ARE RADIO ACTIVE GALACTIC NUCLEI POWERED BY ACCRETION OR BLACK HOLE SPIN?

A growing body of evidence suggests that energetic feedback from active galactic nuclei (AGNs) is suppressing the cooling of hot halos in galaxies and clusters and preventing significant star formation in bulges at late times (Bîrzan et al. 2004; Bower et al. 2006; Best et al. 2006). But how AGNs are powered and how feedback operates are both poorly understood. AGNs are thought to be powered primarily by the gravitational binding energy released from accretion onto nuclear, supermassive black holes (SMBHs). Much of the accretion energy is released promptly in the form of radiation and mechanical outflows. However, the accreted angular momentum can spin-up SMBHs (e.g., Volonteri et al. 2005), storing rotational energy that may be tapped over longer timescales. Spin may therefore play an important role in the formation of extragalactic radio sources (Begelman et al. 1984; Wilson & Colbert 1995).

There are good reasons to investigate spin-powered feedback in galaxies and clusters. First, the energy available in a spinning black hole is significant with respect to the thermal energy of its X-ray atmosphere. A 10⁹M_☉ black hole spinning near its maximal rate stores ${\gtrsim} 10^{62} \,\rm erg$ of energy which may be released in the form of mechanically dominated jets. X-ray images have shown that jet energy couples efficiently to hot atmospheres (Bîrzan et al. 2004; Merloni & Heinz 2008), which elevates the entropy (energy) of the hot gas and suppresses cooling and star formation in galactic bulges at late times (Voit & Donahue 2005). Second, in most spin models, the jetted outflow is coupled to the black hole's rotational energy through poloidal magnetic fields anchored to an accretion disk (Blandford & Znajek 1977; Meier 1999; Beckwith et al. 2010; Krolik & Hawley 2010). These models generally require the field to be confined by the accreting gas, placing an upper limit on the magnetic field strength and hence the power that can be tapped from spin (i.e., $\dot{M} \propto B^2_p\propto P_{\rm jet}$). The connection between jet power, spin, and accretion rate could in principle provide the physical basis for a feedback loop (McNamara et al. 2009). Finally, systems with high jet power and low fuel reserves may have difficulty powering their jets by accretion, making spin power an appealing alternative to accretion power.

Radio jets are thought to form in radiatively inefficient accretion flows (e.g., RIAFs or ADAFs) associated with hot, thick disks accreting far below the Eddington accretion rate (Rees et al. 1982; Narayan & Yi 1995; Narayan & Quataert 2005; Wu & Cao 2008). Several models have been proposed to power and collimate radio jets (Begelman et al. 1984), including the Blandford–Znajek (BZ) mechanism (Blandford & Znajek 1977; Ghosh & Abramowicz 1997) and its variants. The BZ mechanism derives power from a spinning black hole through torques applied by magnetic field lines threading the ergosphere and inner region of the accretion flow. Field lines wind up along the hole's spin axis creating a collimated outflow in the form of a jet. Variants of the BZ model, the so-called hybrid models, are able to boost the power output per gram of accreted mass through the amplification of magnetic flux in the plunge region of the black hole (Reynolds et al. 2006; Garofalo et al. 2010), and through frame-dragging (Meier 2001).

In this paper, we evaluate the roles of spin and accretion in generating powerful AGN outbursts in the cores of clusters. Because current jet models require a substantial level of accretion in order to extract spin power (Nemmen et al. 2007; Cao & Rawlings 2004), we assume at the outset that all systems are ADAFs accreting at the same fraction of the Eddington accretion rate, and we then critique this assumption. Our analysis differs from other analyses in that we do not rely on radio synchrotron power as a measure of jet power (e.g., Cao & Rawlings 2004). Instead, we derive jet power from cluster X-ray cavities taken from the Rafferty et al. (2006) sample, which provide reliable mechanical power estimates that can be compared directly to spin models. Black hole masses were estimated using R-band absolute magnitudes also taken from Rafferty et al. (2006), and folded through the black hole mass versus bulge magnitude relation of Lauer et al. (2007). The objects considered here and their properties are listed in Table 1.

We adopt the model of Nemmen et al. (2007) for relating jet power to the parameters of accreting black holes. Their model follows the hybrid model proposed by Meier (1999, 2001), which relies on the BZ mechanism in rapidly spinning black holes and the Blandford–Payne model (Blandford & Payne 1982) at lower spins. Under the BZ mechanism, magnetic field threading the inner edge of the accretion disk and the ergosphere can tap the spin energy of the black hole to power a jet. The available power is proportional to the square of the spin parameter, j. The power is small unless the spin parameter is close to its maximum value of unity. Under the Blandford–Payne mechanism, magnetic field threading the inner edge of the disk taps the kinetic energy of disk material to drive the jet. This mechanism can power jets even for j = 0, but the BZ mechanism can tap substantially greater jet powers from rapidly spinning black holes

For a given black hole mass and spin parameter, the jet power depends quadratically on the poloidal magnetic field strength (magnetic pressure). Hybrid spin models (e.g., Meier 2001; Nemmen et al. 2007; Benson & Babul 2009) are able to enhance jet power by including field amplification from the rotation of the accretion disk, frame dragging, and so forth. The poloidal magnetic field strength is not an arbitrary parameter, but is determined by the accretion rate through the disk and ergosphere such that $B^2_{P}\propto \dot{M}$ (Meier 1999, 2001; Nemmen et al. 2007). Observational estimates of the spin parameters of radio galaxies (e.g., Cao & Rawlings 2004; Daly 2009) cannot be decoupled from the accretion rate, which is an issue we focus on here.

In Figure 1, we plot jet power against the estimated black hole mass for the hosting brightest cluster galaxies (BCGs). The jet powers span the range 10⁴² erg s^-1 to 10^46.5 erg s^-1, and the estimated black hole masses lie between ∼10^8.5 M_☉ and 10¹⁰ M_☉. Four objects with dynamically determined black hole masses are plotted as blue squares. All fall within the range of black hole masses estimated from bulge luminosities.

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The total energy associated with a maximally spinning 10⁹ M_☉ black hole is ${\sim} 10^{62} \,\rm erg$. Its potential power output is P_rot ≈ 10^44→47 erg s^-1 for spin-down timescales of 10^10→7yr (Martini 2004). The power output, assuming a spin-down period of 10⁸ yr, is shown as the upper solid line labeled "Pure Rotation" in Figure 1. The line lies well above the observations demonstrating that spin is a potentially important power source.

Lacking measurements of their true accretion rates, we assume initially that all systems are accreting at the same rate $\dot{m}$ in units of the Eddington limit, and we evaluate their spin parameters, j, using the Nemmen et al. (2007) model. Here the Eddington accretion rate is of the form $\dot{M}_{\rm Edd}=2.2 \epsilon ^{-1}M_{\rm BH,9} \,M_\odot \, \rm yr^{-1}$, where = 0.1 and black hole mass is given in units of 10⁹ M_☉. We further assume a viscosity parameter α = 0.2, which is within the approximate range expected in a turbulent accretion flow (see Meier 2001; Nemmen et al. 2007). Varying α between 0.04 and 0.3 in Nemmen's model does not change our conclusions significantly.

The solid line labeled "j = 1" in Figure 1 shows the calculated jet power from maximally spinning holes as a function of mass. The parallel broken lines show jet power calculated for lower spin parameters. In order to account for the high jet powers of MS0735 and Hercules A, the accretion rate must be $\dot{m} = 0.02$ or larger. We therefore have adopted this accretion rate in Figure 1. Taken at face value, the data are consistent with spin parameters lying in the broad range between 0.01 ≲ j ≲ 1, and with a median value of ≃0.6. However, due to the number of unknown variables, we are unable to place interesting constraints on the spin parameters of individual objects.

The assumption of constant $\dot{m}$ implies a physical mass accretion rate $\dot{M}$ that increases in proportion to black hole mass. With a black hole mass of about 6.4 × 10⁹ M_☉ (Gebhardt & Thomas 2009), M87 would then be accreting at $\dot{M} \sim 2.8 \,M_\odot \, \rm yr^{-1}$. Accretion at this rate would deplete its molecular gas reservoir in 3 × 10⁶ yr, which is inconsistent with the age of its current AGN outburst $7\times 10^7 \,\rm yr$ (Forman et al. 2007). Moreover, the gravitational binding energy released would dramatically exceed the observed mechanical power and radiation emerging from the nucleus, unless the binding energy is being advected onto the SMBH. Other systems suffer similar problems although their constraints are not as tight. For these reasons, the assumption that all systems are accreting at or near $\dot{m}=0.02$ seems to be unrealistic.

The distribution in Figure 1 is equally consistent with all systems harboring SMBHs with high spin parameters but with broadly varying accretion rates, or with both the accretion rate and spin varying widely. We cannot distinguish between these possibilities, except perhaps in the most powerful systems.

3.1. A Constraint on $\dot{m}_{\rm crit}$

Ignoring spin power for the moment, the accretion rate required to power the AGN in our sample assuming $P_{\rm jet} = \epsilon \dot{M}c^2$ is shown on the right-hand side of Figure 1. The value of in any given system is poorly known and can vary between 0.06 and 0.42 depending on whether we are dealing with respectively, a non-rotating black hole or a maximally spinning black hole. Given this uncertainty, we have adopted = 0.1 for all objects, which has become standard practice in the field. The accretion rates vary from $\dot{M} \simeq 10^{-4} {\, M_\odot \,\rm yr^{-1}}$ in the gE galaxy M84 to several ${\, M_\odot \,\rm yr^{-1}}$ in Hercules A and MS0735. The Bondi accretion rate from a hot atmosphere scales as $\dot{M}_{\rm B} \propto n_e (kT)^{-3/2} M_{{\rm BH}}^2$, where n_e and T are, respectively, the electron density and gas temperature at the Bondi radius, and M_BH is the black hole mass. Bondi accretion can be effective only when the hot atmosphere is sufficiently dense near the Bondi radius to feed the SMBH at a rate consistent with P_jet.

In Figure 2 we plot the ratio of jet power to Bondi accretion power against estimated black hole mass. We assume $P=\eta \epsilon \dot{M}c^2$ where the efficiency of accretion through the Bondi sphere is η = 1. In other words, all of the mass reaching the Bondi radius is assumed to be accreted onto the SMBH. Figure 2 shows that with the exception of the lower power systems residing within or near the shaded region of the plot, Bondi accretion would have great difficulty powering cluster AGN outbursts. Rafferty et al. (2006), using the data presented here, and Hardcastle et al. (2007), using powerful radio galaxies, reached similar conclusions.

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Falling gas temperatures and rising gas densities near the (unresolved) Bondi radii, in addition to the possibility that the black hole masses may be larger than their bulge luminosities imply, would increase the number of objects lying within the shaded region in Figure 2 (see Rafferty et al. 2006 for a thorough discussion). However, this effect will be offset to a degree by the overly optimistic assumption that η = 1. Mass lost to winds blowing from the accretion disk and the need to shed angular momentum from the accreting gas (e.g., Neilsen & Lee 2009; Proga 2009; Pizzolato & Soker 2010) are expected to drive η well below unity (Allen et al. 2006; Merloni & Heinz 2008; Benson & Babul 2009; Li & Cao 2010). For example, Allen et al. (2006) and Merloni & Heinz (2008) found that only a few percent of the matter reaching the Bondi radius is actually converted into jet power, which is consistent with η < 1. Accretion at this level would be able to power low-luminosity AGNs found in elliptical galaxies (Allen et al. 2006). However, it strengthens our conclusion that Bondi accretion from the hot atmosphere alone probably cannot fuel the most powerful AGNs in clusters.

In Figure 3 we plot total molecular gas mass against jet power for the objects with gas mass measurements available in the literature. The molecular gas masses generally lie between 10⁹ M_☉ and 10¹¹ M_☉. Only M87's upper limit of less than 8 × 10⁶M_☉ (Tan et al. 2008) lies substantially below this range. Gas masses were corrected to our adopted cosmology when necessary; details of the gas mass analysis can be found in the references given in the caption to Figure 3. The gas masses needed to fuel the AGNs, M_acc ∼ E_cav/0.1c² = 10⁶ M_☉–10⁹ M_☉, lie well within the observed range seen in Figure 3. Nevertheless, if these AGNs are powered primarily by accretion of molecular gas, a correlation between the gas supply and jet power would be expected. Spin models requiring high accretion rates would also predict a correlation. Yet no correlation is seen between molecular gas mass and jet power within the range of jet power shown in Figure 3. The Spearman rank order correlation coefficients for the sample including and excluding upper limits are 0.35 and 0.60, respectively. These statistical figures of merit confirm the absence of an evident correlation in Figure 3. In fact, for a given jet power the molecular gas reservoirs vary in mass by more than two orders of magnitude. Furthermore, the large gas supply relative to AGN power in most systems suggests that very little molecular gas is currently reaching the black hole.

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The large scatter and absence of a correlation may be related to several factors. The most important factor may be the presence or absence of star formation, which we discuss further below. The high star formation rates in many of the objects in our sample indicate that most of their molecular gas is being consumed by star formation (Rafferty et al. 2006; O'Dea et al. 2008). Some of the gas that is not consumed by star formation may be driven away from the nucleus by AGNs (Sternberg & Soker 2009). In addition, temporal variations in accretion rate related perhaps to dynamical interactions with neighboring galaxies may also be contributing to the scatter. Finally, because in most systems only a small fraction of the molecular gas mass is required to fuel the AGN, a real underlying correlation may be lost in the scatter. Whatever the important factors may be, AGN power seems to be largely decoupled from the total molecular gas supply in these systems.

5.1. Accretion Efficiency per AGN Outburst

Another way to look at this problem is to evaluate the fraction of the available molecular gas mass in the host galaxy that must be consumed by the AGN in order to power it. We refer to this as the accretion efficiency per AGN outburst. We define the accretion efficiency per AGN outburst as E_jet/0.1 M_molc². Using this definition, a plot of accretion efficiency versus molecular gas mass is shown in Figure 4. The figure shows no apparent trend, but instead shows a large range in accretion efficiency as a function of molecular gas mass.

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The median accretion efficiency of the sample is approximately 6 × 10⁻⁴. This figure indicates that for each unit of mass that is accreted onto the black hole, less than 1600 units form into stars. This assumes that most of the remaining molecular gas is consumed by star formation (O'Dea et al. 2008) and not the AGN, which is a reasonable assumption for BCGs. As a point of reference, the average mass accretion efficiency of SMBHs implied by scaling relations between bulge and black hole mass is ≃1.4 × 10⁻³ (Magorrian et al. 1998, Häring & Rix 2004). In other words, for each unit of mass that fell into nuclear black holes, roughly 700 units of mass formed stars. This figure lies below the median for our sample but is well within its variance. The accretion efficiency at a given gas mass varies by more than three orders of magnitude. Therefore, the similarity between the two figures may be a coincidence.

The extremes in accretion efficiency are Abell 1068 and MS0735. On the one hand, Abell 1068 is a cluster with a burgeoning central galaxy that hosts a relatively weak AGN. On the other hand, MS0735's BCG is gas-poor and shows no evidence of star formation, yet it hosts an extraordinarily powerful AGN. Abell 1068's BGG contains ∼10¹¹ M_☉ of molecular gas (Edge 2001) and is experiencing star formation at a rate of ${\sim} 60\, M_\odot\ \rm yr^{-1}$ (McNamara et al. 2004). The BCG has a weak radio AGN indicating a current accretion efficiency below 10⁻⁵. It is a strong far-infrared source (Edge et al. 2010). Most of the infrared luminosity is associated with star formation, but some of may be associated with a buried AGN (Quillen et al. 2008). The energy being released in the infrared by the AGN may indicate a higher accretion rate than its radio power indicates. But the mechanical energy associated with its radio AGN clearly falls well below the sample mean.

Most of the objects in this sample with molecular gas masses above a few 10⁹M_☉ are experiencing star formation and thus bulge growth at some level. All of the objects with gas masses above 10¹⁰ M_☉ are located to the upper left quadrant of Figure 4, and all are experiencing star formation above several tens of solar masses per year (O'Dea et al. 2008). At the same time, all have moderately powerful AGN outbursts and are thus experiencing black hole growth. Rafferty et al. (2006) found that many cooling flow BCGs with star formation and powerful AGN are growing parallel to the slope of the black hole versus bulge mass scaling relations. Rafferty's result is consistent with our finding that the median accretion efficiency also lies close to the expected value from black hole scaling relations. Abell 1068 is an outlier in the sense that its black hole appears to be growing more slowly than expected for its current star formation rate.

With an accretion efficiency of approximately 10%, MS0735 represents the opposite extreme. A search for molecular gas in MS0735 in the CO[1 → 0] emission line by Salome & Combes (2008) revealed an upper limit of ∼10¹⁰ M_☉. An HST image of the BCG has revealed only weak nuclear dust features. Furthermore, its star formation rate, based on both far-ultraviolet (McNamara et al. 2009) and mid-infrared observations (M. Donahue et al. 2011, in preparation), lies below $0.25 \,M_\odot\ \rm yr^{-1}$. Apart from its AGN, the galaxy appears to be dormant, and is similar to other BCGs with gas reservoirs below about 10⁹ M_☉.

The implication is that the ratio of MS0735's molecular gas mass to its total jet power is so small that a substantial fraction of its existing gas supply must have been consumed by its SMBH in the past 10⁸ yr. If so, the gas must have efficiently shed its angular momentum and accreted rapidly onto the SMBH. It must have done so without forming an appreciable number of stars, which would be difficult to understand (see McNamara et al. 2009 for a discussion). Hydra A, MKW3S, and Cygnus A are similar but less extreme. In fact, these objects appear to congregate together at the high efficiency and relatively low gas mass quadrant to the lower right of Figure 4. Given their relatively modest gas masses, it is surprising that they they are among the most powerful AGN known in clusters.

Powerful radio AGN located in relatively gas poor host galaxies have been noticed elsewhere. Ocaña Flaquer et al. (2010) noted relatively modest molecular gas masses of a few 10⁸ M_☉ in powerful, nearby radio galaxies. In addition, Emonts et al. (2007) reported an anti-correlation between radio source size and neutral hydrogen mass in giant elliptical galaxies. Because radio source size is correlated with jet power, the implication is that powerful AGN are inversely correlated with the gas supply of the host galaxy. The trends we are seeing in BCGs may be related to a more general phenomenon of high jet powers associated with relatively gas-poor host galaxies.

Being the most powerful FR II radio source in the nearby universe, Cygnus A is worth a brief discussion. An new analysis of the well-known shock front in the X-ray halo surrounding its radio lobes gives Mach number 1.4, total shock energy $E_s=2\times 10^{60} \,\rm erg$, and a mean jet power of 4 × 10⁴⁵ erg s^-1 (P. E. J. Nulsen et al. 2011, in preparation). This power measurement is substantially less than that of Wilson et al. (2006), which treated the shock as very strong. Powering Cygnus A by accretion would have consumed more than ∼10⁷ M_☉ of gas over the past 1.6 × 10⁷ yr. For comparison, Salome & Combes (2003) found an upper limit of 1.5 × 10⁹ M_☉ of molecular gas in its bulge. Assuming the true mass lies just below this limit, it would harbor enough gas in principle to feed the outburst. Nevertheless, its accretion efficiency exceeds 7 × 10⁻³, placing it among the high accretion efficiency systems in Figure 4.

The AGN outburst energies of Abell 1835 and Zw 3146, both of which are indicated in Figure 4, are comparable to that of Cygnus A. However, their accretion efficiencies are an order of magnitude or so lower, placing them to the upper left in Figure 4. Unlike Cygnus A, their bulges contain ∼10¹¹ M_☉ of molecular gas and they are forming stars at rates approaching $100\, M_\odot\, \rm yr^{-1}$. Their locations in Figure 4 imply that gas-rich systems with high star formation rates are unable to channel fuel onto the nucleus as efficiently as gas-poor systems. It is not clear why this would be so. But we suggest that star formation is consuming the molecular gas so rapidly that it is inhibiting the flow of gas onto the AGN.

Assuming all AGN in this sample are powered by accretion, the large variation in accretion efficiency with respect to gas mass seen in Figure 4 must be contributing to the variation in jet power with respect to gas mass seen in Figure 3. Some of the variation in accretion efficiency may be related to variations in the value of the mass to energy conversion efficiency, , which depends on the spin of the black hole. can vary by a factor of 7 depending on whether the black hole is a non-rotating Schwarzschild black hole or a maximally spinning Kerr black hole. The scatter in Figure 4 is much larger than this factor, so the spin of the black hole alone cannot account for it.

In light of this discussion, it remains unclear whether spin is an important factor in powering radio AGNs. Those systems with high (apparent) accretion efficiencies and small gas reservoirs that would have difficulty powering their AGN by accretion alone may be good candidates for spin powering (see also Paggi et al. 2009, Hart et al. 2009). The objects meeting this criterion our sample: Cygnus A, Hydra A, MS0735, MKW3s, are located to right side of Figure 4. If instead their current AGN outbursts are powered by accretion, then their black holes apparently consumed between one part in a few to one part in one hundred of their entire gas supply, indicating a highly efficient mode of accretion. While it would be tempting to attribute powerful AGN residing in gas poor galaxies to spin, current BZ-based spin models (e.g., Nemmen et al. 2007, Benson & Babul 2009) also require relatively high accretion rates. Therefore, a mechanism that is able to tap spin power efficiently at relatively low accretion rates, i.e., $P_{jet} > \dot{M}c^2$, may be needed to explain these systems. We note that existing BZ models still fail to make $P_{jet} > \dot{M}c^2$.

We have examined two possible scenarios for powering AGNs in BCGs: accretion of cold molecular gas and black hole spin. Understanding how radio AGNs are powered is central to many questions related to the evolution of galaxies and black holes, including how AGN feedback operates at late times (e.g., Croton et al. 2006; Somerville et al. 2008). Although we are generally unable to distinguish between these two related scenarios, we find that AGN power in BCGs would be consistent with both a broad range of spin parameters and accretion rates. We find no significant correlation between jet power and molecular gas mass in these systems. We have identified several powerful AGNs associated with BCGs that have surprisingly low gas reserves. Although accretion of cold gas must be important at some level, this study shows that AGN power is poorly correlated with the total molecular gas mass of the host BCG. Molecular gas is clearly associated with star formation (O'Dea et al. 2008), so perhaps most of the gas is being consumed by star formation before it is able to flow into the nucleus. Bondi accretion from hot atmospheres, which has become a staple in AGN feedback models, may be able to fuel weak AGNs (Allen et al. 2006), but would have great difficulty supplying enough gas to power the most energetic AGNs.

If radio AGNs are powered instead by black hole spin, the observed distribution of jet power implies a broad range of spin parameters, given the spin model adopted here (Nemmen et al. 2007). BZ-based models such as Nemmen's require substantial accretion rates in order to access spin power. Thus, it is impossible to place interesting constraints on the spin parameter based on jet power alone. We have highlighted several powerful AGNs residing in relatively gas-poor bulges, which are good candidates for jet powering by black hole spin. However, they may have difficulty achieving their power output even with spin parameters approaching unity, unless their spin is tapped with high efficiency, i.e., P_jet>Mc² (e.g., Garofalo et al. 2010), or their black holes are more massive than expected.

Our understanding of the accretion process in AGNs will advance significantly in the future when ALMA becomes operational, and we are able to disentangle the molecular gas fueling star formation from the nuclear gas that will eventually plunge into the black hole. Likewise, future large aperture X-ray and optical/IR telescopes with subarcsecond resolution are needed to explore the environments of AGNs nearer to their Bondi spheroids.

We thank M. Ruszkowski, D. Evans, and A. Babul for good suggestions. This research was supported in part by a generous grant from the Natural Sciences and Engineering Research Council of Canada.