<figure><img src="image_1.png" /></figure>

# Preferential Accretion in the Supermassive Black Holes of Milky Way-size Galaxies Due to Direct Feeding by Satellites

N. Nicole Sanchez¹,²,³, Jillian M. Bellovary⁴,⁵, Kelly Holley-Bockelmann²,³, Michael Tremmel¹,⁶, Alyson Brooks⁷, Fabio Governato¹, Tom Quinn¹, Marta Volonteri⁸, and James Wadsley⁹

¹Astronomy Department, University of Washington, Seattle, WA 98195, USA; sanchenn@uw.edu

²Department of Natural Sciences and Mathematics, Fisk University, 1000 17th Avenue N., Nashville, TN 37208, USA

³Department of Physics and Astronomy, Vanderbilt University, PMB 401807, Nashville, TN 37206, USA

⁴Queensborough Community College, New York, NY 11364, USA

⁵Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024, USA

⁶Yale Center for Astronomy & Astrophysics, Physics Department, P.O. Box 208120, New Haven, CT 06520, USA

⁷Department of Physics and Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Road, Piscataway, NJ 08854, USA

⁸Institut d'Astrophysique de Paris, Sorbonne Universités, UPMC Univ Paris 6 et CNRS, UMR 7095, 98 bis bd Arago, F-75014 Paris, France
⁹Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada

Received 2016 September 30; revised 2018 April 19; accepted 2018 April 23; published 2018 June 7

## Abstract

Using a new, high-resolution cosmological hydrodynamic simulation of a Milky Way-type (MW-type) galaxy, we explore how a merger-rich assembly history affects the mass budget of the central supermassive black hole (SMBH). We examine a MW-mass halo at the present epoch whose evolution is characterized by several major mergers to isolate the importance of merger history on black hole (BH) accretion. This study is an extension of Bellovary et al. (2013), which analyzed the accretion of high mass, high-redshift galaxies and their central BHs, and found that the gas content of the central BH reflects what is accreted by the host galaxy halo. In this study, we find that a merger-rich galaxy will have a central SMBH preferentially fed by gas accreted through mergers. Moreover, we find that the gas composition of the inner ~10 kpc of the galaxy can account for the increase of merger-accreted gas fueling the SMBH. Through an investigation of the angular momentum of the gas entering the host and its SMBH, we determine that gas accreted through mergers enters the galaxy halo with lower angular momentum compared to smooth accretion, partially accounting for the preferential fueling witnessed in the SMBH. In addition, the presence of mergers, particularly major mergers, also helps funnel low angular momentum gas more readily to the center of the galaxy. Our results imply that galaxy mergers play an important role in feeding the SMBH in MW-type galaxies with merger-rich histories.

**Key words:** black hole physics – galaxies: kinematics and dynamics – galaxies: spiral – methods: numerical

## 1. Introduction

Supermassive black holes (SMBHs) are thought to exist in almost all massive galaxies (see Kormendy & Ho 2013 for a review). In the canonical picture of black hole (BH) growth, these BHs may become active galactic nuclei (AGNs) during periods of high accretion and wane in periods of quiescence (Begelman et al. 1980; Alexander et al. 2005; Papovich et al. 2006; Volonteri 2012). The host galaxy's size, star formation rate, and other environmental effects may help to influence the growth of the BH residing at its center; however, there are still uncertainties concerning the relationship between these SMBHs and their much larger host galaxies, as well as how they grow and evolve together (Haehnelt & Kauffmann 2000; Di Matteo et al. 2005; Hopkins et al. 2006; Fu & Stockton 2009; Sijacki et al. 2009; Silverman et al. 2009; Micic et al. 2011; Mullaney et al. 2012).

The $M-\sigma$ relation, which relates the SMBH's mass and the velocity dispersion of the host galaxy's central stellar population, gives some insight into the complex interplay between these objects (Ferrarese & Merritt 2000; Gebhardt et al. 2000). A prominent trend appears, as SMBHs tend to scale with the velocity dispersion of the host galaxy bulge. The tightness of the relation is significant and can be seen over several orders of magnitudes in velocity dispersion and BH mass (e.g., Merritt & Ferrarese 2001; Tremaine et al. 2002; Graham et al. 2011; Mcconnell & Ma 2013). Scatter exists

among the low-mass galaxies and a deviation may appear at the high-mass end, where overmassive BHs may reside (Van den Bosch et al. 2007; Moster et al. 2010; Emsellem et al. 2011; Natarajan 2011; Volonteri et al. 2016). However, scatter in less massive galaxies may imply that there are several channels of BH growth at play in the low-mass end of the relation (Micic et al. 2007; Volonteri & Natarajan 2009; Reines et al. 2013; Graham & Scott 2014). One standard explanation for the $M-\sigma$ relation lies in galaxy mergers, which build up galaxies, feed SMBHs, and assemble bulges (e.g., Di Matteo et al. 2005; Shen et al. 2008). Major mergers are thought to supply gas to the central SMBH resulting in feedback which quenches star formation and affects the structure of the galaxy (Schawinski et al. 2010).

Major mergers between massive galaxies are thought to be efficient fueling mechanisms for bright AGNs. Additionally, the most massive, highest-luminosity AGNs (i.e., quasars) reside in incredibly luminous infrared galaxies where star formation is abundant, signifying that major mergers may have recently occurred (Treister et al. 2012). Distorted morphologies are often characteristics of quasar hosts, and companions can also be present around quasars, both of which are evidence that strengthen the possibility of a recent merger having affected their lifetimes (Ellison et al. 2010).

These major mergers can also strongly disturb gas-rich galaxies, producing resonant tidal torques that allow large influxes of material to funnel directly into the center, fueling
bursts of star formation and SMBH accretion (e.g., Sanders et al. 1988; Barnes & Hernquist 1991; Mihos & Hernquist 1996; Sanders & Mirabel 1996; Hopkins et al. 2006; Richards et al. 2006; Reddy et al. 2008; Hopkins & Quataert 2010). At small scales closer to the SMBH, the larger tidal torques from a major merger less effectively drive gas into the innermost region of the galaxy; however, perturbations at all scales from the merger could still drive accretion into the smaller inner region of the galaxy, though the rapid decay of these perturbations may not encourage gas flow. Other large-scale instabilities such as bars and spiral waves are also proficient fueling mechanisms for funneling gas into the galaxy; however, these cases can inhibit small-scale gas accretion through other complications. While there is still some uncertainty regarding the processes that transport gas through the last ~1 kpc to the SMBH, Hopkins & Quataert (2010) have shown that major mergers between gas-rich galaxies can result in non-axisymmetric gravitational instabilities that can drive BH accretion within the innermost ~0.1 pc.

In many less massive and less luminous AGNs, however, there is a clear lack of distorted morphology, close neighbors, and/or other obvious merger evidence (Ryan et al. 2007; Schawinski et al. 2011; Ellison et al. 2013; Hicks et al. 2013). It is also important to note that many of these AGNs exist in spiral galaxies, which are unlikely to have been recently disturbed by major mergers (Schawinski et al. 2011; Kocevski et al. 2012). Nevertheless, some evidence suggests that disturbed galaxies may reform a disk quickly, even after a major merger, as long as it is gas-rich (van Gorkom & Schiminovich 1997). The rapid disk reformation of the galaxy in this paper was previously studied by Governato et al. (2009) (see Section 4). More recently, Treister et al. (2012) has suggested that only the highest luminosity AGNs require fueling via major mergers; ~90% of AGNs across all redshifts are fueled by various other mechanisms, which may include minor mergers, flybys, and smooth accretion, whereby gas is directly accreted via large filaments from the ambient intergalactic medium (Cox et al. 2006; Dubois et al. 2012; Sinha & Holley-Bockelmann 2012; Bellovary et al. 2013; Di Matteo et al. 2017).

Smooth accretion, in particular, may play an important role in fueling these low-mass galaxies. Halos less than $10^{11} M_\odot$ can accrete filaments of unshocked gas; thereafter, gas will shock heat to the virial temperature of the halo (Keres et al. 2005). Even for massive halos, unshocked gas may still penetrate shocked regions to fuel the galaxy (Brooks et al. 2009; Dekel et al. 2009; Nelson et al. 2013). In addition, SMBH feedback, the depositing of energy and momentum back into the gas reservoir during accretion, also affects the overarching structure of the host galaxy (Governato et al. 2010). Secular processes, including bar formation and disk instabilities, may also be prominent forms of accretion for these SMBHs (Kormendy & Ho 2013; Athanassoula et al. 2016).

It is clear that galaxy hosts grow through a variety of channels that depend on mass, environment, and interaction history. Therefore, we want to understand how these different galaxy evolutionary paths translate into SMBH fueling mechanisms, and see how they affect the fueling gas flowing into the SMBH itself. Bellovary et al. (2013) (hereafter, B13) compared simulations of three high-mass, high-redshift galaxies and found that while mergers and smooth accretion both efficiently build up galaxies, no particular dynamical

process was more adept at feeding the SMBH. However, with only minor mergers, these galaxies represented relatively quiet merger histories. Using a similar method as B13, this work examines the SMBH and galaxy fueling mechanisms of a Milky Way-mass (MW-mass) galaxy with a rich merger history. MW-type galaxies host SMBHs on the order of $10^6 M_\odot$, which are likely the most common type of massive BH, yet little is known about them or how they may grow (Kormendy & Ho 2013). Through this examination, we hope to better understand the coevolution of SMBHs and their hosts in this class of galaxy.

In this study we analyze the MW-type galaxy h258, which has a history characterized by major mergers. Since this galaxy is similar to the MW in virial mass, stellar mass, and circular velocity, without a deeper examination we may not recognize the turbulent history from which it results. We will pinpoint the origins of gas entering the SMBH and halo to look for clues about SMBH fueling within this galaxy. By examining its assembly, and its SMBH's fueling, we can determine the accretion rate and gain further understanding about how SMBHs grow over a range of merger histories in galaxies like our own.

## 2. Simulation Parameters

Using the smoothed particle hydrodynamics (SPH) N-body tree code, Charm N-body GrAvity solver (ChaNGa; Menon et al. 2015), we ran an initial dark matter-only (DM-only), uniform resolution volume of 50 h⁻¹ Mpc on a side to identify a MW-mass halo at z = 0 for further examination. This DM-only simulation assumed WMAP 3 parameters (Spergel et al. 2007): Ω_m = 0.24, Ω_Λ = 0.76, H₀ = 73 km s⁻¹, and σ_8 = 0.77. Halo h258 was chosen for its MW-mass at z = 0 and its active merger history. The halo has a virial mass of $M_{vir} = 8.6 \times 10^{11} M_\odot$ at z = 0 defined relative to a critical density, ρ_c, where ρ/ρ_c = 200, and the virial radius is defined as the radius that encloses a density 200 times that of ρ_c. Two recent major mergers characterize the h258 halo at z = 1.8 and z = 1.2. We constructed a “zoom-in” high-resolution simulation on this galaxy, including gas and star particles, using the volume-renormalization of Katz & White (1993), resimulating only a few virial radii from the main halo at the highest resolution from z = 150 to z = 0.

We note that a lower-resolution version of h258 was run using the Gasoline code (Wadsley et al. 2003). Our higher-resolution h258 run has a spline force softening length of 174 pc and initial gas particle masses of $2.7 \times 10^4 M_\odot$. Star particles are created with 30% of their parent gas particle mass, allowing a mass of 8100 $M_\odot$. Halo h258 contains about five million DM particles inside the virial radius at z = 0 and over 14 million DM, star, and gas particles in total. The resolution of both force and mass in these simulations is comparable to the “Eris” simulation which has one of the highest resolutions for an N-body+SPH cosmological simulation of a MW-mass galaxy so far produced (Guedes et al. 2011).

Compared to the previous h258 simulation, the ChaNGa simulated h258 scales better and includes a new improved SPH formalism (Keller et al. 2014). The hydrodynamic treatment now includes a geometric density average—($P_i + P_j$)/($ρ_iρ_j$) rather than $P_i/ρ_i^2 + P_j/ρ_j^2$ where $P_i$ and $ρ_i$ are the particle's pressure and density—in the force expression, in addition to the standard SPH density estimator (Ritchie & Thomas 2001). Adjusting the force expression diminishes the numerical surface tensions due to
shear flows, such as Kelvin-Helmholtz instabilities. We also apply a consistent and entropy-conserving energy equation to account for the modified force expression and correctly model strong shocks, such as Sedov blasts.

Our simulation introduces a uniform UV background at $z \sim 9$ to simulate the cosmic reionization energy using the formula of Haardt & Madau (2012). To model star formation, gas particles can stochastically spawn up to three stars with a star formation efficiency parameter of $c^* = 0.1$ once the density threshold and temperature satisfy conditions for star formation (10.0 amu cm$^{-3}$; $T < 10^4$ K). As shown in Governato et al. (2010), this high-density threshold is necessary to produce bursty star formation events in the high-density peaks of the interstellar medium (ISM). Because we are able to resolve gas smoothing lengths up to 10 times smaller than the gravitational softening length, we are confident that these high-density peaks can be properly tracked and resolved. If all the criteria are met, the probability a gas particle will form a star is given by

$$p = \frac{m_{\text{gas}}}{m_{\text{star}}} (1 - e^{-c^* \Delta t / t_{\text{form}}}) \quad (1)$$

where $m_{\text{star}}$ and $m_{\text{gas}}$ are the star and gas particle masses, $t_{\text{form}}$ is the gas particle's dynamical time, and we set the time between star formation episodes, $\Delta t$, to 1 Myr. Bellovary et al. (2011) describe these star formation criteria; however, they mistakenly exclude the negative sign in the exponent, and we present the corrected version here.

Realistic star formation histories result in galaxies that have realistic density profiles and lie on the observed scaling relations (mentioned in detail below). The lower-resolution simulations mentioned in this paper have a lower threshold, since the high-density peaks are not resolved. These star particles represent a Kroupa initial mass function (Kroupa et al. 1993). Molecular hydrogen and metal-line cooling are not included, though we implement a low-temperature extension to the cooling curve to trace metals (Bromm et al. 2001) and the metal diffusion prescription of Shen et al. (2010). We do not expect the omission of metal cooling to affect our results. Gas that is smoothly accreted onto a galaxy is expected to have low metallicity, so cooling by metals (for example, after gas undergoes a shock) will have low efficiency in this instance. According to Christensen et al. (2014), broad galaxy properties such as rotation curves, star formation histories, and density profiles are consistent across various cooling models; additionally, the primordial cooling model we use here is in excellent agreement with many properties of the more sophisticated molecular ISM model. The effect of metal cooling on the categorization and subsequent evolution of the gas would be negligible.

Supernova (SN) feedback releases $10^{51}$ erg of thermal energy within a “blastwave” radius determined by the equations of Ostriker & McKee (1988). In the affected region, cooling turns off for a time relative to the expansion phase of the SN remnant also determined by the blastwave equation. SN Ia and II rates from Thielemann et al. (1986) and Woosley & Weaver (1995), respectively, are implemented through the Raiteri et al. (1996) method, which uses the stellar lifetime calculations of the Padova group (Alongi et al. 1993; Bressan et al. 1993; Bertelli et al. 1994) to describe stars with varying metallicities. Both the supernova “blastwave” radius and SN (Ia and II) prescriptions are described in detail by Stinson et al. (2006). While it is

true that a different treatment of the ISM and SNe feedback might alter the structure of the ISM, Christensen et al. (2014) examined simulated spiral and dwarf galaxies utilizing similar SNe prescriptions and three different ISM models, and determined that the resulting ISM remained consistent with each other. Additionally, our galaxy is in good agreement with galaxies affected by superbubble SN feedback (Keller et al. 2014).

Simulated galaxies are shown to conform with the observed Tully-Fisher relation (Governato et al. 2009), the size-luminosity relation (Brooks et al. 2011), and the mass-metallicity relation (Brooks et al. 2007; Christensen et al. 2016), in addition to having realistic matter distributions and baryon fractions (Governato et al. 2010; Guedes et al. 2011). The parameter and resolution choices described above allow the galaxies to adhere to the stellar-mass-halo-mass relation at $z=0$ and maintain a realistic period of star formation (Brooks et al. 2007; Maiolino et al. 2008; Moster et al. 2010; Munshi et al. 2013). Given that the simulations are in accordance with observations, we are confident that it reasonably represents growth in the galaxy and its SMBH.

Since there are uncertainties in BH seed formation, we model BH seeding that is broadly consistent with several theories of direct collapse BHs (Couchman & Rees 1986; Abel 2002; Bromm & Larson 2004) and Population III stellar remnants (Loeb & Rasio 1994; Eisenstein & Loeb 1995; Koushiappas et al. 2004; Begelman et al. 2006; Lodato & Natarajan 2006). While this method allows the BH formation process to remain physically motivated, BH seeds form if their parent gas particle matches the criteria required for star formation and also maintains zero metallicity, a requirement of many direct collapse models. A probability of $\chi_{\text{seed}} \sim 0.1$ is applied to determine whether a gas particle (with the above specifications) will become a BH seed with the same mass as its parent gas particle. This probability was chosen to match the predicted occupation fraction of BH seeds at $z \sim 3$ (Volonteri et al. 2008). However, BH particles cease to form once the global metallicity increases due to star formation, resulting in BH seeds only forming early on in the simulation (see Bellovary et al. 2011 for further details).

On many occasions, seed BH particles form one at a time. Feedback from accretion begins immediately after formation, preventing further massive black holes (MBHs) from forming nearby due to the increased temperature. On some occasions, however, more than one MBH seed can form in the same location at the exact same time, because multiple particles meet the formation criteria. In this instance, they often merge quickly. Since we do not resolve the direct collapse process, we do not consider this multiple-seed formation physical; rather, one can consider it a crude form of an initial mass function. The direct collapse seed mass is not well constrained, and the resulting seed acts the same as a single-seed predecessor does throughout the remainder of the simulation.

The requirement that BH seeds must form from zero metallicity gas particles also causes BH formation to be confined in areas of primordial star formation in the earliest and most massive halos in the simulation. In this technique, BH formation is dependent only on local environment, neglecting any large-scale properties of the host halo. We use the sub-grid prescription for modeling the effects of dynamical friction on SMBH orbits from Tremmel et al. (2015), which has been shown to produce realistic sinking times for SMBHs. This
<figure><img src="image_2.png" /><figcaption>Figure 1. The central BH's cumulative mass as a function of time and redshift. The black dashed line indicates the total cumulative BH mass. The black solid line indicates the total accreted gas mass. The blue dotted-dashed line indicates smoothly accreted gas mass that remains unshocked after entering the virial radius of the main halo. The green solid line indicates the gas mass accreted through mergers. The red dashed line indicates accreted gas mass that was shocked upon entry into the halo. Gas tracking begins when the BH exists in a galaxy halo of a non-diminutive size, though the BH did exist and merged with other BHs (around five) prior to this point. Major mergers are marked with gray hatched regions.</figcaption></figure>

prescription, combined with our high resolution to minimize two-body interactions and numerical noise, results in SMBHs that can remain stable at the galactic center while also, when appropriate, experiencing realistic perturbations and sinking timescales during and after galaxy interactions and mergers (Bellovary et al. 2011).

BH mergers occur when they are separated by less than twice the softening length and satisfy (1/2) $\delta v^2 < \delta a \cdot \delta r$ (which is an approximation of being gravitationally bound), where $\delta v$ and $\delta a$ are the velocity and acceleration differences between the two BHs and $\delta r$ is the distance separating them. In addition to gaining mass via mergers, BHs accrete through the Bondi-Hoyle mechanism:

$$ \dot{M} = \frac{4\pi\alpha G^2 M_{\text{BH}}^2 \rho}{(c_s^2 + v^2)^{3/2}}, \quad (2) $$

where $\alpha$ is a constant of order 1, $\rho$ is the density of the surrounding gas, $c_s$ is the sound speed, $v$ is the BH's relative velocity to the gas, and the accretion rate is Eddington-limited. Feedback is applied to surrounding gas with an energy boost determined by the accreted mass as follows: $\dot{E} = \epsilon_r \epsilon_f \dot{M} c^2$ where $\dot{M}$ is the accreted mass, and $\epsilon_r = 0.1$ and $\epsilon_f = 0.03$ are assumed for the radiative efficiency and feedback efficiency, respectively. This energy is distributed as thermal energy to the 32 nearest particles via a kernel probability function. Though other groups use a higher value for feedback, $\epsilon_f = 0.05$ (Sijacki et al. 2007; Di Matteo et al. 2008), we find that $\epsilon_f = 0.03$ in our code produces MBHs in better agreement with MBH-host galaxy scaling relations. However, as our main concern is in the

relative proportion of gas from various origins (see Section 4) and we restrict our analysis of the angular momentum of gas to only the timestep of entry into the main halo, our results are not sensitive to our choices of $\epsilon_r$ or $\epsilon_f$. This same model was additionally used by B13 at a lower resolution and without the addition of the dynamical friction prescription. While the BH seed and accretion models may determine the final mass of the SMBH, by comparing the relative proportions of gas accreted by the BHs, we avoid these model dependencies. Additionally, because gas is categorized as it enters the outskirts of the galaxy, far from any SMBH, the relative fractions accreted by the central BHs are not affected by the accretion and feedback models.

### 3. Simulation Analysis

We first identify halos using the Amiga Halo Finder which uses an overdensity criterion for a flat universe (Knebe et al. 2001; Gill et al. 2004; Knollmann & Knebe 2009) to set the virial radius in the primary halo. We select the primary halo to be the most massive at $z=0$ in the high-resolution region. The central SMBH in the primary halo has a mass of $1.3 \times 10^7 M_{\odot}$ and a velocity dispersion in the bulge of $\sigma \sim 152 \text{ km s}^{-1}$, indicating that h258 lies on the $M-\sigma$ relation. Additionally, the disk scale length is 2.8 kpc, comparable to that of the MW, while the total halo mass, $M_{\text{DM}} = 8.6 \times 10^{11} M_{\odot}$, and stellar mass, $M_* = 5.5 \times 10^{10} M_{\odot}$, show that the galaxy halo fits on the SMHM relation using the correction factors from Munshi et al. (2013).

In this analysis, we retrace each gas particle that was accreted by the halo or SMBH, following the gas back through its journey in the halo and recording its host halo and time of accretion (Brooks et al. 2009). The particles are then classified into types by their method of entrance into the primary halo. Gas that belonged to a different halo than the primary prior to accretion is classified as “clumpy,” entering the primary halo through mergers. All other gas is classified as “smooth” accretion, and is then subdivided into two categories: “unshocked” and “shocked.” Unshocked gas will usually flow into the halo via large-scale, DM filaments (Keres et al. 2005; B13). It is possible for unshocked gas to be dense enough to pierce an already developed shock, allowing it to funnel into the galaxy core where it can be accreted onto the SMBH (Nelson et al. 2013).

However, as we discussed in Section 1, if the galaxy halo is $\gtrsim 10^{11} M_{\odot}$, the gas is known to shock-heat to the virial temperature of the halo. We identify shocked particles through an increase in entropy and temperature using the following criterion:

$$ T_{\text{shock}} \ge 3/8 T_{\text{vir}}, \quad (3) $$

where $T_{\text{vir}}$ is the virial temperature of the halo, $T_{\text{shock}}$ is the temperature of the gas particle, and the minimum change in entropy is

$$ \Delta S \ge S_{\text{shock}} - S_0, \quad (4) $$

where $S_0$ is the initial entropy of the gas particle, and

$$ S_{\text{shock}} = \log_{10}[(3/8T_{\text{vir}})^{1.5}/4\rho_0], \quad (5) $$

where $\rho_0$ is the gas density prior to encountering the shock. Therefore, gas particles must reach both an entropy and temperature threshold to be labeled as “shocked,” and all
smoothly accreted gas that does not is labeled as “unshocked.”
Additionally for a “shocked” classification, the gas must be
entering the virial radius and a minimum galaxy halo mass
($\gtrsim 10^{11} M_{\odot}$) must be reached (see Brooks et al. 2009 for further
details). Since our halo is $\sim 10^{12} M_{\odot}$ by $z=0$, we should
expect to find more shocked gas entering the halo at later times.
Both types of smoothly accreted gas are tracked from the
moment they enter the virial radius until they reach a cutoff
radius at 10% of the virial radius (0.1 $R_{vir}$) at which point SN
feedback may appear as virial shocking and cause contamina-
tion in our estimates of shocked accretion. Thus, gas may be
labeled as shocked if it meets our criteria between the times
when it crosses $R_{vir}$ and when it reaches 0.1 $R_{vir}$. This cutoff
also accounts for any AGN feedback we might encounter.

Once all the gas particles have been individually categorized,
we can use these labels to classify the gas accreted by the
SMBH, and we can better contrast the processes that feed the
galaxy halo and its SMBH in MW-mass halos.

4. Results

The galaxy h258 is characterized by two major mergers; the
first occurs at $z \sim 1.8$ (mass ratio, $q \sim 0.8$) and the second at
$z \sim 1.2$ ($q \sim 1$). Despite its merger-rich history, gas accretion
smoothly increases the cumulative BH mass in h258 through-
out its evolution, as can be seen in Figure 1. The black dashed
line in Figure 1 indicates the total cumulative BH mass
(including both mass from gas and BH mergers), while the
black solid line indicates the total accreted gas mass. The blue
dotted–dashed line represents the gas mass accreted via
unshocked gas, while the green solid line and red dashed line
show the gas mass accreted through mergers and shocked gas,
respectively. Major mergers are indicated by gray hatched
regions.

It is important to point out that the largest part of the mass
budget is not gas at all, but other BHs that have merged with
the SMBH seed; the final distribution of mass in the SMBH
$(1.3 \times 10^7 M_{\odot})$ comes primarily ($\sim$90%) from mergers with
other BHs. This has important implications for gravitational
wave astronomy, increasing the event rate for SMBH assembly
at high redshifts (Holley-Bockelmann et al. 2010).

Although the intent of this paper is to focus on the origin of
the gas accreted by the SMBH, it is worthwhile to examine the
remainder of the SMBH's growth, which consists of BH
mergers. While the contribution from other seed SMBHs
appears significant, we point out that the uncertainties in seed
masses and formation efficiencies result in a large uncertainty
in the exact mass that may be acquired by SMBH mergers.
Additionally, there are repercussions regarding gravitational
waves that we do not consider here, such as recoil upon
merging. We leave a treatment of the dark side of the SMBH
mass budget to a future paper, as it calls for a statistical or semi-
analytic approach to incorporate the effects of seed model, BH
spin, and gravitational wave recoil.

Aside from this significant BH assembly, the largest gain in
accreted SMBH gas mass comes from gas accreted through
mergers after $z \sim 1$. From Figure 1, we see that gas accreted
through mergers makes up the majority of accreted mass
entering the SMBH at early times; however, the transition
between when smooth, unshocked accretion and gas accreted
from mergers dominates is clearly distinguished. While clumpy
gas (green) dominates gas mass accretion in the SMBH at the

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Gas fractions of the gas particles accreted by the main halo (left) and the SMBH (right), distinguished by type. Blue, green, and red distinguish gas gained via smooth accretion that remains unshocked, gas gained through mergers, and smoothly accreted gas that is shocked upon entry, respectively.</figcaption></figure>

earliest time, unshocked gas (blue) overtakes it for a short time
before clumpy gas once again dominates by $z \sim 1.5$.

This low-redshift transition to a clumpy gas preference
results in the large fraction of clumpy gas seen in the accreted
mass fractions in the SMBH (Figure 2). Figure 2 depicts the
fractions of total gas accretion in the galaxy halo and the
SMBH at $z=0$, again differentiated by gas origin. The gas
accreted by the halo is half (56%) comprised of gas accreted
through mergers, with 36% of the gas entering through
unshocked, smooth accretion. The smallest fraction of the total
gas is comprised of shocked gas (8%). Unlike the halo, nearly
three quarters (74%) of the gas accreted by the central SMBH is
accreted via mergers, while only a quarter (24%) is comprised
of unshocked, smoothly accreted gas. Shocked gas makes up
the last 2% of total gas entering the SMBH. It is evident then
that the SMBH more readily accretes gas gained through
mergers. While this result is consistent with the work of Dubois
et al. (2015), which explores how galaxy mergers may be
necessary for triggering BH growth in low mass galaxies, it is
contrary to B13 which found that in high-redshift, high-mass
galaxies, the fractions of gas comprising the SMBH and its host
were nearly the same. While the study by B13 focuses on high-
mass galaxies at high redshift, they all have similar gas
fractions and masses (total masses on the order of $10^{11} M_{\odot}$
and gas masses of a few $10^{10} M_{\odot}$) compared to the immediate
progenitors of h258 (which merge at $z \sim 1.2$ and $z \sim 1.8$). In
addition, the smooth accretion histories are broadly similar, in
that each host galaxy forms a shock front and begins accreting
shocked-mode gas about half way through its evolution
($\sim 6$ Gyr for h258, compared to $\sim 1$ Gyr for the B13 galaxies).
The similar smooth accretion histories, masses, and gas
fractions do point to the gas of merger origin being the key
factor in the difference between our results and those of B13.
We suggest that when major mergers are a key part of a
galaxy's assembly history, these mergers may also drive
SMBH growth.

A previous study by Fu & Stockton (2007) supplied direct
observational evidence that gas from a merger can be funneled
directly into the vicinity of the SMBH ($<1$ pc). Their study
examined a collection of 12 low-redshift quasars, half of which
are characterized by luminous extended emission-line regions
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Fractional radial density profiles of the gas that enters the main halo by $z=0$. All our lines add up to 1 in each radial bin. Gas within the galaxy halo's central 10 kpc is comprised of similar fractions of clumpy, unshocked, and shocked gas compared to that which is accreted by the SMBH (Figure 2). The green, blue, and red lines indicate clumpy, unshocked, and shocked gas, respectively.</figcaption></figure>

(EELRs). These EELRs were found to have metallicities below the mass-metallicity correlation of normal galaxies and are thought to have resulted from massive, galactic superwinds accompanying the creation of the powerful radio jets associated with the quasars. The quasars hosting EELRs were also found to have low-metallicity broad-line regions (BLRs) at their centers, while the quasars without EELRs hosted BLRs with metallicities above $Z_{\odot}$. Fu & Stockton (2007) determined that the presence of these low-metallicity EELRs as well as the similar, low-metallicity BLRs are evidence of a merger with a gas-rich galaxy. Such an interaction may explain both the infusion of low-metallicity gas into the BLRs and the subsequent ejection of that gas by the radio jets, forming the EELRs. Fu & Stockton (2009) do not directly state that the AGN activity was powered by gas directly from the merging galaxy; however, they do infer that the low-metallicity BLR and EELR regions originate directly from the interloper. Therefore it is quite likely that at least some of the gas from the merging galaxy, which seems to venture quite near the SMBH, may be accreted onto it in non-negligible amounts. We specifically traced the fraction of gas accreted via mergers that enters the galaxy ($<10$ kpc from the center) and determined this clumpy gas fraction is comparable to that accreted by SMBH. Figure 3 describes the fractional radial density profiles of the gas in the halo where clumpy, unshocked, and shocked gas are shown in green, blue, and red, respectively. The composition of the gas nearest the SMBH can account for increase we see in the amount of clumpy gas comprising the gas mass of the SMBH over that of the halo. While our study did not measure metallicity or include radio jets, our overall results support the conclusion that gas from incoming galaxy mergers with initially low angular momentum can efficiently lose further angular momentum through dynamical interactions with the larger galaxy, and can therefore be more readily accreted by the SMBH.

To better understand the apparent preference for merger-accreted gas, we examine the angular momentum of the gas at the moment it enters the halo. Figure 4 shows a cumulative distribution of the angular momentum of the gas as it enters the

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Normalized cumulative distribution of angular momentum (kpc km s⁻¹) of the gas particles accreted onto h258 by $z=0$; gas particles accreted onto the main halo (solid lines) and central black hole (dashed lines). The green, blue, and red lines indicate clumpy, unshocked, and shocked gas, respectively.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Normalized cumulative distribution of angular momentum (kpc km s⁻¹) of the gas particles accreted onto the h258 halo at a single timestep ($z \sim 1.2$) during the major merger's greatest influx of accreted gas. About 450,000 gas particles accreted onto the halo at this timestep. Angular momentum of gas particles accreted onto the main halo and central BH are distinguished by solid and dashed lines, respectively. The green, blue, and red lines indicate clumpy, unshocked, and shocked gas, respectively.</figcaption></figure>

halo (solid lines). We further distinguish the gas that enters the SMBH (dashed lines), still considering its angular momentum at the moment of halo entry. The gas is again distinguished by origin (clumpy, unshocked, shocked being green, blue, and red, respectively). We find that the angular momentum of gas entering which eventually reaches the SMBH is lower overall, and that the lowest angular momentum gas is comprised of both clumpy and unshocked gas. This result can be seen in Figure 5, which shows the cumulative distribution of the angular momentum of the incoming gas particles at the time of the greatest influx of accreted gas during the merger at $z \sim 1.2$ (colors and linestyles as in Figure 4). Figure 5 explicitly shows that the gas ending up in the SMBH enters with the lowest angular momentum. Thus a fraction of the gas accreted via the mergers that characterize this galaxy's evolutionary history
may have low enough angular momentum to be efficiently channeled into the center of the primary galaxy. This gas must lose further angular momentum to be efficiently accreted by the SMBH, which likely occurs via the standard picture of gas in the host galaxy losing angular momentum due to torques from the merger dynamics (Capelo et al. 2015). It is important for us to highlight that, since the presumed SMBH accretion method takes place at smaller scales than our resolution limit, we are unable to track the angular momentum loss of the gas through the last few parsecs.

A lower-resolution version of the galaxy h258 was run using the N-body code, Gasoline, like the simulations in B13. Despite fundamental differences in the hydrodynamic implementation and gas physics included and the absence of a dynamical friction prescription, an analysis of this low-resolution h258 results in an SMBH with the same distinct preference for accreting clumpy gas. A second galaxy, h277, was also run using Gasoline; however, this galaxy was characterized by a quiescent merger history (no major mergers) and resulted in a SMBH whose accreted mass fractions mirrored the halo (as seen in B13). The broad consistency between the low- and high-resolution simulation of the same galaxy, and the similar results of a quiescent galaxy to the previous study, indicate that the large-scale gravitational dynamics could be a main driver of the SMBH fueling in this case. We also stress that, while major mergers may not be the only physical mechanisms by which gas can be funneled into the centers of galaxies (the previous study being a strong example of this), mergers between galaxies clearly play an important role when considering the gas accretion of SMBHs.

## 5. Conclusion

This study examines the gas accretion onto the fully cosmological simulation of a MW-size galaxy to redshift $z=0$, with major mergers characterizing its past. We trace the gas into the SMBH at its center and differentiate the gas accreted onto the galaxy halo and SMBH by origin. Gas gained through mergers is classified as “clumpy” gas and smoothly accreted gas is separated into “shocked” and “unshocked” categories. Our goal is to determine what types of gas are primarily feeding the SMBH and the halos of this galaxy class, and to determine what effects the merger history of a galaxy may have on these processes.

A previous study by Bellovary et al. (2013) analyzed high-mass, high-redshift galaxies and found the gas composition of the SMBHs mirror their host halos. Contrary to these previous results, when we examined a galaxy with an active merger history, we determined that the SMBH at the center more readily accretes gas gained through mergers. This remained true both in an older, low-resolution simulation of the same galaxy as well as this current iteration. In both the low- and high-resolution cases, we see a significant increase in the clumpy gas accreted by the SMBH compared to its host. We also note that, in the high-resolution case, we can attribute the increase of clumpy gas to the mergers that characterize h258 and lead to a concentration of this gas residing within the galaxy’s inner ~10 kpc.

The angular momentum of the accreted gas as it enters the galaxy halo sheds some light on the mechanism driving this preferentially accreted clumpy gas. Smoothly accreted gas, which enters the halo with a wide range of angular momentum, is likely to adjust to the net angular momentum of the halo gas;

however, some studies have found that low angular momentum gas can fuel the central SMBH via filaments of smoothly accreted gas (Dubois et al. 2012; Di Matteo et al. 2017). Meanwhile, gas entering through mergers can fall to the galaxy’s center with minimal interaction with the halo gas. This restriction gives merger-accreted gas the advantage of falling more readily to the center and accreting onto the SMBH. Considering all origins of gas, our study is the first to see a clear contribution to gas from merging galaxies directly falling to the center of the primary galaxy and feeding the SMBH.

While the examination of this single, extreme case of a galaxy with an active merger history depicts a class of galaxy with varying SMBH accretion methods, a further study of cases with varying merger histories is required to begin understanding the broad spectrum of MW-mass galaxy accretion (Pontzen et al. 2017). Additionally, examinations of other extreme case, e.g., galaxies with varied but still merger-rich histories, may strengthen the validity of this result. Through this study, we show that the presence of major mergers can play an important role in the final compositions of central SMBHs, but the question of how important these mergers are remains to be seen.

Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. Results were partially obtained using the analysis software Pynbody (https://github.com/pynbody/pynbody). We thank the Fisk-Vanderbilt Masters-to-PhD Bridge program for the funding and support of this research. We also wish to thank the anonymous referee for their thorough reading of the manuscript and their useful comments which greatly improved its quality. J.B. acknowledges generous support from the Helen Gurley Brown Trust. M.V. acknowledges support from NASA award ATP NNX10AC84G.

## ORCID iDs

Jillian M. Bellovary https://orcid.org/0000-0001-7596-8372

Kelly Holley-Bockelmann https://orcid.org/0000-0003-2227-1322

Michael Tremmel https://orcid.org/0000-0002-4353-0306

Alyson Brooks https://orcid.org/0000-0002-0372-3736

Marta Volonteri https://orcid.org/0000-0002-3216-1322

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