Intermediate-mass black holes

Intermediate-Mass Black Hole Feedback in Dwarf Galaxies at High Redshifts


Intermediate-mass black holes (IMBHs: masses between ) historically comprise of an elusive population compared to stellar-mass and supermassive BHs. Recently IMBHs have started to be observed at the centers of low-mass galaxies. Using a modified version of the SPH code GADGET-3, we perform cosmological hydrodynamical simulations of comoving boxes, and investigate the growth and feedback of central IMBHs in dwarf galaxies (DGs). Black Holes of mass are seeded at the centers of halos with . The earliest BHs appear at , and grow thereafter by accreting surrounding gas and by merger with other BHs. Starting from highly sub-Eddington rates (Eddington ratio ), the accretion rate of the BHs increase with time, and reaches for the massive IMBHs by . We find that it is possible to build up IMBHs of a few by , when the BHs are seeded in halos less massive than . The star formation rate density evolution of the DGs (stellar mass ) has a peak plateau between . Star formation is quenched between by BH accretion and feedback. The star formation rate density (SFRD) is reduced by factors up to , when the BHs have grown to a few times . However these IMBHs in DGs are already more massive (at ) compared to the local correlation and that of high- quasars. Our conclusions, based on numerical simulation results, support the scenario that early feedback from IMBHs in gas-rich DGs at can potentially solve several anomalies in the DG mass range within the concordance CDM cosmological scenario of galaxy formation (Silk, 2017). Our results suggest that IMBHs at DG centers grow faster than their host galaxies in the early Universe, and the resulting BH feedback turns the DGs and the BHs dormant.

1 Introduction

Black holes (BHs) are usually observed to be of stellar-mass , or supermassive . Stellar-mass BHs have been historically observed in X-ray binaries existing in our Milky Way and other galaxies (e.g., Bolton, 1972; Cowley et al., 1983; Orosz et al., 2007; Corral-Santana et al., 2016), and more recently in globular clusters (e.g., Maccarone et al., 2007; Giesers et al., 2018). Supermassive BHs (SMBHs) are believed to exist at the centers of active galactic nuclei (AGN), which liberate enormous amounts of feedback energy powered by the accretion of matter (e.g., Rees, 1984; Ferrarese & Ford, 2005). AGN are widely observed through their multi-wavelength emission at all cosmic epochs, , starting from the local Universe up to Gyr ago (e.g., Urry & Padovani, 1995; Goulding & Alexander, 2009; Mortlock et al., 2011).

By natural extension, there should be a population of intermediate-mass black holes (IMBHs) of masses between (e.g., van der Marel, 2004), which are however not as widely observed. Some studies argue that the accreting BHs in ultra-luminous X-ray sources could be IMBHs (e.g., Miller et al., 2003; Sutton et al., 2012; Caballero-Garcia et al., 2018), based on the calculation of the BH mass from a cold thermal disc accreting at sub-Eddington rates.

We do not know how the SMBHs in AGN grew to billions of solar masses. IMBHs are a possible explanation for the origin of SMBHs. The discovery of an universal population of IMBHs can be the key to understanding whether SMBHs can grow from stellar-mass BHs, or whether a more exotic process accelerated their growth soon after the Big Bang. A recent study by Kovetz et al. (2018) suggest that gravitational wave measurements using the advanced LIGO over six years can be used to limit the formation mechanism of IMBHs by the runaway merger of stellar-mass BHs in globular clusters.

Relatively recently, massive BHs have started to be observed hosted in Dwarf Galaxies (DGs). Dynamical BH mass limits detected in nearby dwarfs include several examples such as: in the dwarf elliptical galaxy M32 (van der Marel et al., 1998); in the dwarf lenticular field galaxy NGC 404 (Seth et al., 2010); in the dwarf elliptical galaxy NGC 205 (Valluri et al., 2005); and in the dwarf spheroidal galaxy Ursa Minor (Demers et al., 1995).

Some of the central IMBHs in DGs show signatures of activity in the form of low-luminosity AGN. NGC 4395 is a bulgeless dwarf galaxy with an extremely faint Seyfert 1 nucleus (Filippenko & Sargent, 1989) and an estimated central BH mass (Peterson et al., 2005). Pox 52 (G 1200-2038) is a dwarf galaxy with Seyfert characteristics (Kunth, Sargent & Bothun, 1987), having a central BH of (Thornton et al., 2008). The dwarf starburst galaxy Henize 2-10 (Reines et al., 2011) has an actively accreting massive BH with an order-of-magnitude mass .

The population of DGs with observed AGN signatures have been increasing (e.g., Chilingarian et al., 2018). Izotov & Thuan (2008) presented the spectra of low-metallicity DGs with very-high broad H luminosities, most likely coming from accretion disks around IMBHs (). Performing a systematic search for AGN in DGs using optical spectroscopy from the SDSS, Reines, Greene & Geha (2013) found DGs, with stellar mass between at , hosting active massive BHs with virial BH masses in the range . Using SDSS DR7, Moran et al. (2014) identified nearby low-mass, low-luminosity DGs containing accreting IMBHs () at their centers, and derived a lower limit of a few percent on the fraction of DGs containing AGN.

The stellar mass versus BH mass relationship of IMBHs in DGs is found to be more-or-less consistent with the existing local relation extending linearly (in log-log space) into the lower galaxy mass regime, albeit with a large scatter. IMBH candidates detected using deep X-ray observations (e.g., Schramm et al., 2013; Secrest et al., 2015; Lemons et al., 2015) show that low-mass galaxies with have BHs of . The most-massive ultracompact dwarf galaxy M59-UCD3 with has a massive central BH of (Ahn et al., 2018). The Fornax UCD3 hosting a central corresponds to of the galaxy stellar mass (Afanasiev et al., 2018). Investigating the presence of AGN in nearby dwarf galaxies using mid-infrared emission, Marleau et al. (2017) identified candidates, of which were subsequently confirmed as AGN by other methods. The stellar masses of these galaxies are estimated to be between ; and the black hole masses in the range .

Recently the highest-redshift discovery of AGN in DGs has been made by Mezcua et al. (2018). They present a sample of 40 AGN at with luminosities in the range erg/s. The hosts are DGs with stellar masses between , selected from the Chandra COSMOS-Legacy survey. All these AGN are of type 2 and consistent with hosting IMBHs with masses , and typical Eddington ratios . According to the authors, the observational trends suggest that AGN in DGs evolve differently than those in more-massive galaxies.

AGN influence the formation and evolution of galaxies in the form of feedback, affecting the environment from pc to Mpc scales (e.g., Silk & Rees, 1998; Barai, 2008; Fabian, 2012). Supermassive BHs and host galaxies are argued to coevolve, generating observational trends such as the central BH mass - host galaxy stellar bulge mass correlations (e.g., Magorrian et al., 1998; Gebhardt et al., 2000). The SMBH energy output is often observed as AGN outflows in a wide variety of forms (e.g., Crenshaw, Kraemer & George, 2003; Cicone et al., 2014; Melioli & de Gouveia Dal Pino, 2015; Tombesi et al., 2015; Barai et al., 2018).

Analogous to SMBHs producing AGN feedback, the IMBHs are also expected to have feedback: the energy radiated by IMBHs should affect their host galaxies, possibly driving galactic outflows. BH or AGN feedback mechanism has recently started to be observed in low-mass galaxies. Penny et al. (2017) presented observational evidence for AGN feedback in a sample of quenched low-mass galaxies ; including galaxies showing signatures of an active AGN preventing ongoing star-formation.

AGN feedback operates mostly in the negative form which quenches star formation as seen in simulations (e.g., Scannapieco, Silk & Bouwens, 2005; Barai et al., 2014), and supported by some observations (e.g., Schawinski et al., 2006; Lanz et al., 2016). At the same time, AGN feedback can be positive occasionally, where AGN outflows are found to compress clumpy gas clouds and trigger starbursts, in numerical studies (e.g., De Young, 1989; Zubovas et al., 2013), and observed in jet-induced star formation (e.g., Chambers, Miley & van Breugel, 1987; Zinn et al., 2013). In this work we focus on negative BH feedback effects where star-formation is quenched.

The concordance CDM cosmological scenario of galaxy formation presents multiple anomalies in the dwarf galaxy mass range: e.g. core-cusp, number of DGs. Recently Silk (2017) made an exciting theoretical claim that the presence of IMBHs at the centers of essentially all old DGs can potentially solve the problems. Early feedback energy from these IMBHs can affect the host gas-rich dwarf galaxies at . This early feedback can quench star-formation, reduce the number of DGs, and impact the density profile at DG centers. Dashyan et al. (2017) studied the same problem analytically, and compared AGN versus SN feedback. They find a critical halo mass below which the central AGN can drive gas out of the host halo. This negative feedback effect of AGN is found to be more efficient than SN in the most-massive DGs, where SN is not able to expel the gas.

In this work, we investigate the scenario that IMBHs are present at the centers of dwarf galaxies, by performing cosmological hydrodynamical simulations. Our goals are to (i) test if IMBHs would grow at DG centers in a cosmological environment, and (ii) quantify the impact of feedback from IMBHs on their host DGs, especially the effects on star formation at cosmic epochs .

This paper is organised as follows: we describe our numerical code and simulation setup in §2, present and analyze our results in §3, and in §4 we give a summary of our main findings.

2 Numerical Method

We use a modified version of the TreePM (particle mesh) - SPH (smoothed particle hydrodynamics) code GADGET-3 (Springel, 2005). The sub-resolution physics that we use are described in §2.1 and §2.2. Our different simulation runs are outlined in §2.3.

2.1 Cooling, Star-Formation, SN Feedback

Radiative cooling and heating is implemented by adopting the cooling rates from the tables of Wiersma, Schaye & Smith (2009), which includes metal-line cooling. Eleven element species (H, He, C, Ca, O, N, Ne, Mg, S, Si, Fe) are tracked. Star-formation is implemented following the multiphase effective sub-resolution model by Springel & Hernquist (2003). Stellar evolution and chemical enrichment are computed for the 11 elements (following Tornatore et al., 2007). A fixed stellar initial mass function from Chabrier (2003) is included, in the mass range .

Kinetic feedback from supernovae ejects mass at a rate proportional to the SF rate () as: . The SN wind mass loading factor is taken as (e.g., Tornatore et al., 2007; Barai et al., 2013; Melioli, de Gouveia Dal Pino & Geraissate, 2013), following observations revealing that SN-driven outflow rates are comparable to or larger than SF rates of galaxies (e.g., Martin, 1999; Bouche et al., 2012). We adopt a constant-velocity outflow with SN wind velocity km/s (as was done in e.g. Barai et al., 2015; Biffi et al., 2016).

Run BH Min. Halo Mass for BH Seeding, Seed BH Mass, BH kinetic feedback
name present kick velocity (km/s)
BHs2h1e6v2 Yes
BHs2h1e6v10 Yes
BHs2h4e7v2 Yes
BHs2h7e7v2 Yes
BHs3h1e7v2 Yes
BHs3h2e7v2 Yes
BHs3h3e7v2 Yes
BHs3h3e7v1 Yes
BHs3h4e7v1 Yes
BHs3h4e7v2 Yes
BHs3h4e7v5 Yes
BHs3h4e7v10 Yes
BHs3h5e7v2 Yes
BHs4h4e7v2 Yes
Table 1: Simulation runs and parameters.

2.2 BH Accretion and Feedback

BHs are collisionless sink particles (of mass ) in our simulations. A BH (of initial mass ) is seeded at the center of each galaxy more massive than a total mass , which does not contain a BH already. We test different values of minimum halo mass and seed BH mass in the range: , and .

Gas is considered to accrete onto a BH according to the Bondi-Hoyle-Lyttleton accretion rate (: Hoyle & Lyttleton, 1939; Bondi, 1952), and is limited to the Eddington rate ,


where is the gravitational constant, is the gas density, is the sound speed, and is the velocity of the BH relative to the gas. The quantities , and are computed dynamically within the code at every timestep, using the SPH smoothing method for every BH particle (for details see §2.1 of Barai et al., 2014). We set as a numerical boost factor (as done by e.g., Springel, Di Matteo & Hernquist, 2005; Johansson, Naab & Burkert, 2009; Dubois et al., 2013). The Eddington luminosity is used to express the Eddington mass accretion rate,


where is the mass of a proton, is the speed of light, and is the Thomson scattering cross-section for an electron. A fraction of the accretion rest-mass energy is coupled to the surrounding gas as feedback energy:


Here is the radiative efficiency, and is the feedback efficiency. We adopt the mean value for radiatively efficient accretion onto a Schwarzschild BH (Shakura & Sunyaev, 1973): .

The BH feedback energy is distributed in the kinetic form (introduced in Barai et al., 2014, 2016). Surrounding gas is driven outward at a velocity and mass outflow rate . Given energy conservation,


and using Eq. (4), the outflow rate can be expressed in terms of the BH accretion rate,


We use the values: , and the range km/s.1

The implementation in the GADGET-3 code involves computing physical quantities by kernel-weighted smoothing over gas particles neighboring each BH. The kernel size, or the BH smoothing length , is determined at each timestep by implicit solution of the equation,


where is the kernel estimate of the gas density at the position of the BH, and is the mass of neighboring gas particles.

In particular, the kinetic feedback energy from a BH is distributed to the surrounding gas lying inside a bi-cone volume. The slant height of each cone is , and the half-opening angle is . The cone-axis direction is considered as fixed for each BH, which is randomly assigned during a BH seeding. Gas particles lying within the bi-cone are tracked, and their total mass is computed. The probability for ’th gas particle within the bi-cone to be kicked is calculated:


where is the timestep, and is the mass outflow rate obtained from Eq. (6). A random number , uniformly distributed in the interval , is drawn and compared with . For , the gas particle is given an AGN wind kick, such that its new velocity becomes:


The kick direction is set radially outward from the BH.

We incorporate a scheme for BH pinning, or BH advection algorithm (also done in e.g., Springel, Di Matteo & Hernquist, 2005; Wurster & Thacker, 2013; Schaye et al., 2015). Each BH is repositioned manually at each time-step to the center (minimum gravitational potential location) of its host galaxy. This is done in SPH simulations to correct for dynamical movements of BH particles wandering away from galaxy centers by numerical effects.

We consider that central BHs merge when their host galaxies merge during hierarchical structure formation. When two BH particles come near such that the distance between them is smaller than the smoothing length of either one, and their relative velocity is below the local sound speed, they are allowed to merge to form a single BH (e.g., Sijacki et al., 2007; Di Matteo et al., 2012).

2.3 Simulations

We perform cosmological hydrodynamical simulations of small-sized boxes to probe dwarf galaxies at high redshifts. The initial condition at is generated using the MUSIC2 software (Hahn & Abel, 2011). A concordance flat CDM model is used, with the cosmological parameters (Planck Collaboration, 2015, results XIII): km s Mpc.

The size of the cubic cosmological volume is comoving. We use dark matter and gas particles in the initial condition. The dark matter particle mass is , and the gas particle mass is . The gravitational softening length is set as kpc comoving. Starting from , the box is subsequently evolved up to , with periodic boundary conditions.

We execute a series of simulations, with characteristics listed in Table 1. All the runs incorporate metal cooling, chemical enrichment, SF and SN feedback. The first run has no BH, while the remaining runs include BHs. We vary 3 parameters (which were introduced in §2.2) exploring different BH sub-resolution models: the minimum halo mass for BH seeding , the seed BH mass , and the kick velocity for BH kinetic feedback . These parameters were observed to have the largest effect on the BH growth and feedback. The simulation names are formatted like below, where , , and are numbers in the BH runs.

  • SN : no BH present. This is a control simulation in which only cooling, enrichment, star-formation, and SN feedback are implemented.

  • BHsXhYeZvA : with BH accretion and feedback. The parameter values are, , and km/s.

Halos are identified by executing a Friends-of-Friends (FOF) group finder on-the-fly within our simulations. Galaxies are tracked simultaneously using the subhalo finder SubFind, which associates substructures to FOF halos. The centre of each galaxy is considered as the location of the gravitational potential minimum of its subhalo. We define galaxy stellar mass as the mass of all star particles inside the subhalos obtained by the subhalo finder SubFind. The halo mass of a galaxy, and its virial radius in comoving coordinates , are related such that encloses a density times the mean comoving matter density of the Universe:


where is the present critical density.

3 Results and Discussion

3.1 Large Scale Environment

Figure 1: Projected gas kinematics in the whole kpc simulation box at . The three rows present the following gas properties: overdensity (first row – top), temperature (second), and SFR (third – bottom). The two columns are for different simulations: SN (left) and BHs3h4e7v2 (right). The red circles in the top row depict the virial radius of galaxies in the mass range , while the black circles show the of galaxies. The positions of BHs in run BHs3h4e7v2 are indicated by the magenta cross-points in the top-right panel.

The gas morphology in our simulation box, or the large scale structures, is plotted in Fig. 1. It displays the projected gas kinematics in the whole kpc comoving volume at , for two simulations: SN (left column) and BHs3h4e7v2 (right column). The overdensity (i.e., the ratio between the gas density and the cosmological mean baryon density in the Universe), temperature, and star-formation rate (SFR) of the gas are plotted in the three rows from the top. The black circles in the top row depict the virial radius (defined in Eq. 10) of dwarf galaxies with halo masses in the range . The red circles show the of relatively massive galaxies, those having higher halo masses .

The spatial locations of the BHs within our BHs3h4e7v2 simulation box can be visualized in the top-right panel of Fig. 1. Here the magenta cross-points designate BH positions, overplotted with the gas overdensity. In this run, BHs are seeded at the centres of galaxies with . Therefore all the red circles ( galaxies) and most of the black circles ( galaxies) contain BHs at their centres.

The cosmological large-scale-structure filaments are visible in all the panels of both the runs. There are three Mpc-scale filaments: extending from east to north, from west to north, and from west to south. In addition, there is an overdense region running from the center of the box to the south-west. The filaments consist of dense (yellow and white regions in the top panels), and star-forming (lightgreen, yellow, red and white regions in the bottom panels) gas. The massive galaxies (red circles) lie at the high-density intersections of the filaments, or in the filaments.

In terms of temperature, the immediate vicinity of the dense filaments consists of hotter gas ( K, red regions in the middle panels of Fig. 1), as compared to that in the low-density intergalactic medium and voids (yellow and blue regions). Several mechanisms play together to heat the gas to higher temperatures in the filament vicinity. There are global environmental processes like shock heating during galaxy mergers, and large-scale-structure formation, which are present in both the SN and BHs3h4e7v2 runs. Acting together there are local galactic processes like feedback driven by SN (present in both the columns), and BHs (present in the right column only), which heats the gas, and also often generate outflows.

As they accrete and grow, the BHs provide feedback energy (according to the prescription described in §2.2), which may drive gas outflows. High-velocity gas ejected by central BH feedback propagates radially outward, and shocks with the surrounding slower-moving gas, creating bubble-like gas outflows. Our simulation BHs3h4e7v2 shows the formation of BH feedback-induced outflows, as can be seen in Fig. 1 in the top-right half of the right column panels, around the most-massive BH. The outflows are extended bipolar oval-shaped regions along the north-east to south-west direction, propagating to about . The outflows consist of hot ( K) - visible as red areas in the temperature map (middle-right panel), and low-density gas (top-right panel).

3.2 Black Hole Accretion and Growth

Figure 2: BH mass growth with redshift of the most-massive BH in each run. The different colours discriminate the runs as labelled, which are: BHs2h1e6v2 - red curve, BHs2h1e6v10 - lime-green, BHs2h7e7v2 - cyan, BHs3h1e7v2 - indigo, BHs3h3e7v2 - magenta, BHs3h3e7v1 - brown, BHs3h4e7v1 - green, BHs3h4e7v2 - light-red, BHs3h4e7v10 - black, BHs3h5e7v2 - blue, and BHs4h4e7v2 - yellow.

Fig. 2 presents the BH mass growth with redshift of the most-massive BH for eleven simulations of Table 1. The first BHs are seeded at in our simulations, when the first halos reach the corresponding lower limit . In some of the runs, one of these first seeds grow to become the most-massive BH. However in runs BHs3h4e7v2 (light-red curve) and BHs4h4e7v2 (yellow curve), the BH which becomes most-massive is seeded at later epochs . This variance in the seed epochs is because of the different BH growth modes, as described next.

Each BH starts as an initial seed of . The subsequent growth is due to merger with other BHs and gas accretion. When two galaxies containing BHs merge during hierarchical structure formation, their central BHs merge as well (according to the prescription in §2.2) to form a single larger BH. In addition, BHs grow in mass by accreting dense gas from their surroundings, as galaxies evolve and gas inflows to their centres.

We find that in general, when seeded in larger halos, BHs start to grow later and have an overall smaller growth at the same redshift (comparing indigo and magenta curves, for instance). Furthermore, larger seed BHs grow more massive earlier than smaller seeds (comparing yellow and light-red curves), as naively expected. We also find that varying the and together has a competing effect on the BH mass growth, which might cancel each other. A BH can grow similarly when seeded in smaller halos with a smaller seed mass (red curve), as in larger halos with a higher seed mass (indigo curve).

Figure 3: BH accretion rate (left panel) and Eddington ratio growth with redshift of the most-massive BH in each run.

Fig. 3 displays the accretion rate evolution with redshift, of the most-massive BH in each run: BH mass accretion rate () in the left panel, and Eddington ratio at the right. There is variability of the , whereby it fluctuates by a factor of up to . In the beginning, when the BHs are just seeded, they are accreting at highly sub-Eddington rates with Eddington ratio . The accretion rate grows with time as the BHs grow in mass, and the gas density in the BH vicinity increases by cosmic gas inflow to galaxy centers. However the gas accretion rate remains sub-Eddington always, with Eddington ratio .

We find that the massive BHs grow to a few by in most of our simulations (red, lime-green, indigo, magenta, brown, green, light-red, black, blue, and yellow curves). The accretion rate of these massive BHs has grown to . The exception is the case where BHs of the smallest seed are placed in the largest halos (run BHs2h7e7v2, cyan curve), where the most-massive BH grows up to only. For this BH, gas accretion is always occurring at low Eddington ratios .

The final BH properties reached at depend on the simulation. E.g., in run BHs3h3e7v1 (brown curve): and /yr. In Table 2 we list the final BH mass and the accretion rate of the most-massive BH, together with the final redshift of each simulation run.

Run Final BH mass, BH accretion rate,
name Redshift
Table 2: Final black hole mass and accretion rate of the most-massive BH for the different simulation runs.

3.3 Star Formation Rate Density

Figure 4: Total star formation rate density in simulation volume as a function of redshift, with the different models labelled by the colours. For comparison, the dark-brown and orange curves show two models from Barai et al. (2015), which are SFRD results for more-massive galaxy formation/evolution, from larger volume cosmological simulations.

Stars form in the simulation volume from cold dense gas. Fig. 4 exhibits the global Star Formation Rate Density (SFRD) as a function of redshift, for all the simulations labelled by the different colors. The SFRD (in yr Mpc) is computed by summing over all the SF occurring in each simulation box at a time, and dividing it by the time-step interval and the box volume.

The SFRD rises with time from early epochs , and all the runs behave similarly up to . Most of the simulations reach a maximum SFRD in the form of a plateau between , and the SFRD decreases at and at . We consider the SN run (dark blue curve) without BHs as the baseline, and compare other simulations with it to estimate the impact of BH feedback. The SFRD in simulation BHs2h7e7v2 (cyan curve) is almost similar to that in the run SN, because the BHs are too small there to generate enough feedback. A similar outcome happens in the other runs at , when the BHs are too small.

Star formation mostly occurs over an extended region at galaxy centres, where cosmic large-scale-structure gas inflows and cools. The presence of a central BH quenches star formation, because a fraction of dense gas is accreted onto the BH, and a fraction is ejected out by BH feedback. The processes of BH accretion and feedback suppress SF substantially in most of the runs, from onwards, when the BHs have grown massive and generate larger feedback energy. Compared to the SN case (dark blue curve), the SFRD is reduced by a factor of several in most of the other runs at .

We find that BH accretion and feedback causes a quenching of the SFRD at cosmic epochs , by factors times reduction. The precise redshifts and suppression factors are given in the following for the different simulations (with the same BH outflow velocity km/s):

  • BHs2h1e6v2 (red curve in Fig. 4) at up to times reduction of SFRD,

  • BHs3h1e7v2 (indigo curve) at up to times,

  • BHs4h4e7v2 (yellow curve) at up to times,

  • BHs3h2e7v2 at up to times,

  • BHs3h3e7v2 (magenta curve) at up to times,

  • BHs3h4e7v2 (light-red curve) at up to times,

  • BHs3h5e7v2 (blue curve) at up to times.

Thus, we find that BHs need to grow to a mass a few times , in order to suppress star-formation in dwarf galaxies (of ).

A larger BH outflow velocity () does not change the results substantially. E.g., comparing the red and lime-green curves in Fig. 2, the BH mass growth remains almost the same with and km/s. Increasing decreases the mass outflow rate ( in Eqs. (5) and (6)), in the way favoring an increase in the BH accretion rate, as we see in Fig. 3 at late epochs (comparing red and lime-green curves at ). Further, the smaller mass outflow rate to the environment delays the suppression of star formation (comparing lime-green and red curves in Fig. 4).

3.4 Black Hole - Galaxy Correlation

Figure 5: BH mass versus stellar mass of the galaxies within the simulation volume, at two epochs , in the two panels. The plotting colours distinguish results from different runs. The black lines indicate the observed BH mass versus stellar bulge mass relation for: quasars (Wang et al., 2010) as the solid line, and local galaxies (Marconi & Hunt, 2003) as the dashed line.

The BH - galaxy correlation obtained in our simulations is presented in Fig. 5 as the versus (stellar mass) diagram. It shows all the galaxies within the simulation volume with , at two epochs: in the left panel, and in the right panel. The plotting colour distinguishes results from different runs. Observational data is overplotted as the black lines indicating the BH mass versus stellar bulge mass relationships at different epochs. Local galaxies () are represented by the black-dashed line: (Marconi & Hunt, 2003). The ratio is observed to be steeper at high-. Far-IR and CO bright quasars lie along the black-solid line: median (Wang et al., 2010).

We find a huge scatter in the correlation of the simulated galaxies, especially at low-. In our simulations BHs2h1e6v2 (red symbols in Fig. 5) and BHs3h1e7v2 (indigo symbols), dwarf galaxies with stellar masses between contain BHs in the range at , which are hence already more massive than BHs following the local relation, as well as BHs in quasars. These two are also the runs where SF quenching happens the earliest, implying that the suppression occurs due to BH activities.

BHs in the simulation BHs4h4e7v2 (yellow symbols in Fig. 5) fall on the observed relation of already at . In the run BHs3h2e7v2, BHs lie in between the two correlations at , and have migrated to the relation at the later epoch. Central BHs in the runs BHs3h3e7v2 (magenta symbols), BHs3h4e7v2 (light-red symbols), and BHs3h5e7v2 (blue symbols) more or less follow the local correlation at both the epochs plotted; although their scatter increases substantially in the right panel. When BHs do not grow much (run BHs2h7e7v2, cyan symbols, most-massive reaching only), they always lie significantly below both of the correlations.

At the same time there are studies (e.g., Volonteri & Natarajan, 2009, using semi-analytical models), which find that the existence of the correlation is purely a reflection of the merging hierarchy of massive dark matter haloes.

We find that there is a direct connection between early BH growth and the quenching of SF, which is henceforth caused by resulting BH feedback. In addition, our results of fast BH growth at the centers of dwarf galaxies suggest that these BHs grow faster than their host galaxies in the early Universe.

4 Summary and Conclusions

Intermediate-Mass Black Holes (with masses between ) have historically been an elusive population of BHs, compared to the stellar-mass and supermassive (widely observed at the centers of AGN) BH counterparts. Recently these IMBHs have started to be observed in low-mass galaxies. Our work focuses on the case that IMBHs are formed at the centers of dwarf galaxies. Early feedback from such IMBHs is expected to release energy and affect the host gas-rich dwarf galaxies at , quenching star-formation, reducing the number of DGs, and impacting the density profile at DG centers. This can possibly solve several anomalies in the dwarf galaxy mass range within the concordance CDM cosmological scenario of galaxy formation (Silk, 2017).

We have investigated the growth and feedback of IMBHs at DG centers, by performing cosmological hydrodynamical simulations. We have employed a modified version of the SPH code GADGET-3. It includes the following sub-resolution physics: radiative cooling and heating from a photoionizing background, star-formation, stellar evolution, chemical enrichment for elements, supernova feedback, AGN accretion and feedback. We simulated comoving volumes to probe dwarf galaxies at high redshifts. The mass resolutions are for dark matter particles, and for gas particles. The length resolution is kpc comoving which is the gravitational softening length. The cosmological boxes are evolved with periodic boundary conditions, from up to .

We executed a series of simulations: one of them is a control case with SF-only and no BH; the other runs include BHs and explore different parameter variations of the BH sub-resolution models. In particular, we seed BHs of mass: , at the centers of massive halos with . In addition to and , we also vary the outflow velocity for BH kinetic feedback: km/s.

The earliest BHs appear at in our simulations, when the first halos reach the corresponding lower limit . The BHs are allowed to grow by accreting surrounding gas and by merger with other BHs. As they accrete and grow, the BHs eject out feedback energy, and impact their host DGs. We find the following results for the growth and feedback of IMBHs in our simulations:

  • The BHs grow to intermediate masses a few by , when the BHs are seeded in halos with . The most-massive BH at has: and /yr.

  • BHs seeded in smaller halos grow faster (considering the same redshift) than those seeded in larger halos. E.g. at , the most-massive BH in the simulation has grown to when seeded in halos, while it grows only to when seeded in halos.

  • The effect of increasing or decreasing the parameters and together on the BH mass growth can be the same. E.g., a BH can grow similarly when seeded in smaller halos with a smaller seed mass , as in larger halos with a higher seed mass .

  • The variation in the BH outflow velocity has little effect upon the BH growth, although the increase of the outflow velocity delays the suppression of SF.

  • Starting from highly sub-Eddington rates (Eddington ratio ), the accretion rate of the BHs increases with time, and reaches for the massive IMBHs by .

  • Our simulations probe dwarf galaxies with a stellar mass between . The star formation rate density evolution of these DGs has a wide maximum in the form of a plateau between , and the SFRD decreases at and at .

  • Star-formation is quenched between by BH accretion and feedback. The SFRD is reduced by factors , when the BHs have grown to a mass a few times .

  • There is a huge scatter in the BH - galaxy correlation of the simulated galaxies, especially at low-.

    In our runs where SF quenching happens the earliest, the IMBHs in DGs are already more massive at , as compared to the local correlation and that of high- quasars. Central BHs in some runs (BHs3h3e7, BHs3h4e7, BHs3h5e7) more or less follow the local correlation at .

  • Our result of rapid BH growth at the centers of DGs suggest that these BHs grow faster than their host galaxies in the early Universe. The resulting early BH feedback quenches star formation, and possibly turns the dwarf galaxies (as well as their central BHs) dormant.

  • The IMBHs do not always show indications of BH feedback driven gas outflows. There are only signatures of outflows around the most-massive IMBHs with , as shock-heated low-density gas.

We deduce that intermediate-mass black holes at the centers of dwarf galaxies can be a strong source of feedback. Our cosmological hydrodynamical simulations show that when the IMBHs have grown to , they quench star formation in their host galaxies. At the same time, these IMBHs form the missing link between stellar-mass and supermassive BHs.


We are most grateful to Volker Springel for allowing us to use the GADGET-3 code. This work is supported by the Brazilian Agencies FAPESP (grants 2016/01355-5, 2016/22183-8, and 2013/10559-5); and CNPq (grant 308643/2017-8).


  1. We notice that, although most of the adopted values of the AGN wind velocity in our models are smaller than those inferred from observations of AGN ultra-fast outflows (e.g., Melioli & de Gouveia Dal Pino, 2015; Kraemer, Tombesi & Bottorff, 2018, and references therein), the few tests we performed with more compatible values around km/s did not reveal significant differences in the results (for more details see §3).
  2. MUSIC - Multi-scale Initial Conditions for Cosmological Simulations:


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