with diameters approaching and a cocoon shock enveloping the cavities. These features are discussed in turn in Section 4.
3.1 Surface Brightness
Cluster surface brightness was extracted from the X-ray image for a series of concentric elliptical annuli. The annuli had a spacing of () along the minor axis and were concentric with the shock front. The resulting surface brightness profile, after background subtraction, is shown in Figure 2. An isothermal, single- model (Cavaliere & Fusco-Femiano, 1976), described by
is a poor fit to this profile. Instead, we fit the surface brightness profile with a double- model to account for the excess emission from the cool core of the cluster. The core was best fit by a -model with a normalization of counts/arcsec, a scale radius of , and a of . The normalization of the second component was counts/arcsec, with and . The double- model is a poor fit beyond because of the shock front at , but is a reasonable fit in the cluster centre.
Subtracting the best-fitting double- model from the cluster emission produces the image shown in Figure 3. Two large cavities are easily visible in this image. Sharp edges surround the northeastern (NE) cavity, causing it to be more well-defined than the southwestern (SW) cavity. Bright emission is located at the same radius as the cavities, and could be produced from gas displaced by the cavities. The knot of bright emission east of the centre corresponds to cool, extended emission. The cocoon shock enveloping the cavities is also evident in Figure 3. The large positive residual between is located along the inner edge of the shock front () and is caused by gas that has presumably been displaced by the cavities.
3.2 Projected Profiles
Radial profiles of temperature, density, and abundance were created by fitting spectra extracted from elliptical annuli. Each elliptical annulus was taken to have the same major-to-minor axis ratio () and position angle ( east of north) as the outer shock front, which was determined by eye. The volume of each annulus was calculated assuming prolate symmetry. The inner annuli were created with a fixed radial bin width of along the minor axis, which was chosen based on the spatial resolution of Chandra. These regions contained between and net counts. The remaining annuli were created with the number of counts increasing with radius, with the outermost annulus containing net counts. Projected temperature, density, pressure, abundance, cooling time, and entropy profiles are shown in Figure 4 and are plotted against the semi-minor axis of the annulus.
3.2.1 Spectral Fitting
Projected gas properties were determined by fitting each extracted spectrum with an absorbed single-temperature phabs(mekal) model (Mewe et al., 1985; Mewe et al., 1986; Balucinska-Church & McCammon, 1992; Liedahl et al., 1995) in xspec 12 (Arnaud, 1996). Temperature, normalization, and abundance were allowed to vary while the foreground column density, , was fixed to the Galactic value of (Kalberla et al., 2005; Hartmann & Burton, 1997). This value is consistent with fitted values in the outskirts of the cluster within . Abundance line ratios were set to the values given in Anders & Grevesse (1989) for consistency with previous work.
Density is related to the normalization of the mekal thermal model through the emission integral . The electron and hydrogen densities, and , are taken to be constant within each annulus. All emission in an annulus is assumed to originate from a prolate ellipsoid. Assuming hydrogen and helium mass fractions of and (Anders & Grevesse, 1989) gives . Density can then be determined from the normalization of the thermal model and the volume of the ellipsoid. Pressure is determined from temperature and density using the ideal gas law, .
3.2.2 Temperature Profile
The observed temperature profile, shown in the upper left panel of Figure 4, is consistent with the profiles from Vikhlinin et al. (2005). The mean projected temperature within of the cluster centre is . It rises to a maximum of at , where it drops abruptly to . The temperature beyond this radius is roughly constant at . The sharp drop in temperature at is interpreted as a weak shock front (see McNamara et al. 2005). The ratio between post- and preshock temperatures, , is consistent with the projected temperature jump of expected from the shock measurement. This shock, with a Mach number determined from the surface brightness profile, is discussed further in Section 4.3.
The decrease in temperature at corresponds to cool gas that extends to the southeast, which coincides with the bright residual from Figure 3. This feature is evident in the temperature map discussed in Section 3.3. Significant scatter about the mean temperature is observed at , resulting from excess emission that extends perpendicular to the jet axis. This emission is visible in Figure 3, and may correspond to gas that has been displaced by the cavities.
3.2.3 Abundance Profile
The metal abundance within of the cluster centre is , and then decreases with radius. The abundance rise toward the cluster centre is likely due to enrichment from supernovae in the BCG (de Grandi & Molendi, 2009). From the abundance flattens to , which is typical of cool core clusters (De Grandi & Molendi, 2001; De Grandi et al., 2004). The last radial bin has an abundance of , below the plateau.
3.2.4 Entropy Profile
The entropy index of intracluster gas, defined as , offers a more direct insight into heating and cooling processes than either temperature or density individually. Above the entropy index can be fit by a powerlaw with slope , which is consistent with the slopes found by Voit & Donahue (2005). Toward the centre the mean entropy index appears to flatten toward the central projected value of . However, recent work from Panagoulia et al. (2013) has shown that this may be a resolution effect and that entropy should continue to decrease toward the cluster centre.
3.2.5 Cooling Time
If uncompensated by heating the ICM will radiate away its thermal energy on a timescale , where is the cooling function as a function of metallicity, , and temperature, . The cooling function is determined from the X-ray bolometric luminosity, which is given by and is obtained by integrating the unabsorbed thermal model between and . The cooling time in MS0735, shown in Figure 4, roughly follows a powerlaw with a slope of . The projected cooling time within the central is . Projection effects have a significant effect on central density, and therefore on central cooling time. The deprojected profile is presented in Section 3.4.
Local variations in cluster abundance and temperature are traced using maps created with the contbin 111http://www-xray.ast.cam.ac.uk/papers/contbin method (Sanders, 2006). Cluster emission is grouped into bins that closely follow surface brightness. The minimum signal-to-noise was set to ( net counts) for the temperature map in order to produce an image with high spatial resolution. Accurate abundance measurements require more counts, so a signal-to-noise of ( net counts) was used for this map. A spectrum was extracted from each region produced by contbin and was fit with the absorbed thermal model described in Section 3.2.1. The maps are shown in Figure 5 and are both in broad agreement with the profiles in Figure 4. Point sources have been excluded from these maps.
3.3.1 Temperature Map
The approximate location of the outer shock front is indicated by the black ellipse overlaid on the temperature map (Figure 5, left). A clear temperature jump is seen between the pre- and post-shock bins along the entire shock front. The ratio of postshock to preshock temperature varies between and along the shock front. Accounting for projection effects, these jumps slightly exceed expected jump for the Mach shock reported in this work. See Section 4.3 for a more detailed analysis.
An extended region of cooler emission is seen to the immediate SE of the cluster core, coinciding with the bright emission seen in Figure 1 (right). The temperature of this gas, , is cooler than the surrounding gas. The drop in temperature observed in Figure 4 is consistent with the location of this extended feature.
The central of the temperature map is shown in Figure 6 and is overlaid with VLA radio contours (Bîrzan et al., 2008). Cooler gas (), which likely originates from the centre of the cluster, extends along the direction of the radio jets, implying that the ICM is entrained in the radio jet and is being dragged to high altitudes. This effect has also been observed in Hydra A, where the energy required to uplift the cool gas is comparable to the work required to inflate the cavities (Gitti et al., 2011). Removing the supply of low entropy gas near the cluster centre slows the rate of cooling, which is an important step in regulating AGN feedback (Kirkpatrick et al., 2009).
3.3.2 Abundance Map
The central abundance in MS0735 is roughly and decreases with radius until it reaches . Regions of enhanced abundance are seen toward the end of the radio jets (black contours). A region with lies at the end of the jet pointing to the south. To the north the region lies beyond the extent of the radio jet. This observation is consistent with work done by Kirkpatrick et al. (2009) and Simionescu et al. (2009), who argued that cavities may lift metals to large radii as they rise through the cluster. Kirkpatrick et al. (in prep) measure excess iron emission along the direction of the radio jet in MS0735 out to a radius of . The high metallicity regions in Figure 5 are located at distances consistent with this iron radius.
3.4 Deprojected Profiles
Projected foreground and background emission skews central projected densities and temperatures to higher values. We now correct for this effect by employing deprojected fits to radial profiles. Spectra were extracted from concentric circular annuli containing roughly net counts per annulus. These spectra were area-corrected, then deprojected using the model-independent dsdeproj package described in Sanders & Fabian (2007) and Russell et al. (2008). The absorbed thermal model described in Section 3.2.1 was fit to each of the deprojected spectra, and the resulting profiles are shown in Figure 7. The “onion-peeling” approach of the projct model produces fits that are consistent with dsdeproj. Projected profiles were created using these regions and are plotted alongside the deprojected profiles for comparsion. Two data points are plotted in the central bin due to the presence of multiphase gas, which is discussed in detail in Section 3.5.
Deprojection subtracts the line-of-sight contribution of overlying gas from each annulus. The resulting central density, , is therefore significantly smaller than the central projected density. The deprojected central temperature, on the other hand, is consistent with the projected temperature within . The temperature of the cold phase in the central region is consistent between projected and deprojected profiles.
The projected temperature profile increases smoothly between and , while the deprojected profile varies significantly. The deprojection relies critically on the assumption of spherical symmetry, which clearly fails here and contributes to the bouncing deprojected temperatures. The drop in projected temperature seen at this location in Figure 4 is exaggerated by the deprojection. The pressure profile used for subsequent calculations of cavity and shock properties combines deprojected densities with projected temperature in order to avoid the unstable solutions in the deprojected temperature profile.
At a radius of the projected temperature jumps from a preshock value of to a postshock value of . This temperature jump, , is consistent with the jump observed in Figure 4. The deprojected profile shows a larger jump, , but it is consistent with the projected jump within . The location of this jump is consistent with the location of the shock front, which extends from along its minor axis to along its major axis.
3.5 Multiphase Gas
A single temperature thermal model provides a poor fit to the spectrum of the central below . The spectrum, shown in Figure 8, has a soft excess located between and , resulting in a column density that approaches zero when allowed to vary. This is indicative of lower temperature gas located at the centre of the cluster. A second thermal component was added to the original model, with abundances tied between the two thermal components and the column density fixed to the Galactic value. Applying an F-test, we find the two-temperature model provides a statistically significant improvement to the fit. The best-fitting temperatures are and , and the normalization of the cold component is times smaller than that of the hot component. A single-temperature model is able to model the gas adequately at larger radii.
The density ratio between the cold and hot phases, assuming that they are in pressure balance, is given by . With temperatures of and , the cold gas would be a factor of more dense than the hot gas. The mass ratio between these components can then determined from the normalizations of the xspec thermal models, . Since , the cold, dense gas is times less abundant than the hot gas. The ratio between luminosities is obtained directly from the X-ray bolometric luminosities of the model components, and is .
The cooling time of the hot phase within the central , , is a factor of longer than the projected cooling time within , . The cold component, with a cooling time of , cools on a much shorter timescale than the hot phase. The implied mass deposition rate for a pure cooling model is for the hot phase and for the cold phase. Both of these deposition rates greatly exceed the feeble star formation rate of (McNamara et al., 2009). While cooling gas is apparently able to sustain the AGN, it is not fuelling star formation at an appreciable rate.
The radiative cooling of the central ICM can be suppressed by AGN heating provided cavity power exceeds the X-ray luminosity of the gas. The X-ray luminosities of the hot and cold components are and , respectively. The mean power of the inner cavity system, discussed in Section 5, is , exceeding the combined X-ray luminosity in the central region by a factor of . While this provides ample power to suppress cooling, it is not clear how much of the energy is dissipated within the central region.
AGN feedback can also suppress radiative cooling by physically removing the supply of low entropy gas from the centre of the cluster (Gitti et al., 2011). X-ray cavities have been shown to couple to the metal-rich central gas, dragging it toward large radii as the bubbles rise through the ICM (Kirkpatrick et al., 2009; Simionescu et al., 2009). The temperature map in Figure 6 shows that cool gas is displaced along the direction of the radio jet, implying that gas has been entrained by the radio jet or X-ray cavities and is being displaced from the cluster centre. Using abundance profiles along and perpendicular to the direction of the cavities, Kirkpatrick et al. (in prep) measure a gas outflow rate of being dragged to a radius of . This large mass outflow rate can easily offset the combined mass deposition rate.
3.6 Cooling Region
We define the region in which the cooling time is less than , the look-back time to for concordance cosmology, as the cooling region. In the absence of major mergers, some energy source must make up for the power radiated from within this region in order to suppress cooling in the long term. The cooling radius, , obtained from Figure 7 is , which is consistent with the XMM-Newton analysis of Gitti et al. (2007). A spectrum was extracted from a region with radius and was deprojected using spectra obtained from 3 overlying regions with the same radial width. The total luminosity within the cooling region was estimated by fitting this deprojected spectrum with the absorbed thermal model discussed in Section 3.2.1 and integrating the thermal component between and . The unabsorbed X-ray bolometric luminosity within this region is .
The amount of gas that cools out of the ICM is estimated by adding an mkcflow component to the thermal model. The low temperature limit of this model was fixed to in order to provide an upper limit on the amount gas cooling to low temperatures. The high temperature component was tied to the temperature of the mekal model and allowed to vary. Abundances were also tied between models. The resulting cooling luminosity, , is a small fraction () of the total X-ray luminosity, and corresponds to of gas cooling out of the ICM, which is broadly consistent with the reported by Gitti et al. (2007). With a star formation rate of (McNamara et al., 2009), only a small portion of gas actually cools out of the ICM and forms stars.
4 Large Outburst
Two large cavities, with diameters of , are visible in the X-ray image and are filled by radio emission from the relativistic jet. The cavities are surrounded by a continuous surface brightness edge, corresponding to a weak but powerful shock front. This section presents new, updated measurements of cavity and shock power for the large outburst in MS0735.
The total energy required to inflate a bubble in the ICM is given by its enthalpy,
where is the cavity’s pressure and is its volume. The ratio of heat capacities, , is for a relativistic gas and is for a non-relativistic, monatomic gas. For relativistic contents, the total cavity energy is . The age of an outburst is estimated using three characteristic timescales: the sound crossing time, buoyancy time, and refill time (Bîrzan et al., 2004). In general the sound-crossing time is the shortest, refill time is the longest, and buoyancy time lies in between. We estimate the age of a cavity by the mean of these three timescales and calculate the power required to inflate the cavities as . This age is likely an overestimate of the true age of the bubble, so the powers reported here are underestimates.
The projected sizes and positions of the cavities were determined by eye by fitting ellipses to the surface brightness depressions. The cavities are surrounded by bright rims that are presumably composed of displaced gas. The midpoint of these rims is taken for the measurement of cavity size. The inner (outer) edge of the rim is used to obtain a lower (upper) limit on the projected size of the cavity, which is used to determine the errors on cavity volume and subsequently on cavity enthalpy and power. The northeastern cavity is best fit by an ellipse with semi-major axis , semi-minor axis , and projected distance with a position angle of east of north. The southwestern cavity is best fit by an ellipse with , , and with position angle east of north. Table 2 summarizes the cavity properties and their derived energetics. The temperature, density, and pressure of the surrounding ICM is taken from Figure 7 at a radius corresponding to the centre of the cavities. Projected temperatures and deprojected densities are used in this analysis.
Cavity volumes are calculated using the geometric mean between oblate and prolate ellipsoids, . Upper (lower) limits on cavity volume are determined using the maximum (minimum) projected sizes, with volumes calculated in the same way as the mean volume. The total gas mass displaced by the cavities, assuming they are devoid of X-ray emitting material, is . The electron density, , is taken at a radius corresponding to the centre of the cavity. With volumes of and for the NE and SW cavities, respecticely, the displaced gas masses are and . The work required to inflate the cavities is for the NE cavity and for the SW cavity.
The cavity ages estimated using the buoyancy, sound crossing, and refill timescales are listed in Table 2. The gravitational acceleration, , used to calculate the buoyancy and refill timescales was determined using the MS0735 mass profile from Main et al. (in prep). In general the terminal velocity of bubbles is of the sound speed (Rafferty et al., 2006). In MS0735, however, the large bubble volumes result in supersonic terminal velocities. Neglecting the bubble’s expansion history in the buoyancy timescale therefore underestimates the true cavity age. We use the mean of the buoyancy, sound crossing, and refill timescales in order to estimate bubble age.
The ages of the NE and SW cavities are and , respectively. The age of the surrounding shock front, (see Section 4.3), which should be comparable to the true cavity age, is shorter than the mean rise time. We therefore expect to have slightly overestimated cavity ages, so the calculated power is likely underestimated. The power required to inflate these bubbles is and for the NE and SW cavities, respectively. The total enthalpy () of these cavities is , and the total power is .
The total cavity power of this AGN outburst exceeds the X-ray bolometric luminosity within the cooling radius, , by more than a factor of , easily compensating for radiative losses. At a projected distance of , the majority of the cavity volume is located outside of the cooling region. Unless adiabatic losses from cosmic ray streaming account for a significant fraction of energy dissipation, most of the cavity enthalpy will be carried outside of the cooling region. If this energy is deposited within , where the total gas mass is (Main et al. in prep), the total cavity enthalpy heats the gas by per particle.
4.2 Cavity Rims
Bright rims of cool gas surround many cavity systems (e.g. Fabian et al. 2000; Nulsen et al. 2002; Blanton et al. 2001, 2011), and are also observed in MS0735. The brightest rim appears along the western edge of the NE cavity. A surface brightness profile, centred on the cavity, was created in order to determine the width of the rim. This profile, shown in Figure 9, is created from sectors with an opening angle oriented to the west. Surface brightness is enhanced between to , giving a rim width of .
A spectrum was extracted for the rim and fit with the absorbed thermal model discussed in Section 3.2.1. For comparsion, a spectrum was extracted from a region just outside of the rim with the same opening angle. The rim contains cooler gas than the surrounding gas, with compared to the surrounding . The ratio between densities can be determined directly from the normalization of the thermal model, , and the volume of each region,
We find that the rim is a factor of more dense than the surrounding gas. The pressure ratio between the rim and the ambient gas, , implies that they are in pressure balance.
Radio jets launched by the AGN drive shock fronts into the ICM. MS0735 hosts a continuous, elliptical shock front that encompasses the outer pair of cavities (McNamara et al., 2005). This shock front is modeled as a spherically symmetric point explosion in an intially isothermal atmosphere in hydrostatic equilibrium. The surface brightness profile computed from the model is scaled to fit the preshock profile in the specified energy band. The postshock conditions are then dictated by the Rankine-Hugoniot shock jump conditions for a given Mach number, . A detailed description of the analysis can be found in Nulsen et al. (2005).
The shock front is qualitatively fit by an ellipse with semi-major axis , semi-minor axis , and position angle of east of north. We approximate the elliptical shock front using spherical symmetry by considering only small opening angles around the minor axis of the shock (, roughly to the east and west). We are unable to accurately model the shock along the major axis because of the depression in postshock surface brightness caused by the large cavities. The surface brightness profile extracted from these circular sectors is shown in Figure 10 and is best fit by Mach number ( confidence) at a radius of . This value is marginally () below the measured by McNamara et al. (2005). The difference is likely related to the improved precision yielded by the deeper observation, which provides a more accurate measurement of the pre- and post-shock surface brightness profiles and a more accurate characterization of the depth of the surface brightness discontinuity. The surface brightness of the preshock gas is best fit by the powerlaw with . The corresponding density profile, assuming constant temperature, is with .
From the Rankine-Hugoniot jump conditions, a Mach shock causes a increase in temperature. Projection effects obscure the jump, so that the expected temperature jump is only . From Figures 4 and 7 the observed temperature jump, , is within of the expected jump. A map of the postshock temperature is provided in Figure 11, with the location of the shock front shown as the black ellipse. The postshock temperature is clearly highest along the major axis of the shock, reaching to both the North and South but only to the East and West. This is expected of an elliptical shock front, since the major axis must propagate faster and therefore has a higher Mach number. Due to the large uncertainties in temperature, the jumps along the major and minor axes are not significantly different. However, Figure 11 shows a clear azimuthal trend in temperature, which is indicative of an enhanced temperature jump along the major axis of the shock front.
The shock energy is determined from the point explosion model and depends on preshock temperature and density. The preshock properties are taken from the elliptical profiles in Figure 4, which trace the shock front well. The preshock temperature is specified as with a density of at , resulting in a shock energy of . Using the deprojected profiles in Figure 7 to determine the preshock conditions do not change the result, which is likely only accurate within a factor of .
The main shortcomings of the shock model are in the assumptions of spherical symmerty and a point explosion. Spherical symmetry is a poor description of the elliptical shock front, so the shocked volume is underestimated. The AGN likely drives the shock through a continuous injection of energy, which requires more energy than a point explosion in order to generate the same shock strength. The energy measured here, , is therefore an underestimate of the true shock energy. An improved shock model that does not assume spherical symmetry or a point explosion is required in order to improve the analysis of this weak shock.
The age of the shock determined by the model, , is comparable to the buoyancy and sound-crossing times of the cavities. Since they originate from the same AGN outburst, these ages are likely close to the true value. The shock power, , is slightly smaller than the total cavity power of . Exceeding the X-ray luminosity within the cooling region by a factor of , the shock front also possesses ample power to offset radiative losses. Combined, the cavities and shock front are able to heat the ICM by per particle within , which provides a significant fraction of the per particle required to preheat the cluster gas (Wu et al., 2000).
5 Rejuvenated Outburst
The deep X-ray image reveals two smaller cavities or channels located along the radio jets in the inner of the BCG. Due to their small size relative to the larger cavities and their proximity to the cluster core, the cavities are difficult to disentangle from the gas presumably displaced by the large cavity system. The presence of a second pair of cavities is indicative of a rejuvenated AGN outburst. The inner edge of these cavities are traced by cool rims of displaced gas that are evident in the soft band () image, shown in Figure 12 (left). This image was prepared in the same way as Figure 1, but with energies binned between and .
The right panel of Figure 12 shows five projections taken across the SW inner cavity. The black rectangle in the left panel of Figure 12 shows the projection corresponding to the middle profile. Counts in the energy band were averaged over the width of the projection for each pixel along its length. Several of the profiles show a decrease in brightness, the most significant of which occurs from the cluster centre and reveals a deficit in counts relative to the surrounding bright rims. The decrease in counts toward the NE cavity is much smaller than is seen in the SW cavity, merely flattening instead of producing a clear deficit. This difference likely results from the projection into our line of sight of emission from dense gas, nonuniformly distributed in the cavity rims.
The projected sizes of the two inner cavities are determined in the same manner as the outer cavities (see Section 4.1). The white ellipses in Figure 12 (left) show the cavity sizes adopted here, which use the middle of the rims to determine the mean cavity volume. This approach gives a projected size of , for the inner NE cavity and , for the inner SW cavity. Volumes for these cavities are calculated using the geometric mean between oblate and prolate ellipsoids, or . At projected distances of and from the cluster centre, these cavities displace and of gas in the ICM, respectively.
The mechanical energy required to inflate these cavities, , is for the inner NE cavity and for the inner SW cavity. The mean age of the bubbles, and , give cavity powers of and , respectively. The total mechanical energy () and power for this outburst are therefore and . This cavity power exceeds radiative losses within the cooling region () by a factor of and is times smaller than the outer cavity power, implying that AGN power varies significantly over time. While feeble compared to the outer cavities, the inner cavities are comparable in power to the bubbles in Perseus.
Despite the ample energy in the outer outbursts, a rejuvenated AGN outburst is required in order to continue to offset radiative losses (see e.g. Perseus: Fabian et al. 2006, M87: Forman et al. 2007, Hydra A: Nulsen et al. 2005). The outburst interval in MS0735, given by the difference in mean bubble ages, is . This value ranges between a minimum of when the buoyancy time is used to a maximum of with the refill timescale. Each of these values is shorter than the central cooling time, . The AGN outbursts therefore occur on short enough timescales to prevent the majority of the ICM from cooling. Repeated heating of the central gas supplies enough energy to prevent cooling, and may explain the lack of star formation in the system (McNamara et al., 2009).
5.1 Spectrally Hard Features: An Inner Shock?
Weak shocks are typically produced alongside cavities in an AGN outburst. The gas warmed by shock heating can be traced using a hard band image (Forman et al., 2007), which excludes the portion of the X-ray spectrum that is only weakly dependent on temperature (see Figure 1 of Arnaud 2005). We produce a hard band image by binning cluster emission between and . The hard emission, shown in Figure 13, is fairly circular, with extended emission lying perpendicular to the jet axis. This morphology is quite different than the cooler gas traced by the soft band (Figure 12), which shows emission extending along the jet axis.
The arrows in Figure 13 point to a circular feature that is reminiscent of the shock front in M87 (Forman et al., 2007). A jump in surface brightness is observed at this location, but it is marginal and depends strongly on radial binning. We therefore cannot conclusively determine if this feature corresponds to a shock front. If it is a shock front, then, approximating the density jump from the surface brightness jump, it would have a Mach number of approximately . With a radius of the energy of the shock front is , which is a factor of smaller than the total mechanical energy required to inflate the associated bubbles. The age of this shock is for a preshock temperature of , which translates to a power output of . This shock power is comparable to the total cavity power for the rejuvenated outburst as well as the X-ray bolometric luminosity within the cooling region.
6 AGN Outburst Time Dependence
MS0735 is one among several clusters and groups with two or more pairs of radio cavities embedded in their hot atmospheres. These systems are particularly interesting because they permit a direct indication of AGN power variability over time and the time interval between outbursts, which should be shorter than the cooling time if AGN are regulating cooling (Dunn & Fabian, 2006; Rafferty et al., 2008; Bîrzan et al., 2012). Those known to us are listed in Table 3. We compare the time interval between outbursts in these systems to central cooling time and cavity heating time. We note that this archival sample is heavily biased by selection, as only large bubbles are detectable and multiple outbursts can only be detected for a select range of outburst intervals. There is likely a range in cavity sizes and ages that we are currently unable to detect (McNamara & Nulsen, 2007).
Outburst interval is determined from the difference in ages between inner and outer cavities, with buoyancy times used to determine bubble ages. Outburst intervals are also determined from the period of weak shocks and sound waves. A factor of uncertainty is attributed to all outburst intervals. For bubbles this roughly translates to calculating bubble ages from the sound crossing time and refill time and using those estimates as lower and upper bounds, respectively. The outburst intervals presented here, determined from cavity ages, range from in M87 to in Hydra A. The mean outburst interval of these points is , while sound waves occur on much shorter timescales, with a mean period of .
Central cooling times are obtained from the Rafferty et al. (2008) and Cavagnolo et al. (2009) samples, and are plotted against outburst interval in Figure 14. Outburst intervals determined from bubble ages are plotted as circles, while those determined from weak shocks or sound waves are plotted as triangles. The points are colour-coded based on the central resolution element. Nearby systems, where the achievable resolution is , are shown in white. Grey points correspond to a resolution of and black points are for systems with a resolution that exceeds . The clear separation between these points can be attributed to resolution (Peres et al., 1998). A consistent physical scale would shift the grey and black points to the left, but they tend to be hotter systems so would still have a longer central cooling time than most of the white points. Multiple points are shown for Hydra A, M87, and NGC 5813 because they host bubbles from 3 AGN outbursts, corresponding to 2 outburst intervals.
After accounting for resolution, Figure 14 shows that outburst interval is shorter than or consistent with the mean central cooling time for each system in our sample. AGN outbursts therefore occur on short enough timescales to continually suppress cooling flows (see Rafferty et al. 2008). The mean cooling time for this sample of groups and clusters is , which is a factor of larger than the mean outburst interval. The white points in Figure 14 have a much shorter mean cooling time, , than the points in grey, . These points also have shorter outburst intervals, with a mean outburst interval of compared to . Therefore the points with the smallest resolution element, which have shorter central cooling times, also have shorter outburst intervals. The period of sound waves in M87 (Forman et al., 2007), Perseus (Fabian et al., 2006), Centaurus (Sanders & Fabian, 2008), and A2052 (Blanton et al., 2009) are each an order of magnitude smaller than their central cooling time, implying that weak shocks repeat on timescales short enough to offset cooling in cluster centres.
We define cavity heating time as the amount of time that cavity enthalpy is able to offset radiative losses, . A large outburst offsets cooling for longer times, which could translate to a longer outburst interval. Cavity heating time is compared to outburst interval in Figure 15. For the factor of range in outburst intervals, cavity heating time spans orders of magnitude. We find that outburst interval is shorter than cavity heating time for of the points in our sample. We note that is likely underestimated in NGC 5846 by a factor of a few, as Machacek et al. (2011) report the X-ray luminosity within while the cooling radius is approximately (Cavagnolo et al., 2009).
The majority of systems in Figure 15 (8 of 13) have an outburst interval shorter than their cavity heating time, indicating that heating is continually able to offset radiative cooling over the age of the cluster. Furthermore, the presence of weak shocks and sound waves imply that cavity enthalpy is only a lower limit on the total energy of an AGN outburst, so an AGN outburst will be able to heat the system for longer than the heating time shown in Figure 15. The very small range in outburst intervals relative to the order of magnitude range in heating times suggests that any relationship between these timescales is weak. A much larger sample is required in order to draw any conclusions. The current sample is heavily biased toward nearby systems with large outbursts, and only a small range in outburst interval is detectable.
We have presented an analysis of a deep Chandra observation of MS0735. We find that the mean power required to inflate the large cavity system is , which is the most energetic outburst known. These cavities are encompassed by a continuous, elliptical shock front. We fit a simple hydrodynamical model to the surface brightness profile and obtain a Mach number of . The mean power required to drive this shock front, , is comparable to the power partitioned to the cavities. A clear temperature jump is associated with the shock front, and appears to be stronger along its major axis, where the Mach number must be higher. The power of the AGN outburst is more than enough to offset the modest cooling luminosity of .
We report the detection of a pair of bubbles corresponding to a more recent AGN outburst. These bubbles are located at a projected distance of from the cluster centre, where the outer cavities are no longer able to heat the ICM. The mean power required to inflate these cavities is . A circular feature is observed in the hard band surface brightness, and resembles the weak shock front in M87. The associated surface brightness jumps are marginal, so we cannot conclude with certainty if this is, in fact, a shock front. If it is a shock front, it has a Mach number of approximately and a mean power of .
We detect multiphase gas, with temperatures of and , within of the cluster centre. Evidently, little of this gas condenses out of the intracluster medium. The mean power of the inner cavities is a factor of larger than the combined X-ray luminosities of the two gas phases, and is therefore powerful enough to suppress cooling. Alternatively, the condensation of gas out of the ICM can be prevented by removing the supply of low entropy gas from the centre of the cluster. Cool gas is observed preferentially along the direction of the radio jet, indicating that gas has been entrained by the jet and is being dragged to high altitudes.
With the addition of MS0735, we prepare a sample of clusters and groups with multiple generations of cavities. We also include three systems with detected sound waves, two of which overlap with the cavity sample. We find that the outburst interval is shorter than central cooling time in every system. We also compare outburst interval to the heating time, defined as . We find that the majority of systems in this analysis have a heating time longer than their outburst interval, implying that AGN cycling is able to continually suppress cooling.
We thank the anonymous referee for helpful comments that improved the paper. ANV thanks Julie Hlavacek-Larrondo for helpful comments. ANV, BRM, HRR, and RAM acknowledge support from the Natural Sciences and Engineering Research Council of Canada. BRM acknowledges funding from the Chandra X-ray Observatory Cycle 10 Large Project proposal for MS0735.
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