#  Revealing Gas Inflows towards the Galactic Central Molecular Zone

Yang Su Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China  Shiyu
Zhang  Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China, 96
Jinzhai Road, Hefei 230026, China  Yan Sun  Purple Mountain Observatory and
Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua
Road, Nanjing 210023, China  Ji Yang  Purple Mountain Observatory and Key
Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road,
Nanjing 210023, China  School of Astronomy and Space Science, University of
Science and Technology of China, 96 Jinzhai Road, Hefei 230026, China  Qing-
Zeng Yan  Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China  Shaobo
Zhang  Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China  Zhiwei
Chen  Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China  Xuepeng
Chen  Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China, 96
Jinzhai Road, Hefei 230026, China  Xin Zhou  Purple Mountain Observatory and
Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua
Road, Nanjing 210023, China  Lixia Yuan  Purple Mountain Observatory and Key
Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road,
Nanjing 210023, China

###### Abstract

We study the gas inflows towards the Galactic Central Molecular Zone (CMZ)
based on the gas morphological and kinematic features from the MWISP in the
region of $l=1\fdg 2-19\fdg 0$ and $|b|\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}3\fdg 0$. We find that the near dust lane appears to extend to
$l\sim 15^{\circ}$, in which the end of the large-scale gas structure
intersects with the 3 kpc-ring at a distance of $\sim 5$ kpc. Intriguingly,
many filamentary MCs, together with the bow-like/ballistic-like clouds and
continuous CO features with notable velocity gradient, are finely outlined
along the long structure. These MCs also have relatively large velocity
dispersions, indicating the shocked gas generated by local continuous
accretion and thus the enhanced turbulence along the entire gas structure. We
suggest that the $\sim$3.1–3.6 kpc long CO structure originates from the
accretion molecular gas driven by the Galactic bar. The gas near the bar end
at the 3 kpc-ring region becomes an important reservoir for the large-scale
accreting flows inwards to the CMZ through the bar channel. The inclination
angle of the bar is estimated to be $\phi_{\rm bar}=23^{\circ}\pm 3^{\circ}$,
while the pattern speed of the bar is $\Omega_{\rm bar}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}32.5\pm 2.5\ \,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$. The total
mass of the whole near gas lane is about 1.3$\pm 0.4\times 10^{7}\ M_{\odot}$
according to the calculated $X_{\rm CO}\sim 1.0\pm 0.4\times 10^{20}$ cm-2(K
km s${}^{-1})^{-1}$ from the large-scale 12CO and 13CO data and the
complementary H i data. We revisit the gas inflow rate as a mean value of
1.1$\pm 0.3\ M_{\odot}$ yr-1, which seems to be comparable to the outflow’s
rate of the Galactic nuclear winds after applying the updated lower X-factor
above.

Interstellar medium (847); Molecular clouds (1072); Galaxy kinematics (602);
Milky Way Galaxy (1054); Galaxy structure (622); Milky Way dynamics (1051);
Galactic winds (572);

##  1 Introduction

Galaxies are giant and delicate ecosystems in which material flows in and out.
As the closest galaxy to us, the Milky Way becomes a unique laboratory for
exploring the physical details of the baryon cycle. Benefiting from large-
scale surveys in multi-wavelength, many exciting discoveries have been made in
observational and theoretical studies. One of the most important findings is
the revelation of the existence of the Fermi bubbles (FBs, i.e., Su et al.,
2010) that are directly related to the Galactic nuclear winds (e.g., Sofue &
Handa, 1984; Bland-Hawthorn & Cohen, 2003; Dobler et al., 2010; Heywood et
al., 2019; Ponti et al., 2019, 2021; Predehl et al., 2020; Sarkar, 2024). The
FBs, together with the combined features in multi-wavelengths and multiple
spatial scales, are believed to be associated with past energetic events
(e.g., nuclear activities and intense processes of massive star formation)
near the Galactic Center (GC).

The cold atomic and molecular gas related to the Galactic nuclear winds has
attracted even more attention very recently due to the cold gaseous substances
found in the FBs from the large-scale H i and CO studies (e.g., Lockman &
McClure-Griffiths, 2016; Di Teodoro et al., 2018; Lockman et al., 2020; Di
Teodoro et al., 2020; Noon et al., 2023; Veena et al., 2023). Using the CO
data, we also find that the Galactic nuclear winds have a significant impact
on the Galactic gaseous disk, leading to the material accumulation at the
3-kpc crater-walls (Su et al., 2022) and the gas deficiency in the region of
0.3 kpc$\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}R_{\rm GC}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}$ 3.1 kpc (here $R_{\rm GC}$ is the Galactocentric distance, e.g.,
Burton, 1976; Dickey & Lockman, 1990; Dame et al., 2001; Kalberla & Kerp,
2009; Su et al., 2021). The mass-loading rate of the outflows related to the
Galactic nuclear winds is estimated to be $\sim 2-4\ M_{\odot}$ yr-1 (Su et
al., 2022). Considering additional warm and hot gas in the FBs (Miller &
Bregman, 2016; Krishnarao et al., 2020; Predehl et al., 2020; Zhang & Guo,
2021), the actual mass-loading rate of the Galactic nuclear winds may be even
higher than what is inferred from the cold atomic and molecular gas alone.

On the other hand, there is substantial molecular gas hosting in the region of
$R_{\rm GC}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}$ 300 pc (i.e., the Central Molecular Zone, CMZ). The total
molecular gas in the CMZ is estimated to be 2–6$\times 10^{7}\ M_{\odot}$
(e.g., see Dahmen et al., 1998; Ferrière et al., 2007), corresponding to 3–10%
of all molecular gas in the Galaxy. The origin of the CMZ is probably related
to the episodic accumulation of the gas inflows driven by the gravitational
field of the Galactic rotating bar (see the comprehensive review in Henshaw et
al., 2023). That is, the molecular gas supply along the dust lanes accretion
(or the bar channel) may account for the large amount of material accumulation
in the CMZ. The gas inflow rate onto the CMZ is estimated to be about 0.4–2.7
$M_{\odot}$ yr-1 at a dynamical timescale of tens of Myr (Crocker, 2012;
Armillotta et al., 2019; Sormani & Barnes, 2019; Tress et al., 2020;
Hatchfield et al., 2021).

The above studies show that there seems to be an overall balance between mass
inflow and outflow for the inner 3 kpc region of the Milky Way in the current
period if we ignore the low star formation rate of $\sim$0.1 $M_{\odot}$ yr-1
(Bryant & Krabbe, 2021) in the CMZ. However, the estimations of the mass
inflow and mass outflow rates are model-dependent and are somewhat uncertain.
Therefore, an in-depth and full study of the physical processes of the
accretion gas flowing inward to the CMZ is important for understanding the gas
cycle in the Milky Way. Especially, the comparisons between spatial and
kinematic features in observations and dedicated simulations are fundamental
and crucial in revealing new details and constraining model parameters.

In the letter, we focus on the large-scale inflows of molecular gas towards
the CMZ based on the $l$-$b$-$v$ CO data from the MWISP survey. We describe
the CO and H i data in Section 2. In Section 3, we investigate the
distribution and kinematics of molecular gas along the near dust lane on a
high dynamic range and at $\sim$ 1–2 pc physical resolution (i.e., adopting
$R_{0}$=8.15 kpc from Reid et al., 2019), which is about two orders of
magnitude better than that of the GMCs in nearby galaxies (e.g., Schinnerer &
Leroy, 2024). Our new data clearly show that a large amount of gas is flowing
inwards and bringing the gas to the CMZ. We construct a toy model to
quantitatively delineate the gas kinematics and give a schematic diagram to
explain the CO observations. We discuss the connection between the gas inflow
driven by the Galactic bar and outflow from the Galactic nuclear winds in a
whole picture. Finally, we summarize the new findings and results in Section
4.

##  2 CO and H i data

The CO dataset studied here is from the Milky Way Imaging Scroll Painting
(i.e., the MWISP project, see details in Su et al., 2019). In short, the MWISP
CO data are observed in a region of $l=1\fdg 2-19\fdg 0$ and $|b|\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}3\fdg 0$, which fully covers the molecular gas in the near dust lane
with a spatial and spectral resolutions of $\sim 50^{\prime\prime}$ and $\sim$
0.2 $\,{\rm km}\,{\rm s}^{-1}$, respectively. After cleaning the data, the
reduced 3D cubes (i.e., the position-position-velocity space, hereafter PPV)
with a grid spacing of 30′′ have a typical root mean square (rms) noise level
of  $<$$\sim$ 0.5 K for 12CO and  $<$$\sim$ 0.3 K for 13CO/C18O, respectively.

In this work, the H i data from the all-sky H i survey (Kalberla et al., 2005;
HI4PI Collaboration et al., 2016) are used for large-scale comparisons with
the MWISP CO data. The angular and velocity resolutions of the H i data are
16$\farcm$2 and 1.5 $\,{\rm km}\,{\rm s}^{-1}$, respectively. The typical RMS
sensitivity of the HI4PI data is $\sim$43 mK.

##  3 Results and Discussions

###  3.1 Molecular Gas Flowing towards the CMZ along the Near Dust Lane

Thanks to many spectroscopic data from large surveys (e..g, Dame et al., 2001;
Kalberla et al., 2005; Riquelme et al., 2010b; Jones et al., 2012; HI4PI
Collaboration et al., 2016; McClure-Griffiths & Dickey, 2016; Tokuyama et al.,
2019; Eden et al., 2020; Ginsburg et al., 2020; Schuller et al., 2021) and
many excellent research efforts on the Milky Way, significant progress has
been made in the study of the properties and motion of gas in and around the
Galactic CMZ in the last two decades (e.g., Rodriguez-Fernandez et al., 2006;
Liszt, 2006, 2008; Ferrière et al., 2007; Dame & Thaddeus, 2008; Rodriguez-
Fernandez & Combes, 2008; Riquelme et al., 2010a; Molinari et al., 2011;
Sormani & Magorrian, 2015; Henshaw et al., 2016; Riquelme et al., 2018;
Sormani et al., 2019; Akhter et al., 2021; Busch et al., 2022; Gramze et al.,
2023). On the other hand, a lot of numerical simulations have done a good job
of describing the distribution and evolution of gas in the CMZ and even the
Milky Way (e.g., Fux, 1999; Li et al., 2016, 2022; Sormani et al., 2015, 2018;
Tress et al., 2020; Hatchfield et al., 2021).

Combining observations and theories, we know that the gravitational potential
plays a dominant role in determining the motion of the stars and gas in our
Galaxy (see, e.g., Englmaier & Gerhard, 1999; McKee et al., 2015; Bland-
Hawthorn & Gerhard, 2016). Towards the $R_{\rm{GC}}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}$3 kpc region, the Galactic bar with a non-axisymmetric structure is
particularly important to transport matter from the Galactic disc to the CMZ
and then to the GC (see the recent reviews of Bland-Hawthorn & Gerhard, 2016;
Henshaw et al., 2023; Schinnerer & Leroy, 2024).

However, it is difficult to carefully characterize the structure,
distribution, and motion of the gas flows towards the CMZ by observation
because of our embedded view through the whole Galactic plane. The MWISP CO
survey, which has a large-scale and high-sensitivity triple CO isotope line
data, provides an excellent opportunity for us to delve into the distribution
and kinematics of the molecular gas flowing towards the CMZ.

Figure 1 shows the 12CO $l$-$v$ map in the range of [$l=1\fdg 2$ to $4\fdg 0$,
$-3\fdg 0\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}b\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}+1\fdg 0$] and [$l=4\fdg 0$ to $19\fdg 0$, $-3\fdg 0\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}b\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}-0\fdg 2$] and the total integrated emission from the MWISP data.
The elongated gas structure, which is sketched by the cyan color for the CO
emission and the cyan contours for the corresponding H i emission in the
bottom panel of Figure 1, is perfectly delineated along the near dust lane in
$l\sim[1\fdg 2,10\fdg 3]$ and $v_{\rm{LSR}}\sim[100\,{\rm km}\,{\rm
s}^{-1},280\,{\rm km}\,{\rm s}^{-1}]$. Indeed, the dust lanes (or the
connecting arms) are believed to directly associate with the Galactic bar
(Fux, 1999; Liszt, 2006, 2008; Rodriguez-Fernandez et al., 2006; Marshall et
al., 2008; Sormani & Barnes, 2019).

The major part of the large-scale gas structure lies slightly below the
Galactic plane with a mean value of $b\approx-0\fdg 7$ (or $\sim-70$ pc below
the plane, see Section 3.2.2). This striking feature, together with the
considerable velocity dispersion and velocity gradient of these coherent
clouds, is why we are able to figure this large-scale gas structure out of the
complicated CO emission in the inner Galaxy relatively easily.

Remarkably, the MWISP data clearly reveal many gas structures associated with
the near dust lane, for example, the arc-like and bow-like MCs (Figure 2a), as
well as the ballistic-like CO structure with a length of  $>$$\sim$ 800 pc
(Figure 2b). The moving gas scenario towards the Galactic CMZ is further
supported by the detection of the shocked gas structures with a sharp edge
towards the GC and the increasing velocity and certain velocity gradient along
the dust lane.

That is, the gas is moving away from the observer and is approaching the CMZ
with considerable acceleration along the Galactic bar, leading to the special
CO morphologies (e.g., arc-like, bow-like, and ballistic structures in Figure
2) and the prominent kinematic features (e.g., the very wide CO line
broadening or the large velocity dispersion, and the continuous gas
distribution with a certain velocity gradient shown in Figure 1). These
results provide an excellent indication that the molecular gas flow is heading
towards the CMZ region in the Galactic bar potential. Based on the filamentary
CO structures towards the intersection region (i.e., Sgr E) between the far
dust lane and the CMZ, Wallace et al. (2022) recently proposed a similar
scenario that the gas is being stretched and accelerated by the bar potential
while falling towards the CMZ.

In addition to the above evidence of the gas flows towards the CMZ, some signs
show that the large-scale CO structure has extended to $l\sim 15^{\circ}$ in
the end of the CO lane and is probably accreting the gas near the 3 kpc-ring
(i.e., refer to the 3 kpc arm in Dame & Thaddeus, 2008). We have compiled the
observational evidence below.

1\. Several CO structures at $l\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}10^{\circ}$ are found to be connected in the $l$-$v$ map, indicating
the presence of a large-scale spatially continuous gas structure associated
with the known near dust lane with a similar velocity gradient. These CO
structures often display prominent filamentary morphology along the Galactic
longitude at negative latitude (Figure 2c), which is exactly the same as the
distribution of the known near dust lane in $l\sim 1\fdg 2$ to $10\fdg 3$.
These CO structures, together with many cometary-like and arc-shaped features,
have a relatively large velocity dispersion, showing the enhanced turbulence
(or surrounding shock process) in the whole region;

2\. In fact, some MCs with relatively large CO line dispersion exhibit long-
shell and large arc structures in $l\sim[11^{\circ},15^{\circ}],b\sim[-1\fdg
5,-0\fdg 3],v_{\rm{LSR}}\sim[70\,{\rm km}\,{\rm s}^{-1},130\,{\rm km}\,{\rm
s}^{-1}]$, as well as many bullet CO features embedded in these structures
(see green and red colors for CO emission and the cyan contours for H i
emission in Figure 2c). These $l$-$b$-$v$ features can be interpreted as the
bar-spiral intersection at the low gravitational potential of the bar end,
leading to the accumulation of a large amount of trapped gas with different
velocity in the low shear region.

3\. We find that the large-scale CO structure appears to converge with the
near 3 kpc-ring at $l\sim 15^{\circ}$ and $v_{\rm{LSR}}$ of tens of kilometers
per second, probably indicating a connection between them. Remarkably, a maser
G015.66-00.49 (at a parallax of 0.22$\pm 0.029$ mas and $v_{\rm{LSR}}=-4\,{\rm
km}\,{\rm s}^{-1}$, Reid et al., 2019) is found to be associated with the
elongated MCs (see the purple rectangle in Figure 2c) near the end of the
large-scale CO structure, suggesting a distance of $\sim 5$ kpc for the bar-
spiral intersection region.

According to the above points, we suggest that the large-scale CO structure
(or the whole gas lane, hereafter WGL) extends to $l\sim 15^{\circ}$ and
$b\sim-0\fdg 5$, connecting and accreting gas in the vicinity of the 3 kpc-
ring at a distance of $\sim 5$ kpc, and then transporting material inward
along the bar channel. Meanwhile, in the region where the gravitational
potential of the bar is large, the moving gas is dominated by the Galactic bar
to form the strong compression shock (Figure 2a) and even the bound radial gas
flow (Figure 2b) into the CMZ. The observational evidences related to the
moving gas are also manifested in the prevalent shock structures with the
bright head towards the CMZ (see panels a and b in Figure 2), as well as the
velocity gradient along the WGL revealed by the MWISP large-scale CO
observation (see Figure 1). Based on high-quality MWISP data, we have fully
revealed these new observational details for the first time, supporting the
physical scenario of bar-driven gas inflows from the 3 kpc-ring to the CMZ.

We identified more than 800 MC structures with angular size larger than 2.25
arcmin2 (9 pixels) related to the WGL based on Gaussian decomposition and
clustering algorithm (see details in Henshaw et al., 2019; Riener et al.,
2019; Zhang et al., 2024b). Here, the smoothing parameters of $\alpha$1=1.8
and $\alpha$2=5.4 were used for the Gaussian fitting for the 12CO data with
the 3D grid of $0.5^{\prime}\times 0.5^{\prime}\times 0.5\,{\rm km}\,{\rm
s}^{-1}$. We have marked 64 large MC structures (angular size $>50\
{\rm{arcmin}}^{2}$) on the upper panel of Figure 1. The typical excitation
temperature of the gas is $\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}8\pm 1$ K (assuming the beam filling factor  $<$$\sim$ 1 for these
distant MCs at about 5–8 kpc) according to the peak emission of the 64 large
12CO structures. More than 70% of samples in the 64 MCs have a relatively
small 13CO-to-12CO intensity ratio (i.e., $I(^{13}$CO)/$I(^{12}$CO)$\sim$0.1),
which is roughly half the value of the normal MCs in the Galactic plane
($\sim$0.2 in previous studies, see e.g., Tokuyama et al., 2019; Wang et al.,
2023). We also find that the closer the MCs in the WGL are to the GC, the
greater the velocity dispersion they have. A detailed comparison of the MC’s
properties within the $R_{\rm{GC}}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}3$ kpc region will be shown elsewhere.

###  3.2 Parameters of Moving Gas towards the CMZ

The features of the compressed and shocked molecular gas are well delineated
by the CO data, both along the body of the WGL and at the end of the WGL (or
the bar-spiral intersection region). Figure 3 shows a schematic view of the
observation results. In the diagram, we show that considerable gas is flowing
towards the GC, forming the WGL connecting the 3 kpc-ring and the CMZ. Here,
the gaseous disk at $R_{\rm GC}\sim$3 kpc and the area around it becomes the
main gas reservoir for the large-scale accreting flows inwards to the CMZ.

The morphological and kinematic CO features of the WGL can be approximately
explained by the gas rotation at a certain pattern speed driven by the
Galactic bar potential. In this way, the moving gas driven by the rotation bar
(e.g., Athanassoula, 1992; Fux, 1999; Sormani & Barnes, 2019) can be roughly
described by

$v_{\scriptscriptstyle{//}}=\frac{v_{\rm{LOS}}-(\Omega_{\rm{bar}}-\Omega_{\rm{Sun}})\times{\rm{sin}}(l)}{{\rm{cos}}(\phi_{\rm{bar}}+l)}$
(1)

Here, $v_{\scriptscriptstyle{//}}$ is the gas velocity towards the CMZ region
along the bar (i.e.,
$\vec{v}=\vec{v}_{\scriptscriptstyle{//}}+\vec{v}_{\rm{rot}}$ in the inertial
frame of the Galaxy) and $v_{\rm{LOS}}$ is the measured LOS velocity of the
moving gas. $l$, $\phi_{\rm{bar}}$ are the longitude of the MC in the dust
lane and the Sun-Galactic centre angle, respectively. $\Omega_{\rm{bar}}$,
$\Omega_{\rm{Sun}}$ are rotation speed of the bar and the Sun (e.g.,
$\Omega_{\rm{Sun}}=30.32\pm 0.27\,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$ in
Reid et al., 2019). We discuss these parameters in the following sections
based on the observed large-scale CO features associated with the WGL.

####  3.2.1 Angle between LOS of the Galactic Centre and Bar Major Axis,
$\phi_{\rm bar}$

The inclination angle of the bar ($\phi_{\rm bar}$) with respect to the Sun’s
position is critical in the analysis of gas dynamics and gas structure
characteristics related to the WGL. We have shown that the WGL extends up to
about $l=15^{\circ}$. Interestingly, we find that maser G015.66-00.49 at a
parallax of 0.22$\pm 0.029$ mas and $v_{\rm{LSR}}=-4\,{\rm km}\,{\rm s}^{-1}$
(Reid et al., 2019) is associated with the MC G15.365-0.541 at
$v_{\rm{LSR}}=-0.87\,{\rm km}\,{\rm s}^{-1}$. The MC G15.365-0.541, together
with the nearby CO gas, displays a filamentary structure extended along the
Galactic plane from $l=14\fdg 6$ to $l=15\fdg 7$ (see the CO gas in the purple
rectangle in Figure 2c). Assuming that the elongated structure at a distance
of $\sim 4.9$ kpc (i.e., between the median and the upper limit of the maser
distance) is located close to the end of the WGL, the length of the WGL is
estimated to be $\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}3.6$ kpc, which is slightly larger than the radius of the 3 kpc-ring
(e.g., the Galactocentric distance of the 3 kpc-ring, $R_{\rm ring}\sim$3.1
kpc, see details and Figures 2 and 3 in Su et al., 2021) but reasonable.
Indeed, the estimated length of the WGL here agrees well with the bar’s length
of $\approx$3.5–3.6 kpc from very recent observations (e.g., Lucey et al.,
2023; Vislosky et al., 2024).

The value of $\phi_{\rm bar}$ is thus $\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}20^{\circ}$ by considering the WGL has the longest length of 3.6 kpc
at $l\sim 15^{\circ}$. This result agrees with the CO observation that the WGL
cannot continue to maintain a positive inflow velocity at the point of $l\sim
15^{\circ}$ (i.e., the gas should have $v_{\rm{LSR}}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}0\,{\rm km}\,{\rm s}^{-1}$ at $l\sim 15^{\circ}$ for
$v_{\scriptscriptstyle{//}}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}0\,{\rm km}\,{\rm s}^{-1}$, see Section 3.2.3). Given the deficiency
of atomic and molecular gas within the 3 kpc-ring (e.g., Burton, 1976; Dame et
al., 2001; Su et al., 2022), on the other hand, it is reasonable to define a
minimum length of the WGL of  $>$$\sim$ 3.1 kpc. Given the uncertainties of
the length of $R_{\rm bar}\approx$3.1–3.6 kpc and the distance to the bar end
of $\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}4.9$–5.2 kpc, the estimation of $\phi_{\rm bar}$ is in the range
$20^{\circ}$–$26^{\circ}$.

The value of $\phi_{\rm bar}$ from our estimation is in good agreement with
the previous estimates of $20^{\circ}$–$30^{\circ}$ (e.g., Wegg & Gerhard,
2013; Wegg et al., 2015; Bland-Hawthorn & Gerhard, 2016; Simion et al., 2017;
Shen & Zheng, 2020). Below we use the value of $\phi_{\rm bar}=23^{\circ}\pm
3^{\circ}$ as an input for the derivation of other parameters.

####  3.2.2 Tilted Angle between the Bar and the $b=0^{\circ}$ Plane,
$\theta_{\rm bar}$

Additionally, since the latitude values of the bar traced by the WGL can be
well presented by the CO distribution, the tilt angle of the bar relative to
the $b=0^{\circ}$ plane can be roughly estimated by $\theta_{\rm
bar}={\rm{tan}}^{-1}({\rm{sin}}(\phi_{\rm bar}){\rm{tan}}(b)/{\rm{sin}}(l))$.
The tilt angle is thus $\sim-2\fdg 6\pm 0\fdg 3$ at $l\sim 1\fdg 7$,
$\sim-4\fdg 7\pm 0\fdg 6$ at $l\sim 5\fdg 2$, $\sim-2\fdg 1\pm 0\fdg 3$ at
$l\sim 10\fdg 7$, and $\sim-0\fdg 8\pm 0\fdg 1$ at $l\sim 15\fdg 2$. These
results (also refer to Tress et al., 2020) indicate that the WGL is mainly
located below the Galactic plane at a typical scale of 30–130 pc. The typical
values of the gas lane clouds deviated from the $b=0^{\circ}$ plane are
comparable to or $\sim$3.5 times larger than the standard deviation of the
vertical distribution of the CO clouds in the inner Galactic molecular disk
(e.g., Su et al., 2021).

The total gas mass of the WGL is obviously concentrated below the Galactic
plane, which is the exact opposite of the far dust lane at $l\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}-1^{\circ}$(e.g., Liszt, 2006; Marshall et al., 2008; Sormani &
Barnes, 2019; Akhter et al., 2021). Naturally, the twisted $\infty$ gas
feature in the CMZ (Molinari et al., 2011) appears to be related to the tilted
inflow structures, which may represent the transfer of angular momentum from
the gas reservoir at kpc scales to the GC region at tens of pc scales in the
accretion-driven torques. Moreover, the asymmetric features of the FBs are
probably related to tilted nuclear outflows, which are directly associated
with the tilted gas inflows at various scales from $\sim$kpc to $\sim$pc.

####  3.2.3 Pattern Speed of the Galactic Bar, $\Omega_{\rm bar}$

As an essential parameter for characterizing the bar dynamics, the bar pattern
speed, $\Omega_{\rm bar}$, can be measured from observations. We have shown
that the molecular gas driven by the Galactic bar has an LOS velocity of $\sim
0$ $\,{\rm km}\,{\rm s}^{-1}$ at $l_{\rm max}\approx 15^{\circ}$. This result
can be used to constrain $\Omega_{\rm bar}$. That is, the radial velocities of
the gas should be somewhat greater than $\sim 0$ $\,{\rm km}\,{\rm s}^{-1}$,
i.e., $v_{\scriptscriptstyle{//}}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}0\,{\rm km}\,{\rm s}^{-1}$ near the bar end position or the bar-
spiral intersection region, considering that the material is flowing inward
the CMZ region along the bar channel.

We estimate that the $\Omega_{\rm bar}$ is less than $\sim 30-35\,{\rm
km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$, taking into account possible fluctuations
in the observed LOS velocity of $\sim 0$–$10\,{\rm km}\,{\rm s}^{-1}$ for MCs
close to the region of the WGL end. We find that the estimated $\Omega_{\rm
bar}$ here agrees well with $35-40\,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$
from the recent studies (e.g., Sanders et al., 2019; Shen & Zheng, 2020;
Lucchini et al., 2024; Zhang et al., 2024a). Especially, our estimation is
exactly the same as $\Omega_{\rm bar}=33.29\pm 1.81\,{\rm km}\,{\rm
s}^{-1}\,{\rm kpc}^{-1}$ from the VVV Infrared Astrometric Catalogue and Gaia
DR2 data (Clarke & Gerhard, 2022). This may imply that the WGL is well coupled
with the stellar bar, and the results tend to favor the slow bar scenario in
the current period. The corotation radius, $R_{\rm CR}$, can be approximated
as 5.4–6.3 kpc based on the slower bar model (e.g., see Hilmi et al., 2020).

It should be noted that the movement and evolution of the Galactic bar is
closely related to the gravitational potential distribution and the bar’s
dynamics. At the same time, the bar interacts with the adjacent material,
leading to pattern fluctuations between the bar itself and its surrounding
constituents. Due to the highly dynamical process, the pattern speed of the
Galactic bar may vary over time in one or several rotation periods of the bar
(e.g., $\sim$200 Myr to several Gyr). Indeed, the current slowing rate of the
bar has been well constrained recently (e.g., $-4.5\pm 1.4\ \,{\rm km}\,{\rm
s}^{-1}\,{\rm kpc}^{-1}$ Gyr-1 in Chiba et al., 2021). Finally, other factors
may affect our estimate of $\Omega_{\rm bar}$, for example, some viscous or
turbulent processes associated with the gas driven by the rotation bar.
However, further in-depth analysis of these effects is beyond the scope of
this article. We only use the estimated value of $\Omega_{\rm bar}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}32.5\pm 2.5\,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$ for the
following discussions.

###  3.3 Mass Inflow Rate into the CMZ

Having determined the parameters of $\phi_{\rm bar}$ and $\Omega_{\rm bar}$,
we can infer the process of the gas transport towards the CMZ region along the
bar. The cyan color and cyan contours in Figure 1 display the CO and H i
distribution of the WGL along the bar. The dominant material in the WGL is
molecular gas, and its total mass can be determined from the 12CO emission by
using the CO-to-H2 conversion factor method. We find that the value of $X_{\rm
CO}$ near the GC is probably very different for the MCs in other regions
(e.g., Dahmen et al., 1998; Ferrière et al., 2007; Bolatto et al., 2013; Heyer
& Dame, 2015; Gramze et al., 2023; Kohno & Sofue, 2024a).

We use 12CO and 13CO lines to derive $X_{\rm CO}$ for MCs of the WGL in the
local thermal equilibrium (LTE) method (see, e.g., Su et al., 2015). The area
we focus on is between the region near the 3 kpc-ring and the CMZ region, and
the estimated $X_{\rm CO}$ is about $\sim 1.0\pm 0.4\times 10^{20}$ cm-2(K km
s${}^{-1})^{-1}$ from 17 largest MC samples (angular size $>250\
{\rm{arcmin}}^{2}$) in the WGL assuming $N({{\rm{H}}_{2}})\approx 7\pm 3\times
10^{5}\times N({{}^{13}{\rm{CO}}})$. Here, we find that the conversion factor
from $N({{}^{13}}{\rm{CO}})$ to $N({{\rm{H}}_{2}})$ is between the value at
the $R_{\rm{GC}}\sim$3 kpc region (i.e., $\sim 4\times 10^{5}$ from Frerking
et al., 1982; Milam et al., 2005) and that at the CMZ region (i.e., $\sim
5-10\times 10^{5}$ from Lis & Goldsmith, 1989; Riquelme et al., 2010a, 2018).

The typical value of the $X_{\rm CO}$ for the WGL is $1.0\pm 0.4\times
10^{20}$ cm-2(K km s${}^{-1})^{-1}$, which is very close to
$\sim(0.5-1.0)\times 10^{20}$(K km s${}^{-1})^{-1}$ for the $|l|\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}10^{\circ}$ region from other methods (e.g., see details in
Schultheis et al., 2014). The lower $X_{\rm CO}$ here is consistent with the
lower $I(^{13}$CO)/$I(^{12}$CO) ratio for the inflowing gas presented in
Section 3.1. For the purpose of studying comparison with other work, we
tentatively use the updated value of $X_{\rm CO}=1.0\times 10^{20}$ cm-2(K km
s${}^{-1})^{-1}$ (about 0.5 times the often used value, e.g., see Dame et al.,
2001; Strong et al., 2004; Bolatto et al., 2013; Kohno & Sofue, 2024b) to
estimate the total molecular mass of the WGL.

The molecular gas mass in the WGL is thus 1.1$\pm 0.4\times 10^{7}\ M_{\odot}$
and the velocity gradient along the bar is about 80–90 $\,{\rm km}\,{\rm
s}^{-1}\,{\rm kpc}^{-1}$. In total, the gas mass is about 1.3$\pm 0.4\times
10^{7}\ M_{\odot}$ by counting the additional atomic gas of about 0.2$\times
10^{7}\ M_{\odot}$ for the H i emission associated with the WGL (see the
emission near the black ellipses in the upper panel of Figure 1 and the cyan
contours in the bottom panel of Figure 1). Interestingly, the molecular gas
masses per unit length of the large-scale flows ($\sim 3\times 10^{6}\
M_{\odot}\,{\rm kpc}^{-1}$) is roughly comparable to that of the 3-kpc arm by
adopting the same X-factor value here (see Dame & Thaddeus, 2008). And this
feature can be interpreted by the abundant gas dragged by a rotating bar,
which is shown on the mirror situation for the near 3-kpc structure with
enhanced CO at positive longitude and the far 3-kpc CO at negative longitude
(see Figure 14 in Reid et al., 2016). This symmetrical gas structure is more
common in the barred galaxies (e.g., see Stuber et al., 2023).

Assuming that the far dust lane at $l\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}-1^{\circ}$ is approximately symmetrical with the WGL at
$l\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$>$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}+1^{\circ}$, the average mass inflow rate is thus about 1.1$\pm 0.3\
M_{\odot}$ yr-1 in a typical transport period of $\sim$24 Myr for gas from the
bar end to the CMZ. Here we do not consider the impact of the overshooting
effect (e.g., Sormani & Barnes, 2019), because we do not account for the
amount of overshooting gas re-accreting into the near dust lane from the far-
side lane either (i.e., the CO gas towards us with a relatively small LSR
velocity and the positive longitude, also see Gramze et al., 2023). The
overshot gas may actually re-accrete and flow into the CMZ within several Myr
(Hatchfield et al., 2021), which is about an order of magnitude smaller than
the typical transport period. Taking into account the compensation for the
overshooting gas back from the far dust lane (e.g., refer to the extended
trajectory of red lines of Figure 15 in Wallace et al., 2022), our estimate
does not, in principle, significantly overestimate the overall inflow rate
from the gaseous disk to the region near the CMZ.

The overall distribution of the WGL shows that the current mass transport is
relatively continuous, suggesting that the gas in the CMZ can accumulate
rapidly over a period of several tens of Myr. However, the gas inflows rate to
the CMZ seems to be comparable to the outflows rate (e.g., $\sim 1.5\pm 0.5\
M_{\odot}$ yr-1, see details in Su et al., 2022) driven by the Galactic
nuclear winds after applying the updated lower X-factor above. The general
equilibrium between the outflow and the inflow rate likely indicates that the
accumulation of gas in the CMZ may take a relatively longer time of hundreds
Myr to several Gyr. Our results agree well with the discussion in Henshaw et
al. (2023).

Moreover, the gas distribution along the bar has obvious characteristics of
heterogeneity and clumping, leading to large variations in the instantaneous
inflow rate and subsequent the accumulation of a large amount of materials in
a small region. This process has a significant impact on the star formation
process and star formation rate in the local region. For example, (Anderson et
al., 2020) suggested that Sgr E formed upstream in the far dust lane of the
Galactic bar a few Myr ago, which may be related to the rapid accumulation of
gas in a small region and the successive emergence of star groups therein.
Generally, the gas cycle on the long timescale dominates the large-scale
structural features of the Galaxy as a whole, while the episodic processes,
such as the local individual characteristics of gas flows and the following
stellar/AGN feedbacks, may significantly regulate the dynamics and spatial
distribution of the gas at parsec to hundreds of parsecs scales.

##  4 Summary

By using the MWISP CO data in the region of $l=1\fdg 2-19\fdg 0$ and
$|b|\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}3\fdg 0$, we take a closer look at the gas flowing towards the
Galactic CMZ. The new findings and results are summarized as follows.

1\. The MCs with arc-like and ballistic structures are well delineated along
the near dust lane in the region $l=[1\fdg 2,10\fdg 3]$ and $b=[0\fdg 0,-2\fdg
1$]. The moving and shocked MCs towards the CMZ are further confirmed by the
corresponding wide CO broadening and the large-scale velocity gradient, as
well as the continuous gas structure assembled by a series of bow-like and
bright-edged MCs heading towards the GC.

2\. In addition to the well-known near dust lane at $l\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}10^{\circ}$, more filamentary MCs up to $l\sim 15^{\circ}$ are found
to be the extension of the near dust lane structure in the $l$-$b$-$v$ space.
In $l\sim 10^{\circ}$–$15^{\circ}$, these elongated MCs, together with
cometary-like and long-shell gas structures, also have a relatively large CO
line broadening or velocity gradient. These features are very similar to those
MCs in the near dust lane at $l\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}10^{\circ}$.

3\. The enhanced turbulence of the gas, together with the certain velocity
gradient of the long structure, may originate from large-scale continuous gas
flows with the uniform pattern of motion. In fact, the leading edge of the
radial bar shock is well outlined by these interesting MCs with sharp edge
and/or head-to-tail ballistics towards the GC, as well as many bullet-shaped
MC structures embedded in the shock front.

4\. The large-scale CO gas forms the WGL structure that connects the CMZ and
the 3 kpc-ring. The morphological and kinematic CO features of the WGL provide
robust evidence that a very large amount of molecular gas is moving towards
the CMZ from the 3 kpc-ring. We propose that the large-scale gas structure
well represents radial flows towards the CMZ and the tilted gas flow with
considerable acceleration is driven by the Galactic bar.

5\. The WGL intersected to the $R_{\rm GC}\sim$3.1–3.6 kpc region are
accreting the surrounding material therein and transporting gas towards the
CMZ. The inclination angle and the rotation speed of the WGL are $\phi_{\rm
bar}=23^{\circ}\pm 3^{\circ}$ and $\Omega_{\rm bar}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}32.5\pm 2.5\,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$, respectively.
The result indicates that the large-scale CO structure seems to be coupled
with the stellar bar of our Milky Way. The WGL is below the Galactic plane
with a typical scale of 30–130 pc.

6\. The total gas mass of the WGL is 1.3$\pm 0.4\times 10^{7}\ M_{\odot}$ by
adopting the $X_{\rm CO}=1.0\pm 0.4\times 10^{20}$ cm-2(K km s${}^{-1})^{-1}$
calculated from the MWISP 12CO and 13CO data and the additional H i gas. The
estimated lower $X_{\rm CO}$ agrees with the observational fact of lower
$I(^{13}$CO)/$I(^{12}$CO) ratio for the MCs in the WGL. The velocity gradient
along the bar is about 80–90 $\,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$,
indicating the typical transport period of $\sim$24 Myr for the gas inflows
from the bar end or the bar-spiral intersection region to the CMZ.

7\. The average mass inflow rate towards the Galactic CMZ is thus estimated to
be about 1.1$\pm 0.3$ $M_{\odot}$ yr-1 by considering the roughly symmetrical
inflow structure of the WGL at the positive longitude and the far dust lane at
the negative longitude. If we use the updated lower X-factor above for the
outflow gas, the value of the gas inflow rate seems to be roughly comparable
to the outflow’s rate of $\sim 1.5\pm 0.5\ M_{\odot}$ yr-1 for the Galactic
nuclear winds.

This research made use of the data from the Milky Way Imaging Scroll Painting
(MWISP) project, which is a multi-line survey in 12CO/13CO/C18O along the
northern galactic plane with the PMO-13.7m telescope. We are grateful to all
the members of the MWISP working group, particularly the staff members at the
PMO-13.7m telescope, for their long-term support. MWISP was sponsored by
National Key R&D Program of China with grants 2023YFA1608000 & 2017YFA0402701
and by CAS Key Research Program of Frontier Sciences with grant QYZDJ-SSW-
SLH047. We also acknowledge supports from National Natural Science Foundation
of China through grants 12173090 and 12041305. We are very grateful to the
reviewer for the helpful and constructive comments that have largely improved
this work. The work makes use of publicly released data from the HI4PI survey
which combines the EBHIS in the Northern hemisphere with the GASS in the
Southern hemisphere. The Parkes Radio Telescope is part of the Australia
Telescope National Facility which is funded by the Australian Government for
operation as a National Facility managed by CSIRO. The EBHIS data are based on
observations performed with the 100-m telescope of the MPIfR at Effelsberg.
EBHIS was funded by the Deutsche Forschungsgemeinschaft (DFG) under the grants
KE757/7-1 to 7-3. This publication makes use of data products from the Wide-
field Infrared Survey Explorer, which is a joint project of the University of
California, Los Angeles, and the Jet Propulsion Laboratory/California
Institute of Technology, funded by the National Aeronautics and Space
Administration. PMO 13.7m

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Figure 1:  The upper panel shows the $l$-$v$ diagram of MWISP 12CO emission in
the region [$l=1\fdg 2$ to $4\fdg 0$, $b\leq 1\fdg 0$] and [$l=4\fdg 0$ to
$19\fdg 0$, $b\leq-0\fdg 2$], while the bottom panel displays the integrated
12CO emission of the entire $l$-$b$-$v$ region, overlaid with the gas
associated with the whole near dust lane (see Section 3.1). Note that the gas
inflows of the large-scale gas structure towards the CMZ is highlighted by the
cyan part for the CO emission from the dust lane (i.e., $I(\rm{CO})/100$) and
the cyan contours for the corresponding H i emission scaled by
$I({\rm{\mbox{H\,{i}}}})\times{\rm{tan}}(b)$. The black ellipses in the upper
panel represent the 64 large MC structures (i.e., angular size $>50\
{\rm{arcmin}}^{2}$, and 2$R_{\rm{MC}}\times v_{\rm{FWHM}}$ for the ellipse
size, here $R_{\rm{MC}}$ is the effective radius and $v_{\rm{FWHM}}$ the mean
full width at half-maximum) related to the whole near dust lane, as well as
the red rectangles in the bottom panel for the interesting regions shown in
Figure 2.

Figure 2:  Integrated 12CO emission of three interesting MC structures of the
large-scale CO inflows towards the CMZ. Panel (a) shows the arc-like MCs with
a sharp edge towards the CMZ in the velocity interval of [192, 202] $\,{\rm
km}\,{\rm s}^{-1}$ (blue), [203, 216] $\,{\rm km}\,{\rm s}^{-1}$ (green), and
[222, 237] $\,{\rm km}\,{\rm s}^{-1}$ (red). Panel (b) shows the long
ballistic-like MCs with the bright head towards the CMZ in the velocity
interval of [245, 255] $\,{\rm km}\,{\rm s}^{-1}$ (blue), [256, 264] $\,{\rm
km}\,{\rm s}^{-1}$ (green), and [265, 290] $\,{\rm km}\,{\rm s}^{-1}$ (red).
Panel (c) shows the MCs located near the end of the CO flows in the velocity
interval of [$-31$, 7] $\,{\rm km}\,{\rm s}^{-1}$ (blue), [65, 105] $\,{\rm
km}\,{\rm s}^{-1}$ (green), and [110, 130] $\,{\rm km}\,{\rm s}^{-1}$ (red).
The purple circle and the rectangle represent the maser G015.66$-$00.49 and
the $\sim 0-7\,{\rm km}\,{\rm s}^{-1}$ filamentary MCs located at the bar end,
respectively. The cyan contours are the same as those in Figure 1 for the
corresponding H i emission related to the WGL. Note that the blue color in the
panel (c) roughly traces the near-3 kpc-ring emission (see Dame & Thaddeus,
2008) or the lateral arm indicated in Figure 3.

Figure 3:  Schematic representation of the WGL and the lateral arm based on
the morphological and kinematic features from the MWISP CO data. In the
diagram, the red shaded blocks represent the MCs flowing towards the CMZ,
while the blue shaded blocks show the MCs along the near 3 kpc ring (or the
lateral arm dragged by the rotation bar). The end of the WGL intersects with
the 3 kpc-ring structure at a distance of about 5 kpc. The bar plays an
extremely important role in driving flows and transporting the reservoir gas
at $R_{\rm GC}\sim$3–4 kpc to the CMZ. The red ring represents the CMZ, while
the red dots, red stars, and red triangles represent the Sun, the GC, and the
bar end, respectively. The direction of the moving gas and the Sun is labeled
by the black arrows. Here, the longitude of the near bar end, $l$, is measured
to be about $15^{\circ}$. The inclination angle and the pattern speed of the
bar are estimated to be $\phi_{\rm bar}=23^{\circ}\pm 3^{\circ}$ and
$\Omega_{\rm bar}\mbox{\hskip
1.99997pt\raisebox{2.15277pt}{$<$}\raisebox{-2.15277pt}{$\sim$}\hskip
1.99997pt}32.5\pm 2.5\,{\rm km}\,{\rm s}^{-1}\,{\rm kpc}^{-1}$ (see text),
respectively.