Nuclear Star Cluster Research Articles

Growing black holes through successive mergers in galactic nuclei – I. Methods and first results

ABSTRACT We present a novel, few-body computational framework designed to shed light on the likelihood of forming intermediate-mass (IM) and supermassive (SM) black holes (BHs) in nuclear star clusters (NSCs) through successive BH mergers, initiated with a single BH seed. Using observationally motivated NSC profiles, we find that the probability of an ${\sim }100\hbox{-}\mathrm{M}_\odot$ BH to grow beyond ${\sim }1000 \, \mathrm{M}_\odot$ through successive mergers ranges from ${\sim }0.1~{{\ \rm per\ cent}}$ in low-density, low-mass clusters to nearly 90 per cent in high-mass, high-density clusters. However, in the most massive NSCs, the growth time-scale can be very long ($\gtrsim 1\,$ Gyr); vice versa, while growth is least likely in less massive NSCs, it is faster there, requiring as little as ${\sim }0.1\,$Gyr. The increased gravitational focusing in systems with lower velocity dispersions is the primary contributor to this behaviour. We find that there is a simple ‘7-strikes-and-you’re-in’ rule governing the growth of BHs: Our results suggest that if the seed survives 7–10 successive mergers without being ejected (primarily through gravitational wave recoil kicks), the growing BH will most likely remain in the cluster and will then undergo runaway, continuous growth all the way to the formation of an SMBH (under the simplifying assumption adopted here of a fixed background NSC). Furthermore, we find that rapid mergers enforce a dynamically mediated ‘mass gap’ between about ${50\!-\!300 \, \mathrm{M}_\odot }$ in an NSC.

Distinguishing Dark Matter Cusps from Cores Using Globular Clusters

Globular clusters (GCs) provide valuable insight into the properties of their host galaxies’ dark matter halos. Using N-body simulations incorporating semianalytic dynamical friction and GC−GC merger prescriptions, we study the evolution of GC radial distributions and mass functions in cuspy and cored dark matter halos. Modeling the dynamics of the GC-rich system in the dwarf galaxy UGC 7369, we find that friction-induced inspiral and subsequent mergers of massive GCs can naturally and robustly explain the mass segregation of the GCs and the existence of a nuclear star cluster (NSC). However, the multiple mergers required to form the NSC only take place when the dark matter halo is cuspy. In a cored halo, stalling of the dynamical friction within the core halts the inspiral of the GCs, and so the GC merger rate falls significantly, precluding the formation of an NSC. We therefore argue that the presence of an NSC requires a cusp in UGC 7369. More generally, we propose that the presence of an NSC and the corresponding alteration of the GC mass function due to mergers may be used as an indicator of a cuspy halo for galaxies in which we expect NSC formation to be merger dominated. These observables represent a simple, powerful complement to other inner halo density profile constraint techniques and should allow for straightforward extension to larger samples.

A 3D model for the stellar populations in the nuclei of NGC 1433, NGC 1566, and NGC 1808

Aims. We aim to characterize the properties of the stellar populations in the central few hundred parsecs of nearby galactic nuclei; specifically their age, mass, and 3D geometry. Methods. We use spatially resolved spectroscopic observations of NGC 1433, NGC 1566, and NGC 1808 obtained with SINFONI to constrain a 3D model composed of a spherically symmetric nuclear star cluster (NSC) and an extended thick stellar disk. We computed UV to mid-infrared single stellar population (UMISSP) spectra to determine the age of the stellar populations and construct synthetic observations for our model. To overcome degeneracies between key parameters, we simultaneously fit the spatially resolved line-of-sight velocity, line-of-sight-velocity-dispersion, low-spectral-resolution NIR continuum, and high-spectral-resolution CO absorption features for each pixel. Results. For the three objects, we derive the age and mass of the young and old stellar populations in the NSC and surrounding disk, as well as their 3D geometry: radius for the NSC; thickness, inclination, and position angle for the disk. These results are consistent with published independent measurements when available. Conclusions. The proposed method allows us to derive a consistent 3D model of the stellar populations in nearby galactic centers solely based on a near-infrared IFU observation.

Milky Way globular clusters on cosmological timescales

Aims. We estimate the dynamical evolution of the interaction of globular clusters’ with the Galactic centre that dynamically changed in the past. Methods. We simulated the orbits of 147 globular clusters over a 10 Gyr lookback time using the parallel N-body code ‘φ-GPU’. For each globular cluster, we generated 1000 sets of initial data with random proper motions and radial velocities based on the observed values. To distinguish globular clusters interacting with the Galactic centre, we used the criterion of a relative distance of less than 100 pc. We used four external potentials from the IllustrisTNG-100 database, which were selected for their similarity to the present-day Milky Way, to simulate the structure of the Galaxy at different times. Results. We obtained approximately three to four globular cluster interactions per billion years at distances of less than 50 pc and approximately five to six interactions per billion years at distances of less than 80 pc among the studied 147 globular clusters that had close passages near the Galactic centre. We selected ten of them for detailed study and found almost 100% probability of an interaction with the Galactic centre for six of them. Conclusions. According to our results, the maximum interaction frequency of globular clusters with the Galactic centre in the Milky Way is likely to be a few dozens of passages per billion years within a central zone of 100 pc. This low frequency may not be sufficient to fully explain the relatively high mass (of order 107 M⊙) of the nuclear star cluster in the Milky Way if we consider only the periodic capture of stars from globular clusters during close encounters. Therefore, we must also consider the possibility that some early globular clusters were completely tidally disrupted during interactions with the forming nuclear star cluster and the Galactic centre.

Globular clusters in the Galactic center region: Expected behavior within the infall and merger scenario

In this work, we reexamine the infall and merger scenario of massive clusters in the Milky Way’s potential well as a plausible Milky Way formation mechanism. We aim to understand how the stars of the merging clusters are redistributed during and after the merger process. We used, for the first time, high-resolution simulations with concentrated in the 300 pc around the Galactic center. We adopted simulations developed in the framework of the Modelling the Evolution of Galactic Nuclei (MEGaN) project. We compared the evolution of representative clusters in the mass and concentration basis in the vicinity of a supermassive black hole. We used the spatial distribution, density profile, and the 50% Lagrange radius (half mass radius) as indicators along the complete simulation to study the evolutionary shape in physical and velocity space and the final fate of these representative clusters. We find that the least massive clusters are quickly (< 10 Myr) destroyed. On the other hand, the most massive clusters have a long evolution, showing variations in the morphology, especially after each passage close to the supermassive black hole. The deformation of the clusters depends on the concentration, with general deformations for the least concentrated clusters and outer strains for the more concentrated ones. At the end of the simulation, a dense concentration of stars belonging to the clusters was formed. The particles that belong to the most massive and most concentrated clusters are concentrated in the innermost regions, meaning that the most massive and concentrated clusters contribute a more significant fraction of particles to the final concentration. This finding suggests that the population of stars of the nuclear star cluster formed through this mechanism comes from massive clusters rather than low-mass globular clusters.

Nuclear star clusters as probes of dark matter haloes: the case of the Sagittarius dwarf spheroidal galaxy

ABSTRACT The Sagittarius dwarf spheroidal (Sgr dSph) galaxy is currently being accreted and disrupted by the tidal field of the Milky Way. Recent observations have shown that the central region of the dwarf hosts at least three different stellar populations, ranging from old and metal-poor over intermediate metal-rich to young metal-rich. While the intermediate-age metal-rich population has been identified as part of the galaxy, the oldest and youngest populations belong to M54, the nuclear star cluster (NSC) of the Sgr dSph galaxy. The old metal-poor component of M54 has been interpreted as at least one decayed globular cluster (GC) that was initially orbiting its host galaxy. The youngest population formed in situ from gas accreted into M54 after its arrival at the centre of the host. In this work, we use the observed properties of M54 to explore the shape of the inner density profile of the Sgr dSph galaxy. To do so, we simulate the decay of M54 towards the centre of the dark matter (DM) halo of its host. We model the DM density profile using different central slopes, and we compare the results of the simulations to the most recent observations of the structural properties of M54. From this comparison, we conclude that a GC that decays in a DM halo with a density profile ∝ r−γ and γ ≤ 1 shows a rotational signal and flattening comparable to those observed for M54. Steeper profiles produce, instead, highly rotating and more flattened NSCs which do not match the properties of M54.

Evidence of a Decreased Binary Fraction for Massive Stars within 20 milliparsecs of the Supermassive Black Hole at the Galactic Center

We present the results of the first systematic search for spectroscopic binaries within the central 2 × 3 arcsec2 around the supermassive black hole at the center of the Milky Way galaxy. This survey is based primarily on over a decade of adaptive optics-fed integral-field spectroscopy (R ∼ 4000), obtained as part of the Galactic Center Orbits Initiative at Keck Observatory, and it has a limiting K’-band magnitude of 15.8, which is at least 4 mag deeper than previous spectroscopic searches for binaries at larger radii within the central nuclear star cluster. From this primary data set, over 600 new radial velocities are extracted and reported, increasing by a factor of 3 the number of such measurements. We find no significant periodic signals in our sample of 28 stars, of which 16 are massive, young (main-sequence B) stars and 12 are low-mass, old (M and K giant) stars. Using Monte Carlo simulations, we derive upper limits on the intrinsic binary star fraction for the young star population at 47% (at 95% confidence) located ∼20 mpc from the black hole. The young star binary fraction is significantly lower than that observed in the field (70%). This result is consistent with a scenario in which the central supermassive black hole drives nearby stellar binaries to merge or be disrupted, and it may have important implications for the production of gravitational waves and hypervelocity stars.

Global instability by runaway collisions in nuclear stellar clusters: numerical tests of a route for massive black hole formation

ABSTRACT The centres of galaxies host nuclear stellar clusters, supermassive black holes, or both. The origin of this dichotomy is still a mystery. Nuclear stellar clusters are the densest stellar system in the Universe, so they are ideal places for runaway collisions to occur. Previous studies have proposed the possible existence of a critical mass scale in such clusters, for which the occurrence of collisions becomes very frequent and leads to the formation of a very massive object. While it is difficult to directly probe this scenario with simulations, we here aim for a proof of concept using toy models where the occurrence of such a transition is shown based on simplified compact systems, where the typical evolution time-scales will be faster compared to the real Universe. Indeed our simulations confirm that such a transition takes place and that up to 50 per cent of the cluster mass can go into the formation of a central massive object for clusters that are above the critical mass scale. Our results thus support the proposed new scenario on the basis of idealized simulations. A preliminary analysis of observed nuclear star clusters shows similar trends related to the critical mass as in our simulations. We further discuss the caveats for the application of the proposed scenario in real nuclear star clusters.

Where intermediate-mass black holes could hide in the Galactic Centre

Context. In the Milky Way the central massive black hole, Sgr A*, coexists with a compact nuclear star cluster that contains a sub-parsec concentration of fast-moving young stars called S-stars. Their location and age are not easily explained by current star formation models, and in several scenarios the presence of an intermediate-mass black hole (IMBH) has been invoked. Aims. We use GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2, the best known S-star, to investigate whether a second massive object could be present deep in the Galactic Centre (GC) in the form of an IMBH binary companion to Sgr A*. Methods. To solve the three-body problem, we used a post-Newtonian framework and consider two types of settings: (i) a hierarchical set-up where the star S2 orbits the Sgr A*–IMBH binary and (ii) a non-hierarchical set-up where the IMBH trajectory lies outside the S2 orbit. In both cases we explore the full 20-dimensional parameter space by employing a Bayesian dynamic nested sampling method. Results. For the hierarchical case we find the strongest constraints: IMBH masses > 2000 M⊙ on orbits with smaller semi-major axes than S2 are largely excluded. For the non-hierarchical case, the chaotic nature of the problem becomes significant: the parameter space contains several pockets of valid IMBH solutions. However, a closer analysis of their impact on the resident stars reveals that IMBHs on semi-major axes larger than S2 tend to disrupt the S-star cluster in less than a million years. This makes the existence of an IMBH among the S-stars highly unlikely. Conclusions. The current S2 data do not formally require the presence of an IMBH. If an IMBH hides in the GC, it has to be either a low-mass IMBH inside the S2 orbit that moves on a short and significantly inclined trajectory or an IMBH with a semi-major axis > 1″. We provide the parameter maps of valid IMBH solutions in the GC and discuss the general structure of our results and how future observations can help to put even stronger constraints on the properties of IMBHs in the GC.

Searching for clues of past binary supermassive black hole mergers in nuclear star clusters

ABSTRACTGalaxy mergers are common processes in the Universe. As a large fraction of galaxies hosts at their centres a central supermassive black hole (SMBH), mergers can lead to the formation of a supermassive black hole binary (SMBHB). The formation of such a binary is more efficient when the SMBHs are embedded in a nuclear star cluster (NSC). NSCs are dense and massive stellar clusters present in the majority of the observed galaxies. Their central densities can reach up to $10^7\, {\rm M_{\odot }}\,{\rm pc^{-3}}$ and their masses can be as large as a few $10^7\, {\rm M_{\odot }}$. The direct detection of an SMBHB is observationally challenging. In this work, we illustrate how the large-scale structural and dynamical properties of an NSC can help to identify nucleated galaxies that recently went through a merger that possibly led to the formation of a central SMBHB. Our models show that the merger can imprint signatures on the shape, density profile, rotation, and velocity structure of the NSC. The strength of the signatures depends on the mass ratio between the SMBHs and on the orbital initial conditions of the merger. In addition, the number of hypervelocity stars produced in the mergers is linked to the SMBHB properties. The merger can also contribute to the formation of the nuclear stellar disc of the galaxy.

Correction to: Gravitational waves from the remnants of the first stars in nuclear star clusters

Correction to: Gravitational waves from the remnants of the first stars in nuclear star clusters

The growth of intermediate mass black holes through tidal captures and tidal disruption events

ABSTRACTWe present N-body simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 M⊙. The models are evolved with the N-body code bifrost to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star–BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About ∼20–30 per cent of the stars within the spheres of influence of the black holes form Bahcall–Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500–1300 TDEs, depending on the initial cluster structure. Most (>95 per cent) of the TDEs originate from stars in the Bahcall–Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density, and velocity dispersion of the clusters ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}}\rho \sigma ^{-3}$). We find that TDEs can lead a 300 M⊙ BH to reach $\sim 7000 \, \mathrm{{M}_{\odot }}$ within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters.

Evidence for globular cluster collapse after a dwarf-dwarf merger: A potential nuclear star cluster in formation

Direct observational evidence for the creation of nuclear star clusters (NSCs) is needed to support the proposed scenarios for their formation. We analysed the dwarf galaxy UGC 7346, located in the peripheral regions of the Virgo Cluster, to highlight a series of properties that indicate the formation of a NSC caught in its earlier stages. First, we report on remnants of a past interaction in the form of diffuse streams or shells, suggesting a recent merging of two dwarf galaxies with a 1:5 stellar mass ratio. Second, we identify a number of globular cluster (GC) candidates that are broadly compatible in colour with the main component that is both more extended and more massive. Strikingly, we find these GCs candidates to be highly concentrated towards the centre of the galaxy (RGC = 0.41 Re). We suggest that the central concentration of the GCs is likely produced by the dynamical friction of this merger. This would make UGC 7346 a unique case of a galaxy caught in the earlier stages of NSC formation. The formation of NSCs due to collapse of GCs by dynamical friction in dwarf mergers would provide a natural explanation of the environmental correlations found for the nucleation fraction for early-type dwarf galaxies, whereby denser environments host galaxies with a higher nucleation fraction.

The Influence of Disk Composition on the Evolution of Stars in the Disks of Active Galactic Nuclei

Disks of gas accreting onto supermassive black holes, powering active galactic nuclei (AGN), can capture stars from nuclear star clusters or form stars in situ via gravitational instability. The density and thermal conditions of these disks can result in rapid accretion onto embedded stars, dramatically altering their evolution in comparison to stars in the interstellar medium. Theoretical models predict that, when subjected to sufficiently rapid accretion, fresh gas replenishes hydrogen in the cores of these stars as quickly as it is burned into helium, reaching a quasi-steady state. Such massive, long-lived (“immortal”) stars may be capable of dramatically enriching AGN disks with helium, and would increase the helium abundance in AGN broad-line regions relative to that in the corresponding narrow-line regions and hosts. We investigate how the helium abundance of AGN disks alters the evolution of stars embedded therein. We find, in agreement with analytical arguments, that stars at a given mass are more luminous at higher helium mass fractions, and so undergo more radiation-driven mass loss. We further find that embedded stars tend to be less massive in disks with higher helium mass fractions, and that immortal stars are less common in such disks. Thus, disk composition can alter the rates of electromagnetic and gravitational wave transients as well as further chemical enrichment by embedded stars.

Study of central light distribution in nearby early-type galaxies hosting nuclear star clusters

ABSTRACT We present analysis of 63 nearby (<44 Mpc) early-type galaxies hosting nuclear star clusters using the recently discovered parameter central intensity ratio (CIRI) determined from near-infrared (3.6 $\mu$m) observations with the Infrared Array Camera of Spitzer Space Telescope. The CIRI, when combined with filters involving age and B − K colour of host galaxies, helps identify two distinct classes of galaxies hosting nuclear star clusters. This is independently verified using Gaussian mixture model. CIR shows a positive trend with faint, low-mass, and blue galaxies in the sample, while the opposite is true for bright, high-mass, and red galaxies, albeit with large scatter. The variation of CIRI with central velocity dispersion, absolute B-band magnitude, dynamical mass, and stellar mass of host galaxies suggests that the mass of nuclear star clusters increases with that of host galaxies, for faint, low-mass, young, and blue galaxies in the sample. In bright, high-mass, old, and red galaxies, on the other hand, the evolution of nuclear star clusters appears complex, with no apparent trends. The analysis also reveals that redder galaxies (B − K > 3.76) are more likely to be dominated by the central black hole than the nuclear star clusters, while for bluer galaxies (B − K < 3.76) in the sample the situation is quite opposite.

The Star Formation History of the Milky Way’s Nuclear Star Cluster

We report the first star formation history study of the Milky Ways nuclear star cluster (NSC), which includes observational constraints from a large sample of stellar metallicity measurements. These metallicity measurements were obtained from recent surveys from Gemini and the Very Large Telescope of 770 late-type stars within the central 1.5 pc. These metallicity measurements, along with photometry and spectroscopically derived temperatures, are forward modeled with a Bayesian inference approach. Including metallicity measurements improves the overall fit quality, as the low-temperature red giants that were previously difficult to constrain are now accounted for, and the best fit favors a two-component model. The dominant component contains 93% ± 3% of the mass, is metal-rich (), and has an age of Gyr, which is ∼3 Gyr younger than earlier studies with fixed (solar) metallicity; this younger age challenges coevolutionary models in which the NSC and supermassive black holes formed simultaneously at early times. The minor population component has low metallicity () and contains ∼7% of the stellar mass. The age of the minor component is uncertain (0.1–5 Gyr old). Using the estimated parameters, we infer the following NSC stellar remnant population (with ∼18% uncertainty): 1.5 × 105 neutron stars, 2.5 × 105 stellar-mass black holes (BHs), and 2.2 × 104 BH–BH binaries. These predictions result in 2–4 times fewer neutron stars compared to earlier predictions that assume solar metallicity, introducing a possible new path to understand the so-called “missing-pulsar problem”. Finally, we present updated predictions for the BH–BH merger rates (0.01–3 Gpc−3yr−1).

PHANGS–JWST First Results: A Combined HST and JWST Analysis of the Nuclear Star Cluster in NGC 628

We combine archival Hubble Space Telescope and new James Webb Space Telescope imaging data covering the ultraviolet to mid-infrared regime to morphologically analyze the nuclear star cluster (NSC) of NGC 628, a grand-design spiral galaxy. The cluster is located in a 200 pc × 400 pc cavity lacking both dust and gas. We find roughly constant values for the effective radius (r eff ∼ 5 pc) and ellipticity (ϵ ∼ 0.05), while the Sérsic index (n) and position angle (PA) drop from n ∼ 3 to ∼2 and PA ∼ 130° to 90°, respectively. In the mid-infrared, r eff ∼ 12 pc, ϵ ∼ 0.4, and n ∼ 1–1.5, with the same PA ∼ 90°. The NSC has a stellar mass of , as derived through B − V, confirmed when using multiwavelength data, and in agreement with the literature value. Fitting the spectral energy distribution (SED), excluding the mid-infrared data, yields a main stellar population age of (8 ± 3) Gyr with a metallicity of Z = 0.012 ± 0.006. There is no indication of any significant star formation over the last few gigayears. Whether gas and dust were dynamically kept out or evacuated from the central cavity remains unclear. The best fit suggests an excess of flux in the mid-infrared bands, with further indications that the center of the mid-infrared structure is displaced with respect to the optical center of the NSC. We discuss five potential scenarios, none of them fully explaining both the observed photometry and structure.

Accelerations of stars in the central 2–7 arcsec from Sgr A*

This work presents the results from extending the long-term monitoring program of stellar motions within the Galactic Center to include stars with separations of 2–7 arcsec from the compact radio source, Sgr A*. In comparison to the well studied inner 2 arcsec, a longer baseline in time is required to study these stars. With 17 years of data, a sufficient number of positions along the orbits of these outer stars can now be measured. This was achieved by designing a source finder to track the positions of ∼2000 stars in NACO/VLT adaptive-optics-assisted images of the Galactic Center from 2002 to 2019. Of the studied stars, 54 exhibit significant accelerations toward Sgr A*, most of which have separations of between 2 and 3 arcsec from the black hole. A further 20 of these stars have measurable radial velocities from SINFONI/VLT stellar spectra, which allows for the calculation of the orbital elements for these stars, thus increasing the number of known orbits in the Galactic Center by ∼40%. With orbits, we can consider which structural features within the Galactic Center nuclear star cluster these stars belong to. Most of the stars have orbital solutions that are consistent with the known clockwise rotating disk feature. Further, by employing Monte Carlo sampling for stars without radial velocity measurements, we show that many stars have a subset of possible orbits that are consistent with one of the known disk features within the Galactic Center.

Study on the detectability of gravitational radiation from single-binary encounters between black holes in nuclear star clusters: The case of hyperbolic flybys

With the release of the third Gravitational-Wave Transient Catalogue (GWTC-3), 90 observations of compact-binary mergers by Virgo and LIGO detectors are confirmed. Some of these mergers are suspected to have occurred in star clusters. The density of black holes at the cores of these clusters is so high that mergers can occur through a few generations forming increasingly massive black holes. These conditions also make it possible for three black holes to interact, most likely via single-binary encounters. In this paper, we present a first study of how often such encounters can happen in nuclear star clusters (NSCs) as a function of redshift and whether these encounters are observable by gravitational-wave (GW) detectors. This study focuses on effectively hyperbolic encounters leaving out the resonant encounters. We find that in NSCs single-binary encounters occur rarely compared to binary mergers and that hyperbolic encounters most likely produce the strongest GW emission below the observation band of terrestrial GW detectors. While several of them can be expected to occur per year with peak energy in the LISA band, their amplitude is low, and detection by LISA seems improbable.

Growth of a Massive Black Hole in a Dense Star Cluster Via Tidal Disruption Accretion

Stars that are tidally disrupted by a massive black hole (MBH) may contribute significantly to the growth of the MBH, especially in dense nuclear star clusters. Yet, this tidal disruption accretion (TDA) of stars onto the MBH has largely been overlooked compared to the gas accretion (GA) channel in most numerical experiments until now. In this work, we implement a black hole growth channel via TDA in the high-resolution adaptive mesh refinement code Enzo to investigate its influence on an MBH seed’s early evolution. We find that an MBH seed grows rapidly from 103 to ≳106 M ⊙ in 200 Myr in some of the tested simulations. Compared to an MBH seed that grows only via GA, TDA can enhance the MBH’s growth rate by more than 1 order of magnitude. However, as predicted, TDA mainly helps the early growth of the MBH (from 103–4 to ≲105 M ⊙) while the later evolution is generally dominated by GA. We also observe that the star formation near the MBH is suppressed when TDA is the most active, sometimes with a visible cavity in gas (of size ∼ a few pc) created in the vicinity of the MBH. It is because the MBH may grow expeditiously with both GA and TDA, and the massive MBH could consume its neighboring gas faster than being replenished by gas inflows. Our study demonstrates the need to consider different channels of black hole accretion that may provide clues for the existence of supermassive black holes at high redshifts.