# How does the presence of bar affects the fueling of supermassive black holes
? An IllustrisTNG100 perspective

Sandeep Kumar Kataria 1,2 & M. Vivek,3
1Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong
University, 800 Dongchuan Road, Shanghai 200240, China
2Key Laboratory for Particle Astrophysics and Cosmology (MOE) / Shanghai Key
Laboratory for Particle Physics and Cosmology, Shanghai 200240, China
3Indian Institute of Astrophysics, Bangalore 560034, India
skkataria.iit<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We conduct a statistical study of black hole masses of barred and unbarred
galaxies in the IllustrisTNG100 cosmological magneto-hydrodynamical
simulations. This work aims to understand the role of the bars in the growth
of central supermassive black hole mass and its implications on AGN fueling.
Our sample consists of 1191 barred galaxies and 2738 unbarred galaxies in the
IllustrisTNG100 simulations. To have an unbiased study, we perform our
analysis with an equal number of barred and unbarred galaxies by using various
controlled parameters like total galaxy mass, stellar mass, gas mass, dark
matter halo mass, etc. Except for the stellar mass controlling, we find that
the median of the black hole mass distribution for barred galaxies is higher
than that of the unbarred ones indicating that stellar mass is a key parameter
influencing the black hole growth. The higher mean accretion rate of the black
holes in barred galaxies, averaged since the bar forming epoch (z$\sim$2 ),
explains the higher mean black hole masses in barred galaxies. Further, we
also test that these results are unaffected by other environmental processes
like minor/major merger histories and neighboring gas density of black hole.
Although the relationship between stellar mass, bar formation, and black hole
growth is complex, with various mechanisms involved, our analysis suggests
that bars can play a crucial role in feeding black holes, particularly in
galaxies with massive stellar disks.

###### keywords:

(galaxies:) quasars: supermassive black holes – galaxies: bar –
galaxies:kinematics and dynamics

††pubyear: 2015††pagerange: How does the presence of bar affects the fueling
of supermassive black holes ? An IllustrisTNG100 perspective–How does the
presence of bar affects the fueling of supermassive black holes ? An
IllustrisTNG100 perspective

##  1 Introduction

An Active Galactic Nucleus (AGN) plays a vital role in galaxy evolution by
providing feedback to the host galaxy (Silk & Rees, 1998). In this feedback,
AGNs release part of their rest mass accreted energy to the gas reservoir in
their host galaxy (Fabian, 2012). AGN and stellar feedback are considered
necessary in high and low-mass galaxies, respectively, which explains the
observed galaxy luminosity function. Many semi-analytical and numerical
simulations have shown the importance of feedback (for e.g., Kauffmann &
Haehnelt, 2000; Granato et al., 2004; Springel, 2010). It has been observed
that the most massive galaxies tend to have the most massive SMBHs at their
centers (Kormendy & Ho, 2013). Additionally, there is a correlation between
the mass of the SMBH and the properties of the host galaxy, such as the bulge
mass and velocity dispersion (Ferrarese & Merritt, 2000). These observations
suggest that the growth of SMBHs and the feedback they provide play a crucial
role in shaping the properties of galaxies.

The disk galaxies in the observable universe come in various shapes and sizes
(Binney & Tremaine, 2008). It is well known that non-axisymmetric
instabilities, e.g., bar and spirals in the disk galaxy, play an essential
role in the secular evolution of disk galaxies, leading to the formation of
pseudo bulges whereas classical bulges are formed through merger events
(Kormendy & Kennicutt, 2004). Many N-body simulation studies show the
formation of Box/Peanut/X-shaped bulges in barred galaxies during their
secular evolution via the bending of bar or 2:1 vertical resonances. (Raha et
al., 1991; Pfenniger & Friedli, 1991; Shen et al., 2010; Zana et al., 2019;
Łokas, 2019). As the bar forms and rotates, it exerts torques on the
surrounding material. This torque extracts angular momentum from the inner
regions, causing material to move towards the central region. Thus, the bar
plays a significant role in transporting angular momentum from the central
region to the outer parts of disks, which leads to the transport of material
within the disk (Athanassoula, 2003).

Observations claim that nearly two third of massive disk galaxies possess a
bar in the disks, as evidenced by optical and infrared surveys (Eskridge et
al., 2000; Menéndez-Delmestre et al., 2007; Erwin, 2018). It is understood
that the fraction of barred galaxies is contingent upon the properties of the
host galaxies like mass, as well as the methods employed for identifying bars
within them (Lee et al., 2019). Bars are non-axisymmetric (m=2 Fourier mode)
instabilities that form in kinematically colder disks of galaxies (Ostriker &
Peebles, 1973). Recent advances in observational technology, such as the high
resolving power of the James Webb Space Telescope (JWST), have enabled the
identification of bars at high redshifts (z>1) (Guo et al., 2023). The
fraction of barred galaxies is constant up to z $\sim$ 0.84 for massive spiral
galaxies while the bar fraction decline beyond z $\sim$ 0.3 for low mass
spiral galaxies (Sheth et al., 2008). This suggests that the bar can survive
in disk galaxies for a long time, and its evolution can play a significant
role in disk dynamics. The presence of a central massive concentration like
bulge is shown to be destructive for bar survival in the disk (Nelson et al.,
2018; Shen & Sellwood, 2004; Kataria & Das, 2018, 2019; Kataria et al., 2020;
Jang & Kim, 2022). The surrounding dark matter halo properties also play an
essential role in the formation and evolution of bars and central X-shaped
bulges mostly seen in barred galaxies (Saha & Naab, 2013a; Long et al., 2014;
Collier et al., 2018a, 2019; Kumar et al., 2022; Kataria & Shen, 2022; Ansar
et al., 2023). Recently large-scale magneto-hydrodynamical cosmological
simulations have started producing bars whose properties are qualitatively
similar to the observed ones though relatively smaller in sizes (Rosas-Guevara
et al., 2020; Zhao et al., 2020; Frankel et al., 2022; Rosas-Guevara et al.,
2022).

Bars are essential in transporting gas from the outer disk to the central disk
(Sakamoto et al., 1999). Large-scale bars, also referred to as primary bars,
can transfer gas up to the central kpc region. However, the local viscous
stresses responsible for gas transport (Balbus & Hawley, 1991) becomes
inefficient within the sub-parsec region of disk (Shlosman et al., 1989,
1990). In a theoretical study, Shlosman et al. (1989) suggested “bars within
bars" as a possible mechanism to transport gas inwards in the central sub-
parsec region. This mechanism is motivated by the required fueling of gas in a
given time that can sustain AGN activity. At galactic scales, the primary bars
transport gas to the inner $\sim$ 1 kpc, where gas accumulates. Further, the
gas is sequentially transported inwards when the accumulated gas fraction
becomes high at these scales and becomes susceptible to gravitational
instabilities due to self-gravitation. These instabilities form structures
like nuclear spirals, bars, rings, and clumpy disks that trigger nuclear star
formation and gas inflows. These nuclear instabilities transport gas
efficiently to the inner regions, where another set of instabilities develop
and transport gas further inwards. Using simulations, Hopkins & Quataert
(2010) showed that structures like spirals, rings, bars, etc., in the nuclear
regions are efficient in transporting gas within the central sub-parsec
regions. These simulations contained various models of the interstellar medium
that properly treat star formation and self-gravity of stars and gas, which
are crucial for exploring the central sub-parsec region. This simulation study
nicely supplemented the “bars within bars" proposition of Shlosman et al.
(1989).

Observationally, the approach to study the connection between bars and AGN
activity has been twofold: One approach compared bar fraction in a sample of
AGN host galaxies with that of a control sample of inactive galaxies, and the
second approach searched for differences in AGN activity in barred and
unbarred galaxies (See Storchi-Bergmann & Schnorr-Müller, 2019, for a review).
In the former approach, three studies, Knapen et al. (2000) (79% vs. 59%),
Laine et al. (2002) (73% vs. 50%) and Garland et al. (2023) (59% vs. 44 %)
found that Seyfert galaxies are found to have more bars than non-active
galaxies. (Laurikainen et al., 2004) also found a similar result for SB-type
bars in their analysis. Galloway et al. (2015) created a volume-limited sample
of active and inactive disk galaxies using the Galaxy Zoo 2 project and found
a small but statistically significant increase in the bar fraction of active
galaxies. However, Ho et al. (1997); Mulchaey & Regan (1997); Lee et al.
(2012) detected similar bar fractions for Seyfert galaxies and comparison
galaxies. Following the alternate approach, Alonso et al. (2013) and Alonso et
al. (2018) compared the nuclear activity of barred galaxies with that of
unbarred galaxies and AGN galaxies in paired systems, respectively. In both
studies, barred galaxies showed excess nuclear activity and black hole
accretion rate compared to the control samples. However, Cisternas et al.
(2013) did not find any significant correlation between any of the bar
strength indicators and the degree of nuclear activity. Similarly, (Goulding
et al., 2017a) used Galaxy Zoo 2 project and Chandra X-ray data and showed no
enhancement in the nuclear accretion with the presence of a bar in the host
galaxy. Cheung et al. (2015a) combined the two approaches by comparing a
sample of 120 AGN host galaxies in the redshift range, 0.2 $<$ z $<$ 1.0, with
a control sample of inactive galaxies. They found no significant difference in
the bar fraction among active and inactive galaxies and AGN fraction among
barred and non-barred galaxies. Finally, the most recent study by Silva-Lima
et al. (2022) points out that AGNs are favored in barred galaxies though it
also suggests other mechanisms within the 100 pc region that can feed gas to
AGNs. Clearly, there is no consensus among the observational studies about the
role of bars in AGN fueling.

The new generation of cosmological hydrodynamical simulations offers a
powerful tool to study the role of various galaxy components in the evolution
of galaxies (Vogelsberger et al., 2014a). The suite of these simulations
include EAGLE (Schaye et al., 2015), ErisBH (Bonoli et al., 2016), Illustris
(Vogelsberger et al., 2014b), IllustrisTNG (Nelson et al., 2018) and
MassiveBlack-II (Khandai et al., 2015). These simulations are able to
correctly reproduce many observed properties of galaxies at low redshift.
Among these, the IllustrisTNG project, the successor of the original Illustris
simulations, contains the most recent physical models and an updated
prescription for feedback processes that enable the generation of galaxy
populations whose properties are even closer to reality. There are several
studies that attempted to study the bars in galaxies using these simulations.
Peschken & Łokas (2019) studied the bar formation in galaxies using Illustris
simulation and suggested that a large fraction of bars are formed by mergers
and flyby events. Zana et al. (2018a) demonstrated that the global properties
of bar formation remained unaffected by mergers and flybys in a variant of the
ErisBH simulation. Furthermore, in the context of Eris2k simulations, Zana et
al. (2018b) established that bars are resilient to flyby interactions. Using
the Fourier decomposition method, Rosas-Guevara et al. (2020) showed that bars
are found in 40 % of the IllustrisTNG disk galaxies identified at z=0 in the
stellar mass range 1010.4-11 M⊙. Their study concludes that the cosmological
environment and feedback processes determine the chances of forming bars in a
galaxy. A similar result is obtained by Zhou et al. (2020) in their comparison
study on the bar structure in the Illustris and IllustrisTNG100 (hereafter
TNG100) simulations. However, Zhao et al. (2020) revisited the bar fraction
using the ellipse fitting method and reported that 55% of disk galaxies with
stellar mass M⋆ $\approx$ 1010.6 M⊙ are barred, consistent with observations.
In the high-resolution IllustrisTNG50 simulation, Zana et al. (2022)
demonstrated that massive galaxies have a bar fraction of 60% at z=0, which is
comparable to observed values.

Several observational and theoretical studies suggest that AGN have a
relatively short lifetime, ranging from a few 107–108 years (Martini, 2004;
Wada, 2004; Merloni, 2004). In addition, Wada (2004) suggest that mass
accretion onto black holes is not constant even during the expected duty cycle
of 108 years, but rather consists of multiple shorter episodes lasting 104-5
years. On the other hand, numerical simulations have shown that bars have a
lifetime of around a few Giga years (Rosas-Guevara et al., 2020). This
difference in the timescales may explain the lack of a clear correlation
between the presence of large-scale bars and AGN activity. Nevertheless, the
growth of black holes and AGN activity is the most obvious consequence of gas
accretion onto black holes. So, it may be possible to investigate the
connection between bars and AGN activity by examining the distribution of
black hole masses in these galaxies. However, this is challenging
observationally as the number of AGN with robust black hole mass measurements
remains tiny. Large-volume cosmological simulations like IllustrisTNG offers a
promising alternative as they include a black hole prescription in the
simulation and can resolve morphological features such as bars.

In this work, we use the IllustrisTNG simulation to study the role of bars in
the growth of central supermassive black holes. We use the TNG100 simulation,
which has a nice compromise between a large cosmological volume and
resolution. The paper is structured as follows. In section 2, we discuss the
methods and techniques used in this study. We discuss the results and
discussion in sections 3 and 4, respectively. Finally, we conclude our results
in section 5.

##  2 Methods

###  2.1 IllustrisTNG Simulations

IllustrisTNG simulations are the gravo-magnetohydrodynamical cosmological
simulations (Marinacci et al., 2018; Naiman et al., 2018; Nelson et al., 2018;
Pillepich et al., 2018b, 2019; Springel et al., 2018) which are run with
moving mesh code AREPO (Springel, 2010; Pakmor et al., 2016). IllustrisTNG
simulations are the successor to Illustris simulations (Genel et al., 2014;
Vogelsberger et al., 2014a, c; Sijacki et al., 2015) which incorporates new
physics and new treatment of cosmic magnetic field (Weinberger et al., 2017;
Pillepich et al., 2018a) and these simulations solve magnetohdrodynamics
equations using finite volume Godunov type method coupled with self-gravity
using Tree-PM methods. The IllustrisTNG simulations are made of three
cosmological volumes, TNG50, TNG100, and TNG300, which have comoving box sizes
of roughly 51.7, 110.7, and 302.6 Mpc, respectively. Among these simulations
with increasing box sizes, TNG50 corresponds to the highest resolution, while
TNG300 corresponds to the lowest resolution. We have used TNG100 simulations
for this study (Nelson et al., 2018), which provide a good balance between
cosmological volume and resolution of the simulations. The mass resolutions of
gas and dark matter in TNG100 simulations are given by 1.4$\times 10^{6}$
$M_{\odot}$ and 7.5$\times 10^{6}$ $M_{\odot}$, respectively. The comoving
gravitational softening lengths ($\epsilon$) of the gas and dark matter
particles are equal to 180 pc and 740 pc, respectively. These simulations
incorporate the cosmology from the Planck Collaboration et al. (2016) for
which the parameters are given by $\Omega_{\Lambda}$ = 0.6911, $\Omega_{m}$ =
0.3089, $\Omega_{b}$ = 0.0486, $H_{0}$ = 67.74 Km sec-1 Mpc-1, $\sigma_{8}$ =
0.8159, ns = 0.9667.

In the TNG100 simulation, the black holes are seeded in massive halos having
masses $>$ 7.8 $\times$ 1010 M⊙. The masses of seeded black holes are 1.18
$\times$ 106 M⊙. Supermassive black holes in these simulations can grow
through two mechanisms: black hole mergers and gas accretion through secular
evolution. The black holes accrete gas via pure Bondi accretion rate, limited
by the Eddington rate, as follows: (Weinberger et al., 2017).

$\dot{M}_{BH}=min\big{(}\dot{M}_{Bondi},\dot{M}_{Edd}\big{)}$ (1)

where,

$\centering\dot{M}_{Bondi}=\dfrac{4\pi
G^{2}M_{BH}^{2}\rho}{c_{s}^{3}}\@add@centering$ (2)

$\centering\dot{M_{Edd}}=\dfrac{4\pi
GM_{BH}m_{p}}{\epsilon_{r}\sigma_{T}c}\@add@centering$ (3)

Here, G, MBH, $c_{s}$, and $\rho$ in equation 2 are the Gravitational
constant, black hole mass, sound speed, and density, respectively. In equation
3, mp, $\sigma_{T}$, $\epsilon_{r}$ and $c$ are the mass of the proton, the
Thompson cross-section, the radiative accretion efficiency, and speed of light
in vacuum, respectively. The feedback from the black hole is introduced in two
modes: kinetic and thermal modes. The thermal mode feedback is triggered in
the high accretion state and heats the surrounding gas with continuous thermal
energy. The kinetic mode feedback happens in the low accretion state and emits
energy through kinetic outflows that give momentum to the surrounding gas. The
kinetic mode feedback is efficient and releases energy in a pulsed manner. The
energies released in these two modes are as follows (Weinberger et al., 2017).

$\Delta E_{thermal}=\epsilon_{f,high}\epsilon_{r}\dot{M}_{BH}c^{2}$ (4)

$\Delta E_{kinetic}=\epsilon_{f,low}\dot{M}_{BH}c^{2}$ (5)

Here, $\dot{M}_{BH}$ is the accretion rate of the black hole with mass
$M_{BH}$, $\epsilon_{r}$ is the radiative efficiency typically ranging from
0.1 to 0.2, $\epsilon_{f,high}$ and $\epsilon_{f,low}$ are the fraction of
energy released to the surrounding gas for thermal and kinematic mode,
respectively. In high accretion rate, the energy is liberated at a constant
rate, i.e., $\epsilon_{f,high}=0.1$ ; $\epsilon_{f,high}\epsilon_{r}=0.02$.
The maximum limit on emitted fractional energy for low accretion rate mode is
$\epsilon_{f,low}=0.2$. In TNG100 simulations, for black hole masses less than
$10^{8.5}$, thermal feedback is the main feedback mechanism, and the black
holes are in the high accretion state. In massive black holes,
$M_{BH}>10^{8.5}$, gas accretion is self-regulated via the more efficient
kinetic feedback, which causes their Eddington ratios to drop (Weinberger et
al., 2018).

Figure 8:  The top row shows some examples of face-on stellar density maps for
barred galaxies at z=0 in the TNG100 simulation. The bottom row shows some
examples of face-on stellar density maps for unbarred galaxies at z=0 in the
TNG100 simulation. The sub-halo ids of all galaxies are mentioned on top of
each galaxy. The color bars within each map correspond to the logarithm of the
average stellar volume density in units of kpc-2.

###  2.2 Galaxy Selection Criterion

Our sample consists of rotationally dominated disk galaxies from the TNG100
simulation. The rotation dominance is determined using the parameter
K${}_{rot}=\langle v_{\phi}^{2}/v^{2}\rangle$ (Sales et al., 2010), where
$v_{\phi}$ and $v$ correspond to the rotational component of velocity and
total velocity, respectively. Following Du et al. (2019, 2020), we employed
the criterion, Krot $>$ 0.5, to select the sample of rotationally dominated
disk galaxies. All the disk galaxies have stellar masses greater than 1010 M⊙,
which makes the total sample of disk galaxies equal to 3931. The disk galaxy
sample is categorized into barred and unbarred samples using previous studies
Rosas-Guevara et al. (2020) and Zhao et al. (2020).

Rosas-Guevara et al. (2020) identified the barred galaxies in the TNG100
simulations using the strength of $m=2$ Fourier mode. Their sample consisted
of disk galaxies having stellar masses greater than 1010.4 M⊙. Their study
classified the galaxy as a strongly barred galaxy if the strength of $m=2$
Fourier mode is greater than 0.3. The galaxy is termed to have a weak bar if
the strength of $m=2$ Fourier mode is between 0.2–0.3. This method captures
107 barred galaxies.

In addition, Zhao et al. (2020) used the method of ellipse fitting to identify
bars in TNG100 disk galaxies having stellar masses greater than 1010 M⊙. They
measured the ellipticity and position angle of contours by fitting isodensity
contours as a function of radius. If the maximum ellipticity of contour at a
given radius is higher than 0.4, it is defined as a strong bar and otherwise a
weak bar. Zhao et al. (2020) identified 1179 barred galaxies, an order of
magnitude larger than detected bars in the Fourier method by Rosas-Guevara et
al. (2020). The substantial difference in the number of barred galaxies
between these studies can be ascribed to the dissimilarity in the initial
sample sizes studied. Rosas-Guevara et al. (2020) examined galaxies with a
stellar mass exceeding 1010.4 M⊙, while Zhao et al. (2020) focused on galaxies
with a stellar mass surpassing 1010 M⊙. It is worth noting that the larger
sample size in Zhao et al. (2020) has a lower stellar mass threshold,
eliminating concerns regarding incompleteness or missing galaxies between 1010
and 1010.4 M⊙.

After removing common sources from Rosas-Guevara et al. (2020) and Zhao et al.
(2020) samples, we obtained 1193 barred galaxies. The sample is the sum of all
the barred galaxies coming from the two catalogues, where 93 objects have been
identified by both of them. The remaining sample, i.e., 2738 out of 3931 disk
galaxies, forms the unbarred disk galaxy sample. From hereon, we use the terms
"barred galaxies" and "unbarred galaxies" to specifically denote galaxies with
bars and galaxies without bars, respectively, at a redshift of z=0. Fig. 8
shows the face-on stellar density maps of four barred galaxies and four
unbarred galaxies in the TNG100 simulation.

We obtained parameters like blackhole mass, gas mass, stellar mass, total mass
and dark matter halo mass, etc., for both barred and unbarred galaxies. In
Fig. 9, we show the distribution of total galaxy mass, total stellar mass,
total gas mass, total stellar by halo mass, total gas by stellar mass, and
total gas plus the total stellar mass of both barred and unbarred galaxies.
These distributions show that the median values of various galaxy components
are not similar in the full sample of barred and unbarred galaxies. A
Kolmogorov–Smirnov (K–S) test between the barred and unbarred samples returns
a p-value close to 1 for different parameters pointing to significant
differences in the corresponding distributions. The maximum difference is seen
for the stellar mass parameter. Fig. 9b shows that barred galaxies have larger
stellar mass in comparison to unbarred ones.

##  3 Results

In this section, we compare the distributions of various galaxy properties of
barred and unbarred galaxy sample.

Figure 9: Full sample distribution of various properties of 1193 barred (black histogram) and 2738 unbarred (red histogram) galaxies at z=0, which are used to control the sample; namely (a) total galaxy mass, (b) total stellar mass, (c) total gas mass, (d) total stellar to halo mass ratio, (e) total gas to stellar mass ratio, and (f) sum of gas and stellar mass. Vertical dashed lines show the median values of each distribution.  Figure 10: The black hole mass distribution of full barred (black histogram, 1193 galaxies) and unbarred sample (red histogram, 2738 galaxies) at z=0 shows the dichotomy. Vertical dashed lines show the median values of each distribution. |
---|---
(a) | (b)
|
(c) | (d)
|
(e) | (f)
Figure 11: The distribution of the controlled sample and respective black hole
mass distribution of barred (black histogram) & unbarred (red histogram)
galaxies. The left panel of each sub-figure corresponds to the distribution of
control parameters; (a) total galaxy mass, (b) total stellar mass, (c) total
gas mass, (d) ratio of total stellar and total dark matter halo mass, (e)
ratio of total gas mass and total stellar mass (f) sum of total gas mass and
total stellar mass. The right panel of each sub-figure corresponds to the
distribution of black hole mass at z=0 for the controlled samples. Black/red
vertical lines correspond to the median values of the distribution.

###  3.1 Black hole mass distribution in barred and unbarred galaxies

As discussed in section 2.2, we have used 2738 unbarred galaxies and 1193
barred galaxies for this study. As the primary motivation of this study is to
investigate the role of galactic bars in fueling the AGN, we first compared
the distributions of supermassive black hole mass in these galaxies. Fig. 10
shows the black hole mass distribution for the full sample of barred and
unbarred galaxies at z=0. These distributions clearly show a mass dichotomy
for black hole masses in barred and unbarred samples. We notice that the peak
of the black hole mass distribution for barred galaxies is twice the peak of
the black hole mass distribution for unbarred galaxies. The difference in the
median of black hole mass distributions between barred and unbarred galaxies
is $\Delta M_{BH}\approx 4\times 10^{7}M_{\odot}$ ($\sim$ 42 times the average
gas cell mass of 7.93$\times$105 M⊙). However, the number of unbarred galaxies
in our sample is much larger than barred galaxies, which may introduce a bias
in our study. To remove any such bias, we made the sample size similar for
both barred and unbarred galaxies by creating control samples of unbarred
galaxies based on several control parameters. For e.g., in the control sample
of unbarred galaxies with stellar mass as the controlled parameter, we only
included sources in the unbarred sample with similar stellar mass for each
source in the barred sample. This process makes our barred and unbarred sample
sizes equal, which is equal to 1193 sources. In our study, we have used
several parameters to control the unbarred sample. The control sample
generation is implemented using the k-nearest neighbour (KNN) algorithm in the
controlled parameter space (Guo et al., 2003). The KNN algorithm is a non-
parametric classification and regression technique widely used in data mining
and machine learning. In the context of creating a control sample with similar
parameter distributions, KNN identifies the most similar data point from a
dataset to a given data point in the reference dataset based on their
proximity in the feature space. This control sample ensures a balanced
comparison between the datasets and minimizes bias. The KNN algorithm locates
the nearest neighbour in the unbarred sample for each galaxy in the barred
sample. We discuss the various controlled parameters and the comparison of
black hole mass distributions in the controlled galaxy samples in the
following paragraphs.

####  3.1.1 Sample unbiased using total galaxy mass

The total mass of a galaxy plays an essential role in bar formation processes
(Athanassoula, 2003). Hence, we first used the total galaxy mass as a control
parameter to create unbiased samples of barred and unbarred galaxies. The
total galaxy mass refers to the total mass associated with the stellar,
gaseous, and dark matter components. The left panel of Fig. 11(a) shows the
distribution of total galaxy masses of barred galaxies and the control sample
of unbarred galaxies. The right panel of Fig. 11(a) shows the resulting black
hole mass distributions of unbiased galaxy samples at z=0. Unlike the galaxy
mass distributions for the full sample shown in Fig. 9(a), it is clear that
the control sample generation has indeed made the total galaxy mass
distributions similar for barred and unbarred galaxies. Nevertheless, the
black hole mass dichotomy seen in the comparison of the full sample of barred
and unbarred galaxies persists. The median value of black hole mass
distribution peaks at 0.62 $\times$ 108 M⊙ for unbarred galaxies and 1.02
$\times$ 108 M⊙ for barred galaxies. The average gas cell mass in the TNG100
simulation is 9.43$\times$105 M⊙ which is much smaller than the difference of
median black hole mass in barred and unbarred galaxies. It should be noted
that the halo component makes up the majority of the total mass of a galaxy.
Typically, the halo mass accounts for around 90% of the total mass of the
galaxy, while the stellar and gas components make up 5% each. The difference
in the distribution of black hole mass between barred and unbarred galaxies,
even after controlling by total galaxy mass, suggests that the black hole mass
dichotomy is not driven by the difference in the total galaxy mass between the
two samples.

Figure 12:  The left panel shows the distribution of stellar mass for the
barred (black histogram) and unbarred (red histogram) control samples with no
duplication. The right panel shows the corresponding black hole mass at z=0
for the barred (black histogram) and unbarred (red histogram) control samples.
Black/red vertical lines correspond to the median value of the distribution.

####  3.1.2 Sample unbiased using total stellar mass

It is already known that massive stellar disks are prone to bar-type
instabilities, and bars in galaxies are preferentially seen in high stellar
mass galaxies (Athanassoula, 2003). The bar fraction, as well as the strength
of the bars, are correlated with the stellar mass (Rosas-Guevara et al., 2020;
Díaz-García et al., 2016). In this context, it is worth checking if the
difference in the black hole mass distributions between barred and unbarred
galaxies is influenced by the stellar mass parameter. To check this, we
constructed a control sample of unbarred galaxies using the stellar mass as
the controlled parameter.

Figure 13: The left panel of the plot depicts the distribution of total
stellar mass for both barred and unbarred galaxies, which is truncated at 3
$\times$ $10^{10}$ $M_{\odot}$. The middle panel shows the distribution of the
controlled sample for both barred and unbarred galaxies. In the controlled
sample, we located the nearest neighbors of similar stellar mass barred
galaxies in the full unbarred sample with an upper cutoff. Finally, the right
panel of the plot shows the distribution of black hole mass at z=0 in the
controlled sample. In all three panels, the vertical dashed lines indicate the
median values of the corresponding distributions.

Fig. 9(b) illustrates the total stellar mass distribution of barred and
unbarred galaxies for the full sample, demonstrating that barred galaxies are
predominantly located in massive disks compared to unbarred ones. The median
stellar mass of barred galaxies is nearly twice that of the unbarred sample.
This finding aligns with the observation that bars tend to occur in massive
disk galaxies (Rosas-Guevara et al., 2020). In the controlled sample (left
panel of Fig. 11(b)), the distribution of total stellar mass for barred and
unbarred galaxies is similar, unlike the entire sample. The resulting black
hole mass distribution of barred and unbarred galaxies is shown in the right
panel of Fig. 11(b). It is clear that the controlled sample does not exhibit
the black hole mass dichotomy as seen before in the case of total galaxy mass.
Given the stark difference in the distribution of stellar mass of barred and
unbarred galaxies in the full sample, there arises a valid concern that the
generation of the control sample might not be entirely accurate. When using
the KNN algorithm to create a control sample with similar stellar mass
distributions, we found that the same unbarred galaxies were identified as
nearest neighbors for barred galaxies with stellar masses greater than
$3\times 10^{10}M_{\odot}$. The repeated inclusion of the same galaxy in the
control sample leads to a situation where this particular galaxy holds a
dominating influence over the statistical analysis, which is far from ideal.
To address this issue, we modified our algorithm to prevent duplicates in the
control sample by not allowing the same unbarred galaxy to be the nearest
neighbor of more than one barred galaxy. This modification did not yield a
control sample of unbarred galaxies with an entirely identical stellar mass
distribution to that of barred galaxies. The left panel of Fig. 12 shows the
distribution of stellar mass for the barred galaxies (black histogram) and
unbarred (red histogram) control sample galaxies with no duplication. Even in
cases where duplicates were omitted, the KNN algorithm identified a control
sample of unbarred galaxies generally exhibiting lower masses in comparison to
the barred galaxies. This result is understandable, as the KNN algorithm
prioritizes the selection of the nearest galaxy based on stellar mass. In
situations where nearby galaxies are lacking, the algorithm naturally extends
its search to lower mass values in order to identify suitable counterparts.
Due to the aforementioned difference in the stellar mass distribution, we find
a marginal dichotomy in the black hole mass distribution between barred and
unbarred galaxies when no duplicates in control sample were allowed. The right
panel of Fig. 12 shows the corresponding black hole mass at z=0 for the barred
(black histogram) and unbarred (red histogram) control samples. It is evident
that the most massive barred galaxies significantly influence the black hole
mass distribution in these galaxies. We also note here that we conducted the
analysis without duplicates for all other control parameters as well. However,
we observed that this modification didn’t impact any of the results, mainly
because the initial distributions of the control parameters were not
significantly dissimilar to begin with.

In addition to modifying the algorithm to not include duplicates, we also
tried creating a control sample with an upper limit to the stellar mass to
avoid the high stellar mass galaxies where the KNN algorithm failed to create
an ideal control sample dataset. The left panel of Figure 13 illustrates the
distribution of total stellar mass for the full sample of barred and unbarred
galaxies, with an upper mass limit set at $3\times 10^{10}M_{\odot}$. It is
evident that the total stellar mass distribution of unbarred galaxies is
skewed towards lower masses, with a median mass of $1.23\times
10^{10}M_{\odot}$. Conversely, the distribution for barred galaxies is tilted
towards higher values, with a median mass of $2.7\times 10^{10}M_{\odot}$.
Subsequently, we employed the KNN algorithm to identify nearest neighbors
within this pruned dataset. The middle panel of Figure 13 shows the
distribution of stellar mass of the controlled sample of barred and unbarred
galaxies. The right panel of Figure 13 shows the distribution of black hole
mass at z=0 for the unbiased sample of barred and unbarred galaxies with an
uppercut of $3\times 10^{10}M_{\odot}$ on the total stellar mass. The
distribution of black hole masses at z=0 remains consistent between barred and
unbarred galaxies, even within the pruned dataset. In conclusion, there is no
discernible dichotomy in the distribution of black hole masses between barred
and unbarred galaxies. Notably, the absence of such a dichotomy when
controlling for stellar mass implies that stellar mass might indeed be a
driver for the observed black hole mass dichotomy.

Previous studies have demonstrated a strong correlation between bars in
galaxies and the total stellar mass of the galaxy. The strength of the bars is
directly proportional to the stellar mass. It is, therefore, reasonable to
assume that black hole feeding would also be more efficient in strongly barred
galaxies. If we exclude high-stellar-mass barred galaxies from the sample, we
will inadvertently remove galaxies with efficient black hole feeding from the
analysis. In such a scenario, we would not expect to observe any significant
difference in the black hole mass distributions of barred and unbarred
galaxies.

####  3.1.3 Sample unbiased using total gas mass

Gas content plays an important role in the evolution of disk galaxies. Bars
are thought to drive the gas towards the central regions due to their non-
axisymmetric gravitational potential and facilitate the black hole feeding. In
turn, the presence of gas also can strengthen or weaken the bar structure as
the amount of angular momentum redistribution depends on the material with
which angular momentum is exchanged (Athanassoula, 2003; Athanassoula et al.,
2013). Many observational studies have investigated the dependence of bar
presence and gas content. Davoust & Contini (2004) and Masters et al. (2012)
reported that the bar fraction is significantly lower among gas-rich disk
galaxies than in gas-poor ones. Zhou et al. (2021) reported an increasing
trend in the physical size of the bar with an increase in stellar mass and a
decrease in gas fraction. Given that massive gas disks suppress the bar-type
instabilities, it is important to check the influence of gas mass on the
connection between bars and black hole growth. For this, we unbiased the
unbarred galaxy sample using total gas mass as the controlled parameter. Fig.
9(c) shows the gas distribution in the full sample, which indicates that the
median value of gas mass is marginally higher in unbarred galaxies compared to
barred ones. This is in agreement with the previous studies, which found low
gas fractions in barred galaxies. The left panel of Fig. 11(c) shows a similar
distribution of total gas mass for the barred and unbarred sample after the
controlling exercise. The right panel of Fig. 11(c) shows the corresponding
black hole masses, and it is evident that the dichotomy in the black hole mass
distribution between the two galaxy samples persists even after unbiasing with
the total gas mass parameter. The median value of black hole mass distribution
peaks at 0.47 $\times$ 108 M⊙ for unbarred and 1.02 $\times$ 108 M⊙ for barred
galaxies.

####  3.1.4 Sample unbiased using the ratio of total stellar to total halo
mass

It is well known that massive disks support the formation of bars. Similarly,
many simulations studied the role of dark matter component on bar formation
(for e.g., see, Ostriker & Peebles, 1973; Athanassoula, 2003; Dubinski et al.,
2009). While earlier studies with static halos showed that the gravity of the
halo suppresses bar formation (Ostriker & Peebles, 1973), recent simulations
with live halos reported that the angular momentum exchange enables the bar to
grow stronger and longer (Athanassoula, 2002). Moreover, the halo
concentration, total halo mass, and spin of the dark matter halo are reported
to have an influence on the bar formation (Debattista & Sellwood, 1998;
Athanassoula, 2003; Saha & Naab, 2013b; Collier et al., 2018b). In this
scenario, it is interesting to check how the ratio of stellar mass to halo
mass affects the dichotomy of black hole mass distributions presented earlier.
Fig. 9(d) shows the distribution of the total stellar to total halo mass ratio
for the full sample of barred and unbarred galaxies. A small difference in the
distribution is evident from the median of the distributions marked by
vertical lines. Here again, we unbiased the unbarred sample using the total
stellar to total halo mass ratio, and the resulting distributions are shown in
Fig. 11(d). As seen in the left panel of Fig. 11(d), the distribution of the
ratio of total stellar mass and total halo mass is similar for barred and
unbarred galaxies when the sample is controlled. Despite this similarity, we
find that the dichotomy in the distribution of black hole masses persists even
in the unbiased sample of the barred and unbarred galaxies, as seen in the
right panel of Fig. 11(d).

####  3.1.5 Sample unbiased using the ratio of total gas mass to total stellar
mass

As discussed in previous sections, the stellar and gas mass have opposite
effects on the growth of bar formation. It would be interesting to check the
distribution of black hole mass in the two samples with similar gas to stellar
mass ratios. Fig. 9(e) shows the distribution of the total gas mass to total
stellar mass for the full sample of barred and unbarred galaxies. The medians
of the distributions show marked differences between the barred and unbarred
samples. So, we obtained the unbiased sample using the ratio of total gas to
total stellar mass as the control parameter. We find that the distribution of
the ratio of total gas mass and total stellar mass is similar for barred and
unbarred galaxies when the sample is unbiased (left panel of Fig. 11(e)). Even
in this case, we find that the dichotomy exists in the distribution of black
hole masses in the unbiased sample of the barred and unbarred galaxies, as
shown in the right panel of Fig. 11(e). The median value of black hole mass
distribution peaks at 0.55 $\times$ $10^{8}$ $M_{\odot}$ for unbarred and 1.02
$\times$ $10^{8}$ $M_{\odot}$ for barred galaxies. This result is similar to
the case where we used total gas mass as a controlling parameter, but differ
from the case when total stellar mass was used as the controlling parameter.

####  3.1.6 Sample unbiased using the sum of total stellar mass and total gas
mass

As the central black hole can feed on both stars and gas, the difference in
the amount of total baryonic mass (stellar mass + gas mass) available in the
galaxy can drive the difference in the distributions of black hole mass
between barred and unbarred galaxies. To probe if the total baryonic mass has
any effect on the black hole mass growth, we repeated the unbiasing exercise
for the two samples with the total baryonic mass as the controlled parameter.
We find that the distribution of the total baryonic mass is similar for barred
and unbarred galaxies when the sample is controlled, as seen in the left panel
of Fig. 11(f). Here again, we find that the dichotomy persists in the
distribution of black hole masses even in the unbiased sample of the barred
and unbarred galaxies, as shown in the right panel of Fig. 11(f).

####  3.1.7 Summary of the unbiasing exercises

In this section, we carried out unbiasing the galaxy samples using total
galaxy mass, total stellar mass, total gas mass, star-to-halo mass ratio, gas-
to-star mass ratio, and total baryonic mass as the control parameters. If any
of these parameters drive the black hole mass dichotomy, we should have seen
similar distributions of black hole mass for the unbiased barred and unbarred
galaxies. Except for the stellar mass, we see that the black hole mass
dichotomy is preserved even after the unbiasing exercise. In the case of
stellar mass as the controlled parameter, the distribution of black hole mass
at z=0 is similar for both barred and unbarred galaxies. We attribute the
vanishing of the black hole mass dichotomy after controlling for total stellar
mass to the significant influence of stellar mass in the formation of bars and
the subsequent efficient fueling of the black holes, allowing for their
growth.

###  3.2 Effect of surrounding gas density of galaxy and mergers

In addition to bars, environmental factors such as galaxy mergers can also
contribute to the inflow of gas toward the central regions of a galaxy,
thereby facilitating black hole growth. To accurately assess the impact of
galactic bars on black hole growth, it is crucial to distinguish the effects
of mergers from those of bars (Kormendy & Kennicutt, 2004). In this section,
we explore how non-secular evolution events like galaxy mergers affect our
analysis.

####  3.2.1 Effect of surrounding gas density

We first investigated the impact of gas density around the host galaxy on the
distribution of black hole mass of barred and unbarred galaxies. We eliminated
any bias in our sample by controlling the surrounding host galaxy gas density
as the control parameter. The median black hole mass in barred galaxies peaks
higher than in unbarred galaxies, resulting in the black hole mass dichotomy.

Additionally, we refined our analysis by considering two additional parameters
simultaneously that could influence black hole mass growth: the total mass and
the surrounding neighborhood gas density around the black hole in the host
galaxy. To gauge the surrounding gas density, we employ the "BH_Density"
parameter derived from the TNG100 simulations. This parameter represents the
local comoving gas density, averaged across the BH’s closest neighbors. It
pertains to the density within a comoving radius of the sphere encompassing
256 ±4 nearest-neighbor gas cells around the BH. For the galaxies in our
sample, this measurement spans from 1 kpc to 56 kpc and necessarily reflect
the availability of gas extending beyond the length scales of the bars.

To achieve this, we utilized a 2D KNN algorithm that uses the total galaxy
mass and the gas density in the vicinity of the black hole as anchor points.
This allowed us to identify the nearest neighbors of the unbarred sample
galaxies to those of the barred sample, in terms of these two parameters.

Fig. 14 illustrates the distribution of black hole masses for the unbiased
barred and unbarred samples obtained using this method. We can observe that
the median black hole mass in the unbarred sample (0.6 x $10^{8}$ $M_{\odot}$)
is lower than that in the barred sample (1.01 x $10^{8}$ $M_{\odot}$), which
confirms the black hole mass dichotomy observed in our earlier results.

Figure 14: The distribution of black hole mass at z=0 of barred and unbarred
samples is obtained using the 2D KNN method by choosing the total galaxy mass
and surrounding gas density of the black hole host halo. Black/red vertical
lines correspond to the median value of the distribution. Figure 16:
Distribution of black hole mass at z=0 for barred (black histogram) and
unbarred (red histogram) galaxies without any merger event during their
evolution. Black/red vertical lines correspond to the corresponding median
values of the distribution.

####  3.2.2 Galaxies without major mergers

To disentangle the effect of galaxy mergers, we examined the black hole mass
distribution in individual subhalos hosting galaxy disks and constructed a
merger tree at the subhalo level using the SubLink algorithm (Rodriguez-Gomez
et al., 2015). By tracing the evolutionary history of these galaxies and
excluding those that have undergone major or minor mergers, we can better
understand the specific role of bars in black hole mass growth.

We define the major merger as an event for the parent galaxy (subhalo) when a
satellite galaxy of mass greater than 1/5 of the parent galaxy falls inside
the parent galaxy. In Fig. LABEL:fig:Mergers_barred, we present a scatter plot
showing the number of major mergers that barred galaxies in our sample have
experienced since their formation, plotted against their black hole masses at
z=0. Fig. LABEL:fig:Mergers_unbarred shows a similar scatter plot for unbarred
galaxies. We notice a tendency for the maximum black hole mass to rise as the
number of major mergers experienced by galaxies increases. However, it’s
important to note that this trend doesn’t hold true for galaxies with more
than six major mergers. We also notice from Fig. LABEL:fig:major_mergers that
none of the galaxies in our sample have more than eight major merger events
throughout their evolutionary history. Also, only a few galaxies have gone
through more than five mergers in our sample.

To investigate the role of bars in the growth of black holes, we specifically
selected galaxies that have not undergone any major merger events. This
resulted in 75 barred galaxies and 89 unbarred galaxies. In Fig. 16, we
present the distribution of black hole masses for this subset of galaxies. Our
findings reveal that even in galaxies that have not experienced any major
mergers throughout their evolutionary history, the distribution of black hole
masses in barred galaxies is higher than that in unbarred galaxies. This
suggests that the presence of a bar may enhance the growth of black holes,
strengthening the claim that bars play a significant role in the growth of
black holes in galaxies.

####  3.2.3 Galaxies with small number of minor mergers

Rosas-Guevara et al. (2020), noted that strongly barred galaxies tend to
experience a higher frequency of minor mergers compared to major merger
events. We define a minor merger event as one where the ratio of infalling
galaxies is between 1:10 to 1:100. In Fig. LABEL:fig:barred_minor, we present
a scatter plot showing the black hole masses of galaxies plotted against the
number of minor merger events they have undergone throughout their
evolutionary history. Our results indicate that the total number of minor
mergers is much higher than major mergers, and there is a clear correlation
between the number of minor merger events and the black hole mass of host
galaxies, similar to the trend observed for major mergers. The tendency for
black holes to exhibit greater mass in galaxies that have experienced a higher
frequency of mergers, including both minor and major mergers, can be
attributed to the fact that these galaxies have undergone more substantial
growth, resulting in the proportional growth of their black hole masses. Fig.
LABEL:fig:unbarred_minor shows the number of minor merger events for an
unbarred sample identical to the barred galaxies mentioned above. We can also
see a high frequency of minor merger events compared to major mergers and the
correlation of increasing black hole mass with an increase in minor merger
events. It is evident that a higher number of mergers signifies a more
advanced stage of galactic evolution, leading to an increase in mass.

To eliminate the effect of minor mergers on black hole growth, we only
consider barred and unbarred galaxies that have undergone less than five minor
mergers. The sample size becomes too small when we consider galaxies with no
minor mergers at all. Fig. 18 shows the distribution of black hole masses for
the selected barred and unbarred galaxies. We observe that the dichotomy in
black hole masses between barred and unbarred galaxies remains significant
even after controlling for the effect of minor mergers. This finding provides
further evidence to support the notion that bars play a significant role in
enhancing black hole growth by efficiently funneling gas toward the central
region of the galaxy.

Figure 18: The distribution of black hole masses at z=0 for barred (black
histogram) and unbarred (red histogram) galaxies that have not gone through
more than five minor mergers. Black/red vertical lines correspond to the
corresponding median values of the distribution.

###  3.3 The black hole mass dichotomy with weak and strong bars

We differentiated strongly and weakly barred galaxies based on the Fourier
mode strength cutoff in (Rosas-Guevara et al., 2020) and ellipticity in Zhao
et al. (2020) as explained in section 2.2. Our sample contains 836 strongly
barred galaxies and 357 weakly barred galaxies. To investigate the impact of
bars on black hole growth, we examined the distribution of black hole masses
separately for unbarred, weakly barred, and strongly barred galaxies. Fig. 19
displays the distribution of black hole masses at z=0 for each galaxy type.
The plot indicates that the peak of black hole mass distribution in weakly and
strongly barred galaxies is higher compared to unbarred galaxies. This is
possible if bars facilitate black hole mass growth in galaxies. Additionally,
Fig. 19 suggests that the growth of black holes in strongly barred galaxies is
comparable to that of weakly barred galaxies. This observation may suggest
that although strongly barred galaxies may have a greater availability of gas
being funneled towards their central regions, the strong feedback in these
galaxies may regulate black hole growth to a similar level as in weakly barred
galaxies.

Figure 19: Distributions of black hole mass at z=0 for unbarred (red
histogram), weakly barred (green histogram), and strongly barred (black
histogram) galaxies. Black/green/red vertical lines correspond to the
corresponding median values of the distribution.

###  3.4 Time evolution of bar strength and black hole mass

A potential concern in our current analysis is that barred galaxies are
selected based on their morphology at z=0. However, bars evolve along with
their host galaxy. They form, grow in length and strength, and weaken,
sometimes vanishing altogether, either definitively or temporarily. The
existence of a robust bar at z=0 does not conclusively indicate that the same
bar has persisted from its initial formation. Hence, it may not be correct to
seek a relationship between the final (z=0) black hole mass and the final
(z=0) status of the bar. It may be more appropriate to compare the
instantaneous black hole mass and the co-evolving bar strength. To address
this concern, we first identified the bar-forming epochs within a sub-sample
of galaxies in our dataset. This sub-sample is primarily drawn from the Rosas-
Guevara et al. (2020) study as the time-evolution of bar strengths is readily
accessible from this study. The sub-sample contains 107 and 139 galaxies,
which are barred and unbarred, respectively, at z=0. We then control the
unbarred galaxies by the total galaxy mass at the bar-forming epoch. We
identified a galaxy from the 139 unbarred galaxy sample with a similar total
galaxy mass at the bar-forming epoch for each barred galaxy. Following Rosas-
Guevara et al. (2020), we defined tnorm as the normalized time since the bar
formation time, i.e., tnorm = (tbar \- tlookback)/tbar where tbar is the bar
age (defined above) and tlookback the look-back time. tnorm = 0 corresponds to
tlookback = tbar, whereas tnorm = 1 corresponds to z = 0 (tlookback = 0). Fig.
20 shows the median of the black hole mass (solid lines) and bar strength
(dashed lines) evolution as a function of tnorm. It is clear from the figure
that once the bar forms, there is little evolution in its strength beyond
tnorm $\sim$ 0.2. It is encouraging to note that the bar strength never
crosses the threshold of 0.2 for unbarred galaxies. The difference between the
black hole mass between barred and unbarred galaxies was also maximum at tnorm
$\sim$ 0.2 when the bars grew to their full size. After that, the difference
between black hole masses decreases, possibly due to feedback effects
regulating black hole accretion in the already massive barred galaxies. It is
worth noting that this analysis solely draws upon 107 barred galaxies from the
Rosas-Guevara et al. (2020) sample, a significantly smaller subset compared to
our initial analysis.

While our analysis indicates a general trend of stability in bar strength over
time, it is important to note that individual cases may exhibit variations
influenced by factors such as mergers, flybys, and instabilities.

Figure 20: Time evolution of black hole mass and bar strengths in the barred
and unbarred galaxies with time. Solid and dashed lines corresponds to black
hole mass and bar strength respectively. Here tnorm=0 corresponds to bar
forming epoch and tnorm =1 corresponds to current epoch. Bar strength is
measured as the ratio of m=2 Fourier mode to m=0 Fourier mode of star
particles.

##  4 Discussion

Observational evidence of bar-AGN connection has been argued in various
studies where some studies show that barred galaxies preferentially host AGNs
(Laine et al., 2002; Oh et al., 2012; Galloway et al., 2015; Alonso et al.,
2018; Silva-Lima et al., 2022) while other studies claim no connection between
AGNs and barred host galaxies (Regan & Mulchaey, 1999; Cisternas et al., 2013;
Cheung et al., 2015b; Goulding et al., 2017b). In this study, we have looked
for bar-AGN connections in TNG100 disk galaxies. In previous sections, we
demonstrated that black hole masses of barred galaxies are consistently higher
than those of unbarred galaxies in the TNG100 simulations, even after
accounting for potential biases. This would suggest that the presence of a bar
in a galaxy could play a crucial role in facilitating black hole growth by
channeling gas to the central regions of the galaxy. In this section, we
discuss the implications of our results.

###  4.1 Difference in Black hole Seeding

One possibility for the origin of the black hole mass dichotomy observed in
barred and unbarred galaxies is that it arises from differences in the seeding
of black holes in these systems. In this scenario, barred galaxies may have
experienced earlier or more efficient black hole seed formation compared to
unbarred galaxies, resulting in larger black hole masses at later times.

As previously mentioned, black holes are seeded in massive halos with a mass
exceeding $7.8\times 10^{10}M_{\odot}$. To investigate the seeding time of
black holes in our analysis, we selected controlled barred and unbarred
samples with total galaxy mass as the control parameter and traced the
redshift evolution of black hole counts in these sample galaxies. Fig. 21
displays the black hole counts in the controlled barred and unbarred samples
from redshift 8 to the present epoch. The plot indicates that black holes in
barred galaxies were seeded earlier than those in unbarred galaxies. The
difference in black hole seeding between barred and unbarred galaxies is
prominent during the redshift range of 7 to 2. This finding suggests that the
halos in which bar-forming disks appeared were more massive and formed
earlier. This also explains why the disks of barred galaxies tend to be more
massive, as their respective dark matter halos formed earlier and had more
time to accrete gas than unbarred galaxies, as seen in Fig. 9(b). The question
immediately arises whether the early seeding of black holes in barred galaxies
leads to the observed dichotomy in black hole masses, given the extended
period of gas accretion in barred galaxies. To investigate this, we estimated
the maximum mass that can be accreted by the black hole due to early seeding
alone, from redshift z=7 to z=2.

Fig. 22 depicts the evolution of the mean accretion rate for the barred and
unbarred galaxy samples while controlling for the total galaxy mass. We
observe that the mean accretion rate for both samples increases around
redshift 4. The difference in the mean accretion rate between barred and
unbarred galaxies reaches its maximum value at around redshift 2, after which
the mean accretion rates for both samples begin to decrease. The number of
black holes triggered as a function of redshift shows that unbarred galaxies
lag behind barred galaxies. For instance, by redshift 6, a total of 200 black
holes are already triggered in barred galaxies, whereas in unbarred galaxies,
this happens around redshift 5. However, by redshift 2, the number of black
holes already triggered in barred and unbarred galaxies becomes similar.
Assuming that the difference in accretion rates between barred and unbarred
galaxies remains constant over time and equals the maximum difference observed
at z=2, multiplying the accretion rate difference by the time elapsed between
the time when the difference in black hole seeding is prominent (i.e.,
7>$z$>2) would give us the maximum possible mass difference between the two
samples. The difference between the mean accretion rate of black holes in
barred and unbarred galaxies ($\Delta\dot{M}_{BH}$) from z=7 to z=2 is given
by $10^{6}M_{\odot}/(.978Gyr)$. The maximum difference in black holes mass of
barred and unbarred samples which this early black hole seeding can lead is
given by:

$\Delta M_{BH}\leq\Delta\dot{M}_{BH}\times(t_{z=7}-t_{z=0})=1.4\times
10^{6}M_{\odot}$ (6)

Figure 21: Cumulative distribution of the number of black holes as a function
of redshift in the controlled sample of barred (black curve) and unbarred (red
curve) galaxies. The dashed/black vertical line shows the redshift when barred
and unbarred samples have an equal number of black holes.  Figure 22: The
figure shows the evolution of the mean accretion rate of controlled barred
(black curve) and unbarred (red curve) samples with redshift. The dashed
vertical line shows the redshift when the difference in mean accretion rate is
maximum between barred and unbarred samples. The dot-dashed vertical line
indicates the epoch when the mean accretion rate of black exceeds that in
unbarred galaxies compared to barred ones.  Figure 23: The figure shows the
distribution of the average accretion rate of the black holes between 2 $<$ z
$<$ 0 for the controlled barred (black histogram) and unbarred (red histogram)
samples. Black/red vertical lines correspond to the corresponding median
values of the distribution.

The calculated value of $\Delta M_{BH}$ resulting from the early seeding
effect is approximately one order of magnitude lower than the observed black
hole mass difference between barred and unbarred galaxy samples at z=0, which
is $4\times 10^{7}M_{\odot}$. It is worth noting that this calculation
represents an upper limit on the potential effect of early seeding. The actual
time required for unbarred galaxies to catch up with the number of black holes
in barred galaxies is much shorter. Therefore, we can conclude that early
seeding of black holes in the barred sample alone is unlikely to be solely
responsible for the observed dichotomy between barred and unbarred galaxies in
terms of black hole mass at the current epoch.

Figure 22 also shows that the mean accretion rate of barred galaxies falls
below that of unbarred galaxies at around z$\sim$ 0.2. This trend could be
interpreted as the result of more significant kinetic feedback in barred
galaxies. As discussed in section 2.1, for black holes with masses greater
than $10^{8.5}M_{\odot}$, kinetic feedback is the most effective feedback
mechanism, which imparts momentum to the surrounding gas, regulating the
accretion rate. The majority of the barred galaxy samples have black hole
masses greater than $10^{8.5}M_{\odot}$, whereas only a small fraction of
unbarred galaxies have black hole masses above this threshold, as evident from
Fig. 10. This suggests that the effects of kinetic feedback began to regulate
gas availability for accretion at around redshift 0.2.

###  4.2 Average accretion rates since bar forming epochs

Rosas-Guevara et al. (2020) shows that most of the bars in the disks have
formed around $z\approx 2$. We expect the bar to channel gas in the central
region and enhance the availability of gas in the black hole vicinity (Regan &
Teuben, 2004). To investigate the influence of bars on AGN fueling, we
calculated the average accretion rate of both the barred and unbarred samples
from the formation epoch of bars (z $\sim$ 2) to the present epoch.

Fig. 23 shows the average accretion rate of black holes in the barred and
unbarred samples from z=2 to the current epoch. The plot indicates that the
median value of the accretion rate is higher in barred galaxies than in
unbarred galaxies, with a difference between the two medians
($\Delta\dot{M}_{BH}$) of approximately $3\times 10^{6}M{\odot}/(.978Gyr)$. To
estimate the difference in black hole mass between the two samples, we
multiplied the average accretion rate difference with the elapsed time between
2$<$z$<$0.

$\Delta M_{BH}\approx\Delta\dot{M}_{BH}\times(t_{z=2}-t_{z=0})=4\times
10^{7}M_{\odot}$ (7)

Using the calculated difference in mean accretion rate, we estimated a mass
difference that can account for the observed discrepancy in black hole masses
between the barred and unbarred samples at the current epoch. This mass
difference is comparable to the observed difference in black hole masses
between the two samples (as shown in the right panel of Fig. 11(a)), providing
evidence that the presence of a bar enhances black hole growth by facilitating
gas inflow towards the central regions of a galaxy.

###  4.3 Stellar mass, bar formation and black hole growth

Stellar mass is known to be one of the key factors influencing the formation
and strength of bars in galaxies. Observational studies have shown that the
presence of a bar is more common in massive galaxies than in low-mass galaxies
(for e.g., Cheung et al., 2015a). Also, it has been observationally found that
the fraction of galaxies with bars increases with increasing stellar mass
(e.g., Masters et al., 2012). This trend is also supported by numerical
simulations. For example, simulations by (Athanassoula, 2003) show that bars
are more likely to form in galaxies with massive stellar disks. Zana et al.
(2022) conducted a detailed statistical analysis of the bar population in the
TNG50 simulation, affirming that the prevalence of bars is greater in galaxies
with higher masses. The prevalence of bars in massive galaxies can be
attributed to the fact that the formation of a bar requires a significant
concentration of gas and stars in the central region of a galaxy, which is
more likely to occur in massive galaxies due to their deeper potential wells.
In addition, massive galaxies tend to have more dynamically hot stellar disks,
which are less susceptible to fragmentation and, therefore, more likely to
form bars (Athanassoula, 2003). Additionally, Athanassoula et al. (2013);
Rosas-Guevara et al. (2020) found that the strength and longevity of bars
increase with the mass of the galaxy, with more massive galaxies producing
stronger and longer-lasting bars. One possible explanation for this
relationship is that massive disks are more stable to perturbations, which
allows bars to persist for longer periods. This increased stability arises
because the gravitational potential of a massive disk can absorb the energy of
perturbations more effectively, preventing them from disrupting the bar.
Therefore, there is ample evidence to suggest that stellar mass plays a
critical role in bar formation in galaxies (Fujii et al., 2018). More massive
galaxies tend to have larger, more stable disks that are better suited to
supporting long-lived bars (Bland-Hawthorn et al., 2023).

In our analysis of comparing the black hole masses of barred and unbarred
TNG100 galaxies at z=0, a clear dichotomy is observed in black hole mass
distribution, with the barred galaxies exhibiting higher black hole masses.
Despite controlling the samples with various parameters such as galaxy mass
and gas mass, the dichotomy in the black hole mass distribution between barred
and unbarred galaxies persisted. However, the previously observed dichotomy
disappeared after controlling the samples with the total stellar mass
parameter. This result suggests that the total stellar mass may be a potential
driver for the observed dichotomy in the black hole mass distribution.

It is possible that galaxy mergers play a major role in the formation and
evolution of bars in galaxies. The gravitational interaction and tidal forces
from a galaxy merger can transfer angular momentum to the gas and stars in the
disk, forming bars. Numerical simulations have shown that both major and minor
mergers can lead to bar formation by perturbing the disk and producing non-
axisymmetric features like bars and spirals (Hernquist & Mihos, 1995; Cavanagh
& Bekki, 2020). However, some studies suggest that bars can form and persist
without the need for a merger (Debattista & Sellwood, 1998; Athanassoula,
2003). Furthermore, the studies by Zana et al. (2018a, b) indicate that
external gravitational interactions, such as mergers or flybys, have the
potential to impede the evolutionary process of bars within galaxies. The
exact role of mergers in bar formation and evolution is still a topic of
active research (Ghosh et al., 2021). If galaxy mergers were the reason for
bar formation, it is possible that the same merger events can channel the gas
toward the center enabling black hole growth. If this is the case, the
relationship between bars and black hole mass observed in our analysis may be
indirect and instead be due to the effect of mergers on both bar formation and
black hole growth. To investigate the role of mergers on black hole mass
growth, we constructed a sample of barred and unbarred galaxies that have no
major mergers / a small number of minor mergers. We find that even in this
case, the black hole mass dichotomy exists between barred and unbarred
galaxies. This suggests that while mergers may play a role in bar formation
and subsequent black hole growth, they are not the sole driving factor for the
observed connection between bars and black hole mass.

Bars can transfer the angular momentum within the disk of the galaxy and
channel the gas towards the central regions, where it can fuel star formation
or accrete onto a central supermassive black hole. Observationally, it has
been shown that barred galaxies have a larger molecular gas density in the
central regions compared to unbarred galaxies (Sakamoto et al., 1999).
However, for accretion onto black holes to occur, the gas must be transported
to within a few parsecs of the galaxy center, which is closer than the typical
location of the Inner Lindblad Resonance of the bar. Additional mechanisms
like oscillations of gas flow orbits or bars within bars are invoked to drive
further inflow and feed the AGN (Shlosman et al., 1989). Many double-barred
galaxies have been found through observations. For e.g., Erwin (2004)
presented a catalog of 67 double-barred galaxies. Around one-third of barred
galaxies are found to host a short inner bar of radius $<$1 kpc (Erwin &
Sparke, 2002; Laine et al., 2002; Erwin, 2004). Furthermore, just like the
secondary bars, nuclear instabilities like rings and spirals are also thought
to facilitate black hole fueling. However, it is possible that the gas
transported by bars is consumed in star formation before it can reach the
black hole, thereby limiting the effectiveness of bars in fueling black hole
growth. The relative importance of these processes may depend on various
factors, such as the gas content and dynamics of the host galaxy. Using the
TNG100 simulations, Rosas-Guevara et al. (2020) found that strongly barred
galaxies have a significantly higher median black hole mass compared to
unbarred galaxies, with this difference becoming more pronounced shortly after
the epoch of bar formation. While the mean accretion rate of barred galaxies
decreases significantly after the formation of the bar, primarily due to the
impact of AGN feedback, their analysis clearly suggests that bars have played
a crucial role in facilitating the feeding of black holes in these galaxies,
as well as enhancing central star formation.

Overall, the connection between stellar mass, bar formation, and black hole
growth is complex and multifaceted, with various mechanisms at play, such as
gas inflows due to bars, mergers, secular processes, and feedback effects.
Nevertheless, our analysis in this study indicates that bars can play a
crucial role in feeding black holes, particularly in galaxies with massive
stellar disks.

##  5 Conclusions

In this article, we analyzed the black hole mass distribution in barred and
unbarred galaxies using the TNG100 magneto-hydrodynamic cosmological suite of
simulations. We examined 1193 barred and 2738 unbarred galaxy samples while
controlling for various parameters. Our main findings are listed below:

  * •

There is a clear dichotomy in the distribution of black hole masses in barred
and unbarred galaxies. The median black hole mass of the unbarred sample is
higher than that of unbarred ones, and the difference between median black
hole mass $\Delta M_{BH}\approx 4\times 10^{7}M_{\odot}$.

  * •

We removed any underlying bias in our analysis by creating control samples
with various parameters like total galaxy mass, total stellar mass, total gas
mass, stellar-to-halo mass ratio, gas-to-stellar mass ratio, and total
baryonic mass. Except for the controlling with total stellar mass, we found
that the black hole mass dichotomy is reproduced in all other cases.
Therefore, we conclude that stellar mass is the primary driver of the black
hole mass dichotomy between barred and unbarred galaxies at the current epoch.
This can be attributed to the fact that bars require massive stellar disks for
their formation, and black hole fuelling is more efficient when the bars are
stronger.

  * •

We disentangled the effect of galaxy mergers on black hole growth by removing
galaxies with any major/minor mergers from our analysis. The results of this
analysis also show a higher mean black hole mass for barred galaxies compared
to unbarred galaxies, which further strengthens the role of bars in fueling
black hole activity.

  * •

The seeding of black holes occurs earlier in barred samples compared to the
unbarred sample, in agreement with the earlier studies that bars are formed in
massive galaxies. However, this early seeding effect can only lead to a
maximum black hole mass difference of $3\times 10^{6}M_{\odot}$, much lower
than the observed black hole dichotomy between barred and unbarred samples at
the current epoch.

  * •

The high mean black hole mass in barred galaxies compared to unbarred ones is
explained ($\Delta M_{BH}\approx 4\times 10^{7}M_{\odot}$) with the higher
mean accretion rate from bar forming epoch redshift z$\approx$2 to z=0.

  * •

Therefore, we suggest a potential association between AGN activity and the
presence of a bar within the host galaxy.

Future simulations with higher resolution and improved physical modeling can
provide a more detailed understanding of the physical mechanisms responsible
for the connection between bars and AGN activity, ultimately leading to a more
comprehensive understanding of the co-evolution of black holes and their host
galaxies.

## Acknowledgements

The Authors would like to thank the Referee for the helpful suggestions that
improved the quality of the manuscript. MV acknowledges support from DST-SERB
in the form of core research grant (CRG/2020/1657). The IllustrisTNG
simulations were undertaken with compute time awarded by the Gauss Centre for
Supercomputing (GCS) under GCS Large-Scale Projects GCS-ILLU and GCS-DWAR on
the GCS share of the supercomputer Hazel Hen at the High Performance Computing
Center Stuttgart (HLRS), as well as on the machines of the Max Planck
Computing and Data Facility (MPCDF) in Garching, Germany. The authors thank
all the members of the IllustrisTNG team for making the simulation data
public.

## Data Availability

The data is publicly available on IllustrisTNG website as provided by
IllustrisTNG team. https://www.tng-project.org/data/

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