Black-Hole Feedback and Coevolution

Black holes can inject enough radiation, momentum, and mechanical energy to transform their environments. That energetic possibility is not yet a causal demonstration that feedback sets a galaxy’s stellar mass, quenches its star formation, or creates a black-hole–host relation. A persuasive case must connect the engine to the gas in space and time, close the coupled energy and momentum budgets, and outperform explanations based on shared fuel, halo potential, merger averaging, and selection.

Required background. Probability and inference for gravity supplies causal graphs, selection-aware comparison, and counterfactual reasoning.

Helpful background. Black-Hole Geometry and Mechanics supplies black-hole energy scales; Relativistic Matter and Compact Objects supplies the compact accretor; Black-Hole Astrophysics supplies accretion, winds, and jets; Relativistic Cosmology supplies halo growth and population evolution.

From available energy to coupled work

If a black hole gains gravitational mass $\Delta M_\bullet$ through radiatively efficient accretion with efficiency $\eta$, the emitted radiative energy is

$$E_{\rm rad} = \frac{\eta}{1-\eta}\,\Delta M_\bullet c^2.$$

Only a fraction $\epsilon_{\rm coup}$ reaches the relevant gas in the relevant form:

$$E_{\rm coup}=\epsilon_{\rm coup}E_{\rm rad}, \qquad p_{\rm rad}=\frac{E_{\rm rad}}{c}.$$

A rough comparison scale for bulge gas is

$$E_{\rm bind}\sim f_g M_{\rm bulge}\sigma^2, \qquad p_{\rm bind}\sim f_g M_{\rm bulge}\sigma.$$

These estimates explain why a small coupling fraction can be dynamically important: rest-mass energy is enormous compared with galactic binding energy. They do not show where energy was deposited, whether it radiated away, which phase received it, or whether star formation changed. A momentum-conserving shell, an energy-conserving hot bubble, a narrow jet, and distributed cosmic-ray heating can share the same injected power yet produce different spatial and temporal responses.

The appropriate budget is local and multiphase:

$$\dot E_{\rm in} = \dot E_{\rm thermal} +\dot E_{\rm kinetic} +\dot E_{\rm cosmic\,ray} +\dot E_{\rm radiation} +\dot E_{\rm escape} +\dot E_{\rm loss}.$$

Likewise, the gas supply must be followed from halo inflow through cooling, molecular-cloud formation, stars, outflow, recycling, and black-hole accretion. Measuring one fast ionized component and multiplying it by a single radius does not close this budget.

Two feedback regimes, several physical outcomes

At low Eddington ratio in hot atmospheres, jets inflate X-ray cavities and drive shocks or sound waves. For a cavity in ambient pressure $p$, its enthalpy is

$$H=\frac{\gamma}{\gamma-1}pV,$$

so relativistic contents give $H=4pV$. Dividing by buoyancy, sound-crossing, and refill ages brackets a time-averaged cavity power. Comparing that power with cooling luminosity in a matched aperture is one of the clearest direct energy tests, but projection, unseen cavities, pressure support, age, duty cycle, and the location of dissipation remain consequential McNamara and Nulsen 2007, §§ 3.4–3.10 and 5.1–5.6. A global equality $P_{\rm cav}\simeq L_{\rm cool}$ supports maintenance balance; it does not by itself prove that heat arrives wherever and whenever cooling occurs.

At high Eddington ratio, radiation and disk winds can accelerate ionized, neutral, atomic, and molecular gas. For a phase with characteristic radius $R$, velocity $v$, and mass $M_{\rm out}$, the familiar estimates

$$\dot M_{\rm out}\sim\frac{M_{\rm out}v}{R}, \qquad \dot p_{\rm out}=\dot M_{\rm out}v, \qquad \dot E_{\rm kin}=\frac12\dot M_{\rm out}v^2$$

depend on geometry, density, filling factor, projection, flow history, and the convention relating radius to duration. An outflow proves coupling and motion, not permanent gas removal or quenched star formation. Gas can stall, cool, recycle, or compress other gas and produce a positive or mixed response. Reviews of resolved systems emphasize that driving, coupling, and impact are separate observational questions Fabian 2012, §§ 2–5; Harrison et al. 2024, §§ 3–5.

A causal chain with matched scales

A strong feedback claim needs all of the following links.

1. Engine: infer radiative, wind, or jet output with calibration and beaming uncertainties.
2. Coupling: locate shocks, cavities, accelerated phases, heating, or ionization that connect that output to gas.
3. Response: measure changes in density, temperature, turbulence, cooling, escape, recycling, and star formation over the same aperture.
4. Timing: show that the response follows a physically allowed propagation history despite different AGN and stellar-population clocks.
5. Counterfactual: predict what the same system or population would have done without the intervention.
6. Population consequence: reproduce held-out distributions in mass, color, gas content, star formation, occupation, and redshift.

No single observation normally supplies all six. The AGN varies on timescales far shorter than a galaxy’s integrated star-formation history, while a cavity or fossil outflow averages over a different interval again. Instantaneous anticorrelation can therefore appear even in a causal cycle: accretion peaks, drives a response, fades, and is observed after the gas changes. Conversely, both activity and star formation can rise because a common inflow fuels them.

A causal graph makes the ambiguity explicit. Halo mass, mergers, bars, environment, and gas supply can affect both black-hole accretion and host growth. Conditioning on a detected AGN or resolved sphere of influence can itself create correlations. The black-hole–host scaling page develops these selection effects; Kormendy and Ho show that relations differ among classical bulges, pseudobulges, disks, and merger histories, weakening any one universal coevolution narrative Kormendy and Ho 2013, §§ 6–9.

Counterfactuals in simulations and observations

In a controlled simulation, the relevant intervention changes the feedback channel while holding initial conditions, resolution, stellar feedback, cooling, and black-hole seeding fixed. The comparison must close conservation residuals and demonstrate spatial, mass, and time convergence. If a coupling efficiency was tuned to reproduce a galaxy mass function or black-hole scaling relation, that same relation is not independent evidence; evaluation belongs on gas fractions, entropy profiles, outflow phases, star-formation histories, occupation, and redshift evolution that were not tuned.

Simple “feedback off” experiments can also be misleading. Removing energy injection changes black-hole growth and hence the future engine, so the two branches diverge dynamically. Useful interventions include matched-power changes in geometry or channel, delayed injection, altered coupling to one gas phase, and ensembles over chaotic initial perturbations. The result should state which causal contrast is estimated.

Observations cannot rerun a galaxy, but they can approximate counterfactuals through matched inactive controls, spatially resolved before–after clocks, transverse regions outside a jet or ionization cone, fossil episodes, and population models that include nondetections. A control matched only in stellar mass is inadequate if halo mass, gas content, morphology, merger state, and environment determine both treatment and outcome.

Results and open questions

The evidence cutoff is 2026-08-18. Black-hole coupling is established in several systems; universal causal self-regulation of galaxy growth remains unresolved.

Evidence stream or position	Evidence or result	Counterexample or independent check	Scope, limitation, or open status
Jet maintenance in hot atmospheres	Cavities and shocks provide spatially resolved mechanical calorimetry; powers can match cooling demand	Recompute $4pV/t$ with three ages and test heat deposition within the cooling aperture	Projection, duty cycle, transport, conduction, and unseen phases limit causal closure
Radiative or wind-driven quasar feedback	Multiphase outflows demonstrate gas acceleration across galaxy scales	Close mass, momentum, and energy in all phases and follow escape or recycling	Radius, density, geometry, time averaging, and power source remain major systematics
Causal self-regulation	Energy and momentum scales can produce a limiting black-hole–host relation	Predict gas, star-formation, and residual correlations not used to set the coupling	A successful scaling is not unique evidence for the mechanism
Shared supply or common potential	Gas inflow and halo or bulge structure can correlate black-hole and stellar growth	Compare time-lagged responses and controls matched in gas, halo, merger, and environment	Latent common causes are difficult to measure completely
Merger averaging and selection	Repeated mergers and targeted mass measurements can tighten apparent relations	Forward-select mock parent populations with and without feedback	Requires realistic occupation, measurement, morphology, and follow-up decisions
Positive or mixed feedback	Compression can locally enhance star formation while other phases are removed or heated	Balance stimulated and suppressed star formation over matched space and time	Local triggering need not increase the galaxy-integrated stellar mass
Simulation intervention	Feedback-enabled models can alter massive-galaxy growth and hot-gas structure	Paired runs, conserved budgets, convergence, and held-out observables	Subgrid calibration and compensating stellar feedback limit uniqueness

The discriminating program combines an engine energy history, resolved multiphase gas response, matched inactive controls, and paired simulations under a common likelihood. It tests cooling, gas escape and recycling, star-formation history, black-hole growth, and host scaling simultaneously. Negative or null results in one phase remain informative because they restrict where coupling can hide.

The interpretation could change after a causal time-domain observation, a resolved multiphase energy census, or a controlled simulation comparison with held-out predictions; a selection-corrected revision of black-hole–host relations could also change the conclusion because it changes the correlation the feedback model must explain.

Interpretation and scope

Feedback is an energy-and-information loop: accretion powers an output, the output changes the supply, and the altered supply changes later accretion. “Coevolution” should describe this demonstrated coupling, not merely parallel cosmic histories. The strongest present cases establish substantial mechanical work and plausible maintenance balance; the step from those cases to a universal origin for galaxy demographics remains model dependent.

Generic host demographics without black-hole inference are outside this page’s scope. The detailed cavity methodology appears in jets, feedback, and host environments; the Soltan argument supplies the integrated accretion-energy scale.

Common pitfalls

Comparing total energies only. $E_{\rm coup}>E_{\rm bind}$ is necessary in some expulsion models but is not sufficient without geometry, loss, timing, and multiphase response.

Calling every outflow quenching. Motion can end in escape, recycling, heating, compression, or no measurable change in star formation.

Validating on a tuned relation. A simulation calibrated to a scaling relation must be tested on independent observables and explicit intervention pairs.

Test an energy and momentum claim

A black hole gains $\Delta M_\bullet=10^7M_\odot$ with $\eta=0.10$. Suppose $\epsilon_{\rm coup}=0.005$. A bulge contains $M_g=10^{10}M_\odot$ of relevant gas with $\sigma=200\,\mathrm{km\,s^{-1}}$. Estimate $E_{\rm coup}/(M_g\sigma^2)$ and $(E_{\rm rad}/c)/(M_g\sigma)$. Does either ratio prove quenching?

Solution

Using $M_\odot c^2\simeq1.79\times10^{54}\,\mathrm{erg}$,

$$E_{\rm rad} = \frac{0.10}{0.90}(10^7M_\odot)c^2 \simeq1.99\times10^{60}\,\mathrm{erg},$$

and $E_{\rm coup}\simeq9.9\times10^{57}\,\mathrm{erg}$. The gas comparison scale is

$$M_g\sigma^2 \simeq (10^{10})(1.99\times10^{33}\,\mathrm{g}) (2.0\times10^7\,\mathrm{cm\,s^{-1}})^2 \simeq8.0\times10^{57}\,\mathrm{erg},$$

so the nominal energy ratio is about $1.25$.

For momentum,

$$\frac{E_{\rm rad}}{c} \simeq6.6\times10^{49}\,\mathrm{g\,cm\,s^{-1}}, \qquad M_g\sigma\simeq4.0\times10^{50}\,\mathrm{g\,cm\,s^{-1}},$$

giving a ratio near $0.17$. An energy-conserving bubble can amplify shell momentum beyond the direct radiative value, but only if cooling and leakage permit it. Neither ratio proves quenching: the assumed coupling may not reach the relevant gas, the geometry and duration are unspecified, and the calculation says nothing about cooling, recycling, or the counterfactual star-formation history.

References

• Fabian, Andrew C. “Observational Evidence of Active Galactic Nuclei Feedback.” Annual Review of Astronomy and Astrophysics 50 (2012): 455–489. doi:10.1146/annurev-astro-081811-125521.
• Harrison, Christopher M., et al. “Observational Tests of Active Galactic Nuclei Feedback: An Overview of Approaches and Interpretation.” Galaxies 12 (2024): 17. doi:10.3390/galaxies12020017.
• Kormendy, John, and Luis C. Ho. “Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies.” Annual Review of Astronomy and Astrophysics 51 (2013): 511–653. doi:10.1146/annurev-astro-082708-101811.
• McNamara, Brian R., and Paul E. J. Nulsen. “Heating Hot Atmospheres with Active Galactic Nuclei.” Annual Review of Astronomy and Astrophysics 45 (2007): 117–175. doi:10.1146/annurev.astro.45.051806.110625.