AGN-Disk Hierarchical Assembly

• AGN-disk hierarchical assembly is a model describing the coevolution of supermassive black holes and galactic disks via disk regrowth, gravitational compression, and feedback regulation.
• It demonstrates that disk regrowth deepens the central potential, increasing velocity dispersion and necessitating a 50–80% SMBH mass boost to maintain the MBH–σ relation.
• The framework underscores the role of AGN feedback and secular processes as critical regulators in synchronizing SMBH accretion with evolving galactic structures.

Active galactic nucleus (AGN)-disk hierarchical assembly describes the evolution of supermassive black holes (SMBHs) and their surrounding galactic components through a sequence of coupled, multi-scale processes including disk regrowth, bulge compression, secular and violent gas inflow, disk–star–cluster interplay, and the preservation of critical scaling relations. The paradigm integrates secular disk buildup, merger-driven events, feedback-regulated growth, and the central dynamical effects of gravitationally significant galactic disks, emphasizing:

• The co-evolution of AGN and their host disks, especially in the secular, post-merger era.
• The physical consequences of disk regrowth on the bulge, and thus on the $M_{\mathrm{BH}}$–$\sigma$ relation.
• Trade-offs and regulatory feedbacks necessary to keep SMBHs and bulges on the observed scaling relations as galaxy morphology and mass configurations change.

1. Gravitational Compression During Disk Regrowth

When a galactic disk reassembles around a pre-existing classical bulge containing an SMBH, the additional disk mass deepens the central potential, causing gravitational compression of the bulge. The resulting increase in velocity dispersion ($\sigma$) occurs despite little change in the bulge's stellar mass:

• The canonical $M_{\mathrm{BH}}$–$\sigma$ relation is

$$\log M_{\mathrm{BH}} = \alpha + \beta \log \left(\frac{\sigma}{200\,\mathrm{km\,s}^{-1}}\right)$$

• Disk mass assembly produces a "compression factor" $\mathcal{F}$, given by the ratio $(\sigma/\sigma_0)$, where $\sigma_0$ is the bulge's pre-disk value.
• The dynamical relation for compression includes the bulge and disk mass within the effective radius $R_e$:

$$\left(\frac{\sigma_f}{\sigma_0}\right)^2 \simeq \frac{M_{b,f}(R_{e,f}) + M_d(R_{e,f})}{M_{b,0}(R_{e,0})} \cdot \frac{R_{e,0}}{R_{e,f}}$$

This increase in $\sigma$ would move the galaxy below the standard $M_{\mathrm{BH}}$–$\sigma$ relation unless $M_{\mathrm{BH}}$ grows by a factor $\mathcal{F}^\beta$; for typical parameters, $\mathcal{F} \simeq 1.1$ and $\beta \simeq 4-5$, requiring $M_{\mathrm{BH}}$ to increase by 50–80% to maintain the relation (Debattista et al., 2013).

2. Empirical Evidence: No Offset Between Bulges and Ellipticals

A critical observational result is the lack of any statistically significant offset in the $M_{\mathrm{BH}}$–$\sigma$ relation zero-point ($\alpha$) between classical bulges in disk galaxies and elliptical galaxies. The relation holds true even after accounting for the expected gravitational compression:

• The predicted offset, if SMBHs did not grow in step with bulge $\sigma$, would be

$$\Delta\alpha = -\beta \log \langle \mathcal{F} \rangle$$

with $\langle \mathcal{F} \rangle > 1$ yielding a negative $\Delta\alpha$ for classical bulges.

• Observed samples, however, show no significant zero-point shift.

This implies that SMBHs in disk galaxies must experience substantial mass growth (by 50–80%) as their hosts regrow disks—thereby maintaining the $M_{\mathrm{BH}}$–$\sigma$ relation. The result is a strong argument for AGN feedback, or other mechanisms, finely regulating SMBH accretion in response to changes in the central potential (Debattista et al., 2013).

3. Theoretical and Analytical Frameworks

Semi-analytic and analytic modeling supports these findings by connecting hierarchical disk growth, angular momentum transport, and SMBH accretion. Key elements include:

• Modeling the hierarchical formation of bulges in early mergers, with SMBHs forming rapidly onto the $M_{\mathrm{BH}}$–$\sigma$ relation prior to disk regrowth.
• Parametric fits and dynamical mass argument: for a system initially on the scaling relation, disk assembly leads to $\sigma$ increase and the need for SMBH mass increase by a factor of $\mathcal{F}^\beta$ to prevent a systematic offset.

These models reinforce that the observed scaling is not a product of undisturbed evolution but requires ongoing, regulated SMBH growth during secular disk assembly phases.

4. Implications for AGN Fueling and Secular Evolution

The observed phenomena reveal a scenario where AGN fueling during hierarchical disk assembly can arise from internal, secular processes rather than exclusively from major mergers. Insights include:

• AGN triggering in the cosmic epoch $z \sim 1$–3 is often found in isolated disk galaxies, not in merger remnants, indicating that secular processes—such as bar-driven inflows or minor perturbations—deliver gas to the nucleus (Debattista et al., 2013).
• As the disk assembles and compresses the bulge, gas is funneled toward the SMBH under conditions that naturally enforce the $M_{\mathrm{BH}}$–$\sigma$ relation.

This supports a model where the depth of the central potential well (parameterized by $\sigma$) regulates SMBH growth in a largely self-regulated, feedback-modulated fashion.

5. Consequences for Galaxy and SMBH Coevolution

AGN-disk hierarchical assembly underlines the robust link between SMBH growth and galaxy structural evolution:

• The maintenance of the $M_{\mathrm{BH}}$–$\sigma$ relation during disk regrowth ties the SMBH mass directly to changes in the host's gravitational potential well.
• This robustness holds independently of the detailed mechanism for disk or bulge assembly (e.g., whether via major mergers, minor mergers, or internal disk processes), provided SMBH growth is tuned to track the evolving $\sigma$.

The result is a natural path to the observed cosmic evolution of AGN populations and helps explain why large fractions of SMBH growth can occur in secular, non-merger-driven environments at high redshift.

6. Connections to Feedback and the Structural Evolution of Galaxies

Self-regulated AGN growth—enforced by the preservation of the $M_{\mathrm{BH}}$–$\sigma$ relation—connects to broader feedback and assembly phenomena:

• AGN feedback may play a key role in coupling SMBH accretion rates to the properties of the bulge and disk, potentially quenching or regulating star formation and gas inflow as needed to sustain the scaling relation.
• The empirical maintenance of the $M_{\mathrm{BH}}$–$\sigma$ relation despite ongoing disk assembly highlights feedback processes as a "lockstep" mechanism governing SMBH and galactic evolution.

This understanding informs the interpretation of high-redshift AGN demographics and supports the view that AGN-disk hierarchical assembly is not an incidental feature, but a major process governing galaxy-SMBH coevolution (Debattista et al., 2013).

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In sum, AGN-disk hierarchical assembly provides a quantitative and physical framework for understanding how galactic disks and SMBHs coevolve, particularly through sustained, feedback-modulated growth that sustains the $M_{\mathrm{BH}}$–$\sigma$ relation across cosmic time and morphological transitions.