The MandelZoom project I: modelling black hole accretion through an $α$-disc in dwarf galaxies with a resolved interstellar medium

TL;DR

This study addresses how intermediate-mass black holes grow in dwarf galaxies by resolving the multiphase interstellar medium down to the self-gravity radius of the alpha-disc using the MandelZoom framework. The authors implement explicit stellar feedback, nuclear star clusters, and a subgrid Shakura-Sunyaev disc model within Arepo, achieving sub-parsec resolution to track mass and angular momentum transfer from the ISM to the black hole and its disc. They find that a nuclear star cluster induces a compact, dense circumnuclear disc that can sustain BH accretion at about one percent of the Eddington rate for hundreds of Myr, while driving BH spin-up as coherent inflows persist; SN feedback eventually disrupts the disc, terminating fueling. A key result is that Bondi-Hoyle accretion grossly overestimates growth in this context because it neglects angular momentum and gas phase structure, highlighting the necessity of resolving angular momentum transport in a realistic, multi-phase ISM. Overall, the work demonstrates the critical role of NSCs and high-resolution, multi-scale modeling in predicting IMBH growth and spin in dwarfs and outlines a path toward cosmological simulations that include these processes.

Abstract

While mounting observational evidence suggests that intermediate mass black holes (IMBHs) may be important in shaping the properties of dwarf galaxies both at high redshifts and in the local Universe, our theoretical understanding of how these IMBHs grow is largely incomplete. To address this, we perform high-resolution simulations of an isolated dwarf galaxy with a virial mass of $10^{10}~{\rm M}_{\odot}$ harbouring a $10^4~{\rm M}_{\odot}$ IMBH at its centre at a peak spatial resolution of $\lesssim 0.01$ pc. Within the fully multi-phase interstellar medium (ISM), we incorporate explicit sampling of stars from the initial mass function, photo-ionization, photoelectric heating, individual supernovae (SNe), as well as a Shakura-Sunyaev accretion disc model to track the evolution of BH mass and spin. We find that a nuclear star cluster (NSC) effectively captures the ISM gas and promotes formation of a circumnuclear disc (CND) on scales of $\lesssim 7$ pc. Simultaneously, gravitational torques from the NSC reduce CND angular momentum on (sub-)parsec scales, circularizing the gas onto the $α$-accretion disc and promoting sustained IMBH growth at $\sim 0.01$ of the Eddington rate. While in the innermost regions ($\lesssim 0.5$ pc), star formation is highly suppressed, the CND is susceptible to fragmentation, leading to the formation of massive, young stars. Interestingly, despite an in-situ SN rate of $0.3~{\rm Myr}^{-1}$, the dense CND persists, sustaining BH accretion and leading to its net spin-up. Our study demonstrates the complexity of IMBH accretion within a multi-phase ISM, and paves the way for next-generation studies where IMBH growth in a fully cosmological context can be captured.

Figures (21)

• Figure 1: Effective radius versus mass of NSCs in observed dwarf galaxies with a stellar mass of $10^{5.5}-10^{8.5}\,\rm M_\odot$ from literature Georgiev+2016 and from our current simulation work ( star symbols). The colour indicates the stellar mass of host galaxies of each NSC. Our simulations span the observed range of NSC masses and effective radii, for galaxies of comparable stellar mass. For more information, see Section \ref{['sec:IC']}.
• Figure 2: Distribution of spatial ( left) and mass ( right) resolution as a function of radial distance from the BH for the gas cells in NSC-5pc run at $t=135$ Myr. Colours represent the cell density in each two-dimensional bin. The red dashed line indicates the typical self-gravity radius, $r_{\rm SG} \sim 0.15$ pc. The black dotted line marks the refinement radius, $R_{\rm ref} = 6$ pc. The green dash-dotted line denotes the virial radius, $r_{\rm vir} = 41$ kpc, and the blue solid line denotes the gas target mass for the refinement in the simulation. The innermost region within $r_{\rm SG}$ is very well resolved. For more information, see Section \ref{['sec:refinement']}.
• Figure 3: Slice of the Voronoi tessellation centred at the location of the BH, showing individual gas cells at $t=135$ Myr for NSC-5pc-noSL and NSC-5pc runs. The right panels are ten times zoomed-in images of the left panels. The blue cross mark indicates the location of the BH, and the black-dashed and red-dotted circles represent the refinement radius, $R_{\rm ref}= 6$ pc, and the self-gravity radius, $r_{\rm SG}\sim 0.15$ pc, respectively. For more information, see Section \ref{['sec:refinement-SL']}.
• Figure 4: Visualisation of the NSC-5pc run at $t =135$ Myr. Left: Gas surface density projections within zoom-in boxes of $2~{\rm kpc}, 400~{\rm pc}, 30~{\rm pc}$ (face-on and edge-on), and $3$ pc on a side. The reddish dots in one sub-panel represent the locations of young star particles (age $< 10$ Myr), with the dot size indicating the mass of star particles and the colour encoding their age. The stellar mass range is $6.68-37.9 \,\rm M_\odot$ at this snapshot. In the bottom sub-panel the red-dashed circle presents the self-gravity radius of accretion disc, $r_{\rm SG} \sim 0.15$ pc while the red and blue arrows show the angular momentum versors of the gas within $r_{\rm SG}$ and galactic disc, respectively, while the black arrow indicates the BH spin direction. The BH spin evolves due to the gas inflows through the self-gravity radius of the accretion disc. Right (from the top to the bottom): maps of density-weighted gas temperature, fraction of H$\mathrm{I}$$\mathrm{I}$, density-weighted specific angular momentum, and the Toomre $Q$ parameter. Note that on all scales gas is multiphase, and it exhibits complex morphology and dynamics, with clumpy, filamentary structure and inflowing gas streams on different orbits leading to a warped CND in the centre. For more information, see Section \ref{['sec:overview']}.
• Figure 5: Top two rows: maps of gas surface density, temperature (density-weighted), specific angular momentum (density-weighted), specific torque (density-weighted) exerted on the gas near the BH at $t= 135$ Myr for noNSC and NSC-5pc runs. The projection boxes are aligned with the angular momentum vector of the gas and are centred on the BH. Bottom row: panels show the analogous edge-on maps for NSC-5pc run. Central gas and torque properties are significantly influenced by the presence of the NSC. For more information, see Section \ref{['sec:NSCgas-properties']}.