AGN Dynamical Formation Channel

• AGN dynamical formation channel is defined by the interplay of gravitational instabilities, gas inflows, and angular momentum transport that fuel SMBH growth and trigger nuclear star formation.
• This channel produces a measurable delay between peak star formation and AGN activity, with timing set by gas depletion and stellar conversion processes across scales from 10⁷ to 10⁸ years.
• Dynamically driven gas inflows also form obscuring tori and regulate late-stage star formation, linking SMBH fueling with observed galaxy properties and potential gravitational wave events.

Active Galactic Nucleus (AGN) dynamical formation channels describe the non-stationary, gravitational, and gas-dynamical processes by which central supermassive black holes (SMBHs) are fueled, obscured, and can give rise to the rapid formation and merger of compact objects (including black hole binaries) within galactic nuclei. These channels connect the interplay of large-scale inflows, angular momentum transport, and multi-phase feedback to nuclear star formation, the evolution of SMBH mass, and the signature delay and synergy between starburst and AGN activity. Theoretical, numerical, and observational studies converge on a pathway in which a range of dynamical instabilities, large-scale torques, and gas-rich interactions drive the time-dependent and spatially-varying features defining the AGN phenomenon, with measurable impacts on the timing of star formation, the formation and properties of obscuring tori, and on the efficiency of black hole binary mergers as potential gravitational wave sources.

1. Dynamical Gas Inflow and Angular Momentum Transport

In the AGN dynamical formation channel, large-scale gravitational instabilities—including those induced by galaxy mergers, tidal interactions, or strong disk non-axisymmetries such as bars—generate rapid inflows of cold, dense gas toward the nuclear region (Hopkins, 2011). On central ($\sim$ parsec to $\sim$ kiloparsec) scales, these flows quickly render the nuclear environment gas-dominated, triggering a peak in star formation as the available reservoir increases.

Gravitational torques, primarily acting through non-axisymmetric stellar features (e.g., stellar bars, lopsided disks) and enhanced as stars form in situ, serve to redistribute angular momentum. In regions where the mass is predominantly gaseous, the absence of a substantial collisionless (stellar) component renders angular momentum transport inefficient. Only with progressive stellar conversion does the system enable efficient removal of gas angular momentum, facilitating further inflow all the way to sub-parsec scales. This inefficiency results in a natural bottleneck, stalling accretion onto the SMBH until enough stars are present—a key, generic prediction of dynamical models.

2. Star Formation, Gas Depletion, and the "Infinite Supply" Limit

The peak star formation rate (SFR) in the nucleus follows the arrival and densification of the cold gas, as SFR simply tracks the gas density (Hopkins, 2011). The system generally operates under an "infinite gas supply" approximation: mergers or disk instabilities deliver $\sim 100\times$ more gas than strictly needed for maximum-rate black hole accretion, so BH growth is rarely limited by immediate gas availability.

The delay in SMBH fueling arises dynamically—not from feedback or wind-driven inefficiencies—but from the time required to convert enough gas into stars such that efficient torques can reinitiate inward flow. Once the stellar fraction is sufficient, the inner disk is no longer pure gas, and angular momentum can be funneled away efficiently, restarting SMBH accretion at Eddington or near-Eddington rates even as the overall gas mass (and SFR) decline.

This sequence naturally separates the time of peak SFR (set by gas arrival) from peak AGN activity (set by dynamical torque efficiency), producing the empirical phenomenon of delayed AGN onset after starburst.

3. Characteristic Delays, Scale Dependence, and Mathematical Formulation

The central theoretical result is the prediction that the delay between peak star formation and peak AGN activity is proportional to the gas exhaustion (depletion) time on the relevant spatial scale (Hopkins, 2011). Mathematically, this timescale is

$$\Delta t(R) = \frac{\Sigma_{\rm gas}}{\dot{\Sigma}_*} \approx \epsilon^{-1} t_{\rm dyn}$$

where $t_{\rm dyn}$ is the local dynamical time (typically $t_{\rm dyn} \sim R/V_c$), and $\epsilon$ is the star formation efficiency per dynamical time (in the range $0.006 \lesssim \epsilon \lesssim 0.1$). The delay is typically $10$–$100$ times the local $t_{\rm dyn}$, yielding, e.g., $\sim 10^7\,\rm yr$ on $10$ pc scales and $\sim 10^8\,\rm yr$ on kiloparsec scales. Importantly, this scale-dependence provides a direct diagnostic: measuring SFR and AGN activity at different apertures should show an increasing time offset with larger scales.

4. AGN Feedback and Regulation of Star Formation

A direct consequence of the dynamical delay is that by the time AGN (i.e., black hole) activity peaks, a significant fraction of the original central gas has already been consumed by star formation or expelled by stellar feedback (Hopkins, 2011). As such, the AGN operates not to truncate or quench the initial, most intense starburst, but to mop up residual gas and suppress any remaining or late-time nuclear star formation. This temporally offset feedback mechanism provides a theoretical basis for the observed lack of strong suppression at the onset of major starbursts, and it determines the nature of AGN regulation as being more relevant to low-level, late-stage star formation and gas removal in the nucleus.

5. Observational Diagnostics and Predictions

The dynamical formation channel yields several specific, testable predictions (Hopkins, 2011):

• The delay between SFR and AGN peaks varies systematically with the spatial scale of SFR measurement, scaling as $\Delta t \propto t_{\rm dyn}(R)$.
• Starburst and AGN activity should often be observed with the AGN lagging the starburst by a fraction (10–100) of the local dynamical time, not with perfectly synchronized or reversed timing.
• The bulk of nuclear star formation and mass buildup happens before the SMBH reaches its most luminous phase.
• AGN feedback is most evident or relevant only after substantial gas depletion, in contrast to simultaneous feedback prescriptions.
• The dynamical inefficiencies and delays are an intrinsic property of the physics of angular momentum transport and gas-to-stellar conversions, not a result of fine-tuned stellar winds, turbulence, or supernova models.

Verification could come from high-resolution temporal mapping of SFR and AGN indicators across radial scales, with careful control for scales of measurement and extinction.

6. Relation to Obscuring Structures and Broader AGN Phenomenology

While the dynamical formation sequence above addresses the fueling and timing of SMBH growth, it is naturally embedded in models of AGN "obscuration" as well. Dynamically-driven toroidal structures—characterized by large vertical scale heights ($h/R \sim 1$), substantial clumpiness, and maintained by global gravitational instabilities rather than feedback-driven turbulence—arise as a direct consequence of the same processes that control gas inflow (Hopkins et al., 2011). Bending modes and warps, excited as the gas is driven inward and accumulates eccentric structures, sustain obscuration and fuel supply, with column density distributions (including Compton-thick lines of sight) matching those inferred from X-ray and mid-infrared data when small-scale clumpiness is included and when the torus geometry arises self-consistently from the dynamics.

7. Implications for Galaxy and Black Hole Co-Evolution

The AGN dynamical formation channel elucidates the physical drivers behind observed correlations between galactic star formation, the buildup of galactic bulges, and the timing and growth of central supermassive black holes. Delays in BH fueling set by gas exhaustion timescales provide a natural explanation for the prevalence of post-starburst signatures in AGN hosts. Furthermore, the decoupling of starburst and AGN feedback epochs has important implications for modeling the regulation of SMBH mass, the energy budget available to suppress cooling and gas accretion, and the evolutionary pathways leading to the diversity of observed galaxy properties (e.g., bulge-to-disk ratios, velocity dispersion relations, and nuclear activity cycles).

The dynamical formation framework thus serves as a cornerstone for the integrative understanding of AGN fueling, nuclear star formation, obscuration, and gravitational wave source populations on timescales and spatial scales ranging from kiloparsec mergers to sub-parsec SMBH accretion (Hopkins, 2011).