A critical review of the AGN feedback models

 

I have developed my career over almost 20 years as an engineer. In the astronomy world, but always with engineering roles. As an engineer, you can receive reports of something not working, and what is expected is that you acknowledge and investigate the problem and then find a solution. At some point, you realize that a system has a more fundamental issue, and a completely new approach is necessary. In my opinion, the state of AGN feedback models in the context of cool-core galaxy clusters really falls into this category. In my previous entry, I presented the characteristic curve of cool-core fractions from groups to massive clusters, and showed that there is a discrepancy at the lower mass range, in the domain of galaxy groups.  This problem becomes even more visible when comparing the mid and strong cool-core cluster populations, which are significantly more suppressed in comparison with observations, in contrast with the general cool-core cluster population. 

The plot above, presented in Appendix A of my paper "How the cool-core population transitions from galaxy groups to massive clusters" illustrates the mid (left panel) and mid-to-strong (right panel) cool core cluster populations of the largest Magneticum simulation (Box2b/hr) in comparison with observational data. The discrepancy is clear, and extends to the galaxy cluster regime, even above the mass limit where the observational data samples should be complete and unbiased. Paraphrasing Professor Massimo Gaspari: “We live now probably in a theoretical era of heating catastrophe, in which cooling can be easily halted, but models are rarely checked against overheating.” (from "Solving the cooling flow problem through mechanical AGN feedback")

So, what has happened? There are many different issues that contribute to this problem. One is, of course, the AGN feedback level, which is significantly higher than what can be derived from cavity powers and radio emission in observed low mass end of galaxy clusters, and groups as illustrated by the plot on the left side. This was already pointed out by Prof. Dr. Dunja Fabjan in the comprehensive work "Simulating the effect of active galactic nuclei feedback on the metal enrichment of galaxy clusters" a few years ago. Going back to the origin of this model which was presented in the seminal paper "Supermassive Black Holes in Elliptical Galaxies: Switching from Very Bright to Very Dim" the expectation is that if the AGN  accretion follows the Bondi formula, which is inversely proportional to the entropy, then a self-regulating feedback loop should be established. In this case, the radiative and feedback efficiencies, which are parameters that regulate the energy injected in the surrounding medium following AGN accretion, should not matter that much if they are set to 'reasonable' values. But in reality, we see that the feedback loop does not adjust naturally, and it is very difficult (if not impossible) to set the radiative and feedback efficiencies to values that work at all scales, from galaxy groups up to massive galaxy clusters. For example, the previously mentioned work "Solving the cooling flow problem through mechanical AGN feedback" proposes 3 different values of feedback efficiency for galaxy clusters, galaxy groups, and isolated ellipticals. Also, the detailed observational work "AGN jet power and feedback characterised by Bondi accretion in brightest cluster galaxies" by Yukata Fujia finds a ratio between the AGN power and the so-called “Bondi Power” in the range of 0.001 – 1, spanning 3 orders of magnitude. It is truly a fine-tuning problem, which triggers all my alarms that there is something unnatural in the underlying idea that the AGN feedback can self-regulate to perfectly compensate the radiative looses. 

Unfortunately the problems do not end here. If we look in detail at the situation of the simulated cool-core fractions and AGN feedback at the scale of massive galaxy clusters, they seem to align well with observations; therefore, one would expect the simulated gas and stellar fractions to also match observations, but this is not the case, as illustrated by the figures below. The left panel shows the total (hot + cold) gas fraction in the inner regions (R2500) of simulated and observed galaxy clusters, and the right-hand panel shows the stellar gas fraction for the same region. 

There is clearly a systematic excess of stellar mass, and a corresponding deficit of gas mass, which in reality would be much worse if we looked only at the hot gas, not the total cold + hot gas. So, despite having a better agreement for the AGN feedback at the scale of massive galaxy clusters, it has not properly stopped runaway cooling and star formation. 

The missing link here lies in the spatial distribution of AGN feedback. Even if the level of AGN feedback is well aligned with observations at the scale of massive galaxy clusters, the energy is injected stochastically, but following spherical symmetry in the neighbouring particles inside the so-called ‘black hole sphere of influence’ radius, which decreases as the density increases, following the SPH description for smoothing length (See Eq. 6 from "The cosmological simulation code GADGET-2"). As a result, the AGN feedback generated in lower entropy cores, with higher densities, which actually produce stronger AGN feedback following the Bondi accretion formula, is deposited in smaller regions. This is at odds with observations where we see that the stronger the AGN feedback is, the further it reaches, as illustrated by the plot on the right side.

These problems are not so visible at large scale, and as a matter of fact, the recent compendium of comparisons between observations and the Magneticum simulations shows a good agreement looking at the larger scales of R500 (see "Scaling Relations from Cosmic Dawn to Present Day"). But the AGN feedback model was conceived to prevent problems at the core regions, so a positive check at larger scales does not imply a validation of the AGN feedback model. One interesting example of this is enrichment at large radii. This is usually attributed to the goodness of the AGN feedback models (see Enrichment of the hot intracluster medium: Numerical simulations), but then from observations we see a much stronger difference in the flatness of metallicity profiles comparing disturbed and non-disturbed systems rather than radio-active and radio-quiet systems (see Figures 7 and 8, respectively, from "The non-uniformity of galaxy cluster metallicity profiles").

It is possible to address these problems, adjusting the AGN feedback efficiency to have a better scaling from galaxy groups up to galaxy clusters, and also, it is possible to use different distribution schemas for the injected energy, which scale with the feedback power as seen in observations. In the paper "How the cool-core population transitions from galaxy groups to massive clusters" we present effective models in this direction, also illustrated in the plots below, which show in dark blue the 'corrected' AGN feedback energy injection (left panel), and 'corrected' AGN feedback reach or sphere of influence (right panel).  These alternative models could potentially alleviate overheating problems at the scale of galaxy groups and the excess of star formation at the scale of galaxy clusters.

However, I see these options as technical ‘workarounds’ (using the engineering argon), because in reality the AGN feedback is highly directional, and not distributed spherically as done by the simulations. Some popular lines to improve the AGN feedback models are based on spin, since variations in the AGN spin naturally provide a way to distribute the AGN feedback along different directions. However, a very nice result from Lucas Sala shows that the spin parameter of the AGNs in the center of BCGs actually decreases with the mass of the system (see "Supermassive black hole spin evolution in cosmological simulations with OPENGADGET3"). This has always made a lot of sense to me, since more massive galaxy clusters have typically undergone more mergers, and therefore the spin parameter should tend to 0 according to the isotropic principle (see the illustration below). However, it poses two problems. First, it means that the AGN efficiency (accounting for spin) should actually be higher for galaxy groups than for galaxy clusters, which could cause even stronger overheating for groups and runaway cooling for massive clusters. Secondly, it shows that it is hard for the AGNs of massive galaxy clusters to acquire a higher spin, or change it, which also makes sense since most of the AGNs in massive galaxy clusters are in ADAF mode, with a torus accretion zone rather than a high angular momentum disk.

Finally, some part of the community has always argued that mechanical feedback is the right channel for the AGN feedback in the modern Universe, since almost all AGNs in the center of galaxy clusters are very dim and in radiative mode (see again "Supermassive Black Holes in Elliptical Galaxies: Switching from Very Bright to Very Dim"). It was difficult to argue against mechanical feedback because it was not observable until recently; however, the observations from Hitomi and XRIM point towards very little kinetic energy (low thermal pressure support) in the cores of galaxy clusters as opposed to what is expected from AGN mechanical feedback:

- Hitomi Perseus: "Turbulent pressure support in the gas is 4% or less of the thermodynamic pressure, with large scale shear at most doubling that estimate... A low level of turbulent pressure and bulk shear, in a region continuously stirred by a central AGN and gas sloshing, is surprising and may imply that ICM turbulence is difficult to generate and/or easy to damp." ("The Quiescent Intracluster Medium in the Core of the Perseus Cluster")

- XRIM Centaurus: "The ratio of kinetic to thermal energy density is ∼ 0.03. The velocity dispersion does not increase significantly even in the Central region or in the AGN neighbourhood. This may indicate that the influence of the AGN on the ICM motion in the core is limited." (see "The Bulk Motion of Gas in the Core of the Centaurus  Galaxy Cluster")

- XRIM A2029: "The AGN is currently bright in the radio, but there is no evidence in the X-rays of any AGN driven mechanical disturbance. These characteristics, combined with the low non thermal  pressure support inferred from the low XRISM velocity dispersion, suggest the cluster may currently be in a quiescent phase of AGN feedback" (see "XRISM Reveals Low Nonthermal Pressure in the Core of the Hot, Relaxed Galaxy Cluster A2029")

- Moreover, the simulations that report low levels of turbulent energy compatible with the observations of Hitomi and XRIM neither implement radiative cooling nor AGN feedback (see "Turbulence in Simulated Local Cluster Analogs: one-to-one comparisons between SLOW and XRISM/Hitomi")

So let’s summarize:

- The results from simulations show that the AGN feedback loop does not self-regulate and cannot be adjusted to perfectly compensate for the radiative losses at all scales (from galaxy groups to massive clusters). It is extremely difficult to obtain a balance between radiative losses and AGN feedback, and it does require fine-tuning in the best case.

-Even if the models were perfectly tuned, real AGN feedback is highly directional, and the energy distribution mechanisms are very unclear. This means that still lots of cold gas should be formed in the regions away from the line of sight of the AGN jets.Variation of AGN spin as a way to better distribute the AGN feedback does not work in the modern Universe because most AGNs are in ADAF mode, characterize by low angular momentum accretion driven by torus rather than a thin disk.

- Spin-based models to regulate the AGN efficiency show that the AGNs hosted in the massive clusters have undergone more mergers, and have a lower spin parameter, which means that they should have lower AGN feedback efficiency than AGNs hosted in galaxy groups. However, this could actually increase the overheating problems in galaxy groups and runaway cooling in massive galaxy clusters.

- Since in the modern Universe almost all AGNs in the cores of galaxy clusters are in radio mode, the energy can only be injected in the form of non-radiative channels such as mechanical feedback; however, both Hitomi and XRIM have detected very low levels of turbulent energy, even in the regions surrounding the AGNs.

What do you think? To me, this looks like the underlying idea of AGNs preventing runaway cooling in the cores of galaxy clusters in the modern Universe is shaky, and I think it would be worth looking into other directions rather than trying to hammer this idea any further. Perhaps we should revisit thermal conductivity? This has the advantage of being present everywhere in the cluster core as opposed to directional AGN feedback. But thermal conductivity requires resolving the so-called field length to work effectively, which means that perhaps a higher resolution than the one used so far in the cosmological simulations, such as Magneticum Box2b or Illustris TNG-300 / TNG-Cluster is needed.