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A&A
Volume 692, December 2024
Article Number A213
Number of page(s) 10
Section Astrophysical processes
DOI https://doi.org/10.1051/0004-6361/202452486
Published online 13 December 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

Detections of quasars at redshifts up to z ∼ 7.6 with black hole (BH) masses of ∼109 M⊙ (e.g. Mortlock et al. 2011; Matsuoka et al. 2019; Yang et al. 2020; Wang et al. 2021; Fan et al. 2023; Larson et al. 2023) and now active galactic nuclei (AGNs) at z ≳ 8 with masses of ≳106 M⊙ (Bogdán et al. 2024; Bunker et al. 2023; Maiolino et al. 2024) challenge our understanding of BH formation and growth in the early Universe.

The James Webb Space Telescope (JWST) via the JADES, CEERS, and UNCOVER surveys has now also revealed the existence of more than 300 compact, red objects at z = 4−10 accompanied by broad line emission, the so-called little red dots (LRDs; Matthee et al. 2023, 2024; Harikane et al. 2023; Kocevski et al. 2023; Feeney et al. 2024), which are typically indicative of an AGN. These objects, due to their unusually strong red component in the mid- to far-infrared, may indicate the presence of strong AGN activity. This in turn would indicate that (central) massive black hole (MBH) number densities are much higher than previously thought and hence that MBHs must form much more ubiquitously than previously assumed. Unlike typical AGN-hosting galaxies, they are, for the most part, not accompanied by X-ray (Ananna et al. 2024) or hot dust emission (Williams et al. 2024). Furthermore, when an AGN is assumed present, there is tentative evidence that the spectral energy distribution fits are categorised by high- or super-Eddington accretion and/or over-massive BH/stellar mass ratios (Volonteri et al. 2024; Durodola et al. 2024). All of this (admittedly as of yet somewhat speculative) evidence of higher-than-expected MBH number densities in the early Universe means that it is imperative that we try to understand how rapid and efficient MBH formation at high-z can develop.

The high-z supermassive black hole (SMBH) population as well as the known high-z AGN-dominated galaxies (e.g. GNz-11) and potentially the LRD population seemingly all require early MBH assembly and rapid accretion. As such, the local environment hosting the embryonic BH likely plays a key role in determining the MBH seed mass, the MBH duty cycle, and growth rates. Over the last two decades, significant research has been carried out to determine the birthplaces of MBH seeds and their formation pathways. While light seeds (< 1000 M⊙), born from the remnants of Population III (Pop III) stars, are expected to form ubiquitously in metal-free halos (see Klessen & Glover 2023), it is thought that heavy seeds (> 1000 M⊙) must wait for larger halos to emerge. Therefore, it is very possible that so-called pristine or near-pristine atomically cooled halos are the formation sites of heavy seeds (Oh & Haiman 2002; Bromm & Loeb 2003; Bromm & Yoshida 2011; Regan et al. 2017; Prole et al. 2024a).

Pristine atomically cooled halos can emerge via a variety of environmental pathways. In almost all cases, ordinary star formation in progenitor halos is suppressed until the halo reaches masses ≳107 M⊙ via some suppression mechanism. Examples include immersion in extremely high Lyman-Werner (LW) UV fluxes (J21 ≳ 1000 in units of 10−21 erg s−1 cm−2 Hz−1 sr−1) that suppress H2 formation (e.g. Shang et al. 2010; Regan et al. 2014, 2016, 2017; Regan & Downes 2018; Latif et al. 2013a,b, 2014a; Suazo et al. 2019; Patrick et al. 2023), supersonic baryon streaming motions that prevent gas collapse even if H2 is present (Stacy et al. 2011; Greif et al. 2011; Latif et al. 2014b; Schauer et al. 2017; Hirano et al. 2017), highly supersonic turbulence due to rare, powerful accretion streams (Yoshida et al. 2003; Fernandez et al. 2014; Inayoshi et al. 2015; Latif et al. 2022a), or some combination of the above (Wise et al. 2019). The onset of atomic cooling occurs when a halo’s virial temperature reaches ∼8000 K, with the halo mass required to achieve this being an increasing function with the age of the Universe (Fernandez et al. 2014):

M halo = [ T vir 0.75 × 1800 ( 21 1 + z ) ] 3 / 2 10 6 M ⊙ . $$ \begin{aligned} M_{\rm halo} = \left[\frac{T_{\rm vir}}{0.75 \times 1800} \left(\frac{21}{1+z}\right)\right]^{3/2} 10^6\,\mathrm{M}_{\odot }. \end{aligned} $$(1)

At z = 15, this reaches ∼2 × 107 M⊙. At these masses, catastrophic baryon collapse triggered by the atomic cooling leads to inflow rates of ∼10−3–1 M⊙ yr−1. Stellar evolution models indicate that, at these rates, Pop III stars with masses of a few times 103–105 M⊙ can emerge and later directly collapse into heavy seed BHs (Hosokawa et al. 2013; Woods et al. 2017; Haemmerlé et al. 2018; Hirano et al. 2014, 2015; Herrington et al. 2023; Nandal et al. 2024).

Heavy seeds are currently favoured as the formation pathway for high-redshift SMBHs over normal Pop III stellar BHs – with masses of a few tens to hundreds of solar masses – (light seeds; Susa et al. 2014; Hirano et al. 2014, 2015; Susa 2019; Latif et al. 2022a) because low-mass Pop III stars are born in low-density regions where they cannot rapidly grow and can be ejected from their host halos during supernova (SNe) explosions or gravitational collapse (Whalen et al. 2004; Kitayama et al. 2004; Whalen & Fryer 2012; Smith et al. 2018; Beckmann et al. 2019; Pfister et al. 2019). Although it has been proposed that mechanisms such as super- or hyper-Eddington accretion can overcome these obstacles (Madau et al. 2014; Alexander & Natarajan 2014; Volonteri et al. 2015; Lupi et al. 2016; Inayoshi et al. 2016), radiative or mechanical feedback from the BH appears to make sustained periods of such accretion difficult (Johnson & Bromm 2007; Milosavljević et al. 2009; Alvarez et al. 2009; Smith et al. 2018; Regan et al. 2019; Su et al. 2023; Massonneau et al. 2023). On the other hand, dynamical processes like runaway stellar mergers in dense nuclear clusters could result in stellar masses of a few thousand solar masses (e.g. Portegies Zwart et al. 2004; Devecchi & Volonteri 2009; Katz et al. 2015; Reinoso et al. 2018, 2023; Boekholt et al. 2018). Furthermore, and counterintuitively, feedback in the form of nearby SNe explosions may aid the growth of light seeds by launching gas towards the accreting objects (Mehta et al. 2024).

A MBH born with a mass of 104 − 105 M⊙ will not necessarily reach 107 − 109 M⊙ by z = 5−10. The few cosmological simulations that have created a 109 M⊙ BH by z ∼ 7 have relied on the ‘heaviest’ seeds in the most extreme environments (e.g. Smidt et al. 2018) and find that the MBH must reside at the nexus of rare, unusually powerful accretion streams that grow halos to ∼1012 M⊙ in low-shear environments by z ∼ 6 (Matteo et al. 2012; Feng et al. 2014; Di Matteo et al. 2017; Tenneti et al. 2018; Smidt et al. 2018; Zhu et al. 2022). This fuelling scenario can produce a 4 × 107 M⊙ BH by z = 10.4 (Smidt et al. 2018), like that in UHZ1, but only in one or two dozen halos per cGpc−3. These BHs are more likely the tip-of-the-iceberg, with the more common outcome being BHs with masses in the range 104 − 105 M⊙. It is these BHs with higher number densities and lower seed masses (Regan & Volonteri 2024; McCaffrey et al. 2024) that may be the seeds for the LRDs and other AGN-hosting galaxies that have number densities in the range ∼10−5 − 10−3 cMpc−3 (Pérez-González et al. 2024; Greene et al. 2024; Kocevski et al. 2024).

As the maximum mass halos can achieve before the onset of collapse is limited by the atomic cooling threshold of a few times 107 M⊙, this also theoretically limits the maximum inflow rates onto the central BH seed. Here we investigate whether rapid halo assembly via atomic halo collisions can further drive up accretion rates and boost the masses of BH seeds compared to isolated halos, ultimately leading to the SMBH population currently being detected at high redshifts.

The structure of the paper is as follows: In Sect. 2 we discuss our numerical method, including the simulation code, initial conditions, chemistry solver, and our implementation of sink particles. We present the results of our simulations in Sect. 3 and discuss them in Sect. 4. In Sect. 5 we highlight a few caveats. We conclude in Sect. 6.

2. Numerical method

2.1. AREPO

The simulations presented here were performed with the moving mesh code AREPO (Springel 2010) with a primordial chemistry set-up described in Sect. 2.3. AREPO combines the advantages of adaptive mesh refinement (Berger & Colella 1989) and smoothed particle hydrodynamics (Monaghan 1992) with a mesh made up of a moving, unstructured, Voronoi tessellation of discrete points. AREPO solves hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order un-split Godunov scheme with an exact Riemann solver.

2.2. Initial conditions

We modelled our primordial halos as Navarro-Frenk-White (Navarro 1996; Navarro et al. 1997) dark matter (DM) distributions, normalised to give the desired mass within the desired radius. We modelled the DM as particles of mass 100 M⊙ with a gravitational softening length of 0.1 pc. The baryonic gas component was initialised as an isothermal sphere (ρ ∝ r−2) at 100 K with a central density of 10−25 g cm−3 spanning out to its Jeans length of ∼360 pc. The central density was chosen to represent a halo on the brink of collapse (e.g. Greif et al. 2008; Schauer et al. 2021; Prole et al. 2023). The halos were placed in a background medium of density 10−28 g cm−3. We took the appropriate chemical abundances of H2, H+, D+, and HD from Greif et al. (2008) as xH2 = 10−5, x H + = 10 − 4 $ x_{\mathrm{H}^{+}} = 10^{-4} $, x D + = 2.6 × 10 − 9 $ x_{\mathrm{D}^{+}} = 2.6\times 10^{-9} $, and xHD = 3 × 10−8, respectively. The simulation box had a side length 9600 pc and was seeded with a randomly generated Burgers (1948) turbulent velocity field. The turbulence at these spatial scales and initial gas densities has been shown through cosmological simulations to be supersonic (e.g. Prole et al. 2023); we therefore scaled the velocity field to obtain an rms velocity of 2 times the sound speed: vrms = 1.82 km s−1. We set up four controlled numerical tests at z = 15 as follows:

  1. At our adopted redshift of z = 15, minihalos typically collapse once they reach a mass of ∼106 M⊙ in the absence of a LW radiation field. We therefore set our control set-up as the isolated collapse of a minihalo with 106 M⊙ in DM and used the cosmological baryon to DM mass ratio of 0.15 to give a gas component of 1.5 × 105 M⊙. Generating this gas mass with a 100 K isothermal density profile of central density 10−25 g cm−3 requires a halo radius Rmini = 300 pc, which results in the production of an initially Jeans unstable cloud.

  2. At our adopted redshift of z = 15 and in the presence of a strong LW radiation field, collapse will be delayed until the halo reaches a few times 107 M⊙ where atomic cooling can facilitate the collapse (e.g. O’Shea & Norman 2008). We therefore create an isolated atomic halo with 2 × 107 M⊙ in DM with a baryonic component of 3 × 106 M⊙, requiring a radius Ratomic = 1600 pc. While this configuration is initially Jeans unstable, we set the LW background to a value of J21 = 10 in units of 10−21 erg s−1 cm−2 Hz−1 sr−1 to delay the collapse until the gas reaches the atomic cooling limit of 8000 K.

  3. We simulate the merger of two of the above described atomic halos with a halo-halo collision in the presence of a J21 = 10 LW field. The halo centres were given positional offsets from the box centre of ±Ratomic along the x axis. As the simulation timestep becomes shorter as the density of the gas increases, the period of time we can simulate once the gas reaches the maximum threshold density is significantly shorter than the simulated period prior to this point. It is therefore computationally convenient for the gas to reach its maximum threshold density near to the time when the centres of the halos meet. We experimentally determine that these halos will collapse in roughly 60 Myr. We therefore set the initial collision velocity of the each halo in the x direction to be ±25 km s−1. Such velocities are consistent with those seen in previous studies of colliding flows (e.g. Latif et al. 2021).

  4. A more likely scenario than a head on collision is an indirect halo collision resulting in a fly-by event between the central density peaks of the halos. We therefore also simulate a collision with a small angular offset in the collisional velocity vectors. The left and right halos are given angular velocity offsets from the x axis of +π/24 and −π/24, respectively. This gives an impact parameter (point of closest approach) of ∼200 pc.

2.3. Chemistry

Collapse of primordial gas is closely linked to the chemistry involved (e.g. Glover et al. 2006; Yoshida et al. 2007; Glover & Abel 2008; Turk et al. 2011; Klessen & Glover 2023; Prole et al. 2024b). We therefore use a fully time-dependent chemical network to model the gas. We use the treatment of primordial chemistry and cooling originally described in Clark et al. (2011), but with updated values for some of the rate coefficients, as summarised in Schauer et al. (2019). The network has 45 chemical reactions to model primordial gas made up of 12 species: H, H+, H−, H 2 + $ ^{+}_{2} $, H2, He, He+, He++, D, D+, HD, and free electrons. Optically thin H2 cooling is modelled as described in Glover & Abel (2008): we first calculated the rates in the low-density (n → 0) and local thermodynamic equilibrium (LTE) limits, and then smoothly interpolated between them as a function of n/ncr, where ncr is the H2 critical number density above which collisions are so frequent that they keep the populations close to their LTE values. To compute the H2 cooling rate in the low-density limit, we accounted for the collisions with H, H2, He, H+, and electrons. To calculate the H2 cooling rate in the optically thick limit, we used an approach based on the Sobolev approximation (Yoshida et al. 2006; Clark et al. 2011). Prior to the simulation, we computed a grid of optically thick H2 cooling rates as a function of the gas temperature and H2 column density. During the simulation, if the gas is dense enough for the H2 cooling to potentially be in the optically thick regime (ρ > 2 × 10−16 g cm−3), we interpolated the H2 cooling rate from this table, using the local gas temperature and an estimate of the effective H2 column density computed using the Sobolev approximation. In addition to H2 cooling, we also accounted for several other heating and cooling processes: cooling from atomic hydrogen and helium, collisionally induced H2 emission, HD cooling, ionisation and recombination, heating and cooling from changes in the chemical make-up of the gas and from shocks, compression and expansion of the gas, three-body H2 formation, and heating from accretion luminosity. For reasons of computational efficiency, the network switches off tracking of deuterium chemistry at densities above 10−16 g cm−3 and instead HD cooling is calculated assuming that the ratio of HD to H2 at these densities is given by the cosmological D to H ratio of 2.6 × 10−5. The adiabatic index of the gas was computed as a function of chemical composition and temperature with the AREPO HLLD Riemann solver.

2.4. Sink particles

The simulation mesh must be refined during a gravitational collapse to ensure the local Jeans length is resolved. During the collapse, we resolved the mesh such that the Jeans length (Jeans 1902; Bonnor 1957) was resolved by 16 cells up to a threshold density, ρsink, above which a sink particle (Bate et al. 1995) is introduced to represent the dense gas, preventing artificial instability in cells whose Jeans lengths continue to decrease below the minimum cell length.

We have shown in previous studies that the degree of fragmentation in metal-free gas is highly dependent on numerical resolution, with higher resolution simulations exhibiting more fragmentation (Prole et al. 2022a,b). We therefore expect that the masses achieved by the sink particles in this study would be lower if we employed higher resolutions. What is not known is whether any trends discovered during the halo collisions in the current experiment are resolution dependent. To that end, we repeated the simulations with threshold densities of 10−18 g cm−3 and 10−16 g cm−3. The threshold densities were chosen such that sink particles form after the gas achieves its minimum temperature of ∼100 K at ∼10−20 g cm−3 and has begun its rise in temperature towards the formation of a protostar. We chose our sink particle accretion radius to be the Jeans length at the sink creation density, calculated using the temperature-density relation provided in Prole et al. (2022a). We set the minimum gravitational softening length for gas and sink particles as Lsoft = Rsink/2 and the minimum cell length Lmin = Rsink/4. The sink particle parameters are given in Table 1. At these resolutions, our sink particles likely represent a dense stellar cluster rather than a single massive star (e.g. Prole et al. 2023). The higher resolution simulation (ρsink = 10−16 g cm−3) is henceforth taken to be the fiducial case, providing the data in all of the figures unless stated otherwise.

Table 1.

Simulation parameters.

Our sink particle implementation was introduced in Wollenberg et al. (2020) and Tress et al. (2020). A cell is converted into a sink particle if it satisfies three criteria:

  1. The cell reaches a threshold density.

  2. It is sufficiently far away from pre-existing sink particles so that their accretion radii do not overlap.

  3. The gas occupying the region inside the sink is gravitationally bound and collapsing.

Likewise, for the sink particle to accrete mass from surrounding cells, the cell must meet two criteria:

  1. The cell lies within the accretion radius.

  2. It is gravitationally bound to the sink particle.

A sink particle can accrete up to 90% of a cell’s mass, above which the cell is removed and the total cell mass is transferred to the sink. The sink particle treatment also includes the accretion luminosity feedback from Smith et al. (2011) and the sink particle merger routine from Prole et al. (2022a).

3. Results

In Fig. 1 we show density and temperature slices of the initial conditions for the direct and fly-by collision scenarios, along with respective slices of both collisions at a point just before the formation of the first sink particle. While the initial conditions are idealised isothermal spheres, as the outskirts of the halos collide in the x direction, the overlapping regions create a plane of enhanced density in the y − z plane, which is shock heated up to the atomic cooling limit of ∼104 K.

thumbnail Fig. 1.

Density (top) and temperature (bottom) slices of the simulation box (9.6 kpc) for the halo collision scenarios. Left: Initial conditions for both direct and fly-by collision simulations. Middle: Direct collision shown just before the formation of the first sink particle. Right: Fly-by collision shown just before the formation of the first sink particle.

In Fig. 2 we compare the density-temperature profile of the merging halos with that of the isolated mini and atomic halos at a point just before the formation of the first sink particle. This occurred roughly 60 Myr after the simulation started in both the collision scenarios and the isolated atomic halo scenario, while it occurred after around 45 Myr in the isolated minihalo case. Referring to the top row of panels, gas falling into the minihalo follows the well-established rise to 103 K and fall to 102 K indicative of efficient H2 production and cooling. Likewise, the atomic halo behaves as in previous studies; the H2 abundance is reduced by the external LW field, allowing it to grow to 107 M⊙ where temperatures reach the atomic cooling limit of 104 K and Lyman-α cooling facilitates the proceeding collapse. For the halo merger scenarios, low-density gas is also heated up to the atomic limit by the highly supersonic motions of the gas and the shocks created by the collision. There are also elevated H2 fraction features at densities around 10−24 g cm−3 (middle row), likely caused by the increase in fractional ionisation (bottom row) produced by the shocks during the collision, as the H2 formation rate is dependent on the availability of free electrons.

thumbnail Fig. 2.

2D histograms of gas properties for the four scenarios at a time just before the formation of the first sink particle, colour-coded according to the number of cells. We show the temperature (top), H2 abundance (middle), and ionisation fraction (bottom) as a function of density.

In Fig. 3 we show the growth of the most massive sink particle in all four simulations for both resolutions tested. By the end of the simulations, the direct collision scenario did not produce a more massive sink particle than isolated atomic halo case, regardless of resolution. In both cases, the accretion rate onto the sink experiences a brief (1−2 Myr) spike followed by sharp decline, occurring around 5 Myr after its creation. To explore why this happens, we show gas density slices of the interaction between the high-density centres of the colliding halos, along with the underlying DM distributions in Fig. 4. The DM consists of collisionless particles; hence, the two central DM halos pass through each other during the interaction. On the other hand, the high-density gas from the two halos collides and is ripped from its respective DM peak. The bulk of the gas is left in the centre, pulled equally in both directions by the diverging DM distributions, while the collisionless sink particle is pulled through and subsequently out of the high-density gas with the right-hand-side (RHS) DM potential, causing the accretion peak and subsequent drop-off, as the sink particle is removed from its accretion source. This process is mirrored on the left-hand side (LHS) of the interaction, with the high-density gas leaving with the LHS DM peak despite having not formed a sink particle yet, showing that the ejection is not a numerical artefact caused by the sink particle routine. The interaction is comparable with observations of the ‘Bullet Cluster’ 1E0657−56 (Markevitch et al. 2002; Markevitch & Vikhlinin 2007), which has been used as evidence for the existence of DM due to the offset between the X-ray emission and the nearby gravitational lensing centres (Clowe et al. 2006). Here the collision-dominated hot plasma was separated from the collisionless stellar and DM components, just as we see in our direct collision simulation.

thumbnail Fig. 3.

Sink particle evolution for the four halo scenarios as a function of time, shown for both resolutions tested. Top: Mass of the most massive sink particle. Middle: Accretion rate onto the most massive sink particle; regions with no data indicate periods of zero accretion. Bottom: Total number of sink particles formed.

thumbnail Fig. 4.

200 pc zoom slices showing the time evolution of the direct halo collision. Top: Density projection of the interaction between the two high-density peaks of the halos. The green star indicates the sink particle. Bottom: Underlying DM distribution shown with the contours of a 2D histogram of the DM particle positions. The slices are shown at 60 Myr and 1.5, 2.5, and 4.5 Myr later.

While the direct collision hindered accretion, the remaining three scenarios all produced sustained accretion throughout the simulations, with the fly-by collision providing the best conditions for growth. It has been shown in previous works that larger halo masses increase the accretion onto the central objects (O’Shea & Norman 2008; Bromm & Loeb 2003; Bromm & Yoshida 2011; Wise et al. 2019; Latif et al. 2022b; Prole et al. 2024b). In our high resolution (low resolution) case, we see a factor of 1.3 (1.5) boost in mass when comparing the isolated minihalo with the more massive atomic halo case, growing to 3500 and 4500 (5700 and 8300) M⊙ by the end of the simulation, respectively. On top of this, we also see a further enhancement of a factor of 2.2 (2.5) during the fly-by collision, giving a factor of 2.9 (3.6) times the mass achieved by the minihalo, giving a final mass of 104 (2.08 × 104) M⊙ by the end of the simulation. We investigate the reason for this in Fig. 5, where we show density slices of the fly-by encounter. The accretion onto the sink particle was initially similar to that of the isolated atomic halo, as the sink particle formed outside of the high-density, shocked region. However, once the sink particle entered the hot (atomic cooling) dense gas after ∼4 Myr, it was able to accrete more efficiently and the growth gains compared to the isolated halo scenario became more apparent. The sink particle remained in the shocked region throughout the remainder (6 Myr) of the simulation. The result that objects accreting within the dense, shocked region of the collision experience increased accretion rates is seemingly resolution independent.

thumbnail Fig. 5.

Density (top) and temperature (bottom) slices of the inner 500 pc of the fly-by collision simulation, shown at the formation of the first sink particle (60 Myr) and 5 Myr and 10 Myr later. Sink particles are represented by green stars.

In Fig. 6 we compare the distribution of mass as functions of density and distance from the sink particle at t = 5 Myr after the formation of the first sink particle (when the sink particle is deeply embedded in the dense, shocked region; see the middle panel of Fig. 5). From the left panel we see that the collision produces increased masses across the entire simulated range of densities. The right panel shows the cumulative mass as a function of radius from the most massive sink particle, showing that the mass gains reside from ∼100 pc outwards, but also from within the inner few parsecs. We highlight the density ranges where the fly-by collision hosts significantly more gas than the isolated scenarios in Fig. 7. For the isolated minihalo and atomic halo scenarios, we show the mass of gas existing at or above density thresholds, divided by the values achieved by the fly-by collision (i.e. the black and blue lines from Fig. 6 divided by the red line from the same figure). From this, we see the mass gains compared to the isolated atomic halo mainly reside in the low density range of 10−26–10−24 g cm−3 and the high density range of 10−19–10−17 g cm−3. The increased mass at these densities is more than could be explained by the doubling of gas given from simply having 2 halos present during the merger instead of a single halo. From Fig. 2 it is clear that the increase in lower-density mass is made up of the hot shocked gas in the collisional plane.

thumbnail Fig. 6.

Mass weighted gas profiles for the isolated halo types and the fly-by collision scenario, compared at 5 Myr after the formation of the first sink particle, i.e. when the sink particle is deeply embedded in the dense, shocked region (see the middle panel of Fig. 5). Left: Mass of gas at or above density thresholds as a function of the density threshold. Right: Cumulative mass as a function of radius from the sink particle.

thumbnail Fig. 7.

Mass of gas existing at or above density thresholds divided by the values achieved by the fly-by collision for the isolated minihalo and atomic halo scenarios (i.e. the black and blue lines from Fig. 6 divided by the red line from the same figure). This highlights the density ranges in which the fly-by collision hosts significantly more gas than the isolated scenarios.

While we did not follow the simulation until the sink particle emerged from the LHS of shocked region, the time periods simulated here are already too long to neglect SNe feedback. For reference, during the 6 Myr period the sink particle spends in the shocked region, any unresolved fragmentation and resulting star formation would result in SNe feedback from any stars with masses higher than ∼20 M⊙, while even the highest resolution simulations (hence the least conductive to massive star formation due to fragmentation-induced starvation) show the formation of Pop III stars with masses of a few tens of M⊙ (Prole et al. 2023, 2024a). A recent study by Mehta et al. (2024) showed that SNe feedback can actually aid accretion in some cases by shocking the gas towards other accreting bodies. It is therefore not obvious if further shocking the dense collisional plane via the inclusion of SNe feedback would help or hinder BH seed growth.

The realised boost to BH seed accretion during the collision is important because enhanced accretion is typically only attainable by increasing the mass of the halo when considering isolated halo collapses. This has the limitation that the maximum halo mass that can be achieved before collapse is set by the onset of atomic cooling, meaning halos cannot resist collapse past masses of a few times ∼107 M⊙, even in the presence of extremely high LW radiation intensities (Prole et al. 2024a), steaming velocities (Schauer et al. 2021) or colliding flows (Latif et al. 2022b). Boosting the initial seed masses via halo mergers may therefore be the only mechanism that can overcome this physical barrier to BH seed growth.

4. Discussion

In a Λ cold dark matter (CDM) context, structure formation occurs via bottom-up hierarchical growth with frequent mergers (e.g. Peebles 2015). The first halos are expected to start collapsing from z ∼ 30 onwards (Klessen & Glover 2023) and we now have observations of 109 M⊙ SMBHs existing by z ∼ 11 (Bunker et al. 2023; Maiolino et al. 2024). While isolated halos can have their accretion supply cut off when stellar feedback evacuates gas from the halo, mergers can continue to bring fresh gas into the halo. Through multiple halo mergers similar to that of this work, the central BH seed could continue to grow at accelerated rates for significantly extended periods of time when compared to an isolated collapse, giving them a better chance at achieving observed SMBH masses.

At z ∼ 11, the age of the Universe is roughly 400 Myr. Cosmological simulations show that atomic cooling halos collapse by z ∼ 15 (Xu et al. 2016; Wise et al. 2019; Regan et al. 2020; Latif et al. 2022b), giving them of the order of 100 Myr to undergo multiple mergers. While the simulated period in this investigation took roughly 70 Myr, the initial conditions represented the very early stages of collapse and the velocities were fine tuned to match the collapse time. In reality, mergers can occur at any stage during or after the initial collapse and multiple mergers can take place simultaneously. Additionally, it is unlikely that merging halos would be at similar stages of their collapse, and massive halos would likely merge with multiple smaller halos that are yet to have had their collapse triggered by reaching the mass threshold for collapse. The result is that halo-halo mergers can occur over a wide range of timescales, which allows for many mergers during the 100 Myr time window.

Furthermore, the most realistic mechanism of rapid halo growth is successive minor mergers of low-mass halos. While we have shown that major mergers with pre-established 107 M⊙ halos can boost the accretion rate onto the central BHs, it remains unclear what effect frequent minor mergers with (for example) a 106 M⊙ minihalo would have on the growth prospects of the central objects. While the shocked gas may initially increase accretion rates as we have seen here, successive collisions may disrupt accretion through dynamical heating.

This experiment is the motivation for future work where we will investigate BH seed formation within halos undergoing rapid mergers in a more realistic cosmological setting. Halos experiencing rapid mergers are likely to be compact and perhaps host unusual star formation histories, which could shed light on the formation of LRDs and GNz-11 type galaxies.

5. Caveats

The initial conditions presented here are idealised to test the specific concept that halo mergers can facilitate high-mass BH seed formation. As a result, the halos lack significant substructure. In future work, we aim to test the results of this work with initial conditions more in line with ΛCDM cosmology, by sampling the expected primordial power spectrum and performing cosmological simulations.

We did not include magnetic fields in these simulations. While studies of primordial magnetic fields suggest that they can increase the mass of protostars (e.g. Peters et al. 2014; Turk et al. 2012; Saad et al. 2022; Hirano & Machida 2022; Stacy et al. 2022) and SMBHs (Latif et al. 2013c, 2014c), the fields have no effect when they are properly resolved, distributing the magnetic energy from the small-scale turbulent dynamo (Schober et al. 2012) to smaller spatial scales (Prole et al. 2022b).

Ideally, we would resolve up to the protostellar formation density of 10−4 g cm−3 (Greif et al. 2012), which is currently computationally unfeasible for the period of time we aimed to simulate. Failure to resolve protostellar densities means we have not achieved numerical convergence. However, the important factor in these simulations is not the specific sink particle masses, but rather the relative difference between the masses produced in an isolated collapse versus the merger scenario.

6. Conclusions

This investigation aimed to test to what extent halo-halo mergers affect the growth of SMBH seeds. To that end, we performed simulations of the collapse of an isolated minihalo and an atomic halo and compared them to direct and fly-by halo-halo collisions. The total simulated period was 70 Myr, and we followed the evolution of the sink particle for the final 10 Myr. The sink particles in the collision set-ups spend the final 6 Myr embedded in the dense, shocked region. We have shown that:

  1. Halo collisions create a higher-density central environment where BH seeds can accrete at higher rates.

  2. For direct collisions, the gas density peaks are disrupted by the interaction because the collisionless DM peaks pass through each other while the colliding gas is left in the centre, removing the BH from its accretion source.

  3. When the central density peaks instead experience a fly-by interaction, the BH remains embedded in the dense gas and maintains higher accretion rates compared to the isolated halo cases.

  4. For the fly-by simulation, the final mass of the BH is a factor of 2 higher than that of the isolated atomic halo, and a factor of 3 higher than the minihalo case, reaching 104 M⊙ via the ∼0.03 pc accretion radius of the sink particle.

  5. As the maximum halo mass before collapse is determined by the atomic cooling limit of a few times 107 M⊙, the ability of halo-halo mergers to further boost the rates of accretion onto the central object may play a crucial role in growing SMBH seeds, which is needed to explain recent observations of seemingly over-massive BHs at z ∼ 7.

While this work utilised idealised initial conditions, it serves as a base for future investigations where we will study halo collisions in a cosmological context using realistic initial conditions more in line with ΛCDM cosmology.

Acknowledgments

LP and JR acknowledge support from the Irish Research Council Laureate programme under grant number IRCLA/2022/1165. JR also acknowledges support from the Royal Society and Science Foundation Ireland under grant number URF\R1\191132. The simulations were performed on the Luxembourg national supercomputer MeluXina. The authors gratefully acknowledge the LuxProvide teams for their expert support. The authors wish to acknowledge the Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support. The authors acknowledge the EuroHPC Joint Undertaking for awarding this project access to the EuroHPC supercomputer Karolina, hosted by IT4Innovations through a EuroHPC Regular Access call (EHPC-REG-2023R03-103). RSK and SCOG acknowledge financial support from the European Research Council via the ERC Synergy Grant “ECOGAL” (project ID 855130), from the German Excellence Strategy via the Heidelberg Cluster of Excellence (EXC 2181 – 390900948) “STRUCTURES”, and from the German Ministry for Economic Affairs and Climate Action in project “MAINN” (funding ID 50OO2206). RSK is grateful for computing resources provided by the Ministry of Science, Research and the Arts (MWK) of the State of Baden-Württemberg through bwHPC and the German Science Foundation (DFG) through grants INST 35/1134-1 FUGG and 35/1597-1 FUGG, and also for data storage at SDS@hd funded through grants INST 35/1314-1 FUGG and INST 35/1503-1 FUGG. RSK also thanks the Harvard-Smithsonian Center for Astrophysics and the Radcliffe Institute for Advanced Studies for their hospitality during his sabbatical, and the 2024/25 Class of Radcliffe Fellows for highly interesting and stimulating discussions.

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All Tables

Table 1.

Simulation parameters.

In the text

All Figures

thumbnail Fig. 1.

Density (top) and temperature (bottom) slices of the simulation box (9.6 kpc) for the halo collision scenarios. Left: Initial conditions for both direct and fly-by collision simulations. Middle: Direct collision shown just before the formation of the first sink particle. Right: Fly-by collision shown just before the formation of the first sink particle.
In the text
thumbnail Fig. 2.

2D histograms of gas properties for the four scenarios at a time just before the formation of the first sink particle, colour-coded according to the number of cells. We show the temperature (top), H2 abundance (middle), and ionisation fraction (bottom) as a function of density.
In the text
thumbnail Fig. 3.

Sink particle evolution for the four halo scenarios as a function of time, shown for both resolutions tested. Top: Mass of the most massive sink particle. Middle: Accretion rate onto the most massive sink particle; regions with no data indicate periods of zero accretion. Bottom: Total number of sink particles formed.
In the text
thumbnail Fig. 4.

200 pc zoom slices showing the time evolution of the direct halo collision. Top: Density projection of the interaction between the two high-density peaks of the halos. The green star indicates the sink particle. Bottom: Underlying DM distribution shown with the contours of a 2D histogram of the DM particle positions. The slices are shown at 60 Myr and 1.5, 2.5, and 4.5 Myr later.
In the text
thumbnail Fig. 5.

Density (top) and temperature (bottom) slices of the inner 500 pc of the fly-by collision simulation, shown at the formation of the first sink particle (60 Myr) and 5 Myr and 10 Myr later. Sink particles are represented by green stars.
In the text
thumbnail Fig. 6.

Mass weighted gas profiles for the isolated halo types and the fly-by collision scenario, compared at 5 Myr after the formation of the first sink particle, i.e. when the sink particle is deeply embedded in the dense, shocked region (see the middle panel of Fig. 5). Left: Mass of gas at or above density thresholds as a function of the density threshold. Right: Cumulative mass as a function of radius from the sink particle.
In the text
thumbnail Fig. 7.

Mass of gas existing at or above density thresholds divided by the values achieved by the fly-by collision for the isolated minihalo and atomic halo scenarios (i.e. the black and blue lines from Fig. 6 divided by the red line from the same figure). This highlights the density ranges in which the fly-by collision hosts significantly more gas than the isolated scenarios.
In the text

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