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

TL;DR

This study examines how stellar feedback channels regulate the growth of intermediate-mass black holes embedded in nuclear star clusters within dwarf galaxies by resolving gas inflows from the galactic ISM down to the self-gravity radius of the accretion disc. Using the MandelZoom II framework, the authors run high-resolution simulations that separately and jointly vary early radiative feedback and supernova feedback, as well as star-formation and numerical parameters, to follow the emergence and destruction of circumnuclear discs feeding the black hole. They find that radiative feedback suppresses fragmentation and builds larger CNDs, SN feedback heats and disperses the ISM and can disrupt the CND, and the combination of both leads to intermittent CND cycles that regulate BH fueling and spin-up. The results demonstrate the necessity of including multiple stellar feedback channels in galaxy-scale simulations to understand IMBH growth, with implications for observing IMBHs with facilities like SKA, Rubin, and LISA, and for connecting local IMBH growth to high-redshift supermassive BHs observed by JWST.

Abstract

We present a suite of high-resolution simulations to study how different stellar feedback channels regulate the growth of central intermediate-mass black holes (IMBHs) in dwarf galaxies hosting nuclear star clusters (NSCs). We employ a super-Lagrangian refinement scheme to resolve the self-gravity radius of the $α$-accretion disc ($<0.01$~pc) and follow the gas inflows from the interstellar medium (ISM) to the black hole (BH), allowing for the self-consistent emergence of circumnuclear discs (CNDs). In the absence of stellar feedback, as expected, the galactic disc fragments excessively, producing a massive CND. When radiative stellar feedback is included, fragmentation is suppressed, with even more massive CNDs forming and feeding the IMBH. With supernova (SN) feedback only, clustered SNe strongly heat the ISM, yielding both the lowest CND masses and BH accretion rates. When both radiative stellar feedback and SNe are included, the CND becomes intermittent: it survives for $10$--$100$~Myr, and is then destroyed by feedback before being replenished by fresh galactic inflows, while substantial BH growth still takes place. These results highlight the critical importance of accurately modelling the combined effects of key stellar feedback processes to understand IMBH growth. Our simulation suite brackets the likely range of CND states, with IMBHs exhibiting significant growth and systematic spin-up in all dwarf galaxy models explored. These findings bode well for the detection of IMBHs with future observational facilities such as SKA, the Rubin Observatory, and LISA, and make them highly relevant progenitor candidates of the high-redshift supermassive BHs observed by JWST.

Figures (10)

• Figure 1: Visualisation of our simulation setup. (a) Face-on gas column density projection of the full run in a box of $2$ kpc on-a-side at $t=136$ Myr. (b) NSC surface density projection in a $40$ pc box. Coloured dots mark the positions of stars formed during the simulation; the dot colours correspond to stellar ages. (c) Zoom-in, face-on view of the surface gas density projection in a $40$ pc box. Due to the NSC potential, gas inflows effectively form a CND with a radius of approximately $6$ pc. The reddish dots indicate massive young stars ($M_\star > 5~\,\rm M_\odot$, age $< 35~\mathrm{Myr}$) which are responsible for stellar feedback. The dot size scales with stellar mass, ranging from $5.12~\,\rm M_\odot$ to $18.2~\,\rm M_\odot$. The black dot marks the BH position. (d) Zoomed-in, edge-on view of the gas surface density projection in a $40$ pc box. The CND is warped as the angular momentum of the inflowing gas changes over time. (e) Voronoi slice plot of a $2$ pc box region illustrating the super-Lagrangian refinement, where gas cell sizes decrease toward the BH and achieve a spatial resolution of $<0.01$ pc. At the self-gravity radius, $r_{\rm SG}\sim0.15$ pc, the gas is resolved with $\sim2000$ cells. (f) Sketch of our subgrid BH accretion model. At $r_{\rm SG}$, we measure the inflow rates of mass and angular momentum, which are then used to update the $\alpha$-disc mass and angular momentum. Based on the $\alpha$-disc model Shakura+Sunyaev1973 and the Lense–Thirring effect Bardeen+Petterson1975, the subgrid model computes the evolution of the BH mass, BH spin, accretion disc mass and angular momentum. See Section \ref{['sec:bh-model-method']} for further details.
• Figure 2: Face-on projections of the galactic disc. Simulation results at $t=140$ Myr for four different stellar feedback schemes. Top row: Gas column density in a $2$ kpc box. Second row: Zoomed-in view of the gas column density in a $200$ pc box. Third row: Density-weighted temperature. Fourth-rows: $\ion{H}{II}$ fraction. Bottom row: Locations of young stars overlaid on the gas column density background. The dot colours indicate stellar ages. The thermodynamic state and morphology of the ISM are strongly affected by the stellar feedback combination, but all simulations consistently form a cold dense CND within $\lesssim 10$ pc at the centre. See Section \ref{['sec3:gas-proj']} for further details.
• Figure 3: The time evolution of SFR of simulations within the $r=1$ kpc region for our simulations. The left-hand panel shows that the early stellar feedback leads to much smoother SFRs due to the suppression of excessive disc fragmentation, while the additional inclusion of SN feedback (the full model) introduces slightly burstier SFR evolution. The right-hand panel shows that our SFR evolution is robust against reasonable changes in our star formation prescription, while, as expected, lower initial gas metallicities affect gas cooling efficiency and hence the SFR. See Section \ref{['sec:sfr']} for further details.
• Figure 4: Time evolution of the radial profiles of gas density (density-weighted) and SFR surface density. The red lines show the evolution of the CND radius, while the green lines mark the evolution of the self-gravity radius of the accretion disc. The evolution of the ISM, the CND properties and the spatial distribution of SFRs vary with different stellar feedback channels and numerical setups explored. In all simulations that incorporate the combined effect of stellar radiation and SN feedback the CND is periodically disrupted and exhibits intermittent evolution. See Section \ref{['sec:3d']} for further details.
• Figure 5: Evolution of CND gas and stars. Top and fifth rows: SFR within 10 pc ( blue lines), mass inflow rate into the accretion disc ($\dot{M}_{\rm in}$; red lines), and BH accretion rate ($\dot{M}_{\bullet}$; black lines). Second and sixth rows: inflow ( green lines) and outflow ( orange lines) rate at $r=10$ pc. Third and seventh rows: enclosed gas mass within the central $10$ pc. The total gas mass is shown in black, and we also show gas mass split up in different phases, where the definitions of HIM, WIM, WNM, and CNM are provided in Section \ref{['sec:CNDcycle']}. Forth and bottom rows: number of SNe events ($N_{\rm SNe}$; red, green, black bars) within three different radii and massive stars producing EUV/FUV photons within 10 pc ($N_{\rm FUV\star}$; magenta lines) formed within each time bin ($\Delta t=15$ Myr). EUV/FUV feedback prevents excessive fragmentation of the ISM, allowing more gas to flow into the circumnuclear region, while SN feedback suppresses fragmentation within the CND, making in-situ star formation episodic. Only when both feedback processes operate together does the CND undergo cyclic formation and destruction, leading to episodic accretion onto the BH accretion disc. See Section \ref{['sec:CNDsfr-BHAR']} for details.