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The MandelZoom project II: the impact of stellar feedback on black hole accretion through an $\alpha$ -disc in dwarf galaxies with a resolved interstellar medium

This study utilizes high-resolution simulations to demonstrate that while different stellar feedback mechanisms significantly modulate circumnuclear disc formation and intermediate-mass black hole accretion rates in dwarf galaxies, the inclusion of combined feedback processes still permits substantial black hole growth and spin-up, supporting their role as progenitors for high-redshift supermassive black holes.

Original authors: Eun-jin Shin, Matthew C. Smith, Debora Sijacki, Martin A. Bourne, Sophie Koudmani

Published 2026-03-30

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CC BY 4.0

Original authors: Eun-jin Shin, Matthew C. Smith, Debora Sijacki, Martin A. Bourne, Sophie Koudmani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a dwarf galaxy as a bustling, small town. In the very center of this town sits a "black hole," which we can think of as a giant, hungry vacuum cleaner waiting to eat gas and dust. But this vacuum cleaner isn't just sitting there; it's surrounded by a swirling ring of gas called a Circumnuclear Disc (CND). Think of this ring as a giant, rotating pizza dough being tossed in the air, ready to be eaten by the black hole.

The main question this paper asks is: What happens to this pizza dough when the town's stars start acting up?

Stars aren't just quiet lights; they are active neighbors. When they are born, they blast out radiation (like a heat lamp). When they die, they explode as supernovae (like massive fireworks). The authors of this paper ran super-computer simulations to see how these "stellar neighbors" affect the black hole's ability to eat.

Here is the story of their findings, broken down into simple concepts:

1. The Setup: The Town and the Pizza

The scientists built a digital model of a small galaxy. In the center, they placed a Nuclear Star Cluster (NSC)—a dense crowd of old stars—and a medium-sized black hole (an Intermediate-Mass Black Hole, or IMBH). They used a special "zoom lens" in their computer code that allowed them to see details as small as 0.01 light-years (which is incredibly tiny on a galactic scale). This let them watch the gas flow all the way from the edges of the town right into the black hole's mouth.

2. The Four Scenarios: How the Neighbors Behave

The team ran four different versions of the simulation, changing how the stars behaved:

Scenario A: The Quiet Town (No Feedback)
- What happened: The stars didn't blast anything. The gas in the town clumped together easily, forming a massive, thick pizza dough ring.
- Result: The black hole got a steady, smooth meal. But because the gas clumped so easily, it turned into too many stars, eating up the food before the black hole could get it all.
Scenario B: The Heat Lamps Only (Radiation Feedback)
- What happened: The stars turned on their "heat lamps" (radiation) but didn't explode. This heat kept the gas from clumping too much.
- Result: Surprisingly, this made the pizza dough ring bigger and heavier. Because the gas didn't turn into stars as fast, more of it stayed available to fall into the black hole. The black hole ate more efficiently!
Scenario C: The Fireworks Only (Supernova Feedback)
- What happened: The stars didn't blast heat, but they exploded like fireworks. These explosions were so powerful they blew the gas away, heating the whole town up.
- Result: The pizza dough ring got very thin and scattered. The black hole got very little to eat. The explosions were so effective at clearing the gas that the black hole almost starved.
Scenario D: The Full Package (Heat Lamps + Fireworks)
- What happened: This is the most realistic scenario. The stars blast heat first, then explode later.
- Result: This created a cycle of life and death for the pizza ring.
  1. The heat lamps keep the gas from clumping too early, letting a ring form.
  2. The ring gets heavy and starts making new stars.
  3. Those new stars explode (fireworks), blowing the ring apart completely.
  4. The town cools down, fresh gas flows in from the outskirts, and a new ring forms.
- The Cycle: This happens every 10 to 100 million years. The black hole eats in bursts. It gorges itself, then starves while the ring rebuilds, then gorges again.

3. The Big Surprise: The "Destruction" Paradox

The most fascinating discovery is in Scenario D. You might think that if the stars destroy the food ring, the black hole would stop growing. But the opposite happened!

When the stars explode and blow the ring apart, it actually pushes some of the gas inward, giving the black hole a sudden, massive feast. It's like a chef throwing a pie into the air; when it lands, it splatters everywhere, but some of it lands right in the customer's mouth. The black hole grows in "episodes"—big bursts of eating followed by quiet periods.

4. Why This Matters for the Universe

The "Missing" Black Holes: We know there are huge black holes in big galaxies, but we haven't found many "medium-sized" ones in small galaxies. This paper suggests they are there, but they are eating in bursts. They might be quiet for millions of years, then suddenly light up as they swallow a fresh ring of gas.
The Seeds of Giants: The black holes in these small galaxies today might be the "seeds" that grew into the super-massive giants we see in the centers of big galaxies today. If they can grow efficiently in these small, messy towns, they could have grown fast enough in the early universe to become the giants we see now.
Future Detection: Because these black holes eat in bursts, they might light up briefly. New telescopes (like the SKA, Rubin Observatory, and LISA) are being built specifically to catch these fleeting moments.

The Takeaway

The universe is a chaotic place. The growth of black holes isn't a smooth, steady process like a river flowing. Instead, it's more like a feast-and-famine cycle driven by the stars around them.

No stars acting up? The black hole eats steadily but slowly.
Stars exploding? The black hole starves.
Stars doing both? The black hole gets the best of both worlds: it gets massive rings of food, which then get blown apart, sending a huge wave of food straight into its mouth.

The authors conclude that to understand how black holes grow, we can't just look at the black hole; we have to watch the whole neighborhood, because the stars are the ones holding the keys to the food supply.

1. Problem Statement

The origin and growth of Intermediate-Mass Black Holes (IMBHs; $10^2–10^5 M_\odot$ ) in dwarf galaxies remain a critical unsolved problem in astrophysics, particularly regarding their role as progenitors of high-redshift Supermassive Black Holes (SMBHs). A central challenge is understanding how IMBHs efficiently accrete gas in the shallow potential wells of dwarf galaxies, where stellar feedback can easily disrupt gas reservoirs.

Previous studies often lacked the spatial resolution to resolve the self-gravitating radius of the accretion disc or failed to simultaneously model the complex interplay between galactic-scale inflows, Nuclear Star Clusters (NSCs), Circumnuclear Discs (CNDs), and various stellar feedback channels (radiation, supernovae). This paper aims to bridge this gap by investigating how different stellar feedback mechanisms regulate the formation, stability, and destruction of CNDs and, consequently, the accretion and spin evolution of central IMBHs.

2. Methodology

The authors employed a suite of high-resolution hydrodynamical simulations using the AREPO code (moving-mesh gravito-hydrodynamics solver) within the MandelZoom framework.

Initial Conditions: Simulations modeled an isolated dwarf galaxy ( $10^{10} M_\odot$ ) resembling a WLM-type system, containing a dark matter halo, a baryonic disc, and a pre-existing Nuclear Star Cluster (NSC) hosting a $10^4 M_\odot$ black hole (BH).
Resolution Scheme: A super-Lagrangian refinement strategy was implemented. While the outer galactic regions had a resolution of $\sim 1.75$ pc, the refinement zone around the BH achieved sub-0.01 pc resolution. This allowed the simulation to fully resolve the self-gravity radius ( $r_{SG} \sim 0.05–0.6$ pc) of the accretion disc, enabling a self-consistent treatment of gas inflow from the Interstellar Medium (ISM) down to the BH.
Physics Models:
- Star Formation: Explicit sampling of the Initial Mass Function (IMF) for individual massive stars.
- Stellar Feedback: The study systematically varied feedback channels:
  - No Feedback (noFB): Baseline.
  - Radiative Only (PIPE): Photoionization (PI) and Photoelectric (PE) heating.
  - Supernova Only (SN): Core-collapse SNe (8–35 $M_\odot$ ).
  - Full Physics (full): Combination of PI, PE, and SNe.
- Accretion Model: A subgrid $\alpha$ -disc model (Shakura & Sunyaev) coupled with Lense-Thirring precession (Bardeen & Petterson). Mass and angular momentum fluxes were measured at $r_{SG}$ to update the BH mass and spin.
Simulation Suite: A total of 9 simulations were run over 450 Myr, varying feedback models, star formation thresholds, gas softening lengths, and initial metallicities (including a low-metallicity $Z=0.01 Z_\odot$ case).

3. Key Contributions

Resolution of the Accretion Disc: Unlike previous works, this study resolves the self-gravity radius of the accretion disc, allowing for a physically motivated calculation of angular momentum transport and BH spin evolution rather than relying on Bondi-Hoyle-Lyttleton approximations.
Systematic Feedback Comparison: The paper isolates the specific impacts of radiative feedback versus supernova feedback on the CND lifecycle, a regime previously difficult to disentangle.
CND Lifecycle Characterization: It provides a quantitative description of the CND as a dynamic, episodic structure rather than a static reservoir, linking its survival directly to the timing of in-situ star formation and feedback.

4. Key Results

A. Impact on the Interstellar Medium (ISM) and Star Formation

No Feedback: The disc fragments excessively, leading to massive starbursts and a rapidly declining Star Formation Rate (SFR) as gas is consumed.
Radiative Feedback Only: Suppresses fragmentation, leading to smoother, sustained star formation. Interestingly, this results in the most massive CNDs because gas is not heated enough to escape the potential well but is prevented from forming stars in the outer disc, funneling it inward.
Supernova (SN) Feedback Only: Clustered SNe strongly heat the ISM, creating large voids and suppressing the CND mass. However, the CND survives the entire 450 Myr simulation, providing a continuous, albeit reduced, gas supply to the BH.
Full Feedback (Radiative + SN): This is the most realistic scenario. Radiative feedback from massive stars heats and diffuses the outer CND, making it susceptible to subsequent SN explosions. This leads to a cyclic behavior: the CND forms, survives for 10–100 Myr, is completely disrupted by SNe, and is then replenished by fresh galactic inflows.

B. Black Hole Accretion and Growth

Accretion Modes:
- No Feedback: Smooth accretion with occasional bursts from clump mergers.
- Radiative Only: Bursty accretion driven by feedback-induced gas compression.
- SN Only: Continuous but suppressed accretion (CND survives).
- Full Feedback: Episodic accretion. BH growth occurs in bursts corresponding to CND formation phases, separated by quiescent periods where the CND is destroyed.
Growth Efficiency: Despite the episodic nature, the Full Feedback model results in significant BH growth (20–30% mass increase), outperforming the SN-only model. The Low Metallicity and Reduced Softening runs showed the highest accretion rates, as lower cooling efficiency and higher densities allowed larger gas reservoirs to accumulate.
Spin Evolution: In all models, the BH spin parameter ( $a_\bullet$ ) increased from an initial 0.7 to $>0.8$ due to coherent, aligned accretion from the CND.

C. The CND Cycle

The study establishes that the CND is not a permanent structure in the presence of full stellar feedback. The cycle is driven by:

Inflow: Galactic gas loses angular momentum via the NSC potential, forming a CND.
Star Formation: In-situ star formation occurs, producing massive stars.
Radiative Heating: Early feedback (PI/PE) diffuses the gas, reducing its stability.
Disruption: SNe explode, completely evaporating the CND.
Replenishment: The cycle restarts as new gas flows in from the galactic disc.

5. Significance and Implications

IMBH Detectability: The results suggest that IMBHs in dwarf galaxies can grow significantly even with strong feedback, reaching Eddington ratios of $f_{Edd} \sim 0.01–0.3$ . This implies they should be detectable as low-luminosity AGNs by future facilities like SKA, Rubin Observatory, and LISA.
High-Redshift Progenitors: The finding that low-metallicity environments (simulated in the lowZ run) promote higher BH growth supports the hypothesis that IMBHs in the early Universe (low metallicity) could rapidly grow into the SMBHs observed by JWST.
Modeling Necessity: The paper emphasizes that accurate modeling of IMBH growth requires the simultaneous inclusion of all stellar feedback channels. Ignoring radiative feedback leads to overestimation of CND stability, while ignoring SNe leads to underestimation of CND disruption.
Future Work: The authors note that while AGN feedback was not included, the simulated accretion rates suggest IMBHs could drive observable outflows. Future work will incorporate AGN feedback and magnetic fields to refine these predictions.

In conclusion, the MandelZoom II project demonstrates that the interplay between stellar feedback and nuclear star clusters creates a self-regulating, episodic fueling mechanism for IMBHs, providing a robust pathway for their growth in dwarf galaxies and their evolution into high-redshift SMBHs.