Black Hole Spin-Dependent Hybrid AGN Feedback

• Hybrid AGN feedback combines kinetic (jet-driven) and thermal processes, leveraging black hole spin to regulate gas dynamics and star formation.
• High black hole spin enhances jet power via the Blandford–Znajek mechanism, with efficiency increasing steeply with the spin parameter.
• This framework explains key observational phenomena like multiphase outflows, cooling flow regulation, and anisotropic feedback in galaxies and clusters.

Black hole spin‐dependent hybrid jet/thermal AGN feedback refers to the combination of kinetic (jet-driven) and thermal (radiative or wind-driven) feedback processes in active galactic nuclei (AGN), with a central focus on how the spin of the supermassive black hole modulates the efficiency, geometry, and impact of these feedback modes. This concept integrates advanced numerical models and observational diagnostics to explain the self-regulation of black hole growth, star formation quenching, gas thermodynamics, and the multiphase structure of galaxy and cluster environments.

1. Fundamental Mechanisms of Hybrid Jet/Thermal AGN Feedback

Hybrid AGN feedback models implement two principal feedback channels that operate depending on the black hole's accretion state:

• Kinetic (Jet) Feedback: At low accretion rates relative to the Eddington limit, feedback is deposited in kinetic form as highly collimated, bipolar jets. The kinetic feedback mode is commonly implemented via the injection of momentum and energy in a cylindrical or conical region, simulating relativistic AGN jets that displace and heat the surrounding gas through shock waves, bubble inflation, and turbulence generation.
• Thermal (Radiative/Quasar) Feedback: At higher accretion rates (near-Eddington), energy is released as thermal or radiative feedback—often modeled as isotropic heating or ultra-fast (wind) outflows that heat and ionize the interstellar or intracluster medium through bubbles, blast waves, or pressure-driven expansion.

The transition between these modes is governed by the dimensionless accretion rate $\chi = \dot{M}_{\rm BH}/\dot{M}_{\rm Edd}$, with a critical value (commonly $\chi \sim 0.01$) dictating the switch from thermal to kinetic dominance (Dubois et al., 2011, Dubois et al., 2011, Weinberger et al., 2016, Huško et al., 2023).

The total AGN power output in hybrid models is often expressed as: $$\dot{E}_{\rm AGN} = \epsilon_f\,\epsilon_r\,\dot{M}_{\rm BH} c^2,$$ where $\epsilon_r$ is the radiative efficiency (spin-dependent), $\epsilon_f$ is the feedback coupling efficiency, and $\dot{M}_{\rm BH}$ is the black hole accretion rate.

2. Black Hole Spin and Jet Feedback Efficiency

The spin of the black hole is a critical parameter controlling jet power through the extraction of its rotational energy, typically via the Blandford–Znajek (BZ) mechanism. The BZ jet power for a Kerr black hole is given by: $$P_{\rm jet}^{\rm BZ} \propto B_\perp^2 R_H^2 j^2 c,$$ where $B_\perp$ is the magnetic field at the horizon, $R_H$ is the horizon radius, $j$ is the dimensionless spin parameter, and $c$ is the speed of light (Chen et al., 10 Oct 2024, Daly, 2019, Talbot et al., 2020). Magnetohydrodynamic simulations show that the jet efficiency $\epsilon_j(a)$ depends sharply on spin:

• At low spin ($a \ll 1$), $\epsilon_j \propto a^{2}$,
• At high spin, $\epsilon_j \propto a^{4}$ or steeper (Huško et al., 2023, Huško et al., 2022).

Thus, rapidly spinning black holes can launch highly efficient, collimated jets capable of impacting gas up to host galactic and even cluster scales, with kinetic luminosities that may exceed the accreted rest mass energy per unit time in extreme cases (Huško et al., 2022).

The orientation of the jet is also set by the black hole spin axis, which can evolve under accretion torques and the Lense–Thirring effect, resulting in jet precession or reorientation, affecting the angular distribution of feedback energy (Huško et al., 2022, Talbot et al., 2020, Talbot et al., 2021).

3. Hybrid Feedback: Role of Accretion, Magnetic Fields, and Disc–Jet Coupling

While spin sets an upper bound on the extractable energy for jet feedback, the realized jet power also depends on:

• The accretion disk luminosity, controlled by $\dot{M}_{\rm BH}$ and $\epsilon_r(a)$,
• The magnetic field topology and flux threading the event horizon, often set by the corona or magnetically arrested disk (MAD) state (Chen et al., 10 Oct 2024, Daly, 2019).

Hybrid models increasingly recognize the importance of disc-driven magnetic flux and coronal processes, incorporating both BZ (spin-dependent) and Blandford–Payne (disk-driven, spin-independent) components: $$P_{\rm jet}^{\rm hybrid} \sim P_{\rm jet}^{\rm BZ} + P_{\rm jet}^{\rm BP},$$ where $P_{\rm jet}^{\rm BP}$ arises from magnetocentrifugal launching in the accretion disk and scales with accretion rate/magnetic field but not directly with spin (Chen et al., 10 Oct 2024).

Empirical studies, for example, show only a weak direct correlation between radio luminosity and $j$, but a strong link between radio-loudness and spin, suggesting that while spin is necessary for powerful jets (especially in radio-loud systems), efficient accretion and strong magnetic fields are also required for prominent jet activity (Chen et al., 10 Oct 2024, Velzen et al., 2013).

4. Impacts on Host Galaxy, Cluster, and Observational Diagnostics

Hybrid spin-dependent AGN feedback produces a range of observational phenomena:

• Gas Redistribution: AGN jets displace central gas, inflate low-density cavities, and drive multiphase outflows and turbulence, rearranging the density and entropy profiles of the host medium (Dubois et al., 2010, Li et al., 2014, Bourne et al., 2017, Huško et al., 2022, Talbot et al., 2021, Talbot et al., 2023).
• Star Formation Quenching: By heating or evacuating cold gas reservoirs, AGN feedback strongly suppresses central star formation, often reducing stellar mass buildup by factors of several, particularly in massive systems (Dubois et al., 2010, Weinberger et al., 2016, Huško et al., 2022).
• Cooling Flow Regulation: Feedback cycles induced by accretion-triggered jet episodes efficiently regulate cooling flows in cluster cores, with the observed gas mass and temperature profiles matching $\beta$-models and cool-core/non-cool-core transitions in X-ray clusters (Dubois et al., 2010, Li et al., 2014, Huško et al., 2022, Huško et al., 2023).
• Obscuration and Outflow Geometry: High-spin black holes produce more isotropic luminosity patterns, enabling quasi-spherical outflows that can efficiently clear obscuring gas in all directions and halt accretion; low-spin systems yield strongly anisotropic, polar-focused outflows, with persistent obscuration in the disk plane (Ishibashi, 2020, Bollati et al., 2023).
• Multiphase Outflows and Backflows: Kinetic jets launch both hot, fast, collimated outflows and dense, cold, mass-loaded components (entrained or fallback gas), with entrainment fractions reaching up to $\sim10\%$ of the circumnuclear disc mass in simulations (Talbot et al., 2021, Talbot et al., 2023).

Numerical and observational studies reveal that while the total jet/thermal power is well-constrained by bolometric disk luminosity and outflow energetics, the coupling of feedback to gas, and thus its impact on galaxy evolution, depends on both the black hole spin and feeding conditions (Velzen et al., 2013, Daly, 2019, Bollati et al., 2023).

5. Feedback Anisotropy, Spin Evolution, and Quenching Cycles

The geometry and episodicity of AGN feedback are directly affected by the spin and angular momentum dynamics:

• Anisotropy: High spin produces nearly isotropic feedback, fostering rapid gas clearing and potentially more effective self-quenching and slower subsequent mass and spin growth; low spin confines feedback to narrow cones, allowing more extended gas inflow and faster black hole growth (Ishibashi, 2020, Bollati et al., 2023).
• Spin Evolution: Feedback is self-regulating—accretion of high-angular momentum material can spin up the black hole, while prolonged jet launching can spin it down via extraction of angular momentum, possibly driving the system toward a low-spin equilibrium and episodic quenching cycles (Talbot et al., 2020, Huško et al., 2023, Huško et al., 2022).
• Precession and Misalignment: Jet orientation can be set by the evolving spin vector, with subsequent precession, especially during chaotic accretion or in the context of mergers, impacting where energy and momentum are deposited and thus altering star formation/disk evolution (Talbot et al., 2021, Talbot et al., 2023).

These feedback cycles are particularly relevant for understanding the long-term galaxy evolution through AGN self-regulation, with implications for bimodal AGN populations (radio-loud vs. radio-quiet) and the persistence of multiphase gas in massive halos (Chen et al., 10 Oct 2024, Daly, 2019, Velzen et al., 2013).

6. Key Mathematical Formulations

Several feedback models share common formulas:

Physical Quantity	Formula	Spin Dependence
Jet Power (BZ mechanism)	$P_{\rm jet}^{\rm BZ} \propto B_\perp^2 R_H^2 j^2 c$	$j^2$ (primary)
Jet Power (Hybrid)	$$P_{\rm jet}^{\rm Hybrid} = 2\times10^{47}\,\alpha\,f^2\,\left(\frac{B_{\rm pd}}{10^5\,G}\right)^2 \left(\frac{m}{10^9M_\odot}\right)^2 j^2$$	$j^2$; $B_{\rm pd}$ set by disk/corona properties
AGN Feedback Rate	$$\dot{E}_{\rm AGN} = \epsilon_f\,\epsilon_r\,\dot{M}_{\rm BH} c^2$$	$\epsilon_r = \epsilon_r(j)$
Spin Evolution	$$\frac{da}{d\ln M_{\rm BH}} = \ell_{\rm in} - 2 a e_{\rm in} - s_j$$	$s_j$ captures spin loss from jets

In hybrid spin-dependent feedback, predictions for AGN outflow energetics, galaxy quenching, and disk/jet morphology hinge on these mathematical couplings.

7. Synthesis and Astrophysical Implications

Spin-dependent hybrid jet/thermal AGN feedback emerges as a robust framework connecting the microphysics of black hole accretion, jet launching, and radiative winds with the macro-evolution of massive galaxies and galaxy clusters. Key points include:

• Effective AGN feedback in both jet and thermal channels requires not only high black hole spin but also favorable disk/corona properties and sustained accretion states (Chen et al., 10 Oct 2024, Daly, 2019, Huško et al., 2022).
• The efficiency and form of AGN feedback are time-variable, dictated by self-consistent spin evolution, accretion rate, jet precession, and ISM (interstellar medium) or ICM (intracluster medium) structure (Talbot et al., 2020, Talbot et al., 2023).
• Observational signatures, including jet/lobe radio power, X-ray cavities, multiphase filamentary structure, and radio-loud/radio-quiet AGN demographics, are best explained within a hybrid spin-modulated paradigm that accounts for both mechanical (jet) and radiative (thermal) feedback, as well as their joint effects (Velzen et al., 2013, Bollati et al., 2023, Ishibashi, 2020).

This spin-dependent framework serves as the backbone for contemporary and future cosmological simulations and observational strategies aimed at unraveling the coevolution of supermassive black holes and their host galaxies.