MACER3D: 3D AGN Feedback Simulations

• MACER3D Simulations are a suite of advanced three-dimensional hydrodynamical models that investigate AGN feedback and gas dynamics in galaxies.
• They incorporate enhanced subgrid physics, realistic turbulence, and precise radiative cooling to capture multiscale interactions from the Bondi radius to the circumgalactic medium.
• Simulations yield robust predictions for observed properties such as AGN duty cycles, X-ray luminosities, and the interplay between AGN and star formation across diverse galactic environments.

MACER3D Simulations are a suite of three-dimensional hydrodynamical simulations designed to investigate the role of active galactic nucleus (AGN) feedback and associated gas dynamics in galaxy evolution. Based on the MACER (Massive AGN Controlled Ellipticals Resolved) approach, MACER3D advances beyond previous two-dimensional models by incorporating enhanced subgrid physics, realistic turbulence, spatially resolved radiative cooling, discrete supernova feedback, and self-consistent AGN accretion/feedback coupling—enabling robust, multiscale simulations of galaxy-scale feedback phenomena spanning the Bondi radius to the circumgalactic medium (Zhang et al., 8 Apr 2025, Su et al., 23 Oct 2025).

1. Dimensionality and Physical Motivation

MACER3D achieves a significant methodological advance by transitioning from axisymmetric two-dimensional (2D) to fully three-dimensional (3D) simulations. The move to 3D eliminates the artificial inverse kinetic energy cascade and axisymmetric constraints inherent to 2D, permitting the physically accurate modeling of nonaxisymmetric instabilities (such as spiral features, clumpy and turbulent flows, and filamentary inflows/outflows). This dimensional enhancement is essential for capturing the full turbulence cascade and realistic mixing of metals, energy, and momentum in the interstellar and circumgalactic media. It further allows for the emergence of complex spatial structures observed in real galaxies, which are suppressed or absent in 2D (Zhang et al., 8 Apr 2025).

2. Simulation Framework and Initial Conditions

MACER3D is implemented atop the Athena++ codebase, operating in spherical coordinates $(r, \theta, \phi)$ to efficiently resolve both the Bondi radius (typically $\sim 25\,\mathrm{pc}$ in massive ellipticals; as small as 7 pc in dwarf galaxies) and galactic–halo scales (up to $\sim 250\,\mathrm{kpc}$). The computational grid is logarithmically spaced in radius to capture the required dynamic range, reaching spatial resolutions of 0.3 pc at the innermost boundary. The simulated galaxy comprises a central SMBH, a stellar Jaffe profile,

$\rho_*(r) = \frac{M_* r_*}{4\pi r^2(r_* + r)^2},$

an NFW or beta-model dark matter halo, and a gas component with metallicity gradients. Gas is initialized in hydrostatic equilibrium and, in disk galaxies, follows an exponential–sech$^2$ disk and bulge profile: $$\rho_\mathrm{disk}(R, z) = \frac{M_\mathrm{disk}}{2\pi z_0 R_0^2} \exp(-R/R_0)\,\mathrm{sech}^2(z/z_0)$$

$$\rho_\mathrm{bulge}(r) = \frac{M_\mathrm{bulge}}{2\pi} \frac{r_0}{r(r + r_0)^3}$$

Boundary conditions are formulated to maintain hydrostatic equilibrium and to absorb or outflow gas as appropriate; feedback is injected at the inner boundary according to the computed AGN state (Zhang et al., 8 Apr 2025, Su et al., 23 Oct 2025).

3. Subgrid Physics: Cooling, Metallicity, and Feedback

Advanced Cooling and Metal Enrichment

MACER3D replaces empirical cooling/heating functions with multi-dimensional tables (density, temperature, metallicity, redshift, AGN flux) calculated via Cloudy. Integration of the energy equation uses the exact Townsend method: $$\int_{T^n}^{T^{n+1}} \frac{dT}{\Lambda(T)} = -\frac{(\gamma-1)\mu\rho}{k_B \mu_e \mu_i m_p \Delta t}$$ Metallicity is treated as a passive scalar field and is spatially resolved, coupling back into the cooling process and enabling tracking of enrichment from both stellar evolution and supernova yields—essential for reproducing observed metal distributions in galactic halos (Zhang et al., 8 Apr 2025).

Discrete Supernova Feedback

Supernovae (SN) are implemented as discrete, Poisson-sampled events: $$P(N_\mathrm{SN}; \mu_\mathrm{SN}) = e^{-\mu_\mathrm{SN}} \frac{\mu_\mathrm{SN}^{N_\mathrm{SN}}}{N_\mathrm{SN}!}$$ where $\mu_\mathrm{SN}$ is the expected number of SNe per timestep per region. Each event injects local thermal energy and momentum to the gas. This stochastic prescription contrasts with the spatially smoothed, continuous heating used in previous models and is critical for generating realistic turbulence, clumpy ISM structure, and metal mixing (Zhang et al., 8 Apr 2025).

4. AGN Accretion and Feedback Modeling

MACER3D employs black hole accretion theory to self-consistently model AGN energy and momentum injection:

AGN Mode	Trigger	Wind Prescriptions	Radiative Efficiency
Cold (quasar)	$\dot{M}_\mathrm{BH} > 0.02\,\dot{M}_\mathrm{Edd}$	$$\dot{M}_\mathrm{wind,cold} = 0.28 (L_\mathrm{bol}/10^{45}\,\rm erg\,s^{-1})^{0.85}$$, prescribed wind velocity	$\epsilon_\mathrm{cold} = 0.1$
Hot (radio)	$\dot{M}_\mathrm{BH} < 0.02\,\dot{M}_\mathrm{Edd}$	$$\dot{M}_\mathrm{wind,hot} = \dot{M}_{\rm in} - \dot{M}_\mathrm{BH}$$, $$v_\mathrm{wind} \propto v_\mathrm{K}(r_\mathrm{tr})$$	$$\epsilon_\mathrm{hot}(\dot{m}) = \epsilon_0 (100\,\dot{m})^a$$

The accretion rate is calculated directly from resolved flows at the inner radius. The hot mode employs a truncated thin disk/radiatively inefficient flow, with wind velocity scaling with the local Keplerian speed. Feedback is injected with prescribed angular dependence (e.g., $\cos^2 \theta$ profiles), and all AGN outputs—radiation, winds—are dynamically coupled to the galactic gas (Zhang et al., 8 Apr 2025).

5. Applications: Galaxy Evolution and AGN–Star Formation Coupling

Massive Elliptical Galaxies

Simulations of isolated massive ellipticals using MACER3D demonstrate tightly coupled AGN and SN feedback operating over gigayear timescales (Zhang et al., 8 Apr 2025). Key findings:

• AGN and star formation rate (SFR) display strong temporal correlation, both regulated by central gas supply.
• Fiducial models with both AGN and SN feedback reproduce observed AGN duty cycles (several percent) and cycle timescales ($\sim 10^2$ Myr).
• Feedback maintains long-term galactic quiescence but allows short starburst episodes temporally associated with AGN outbursts.
• Combined feedback enhances halo-scale metal enrichment and matches observed X-ray properties (luminosity, cavities, bubbles).

Starburst Dwarf Galaxies and Positive AGN Feedback

MACER3D simulations of starburst dwarf galaxies demonstrate that moderate AGN feedback—when operating alongside SN feedback—can enhance star formation rates by $\sim 25\%$ compared to SN-only models (Su et al., 23 Oct 2025). The mechanism involves AGN-driven outflows compressing the ISM into dense, rapidly cooling regions conducive to star formation. SN feedback plays a regulatory role by preventing overly powerful AGN outflows that would otherwise expel gas, thus establishing a synergistic regime of “positive” AGN feedback. This result is in strong agreement with observed properties of systems like Henize 2-10, including spatially coincident outflows, shock-compressed gas (at 70 pc), and matched SFR/black hole mass.

6. Model Validation and Observational Concordance

MACER3D results across different galaxy mass regimes are consistent with key observational diagnostics:

• AGN duty cycles of several percent with $10^2$ Myr timescales match those inferred from AGN population studies.
• Simulated soft X-ray luminosities ($L_X \simeq 2$–$3 \times 10^{41}$ erg s$^{-1}$ on average) and transient features (bipolar bubbles, cavities) are in close agreement with Chandra and eROSITA observations.
• For starburst dwarfs, the boost in SFR and spatial morphology of star-forming clumps reflect properties of well-studied galaxies such as Henize 2-10 (Su et al., 23 Oct 2025).

7. Advancements over MACER2D and Future Outlook

Key improvements from MACER2D to MACER3D include:

• Full 3D turbulence, enabling accurate energy cascade and metal mixing.
• High-resolution near the Bondi radius, supporting direct, non-parametric calculations of accretion rates and feedback.
• Generalization to non-axisymmetric morphologies, broadening the model’s applicability to disks, dwarfs, and potentially multi-component systems.

A plausible implication is that MACER3D, through its physically rich and fully three-dimensional treatment, is positioned for future extensions such as explicit inclusion of magnetic fields and cosmic ray physics, and for application to a wider range of galactic environments. Its findings highlight both regulatory and triggering roles of AGN feedback in galaxy evolution, challenging the paradigm of purely suppressive AGN feedback (Zhang et al., 8 Apr 2025, Su et al., 23 Oct 2025).