2020 Vol. 20 No. XX, 000–000

11institutetext: Department of Astronomy, School of Physics and Astronomy,
Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;
email<EMAIL_ADDRESS>
22institutetext: Shanghai Key Laboratory for Particle Physics and Cosmology,
Shanghai 200240, China
33institutetext: Department of Astronomy, Nanjing University, Nanjing 210093,
China<EMAIL_ADDRESS>
Received 2020 September 16; accepted 2020 XXX

# The Bar and Spiral Arms in the Milky Way: Structure and Kinematics

Juntai Shen 1122 Xing-Wu Zheng 33

###### Abstract

The Milky Way is a spiral galaxy with the Schechter characteristic luminosity
$L_{*}$, thus an important anchor point of the Hubble sequence of all spiral
galaxies. Yet the true appearance of the Milky Way has remained elusive for
centuries. We review the current best understanding of the structure and
kinematics of our home galaxy, and present an updated scientifically accurate
visualization of the Milky Way structure with almost all components of the
spiral arms, along with the COBE image in the solar perspective. The Milky Way
contains a strong bar, four major spiral arms, and an additional arm segment
(the Local arm) that may be longer than previously thought. The Galactic boxy
bulge that we observe is mostly the peanut-shaped central bar viewed nearly
end-on with a bar angle of $\sim 25-30^{\circ}$ from the Sun-Galactic center
line. The bar transitions smoothly from a central peanut-shaped structure to
an extended thin part that ends around $R\sim 5\;{\rm kpc}$. The Galactic
bulge/bar contains $\sim 30-40\%$ of the total stellar mass in the Galaxy.
Dynamical modelling of both the stellar and gas kinematics yields a bar
pattern rotation speed of $\sim 35-40\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$,
corresponding to a bar rotation period of $\sim 160-180$ Myr. From a galaxy
formation point of view, our Milky Way is probably a pure-disk galaxy with
little room for a significant merger-made, “classical” spheroidal bulge, and
we give a number of reasons why this is the case.

###### keywords:

Galaxy: structure; Galaxy: bulge; Galaxy: kinematics and dynamics; galaxies:
spiral; galaxies: structure

##  1 Introduction

What the Milky Way looks like has long been a mystery. There are three main
reasons why this problem has been unsolved for so long. One is that most of
the visible stars lie in the Galactic thin disk. Our solar system lies nearly
in the mid-plane of that disk, far from the center of the Milky Way, and from
our vantage point we cannot distinguish structures in the Milky Way because of
projection effects. The difficult situation that astronomers face is best
illustrated by a famous Chinese classic poem by Su Dongpo in the Song dynasty:
“I don’t see the true face of Mountain Lushan because I myself am on the
mountain”. Secondly, thick dust clouds block optical light from distant stars
in the disk of the Milky Way. Thirdly, most stars are very distant. The stars
in the closest major arm of the Milky Way, the Sagittarius-Carina arm, are
about 1400 pc from us. As a result, we may never take a real optical picture
of the Milky Way, so instead we create models based on measuring distances to
objects that trace Galactic structure. A successful Galactic model must also
explain the motions of gas and stars in the gravitational potential of the
Milky Way. The challenge is to synthesize all the direct and indirect
information to weave a complete picture of the Milky Way.

The most prominent features of the visible part of the Milky Way are the
Galactic bar and spiral arms. This review focuses mainly on the structure and
kinematics of the Galactic bar/bulge and spiral arms, on which the famous
Hubble classification scheme of spiral galaxies is based. Only with accurate
information of Galactic bar/bulge and spiral arms can we pinpoint the exact
location of the Milky Way in the Hubble sequence of spiral galaxies.

For nearly a hundred years, the story of building a picture of the Milky Way
has been the story of finding good tracers of spiral structure and credible
methods of measuring their distances. The global spiral structure of the
Galaxy first became apparent through study of the 21-cm line of neutral
hydrogen. Oort et al. (1958) produced a map using the intensity and Doppler
shift of the 21-cm line to extract kinematic distances under the assumption
that hydrogen clouds are in pure circular rotation about the Galactic center.
This map showed long arcs of gas that resembled the spiral features in optical
images of external galaxies. By using kinematic and spectrophotometric methods
to determine the distances of young OB stars and giant HII regions, Georgelin
& Georgelin (1976) constructed a picture of the Milky Way with four spiral
arms. In the 2010s Lumsden et al. (2013) used their Red MSX Source survey to
map the structure of the Milky Way using about 1650 massive young stellar
objects (MYSOs) and HII regions. Their model of the Milky Way (Urquhart et al.
2014; Cabrera-Lavers et al. 2007) also had four spiral arms. However, they did
not delineate arm locations accurately because of the dispersion of MYSO
properties. By counting the near-infrared and mid-infrared stars near the
tangent point from the Spitzer/GLIMPSE (Galactic Legacy Mid-Plane Survey
Extraordinaire) and COBE/DIRBE/ZSMA surveys of the Galactic plane, Benjamin et
al. (2005) and Drimmel (2000) reported that the Milky Way has only two major
stellar arms, the Perseus arm and the Scutum-Centaurus arm. Using a combined
tracer sample of Galactic HII regions, GMCs, and 6.7 GHz methanol masers, Hou
& Han (2014) outlined the spiral structure and found that models of three-arm
and four-arm logarithmic spirals are able to connect most spiral tracers (also
Hou et al. 2009).

Such disagreements about the spiral structure of the Milky Way might be
explained by the different tracers and different approaches used to determine
their distances by different researchers. Kinematic and spectrophotometric
methods to determine the distances of MYSOs and giant HII regions suffer
considerable uncertainties because of inadequacies in the velocity-to-distance
and luminosity-to-distance relationships (Burton et al. 1992). Total star
counts may not allow good mapping of the spiral arms in the Milky Way, where
there might be different contents of evolved stars and gas.

Accurate distance measurement is crucial in resolving the disagreements among
different groups. Trigonometric parallax provides the most reliable distance
determination for a stellar object, and has revolutionized the field in the
last twenty years. It is a completely geometric method, independent of any
assumptions or astrophysical models. Interstellar masers, such as those of
water vapor ($\mathrm{H}_{2}O$) and methanol ($\mathrm{C}H_{3}OH$), are the
most important signposts to high-mass star-forming regions (HMSFRs) along the
spiral arms in the Milky Way. The microwave emission from such masers
penetrates the dust and gas in the disk of the Galaxy and can be very bright,
so that they can be detected over the entire Milky Way. Masers are very
compact objects within complexes of size 20-30 pc (Reid & Moran 1981) and are
ideal for precise parallax measurements. The Bar and Spiral Structure Legacy
(BeSSeL) survey aims to determine accurate distances of HMSFRs in the bar and
spiral arms of the Milky Way by measuring the trigonometric parallaxes of the
methanol and water masers with which they are associated. The spiral structure
with unprecedented accuracy revealed by the BeSSeL survey is summarized in §
3.

Compared to the spiral arms, little was known about the structure of the Milky
Way bar until relatively recently since the central bar is still much further
away from the Sun than the nearby spiral arms. Before the 1990s the Milky Way
was once considered as an unbarred galaxy to most of the astronomical
community. The widely-held but erroneous belief that the Milky Way is unbarred
puzzled many theorists since dynamically “cold” galactic disks were known to
be violently unstable to large-scale instabilities that can result in a strong
bar. Intriguingly, based on the unbarred “fact” of the Milky Way Ostriker &
Peebles (1973) deduced that there must be a significant amount of dark mass
hidden in the Galactic halo in order to keep the Milky Way stable from forming
a bar, well before a dark matter halo was firmly inferred from flat rotation
curves of many nearby galaxies.

The first hint of a bar structure in the Milky Way was the substantial
departures from circular motions of HI gas in the central parts of the Galaxy.
The Leiden astronomers (Oort & Rougoor 1959; Rougoor & Oort 1960) explained
the observed HI gas in the “forbidden regions” of the longitude-velocity
($l-v$) diagram as an “expanding arm” or “expanding ring” from the center. de
Vaucouleurs (1964) correctly interpreted these observations as the non-
circular gas kinematics induced by a central bar. Binney et al. (1991)
demonstrated convincingly that many important central gas features on the
$l-v$ diagram can be explained with the main orbital families in a barred
galaxy. Nowadays the non-circular gas features in the $l-v$ diagram are
interpreted through more sophisticated gas dynamical models, thus providing
important constraints on the properties of both the bar and spiral arms (see §
2.4.2 for more details).

Figure 1: Top: the conceptual picture of the Milky Way with its bar, four
major spiral arms, a subsidiary Local arm, and 3-kpc arms. This artistic
visualization also contains various important components such as gas, dust,
molecular clouds and filaments, HII regions, young OB stars, and young star
clusters. The Sun is marked with a circled red dot in the Local arm. The bar
angle between the bar major axis and the Sun-Galactic center line is around
$25-30^{\circ}$. The Galactic rotation is in the clock-wise direction.
(Credit: Xing-Wu Zheng & Mark Reid BeSSeL/NJU/CFA). Bottom: the Milky Way seen
in the infrared band by Diffuse InfraRed Background Experiment (DIRBE) on
board NASA’s COBE satellite (left-right flipped from the original image to be
more consistent with the face-on picture).

The near-infrared images from NASA’s COBE satellite revealed clearly that the
Milky Way contains an asymmetric parallelogram-shaped boxy bulge in the center
(Weiland et al. 1994, also Figure 1). The asymmetry may be explained by a
tilted bar; the near end of the bar is closer to us than the far side,
consequently it appears to be bigger and taller than the other side (Blitz &
Spergel 1991). Although the structural parameters and orientation of the
Galactic bar, mapped with various stellar tracers, are still being actively
updated (see § 2.1 for more details), the existence of a bar in the Milky Way
has been firmly established since COBE. In § 2.2 we review the properties of
the intriguing “X-shaped structure” in the Galactic bar/bulge discovered about
ten years ago. We discuss briefly in § 2.3 the result of dynamical models of
the Milky Way bar. The measurement of the Galactic bar pattern rotation speed
using stellar and gas kinematic data is reviewed in § 2.4.

The structural components of the Galactic bulge/bar also have to be understood
in the context of the chemical composition and the age of the bulge stars,
which contain key information constraining the formation history of the Milky
Way. Bulge stars have a broad metallicity distribution (McWilliam & Rich 1994;
Zoccali et al. 2008) and are $\alpha$-enhanced. The bulk of bulge stellar
population is as old as $\sim 10$ Gyr (e.g., Ortolani et al. 1995; Lecureur et
al. 2007; Clarkson et al. 2008; Valenti et al. 2013; Hasselquist et al. 2020),
including some of the oldest stars in the Milky Way (e.g. Howes et al. 2014;
Schlaufman & Casey 2014). So most bulge stars must have experienced a rapid,
early formation, yet it becomes unambiguous that they are part of the boxy
bulge/bar from star counts (see § 2.1) and dynamical models. In § 2.3 we also
review the (chemo-)dynamical models of the Galactic bulge/bar attempting to
link its main dynamical and chemical properties.

Figure 1 shows an artistic impression of the majestic Milky Way structure
viewed face-on, along with the infrared observation by COBE as viewed from our
own solar perspective. The Milky Way probably has a strong peanut-shaped bar
with two pairs of spiral arms and a subsidiary Local arm (see § 3). Its Hubble
type may be somewhere between SBb and SBc types.

##  2 The Galactic Bar

The study of the Galactic bar/bulge has progressed enormously in the last ten
years thanks to many large surveys and sophisticated (chemo-)dynamical tools
striving to model these large datasets. We summarize the main results to date
on the structure and kinematics of the Galactic bar. Other extensive reviews
of the Galactic bar/bulge can be found in Rich (2013); Gonzalez & Gadotti
(2016); Bland-Hawthorn & Gerhard (2016); Barbuy et al. (2018).

###  2.1 Basic Structural Properties

The Milky Way contains an asymmetric box-shaped bulge (Maihara et al. 1978;
Weiland et al. 1994; Dwek et al. 1995). The connection of this boxy structure
with an edge-on bar is strong; the COBE infrared image in Figure 1 shows a
parallelogram-shaped distortion that is naturally explained by a bar as a
perspective effect: the near end of the bar (positive longitude $l$) is closer
to us than the far end (negative longitude $l$). Consequently the vertical
extent of the bulge is greater on the near side than on the far side (Blitz &
Spergel 1991). The case became even more compelling when Shen et al. (2010)
built a simple $N$-body model of the Galaxy that self-consistently develops a
bar. Not only their thickened bar, as seen from the Sun, resembles the boxy
bulge of our Galaxy, the model also matches the BRAVA (Rich et al. 2007)
stellar kinematic data covering the whole bulge strikingly well with no need
for a classical bulge made in prior mergers. Thus it is quite likely that the
bulk of the bulge is simply an edge-on triaxial bar (more details in § 2.3).

As in external barred galaxies, the Galactic bar consists predominantly of
stars instead of gas or dust. Thus the structural properties of this triaxial
bar/bulge can be directly determined more precisely from observations if one
can find a good standard candle to trace the bar. As of now the best tracer to
study the structure of the Galactic bulge is red clump giants (RCGs). RCGs are
Helium-core burning stars, and are the metal-rich equivalent of the horizontal
branch stars. RCGs have a narrow range of absolute magnitudes and colors with
weak metallicity dependence (e.g. Zhao et al. 2001; Salaris & Girardi 2002),
thus can be used as a good distance indicator. They are also abundant enough
and sufficiently bright to be seen out to the Galactic bulge, thus well-suited
to investigate the structural properties of the bulge. From the magnitude
distribution of the RCGs one can derive line-of-sight densities and combine
many line-of-sight density measurements to get the full three-dimensional
density distribution of the bulge.

Using 0.7 million RCGs from the Optical Gravitational Lensing Experiment
(OGLE) project, Stanek et al. (1997) modelled the Galactic bar by fitting the
observed luminosity functions in the red clump region of the color-magnitude
diagram. Their models have a bar angle of $20^{\circ}-30^{\circ}$ (defined as
the angle between the bar major axis and the Sun-Galactic center line), with
axis ratios corresponding to $x_{0}:y_{0}:z_{0}=1.00:0.43:0.29$ ($x_{0},y_{0}$
are the semi-major, semi-minor bar axis scalelengths in the Galactic plane,
respectively, and $z_{0}$ is the vertical bar scalelength). Cao et al. (2013)
updated the bar structural parameters with nearly 3 million stars in OGLE III
survey. They found a nearly prolate bar with an axial ratio of
$x_{0}:y_{0}:z_{0}\approx 1.00:0.43:0.40$ with $x_{0}=0.67\;{\rm kpc}$. Their
bar angle is $29\pm 2^{\circ}$, slightly larger than the value obtained from a
similar study based on OGLE-II data (Rattenbury et al. 2007).

The Vista Variables in the Via Lactea (VVV) survey (Saito et al. 2012) offers
a unique opportunity to study the Galactic bulge. The depth of VVV exceeds
that of Two Micron All Sky Survey (2MASS) by $\sim 4$ mag, allowing the
detection of the entire RCG population in most of the bulge region except the
most highly extinct and crowded regions ($|b|<1^{\circ}$). With nearly 8
million RCGs from VVV, Wegg & Gerhard (2013) measured the three-dimensional
density distribution of the Galactic bulge covering the inner $(\pm
2.2\times\pm 1.4\times\pm 1.1)\;{\rm kpc}$. Their measurement is non-
parametric with an assumption that the three-dimensional bulge is eightfold
mirror triaxially symmetric. They found a bar angle of $27\pm 2^{\circ}$. The
resulting density distribution shows a highly elongated bar with face-on
projected axis ratios $\approx(1:2.1)$ at $\sim 2\;{\rm kpc}$ along the bar
major axis. The density falls off roughly in an exponential manner along the
bar axes, with axis ratios $(1.00:0.63:0.26)$ and exponential scalelengths
$(0.70:0.44:0.18)\;{\rm kpc}$. The axial ratio varies with radius as the true
shape of the bar deviates from an ellipsoid to become peanut-shaped (see §
2.2).

Unlike Wegg & Gerhard (2013), Simion et al. (2017) adopted a parametric
approach to model the RCGs in VVV with an analytic function that describes the
full 3D bulge density distribution summed to a background population
consisting of the thin and thick disks, generated with Galaxia (Sharma et al.
2011). For the bulge density distribution they tested an exponential-type
model, a hyperbolic secant density distribution and a combination of the two.
The best-fit parametric model of the bulge density is exponential with an axis
ratio of $(1.00:0.44:0.31)$ and provides a good fit with a median percentage
residual of 5% over the fitted region. Describing the stellar distribution in
the bulge with an analytic function clearly gives a more portable solution
which can be straightforwardly used in other bar/bulge dynamical modeling.
They found that there exists a strong degeneracy between the bar angle and the
dispersion of the RCG absolute magnitude distribution. Simion et al. (2017)
found the bar angle to be at least $20^{\circ}$, which is, however, strongly
dependent on the assumptions made about the intrinsic luminosity function of
the bulge. Shen et al. (2010) also provided some constraints on the bar angle.
They found that their best model tends to prefer a bar angle of $\sim
20^{\circ}-30^{\circ}$ to match the velocity profiles and the photometric
asymmetry. This angle agrees reasonably well with the other independent
studies.

Figure 2: The Galactic boxy bulge and long bar reconstructed by combining
various NIR surveys. Top: the inner Galaxy in solar perspective. Middle: Face-
on projection of best-fitting RCG star count model. Bottom: side-on view of
the bar/bulge along the intermediate axis. Adapted from Wegg et al. (2015).

Based on stars counts from the Spitzer/GLIMPSE survey, Benjamin et al. (2005)
argued for another planar long bar passing through the GC with half-length 4.4
kpc tilted by $\sim 45^{\circ}$ from the Sun-GC line (dubbed as the “long
bar”), which seems misaligned with the boxy bulge bar (see also Cabrera-Lavers
et al. 2007). If the large misalignment were real, then the co-existence of
the long bar with the similarly-sized bulge bar is dynamically puzzling as
their mutual torque tends to align the two bars on a short timescale, unless
their size ratio is extreme ($0.1\sim 0.2$) as in some double-barred galaxies
(Erwin & Sparke 2002; Debattista & Shen 2007; Shen & Debattista 2009). Wegg et
al. (2015) investigated in greater detail the Galactic long bar outside the
bulge, using a larger and more uniform RCG combined sample from United Kingdom
Infrared Deep Sky Survey (UKIDSS), 2MASS, VVV, and GLIMPSE surveys. They found
that the long bar extends to $l\sim 25^{\circ}$ at $|b|\sim 5^{\circ}$ and to
$l\sim 30^{\circ}$ at lower latitudes. The bar angle of the long bar is about
$29.5^{\circ}$, nearly aligned with the boxy bulge/bar at $|l|<10^{\circ}$.
The best model in Wegg et al. (2015) at various projections is shown in Figure
2. The scale height of RCG stars smoothly transitions from the boxy bulge to
the thinner long bar, indicating that the boxy bulge and the thin long bar may
be different components of the same coherent bar structure as seen in
simulations (e.g., Athanassoula 2005; Martinez-Valpuesta & Gerhard 2011; Li &
Shen 2015) and in some external galaxies. There seem two scale heights in the
long bar: a 180 pc thin bar component and a 45 pc “superthin” bar components
which exist predominantly towards the bar end. They also constructed
parametric models for the red clump magnitude distributions and find a total
bar half-length of $5.0\pm 0.2\;{\rm kpc}$ (including the super thin bar
component). Thus the boxy-peanut barred shape in the inner $\sim 2\;{\rm kpc}$
transits smoothly outwards into a long thin bar with a half-length of $5.0\pm
0.2\;{\rm kpc}$, with a consistent bar angle of $\sim 28^{\circ}$ or so.

###  2.2 Peanut-/X-shaped Structure

McWilliam & Zoccali (2010, hereafter MZ10) and Nataf et al. (2010) reported a
clear double-peaked magnitude distribution of the RCGs in many Galactic bulge
fields (often termed the “split red clumps”) in the 2MASS and OGLE data,
respectively. This phenomenon of split red clumps was initially puzzling.
Since RCGs are a good distance indicator, MZ10 suggested that the bimodality
is hard to explain with a naive tilted ellipsoidal bar since the line of sight
crossing the bar can only result in stars with one distance. Nataf et al.
(2010) speculated that one RCG population belongs to the bar and the other to
the spheroidal component of the bulge. Another puzzling fact is that distances
of the bright and faint RCGs are roughly constant at different latitudes,
which was hard to understand with a naive straight bar. MZ10 proposed that the
observed evidence can be well explained with a vertical “X-shaped structure”
in the bulge region. The existence of this structure was later confirmed by
various groups (Saito et al. 2011; Ness et al. 2012; Nataf et al. 2015). They
found that the X-shaped structure exists at least within $|l|\leq 2^{\circ}$,
and displays front-back symmetry. At $|b|<5^{\circ}$, two RCGs begin to merge
due to severe dust extinction and foreground contamination (MZ10; Wegg &
Gerhard 2013). Incorporating proper motions from the VVV Infrared Astrometric
Catalogue (VIRAC) and Gaia DR2, Sanders et al. (2019a) and Clarke et al.
(2019) verified that the differential rotation between the double peaks of the
magnitude distribution of RCGs indeed confirms the X-shaped nature of the bar-
bulge, thus ruled out the alternative explanation that the observed split red
clumps is due to a population effect (Lee et al. 2015).

Figure 3: Demonstration of the X-shape structure in the S10 bar model. The
upper panel shows the side-on view of the model and the lower panel shows the
residual after fitting and subtracting the underlying smooth light
contribution. The vertical X-shaped structure is highlighted in this residual
image. The length unit is $R_{\rm d}=1.9\rm\;kpc$. Reproduced from Li & Shen
(2012).

The X-shaped structure cannot be explained straightforwardly in classical
bulge formation scenarios, but it can develop naturally in the bar thickening
process. A realistic bar is not a purely triaxial ellipsoid since it usually
thickens through the vertical buckling instability or resonant trapping after
a cold disk suffers from the in-plane bar-forming instability. As a result, a
steady bar often acquires a boxy/peanut shape after the dynamical
instabilities. This is relatively well known in both the bar dynamics
community (Combes & Sanders 1981; Combes et al. 1990; Raha et al. 1991;
Pfenniger & Friedli 1991; Athanassoula 2005; Martinez-Valpuesta et al. 2006;
Shen et al. 2010) and the external galaxies with a boxy/peanut-shaped bulge
(e.g., Bureau & Freeman 1999; Bureau et al. 2006; Laurikainen et al. 2014).

The Milky Way bar is no exception to the peanut shape. A buckled bar in
numerical simulations naturally reproduces the observed X-shape properties in
many aspects (Li & Shen 2012; Ness et al. 2012). Li & Shen (2012) analysed the
best-fitting Milky Way bar/bulge model in S10 and found that an X-shaped
structure is clearly recognizable in the side-on view (top panel of Figure 3).
They also demonstrated that it can qualitatively reproduce many observational
results of the X-shaped structure, such as the double-peaked distribution in
distance histograms (MZ10, Nataf et al. 2010) and number density maps (Saito
et al. 2011). The bottom panel of Figure 3 highlights the nearly symmetric
“X-shaped structure” after the underlying smooth component is subtracted from
the side-on bar model. The extent of the “X-shape” is roughly 3 kpc and 1.8
kpc along the bar major axis and in the vertical direction, respectively. The
X-shape has a similar tilting angle as the bar, but extends to only about half
the bar length. As in observations, at a given latitude $b$ the peak positions
are roughly constant, and the further peak becomes gradually stronger at
decreasing $l$; at a given longitude $l$ the separation of the two peaks
increases as $|b|$ increases. Li & Shen (2012) estimated that the light
fraction of this X-shaped structure is about 7% of the whole bulge. Portail et
al. (2015a) performed more sophisticated modeling based on the reconstructed
bulge volume density from VVV survey (Wegg & Gerhard 2013), and found an off-
centered X-shape comprising about 20% of the bulge mass.

Figure 4: 3D isodensity surfaces of a strongly buckled bar in $N$-body
simulations. The left and middle panels show the face-on and side-on
appearance of the bar, respectively. The right panel shows an edge-on view at
a bar angle of $25^{\circ}$. Adapted from Li & Shen (2015).

However, the true three-dimensional shape of the X-shaped structure is not as
simple as a letter “X” with four or eight conspicuous arms. Figure 3 may give
such a biased impression because human eyes tend to be drawn by small-scale
density enhancements. The true three-dimensional shape of the X-shaped
structure is actually more like a peanut. This is demonstrated in Li & Shen
(2015) who estimated the 3-D volume density of $N$-body bar models with an
adaptive kernel smoothing technique (Silverman 1986; Shen & Sellwood 2004).
Figure 4 shows clearly that the morphology of a strongly buckled bar
transitions gradually from a central boxy core to a peanut bulge, and then to
an extended, thin bar. This was also found in the observations with larger and
more uniform samples of RCGs (Wegg & Gerhard 2013; Wegg et al. 2015; Simion et
al. 2017). But the peanut-shaped bulge can still reproduce qualitatively the
observed double-peaked distance distributions that were used to infer for the
discovery of the X-shape. Li & Shen (2015) demonstrated that the pinched
concave isodensity contours of the inner peanut structure can enhance our
visual perception of an letter “X”. Note that the central boxy core is shaped
like an oblong tablet, extending within $\sim$ 500 pc or $|b|\sim 4^{\circ}$
near the Galactic plane. From the solar perspective, lines of sight passing
through the central boxy core do not show bimodal distributions, in agreement
with observations (MZ10; Wegg & Gerhard 2013).

Until quite recently it was widely believed that the peanut-shape of a bar is
supported by orbits trapped around the 3D $x_{1}$ family, also known as banana
orbits due to their banana shape when viewed side-on (e.g., Patsis et al.
2002; Skokos et al. 2002; Athanassoula 2016). The backbone orbits of a 3D
buckled bar are the $x_{1}$ tree, i.e., the $x_{1}$ family plus a tree of 3D
families bifurcating from it (Pfenniger & Friedli 1991). Portail et al.
(2015b), however, proposed that ‘brezel-like’ orbits are instead the main
contributor to the peanut shape. Such orbits may be related to the so-called
“$x_{1}mul_{2}$” orbit family (Patsis & Katsanikas 2014). Qin et al. (2015)
also showed from the kinematics of a simulated boxy peanut-shaped bar that
stars in the bar do not show a clear sign of streaming along banana orbits.
Abbott et al. (2017) found that only ‘fish/pretzel’ orbits and ‘brezel’
orbits, comprising 7.5 per cent of the total mass, show a distinct X-shape in
unsharp masked images, but nearly all bar orbit families contribute some mass
to a 3D boxy peanut-shaped bar (also see Parul et al. 2020). Clearly we need
more in-depth investigations on the orbital structure and vertical resonant
heating process (e.g. Quillen et al. 2014; Sellwood & Gerhard 2020) to make
more specific predictions for the Galactic bar.

Although the buckling instability has been demonstrated to be sufficient to
thicken the Galactic bar into the peanut shape as shown in many previous
studies (e.g., Shen et al. 2010), it is unclear if it is the only way.
Sellwood & Gerhard (2020) carefully studied three mechanisms for bar
thickening: the well-known buckling instability, vertical excitation of bar
orbits as a 2:1 vertical resonance sweeps out along the bar (Quillen et al.
2014), and gradually trapped bar orbits into the 2:1 vertical resonance. They
found the fourth-order Gauss-Hermite coefficient $h_{4}$ profile of the
vertical velocity distribution (see also Debattista et al. 2005) may be a good
diagnostic to discriminate between a bar made via the buckling instability
from the other two mechanisms. It remains hopeful that better proper motion
data in the future will distinguish the thickening mechanism responsible for
the Galactic bar. If the Galactic bar indeed experienced a buckling
instability, then the X-shaped or peanut-shaped structure becomes nearly
symmetric with respect to the disk plane $\sim$ 2 Gyr after the instability
gradually saturates. Thus the observed symmetry (MZ10) might imply that the
X-shaped structure in the Galactic bulge has been in existence for at least a
few billion years (Li & Shen 2012).

The existence of the X-shaped structure in our Milky Way provides additional
evidence that the Galactic bulge is shaped mainly by internal disk dynamical
instabilities instead of mergers, because no other known physical processes
can naturally develop such a structure.

###  2.3 Dynamical Models of the Galactic Bar/bulge

Building a dynamical model of the Milky Way bulge/bar requires stellar or gas
kinematics as constraints. Based on the Schwarzschild orbit-superposition
method, Zhao (1996) developed the first 3D rotating bar model that fits the
density profile of the COBE light distribution and scarce kinematic data at
Baade’s window. His model then was constructed with 485 orbit building blocks,
and little stellar kinematic data were available to explore the uniqueness of
this model, unfortunately.

The Bulge Radial Velocity Assay (BRAVA) project aims to study the stellar
kinematics covering the whole Galactic bulge with $\sim 9000$ M giants as
tracers (Rich et al. 2007). These giants provide most of the box-shaped 2
$\mu$m light distribution that hints for the presence of a bar. The BRAVA
results show that the boxy bulge rotates nearly cylindrically, i.e., rotation
is roughly constant regardless of the height above the disk plane (Howard et
al. 2009; Kunder et al. 2012). BRAVA kinematics also put the Galactic bulge
near the “oblate isotropic rotator” line in the so-called Binney’s $V_{\rm
max}/\sigma-\epsilon$ diagram (Binney 1978), which shows that the bulge is not
a hot, slowly-rotating system supported by random motions. The Abundance and
Radial velocity Galactic Origins Survey (ARGOS) obtained radial velocities and
stellar parameters for an even larger sample of 28000 stars in the bulge and
inner Milky Way (Freeman et al. 2013). The clear cylindrical rotation of the
bulge was confirmed in the ARGOS (Ness et al. 2013) and the Giraffe Inner
Bulge Survey (GIBS) data (Zoccali et al. 2014). These much better kinematic
data with more complete spatial coverage provide crucial constraints for
better dynamical models.

$N$-body simulations of the Galactic bar/bulge have provided insight on its
formation and evolution. For example, the S10 $N$-body model was initially
designed to match the BRAVA data without too many free parameters to tweak. It
is one of the simplest evolutionary bar models that developed naturally from
the bar instability of a cold massive precursor disk. Despite its simplicity,
it has enjoyed successes in many aspects. The physical processes shaping the
structural formation of the Galactic bar/bulge are well understood; the in-
plane bar instability gives rise to a massive bar that then got thickened
vertically into a boxy/peanut/X shape in the subsequent firehose/buckling
instability (see Sellwood 2014 for a comprehensive review on these
instabilities). The best-fitting model of S10 also naturally reproduces many
other observational results reasonably well, e. g., excellent match to the
stellar kinematics, the bar angle of $20^{\circ}-30^{\circ}$, a reasonable bar
length ($\sim 4\;{\rm kpc}$), a bar pattern speed of $\sim 40\;{\rm
km~{}s^{-1}}{\rm kpc}^{-1}$, the vertical metallicity gradient (Martinez-
Valpuesta & Gerhard 2013, Liu & Shen 2021), and gives an upper mass limit on a
possible classical bulge. A drawback of S10 model is its adoption of a rigid
dark matter halo for simplicity, thus it omitted the dynamical friction
between the bar and halo which may affect the long-term evolution of the bar.
Fortunately, the low mass fraction of a cored dark matter halo in the bar
region (Portail et al. 2017a) warrants that such bar-halo dynamical friction
may not be too strong in the Milky Way. Simple bar models like S10 may serve
as a physically-motivated starting point, then more chemo-dynamical
complexities of the Milky Way bulge may be gradually incorporated into it. Di
Matteo et al. (2015), Fragkoudi et al. (2018), and Di Matteo et al. (2019)
showed further how adding a second, thick disk in their $N$-body simulations
may further improve the chemo-kinematic relations we describe below (Figure
5). Debattista et al. (2017) demonstrated how initially co-spatial stellar
populations with different in-plane random motions separate when a bar forms.
Although $N$-body simulations can provide the full evolutionary history from
plausible initial conditions, they are inflexible in the sense that numerous
trials of different initial configurations are required to reproduce the
desired results, which are not always controllable, thus limiting the
systematic exploration of parameter space to match the observational results.

The made-to-measure (M2M) method (Syer & Tremaine 1996) is a complementary
alternative to $N$-body models, and is more flexible in steering models to
match a large number of data constraints. In this approach one first
constructs a reasonable $N$-body model with the essential physics to match the
galaxy under study. The weights of the particles are slowly adjusted as
particles proceed in their orbits until the time-averaged density field and
other observables converge to the observational value, through a weight
evolution equation according to the mismatch between the model and target
observables. The M2M method has been continuously tested and improved in
various implementations (e.g. Bissantz et al. 2004; de Lorenzi et al. 2007;
Dehnen 2009; Long & Mao 2010, 2012; Hunt & Kawata 2013; Portail et al. 2015a;
Long & Mao 2018), and has become an important tool in the dynamical modelling
of the Milky Way bar/bulge. Portail et al. (2017a) built made-to-measure
dynamical models that fit the RCG density from the VVV, UKIDSS, and 2MASS
survey, kinematics from BRAVA, ARGOS, and OGLE surveys. Their models gave a
bar pattern speed of $39.0\pm 3.5\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$. The total
dynamical mass in their model for the bulge volume ($\pm 2.2\times\pm
1.4\times\pm 1.2$ kpc along the bar principal axes) is $1.85\pm 0.05\times
10^{10}M_{\odot}$, with a low dark matter fraction of $17\pm 2\%$. Their
results also implied a core or shallow cusp profile of the dark matter halo
inside $\sim 2\;{\rm kpc}$. The stellar mass inside the bulge volume is $\sim
1.52\times 10^{10}M_{\odot}$, roughly consistent with stellar mass estimate
($\sim 2.0\pm 0.3\times 10^{10}M_{\odot}$) by Valenti et al. (2016) within
$|b|<9.5^{\circ}$ and $|l|<10^{\circ}$ considering that it is a bigger spatial
volume than in Portail et al. (2017a).

Figure 5: Rotation and velocity dispersion profiles in the ARGOS observations
towards the Galactic bulge fields from Ness et al. (2013). The three columns
correspond to three different metallicity bins, decreasing from left to right.
Different symbols represent stars in different fields. Reproduced from Ness et
al. (2013).

Observations also reveal distinctly different kinematic properties between the
relatively more metal-rich and metal-poor stars in the Galactic bar/bulge. For
example, Babusiaux et al. (2010) showed that the more metal-rich population
has bar-like kinematics and the more metal-poor population is likely
associated with an old spheroid or a thick disk (also see Hill et al. 2011;
Rojas-Arriagada et al. 2014). The metal-rich population demonstrates smaller
velocity dispersion and is less $\alpha$-enhanced compared to the metal-poor
one (Johnson et al. 2011; Uttenthaler et al. 2012; Zoccali et al. 2017),
although the rotation curves are similar for three different metallicity bins
(Figure 5). Based on the ARGOS sample, Ness et al. (2012) found that the
X-shaped structure is shown in the metal-rich stars ($\rm[Fe/H]>-0.5$) rather
than the metal-poor ones ($\rm-1.0<[Fe/H]<-0.5$) (also see Uttenthaler et al.
2012; Gilmore et al. 2012), indicating the more metal-rich stars are pre-
dominantly tracing the boxy bar/bulge.

These chemo-kinematic relations set key constraints for dynamical models
including chemical information. Portail et al. (2017b) built a self-consistent
chemodynamical model to fit observational results for the galactic bulge, bar,
and inner disk. They extended the M2M dynamical model from Portail et al.
(2017a) to reproduce the observed metallicity-dependent density distribution
and kinematics. They found most metal-rich stars ($\rm[Fe/H]\geq-0.5$) belong
to the bar component, while the metal poor stars ($\rm[Fe/H]\leq-0.5$) outside
the central kpc are more likely to have a thick disk origin. Their model could
also reproduce the observed vertex deviations in Baade’s window (Soto et al.
2007; Babusiaux et al. 2010). As proper motions from Gaia and VIRAC and other
chemical abundances from large spectroscopic surveys are being included as
model constraints, chemo-dynamical models will become more powerful in
revealing the detailed dynamics and formation history of the Milky Way
bulge/bar.

####  2.3.1 Is There a Classical Bulge Component?

Key information about the galaxy formation and evolution may be learned by
studying galactic bulges. It is generally expected that major mergers between
galaxies tend to create a classical bulge bearing a resemblance to ellipticals
in many aspects, while the slower internal secular evolution processes in a
disk galaxy (Sellwood 2014) tend to build up a disk-like “pseudobulge”
(Kormendy & Kennicutt 2004).

Now it is widely accepted that the bulk of the Galactic bulge is actually the
boxy/peanut-shaped part of the Galactic bar. Although most bulge stars are old
($>$ 10 Gyr), but the assembly epoch of the bulge structure itself may not be
that ancient. There are a number of reasons why an old classical bulge made in
prior mergers or a monolithic collapse is unlikely to be significant in the
Milky Way.

First, a classical bulges is like a mini-elliptical galaxy, which stays on the
“fundamental plane” of ellipticals, i.e., the tight correlations between
galaxy size, central surface brightness, and velocity dispersion. So there is
not much freedom to postulate classical bulges having arbitrary properties,
such as low surface brightness, to make them hard to detect (Kormendy et al.
2010). A very low-mass classical bulge tends to have high surface brightness
and large effective radius predicted from fundamental plane correlations, and
it is much denser than a star cluster or a disky pseudo-bulge. Kormendy &
Bender (2019) estimated that a classical bulge with a bulge-to-total
luminosity ratio $B/T=0.02$ corresponds to an absolute magnitude of
$M_{V}\approx-16.3$, i.e. similar to that of M32 ($M_{V}\approx-16.7$), and
has an effective radius of $100\sim 200$ pc. The fact that we can even detect
the tiny nuclear star cluster ($R_{e}\sim 4$ pc) in the Galactic center shows
that the Milky Way does not contain a small classical bulge with a mass of
$\sim 2\%M_{\rm disk}$, otherwise we would have only observed a dense
classical bulge instead of the nuclear star cluster.

Secondly, the metal-poor stars ($\rm-1.0<[Fe/H]<-0.5$) in the bulge are
unlikely to belong to a classical bulge. Shen et al. (2010) also tested
whether or not a significant classical bulge is present, since it could have
been spun up by the later formation of a bar, flattened thereby and made hard
to detect. They found that including a classical bulge with $\geq$ 10% of the
disk mass considerably worsens the fit of the model to the data, even if the
disk properties are accordingly re-adjusted. If the pre-existing classical
bulge is overly massive, then it becomes increasingly hard to match both the
mean velocity and velocity dispersions simultaneously (see also Saha et al.
2012). Such a small bulge can neither explain the large fraction of metal-poor
stars (Ness et al. 2013; Zoccali et al. 2018), nor the increasing fraction
with latitude $b$ (Di Matteo et al. 2014). Also if the metal-poor stars were
to be associated with a classical bulge, then the rotation velocity of the
metal-poor stars will be significantly slower than that of the metal-rich
ones, which is inconsistent with observations (e.g., Figure 5). In addition, a
10%$M_{\rm disk}$ classical bulge will have a steeply rising surface
brightness per the fundamental plane correlations, which is inconsistent with
the nearly exponential minor-axis profile shown in the NIR data (Launhardt et
al. 2002).

Thirdly, the more centrally concentrated RR Lyrae population (Dékány et al.
2013; Pietrukowicz et al. 2015; Kunder et al. 2016, 2020) are unlikely to be
associated with the classical bulge. They only account for less than 1% of the
total mass of the bar traced by RCGs, and their metallicity (median
$\rm[Fe/H]\sim-1.0$) is much more metal-poor than the bulk of the metal-poor
population in GIBS and Gaia-ESO (Rojas-Arriagada et al. 2014; Zoccali et al.
2018). It has been suggested that these RR Lyrae stars might represent the
inner extension of the halo confined to the inner Galaxy (Pérez-Villegas et
al. 2017; Savino et al. 2020), but Du et al. (2020) demonstrated that this is
unlikely the case with a large RR Lyrae sample from OGLE-IV with Gaia DR2
proper motions.

Fourthly, Clarke et al. (2019) found that the proper motion correlation map
displays a clear quadrupole pattern in all magnitude slices of RCGs, showing
no evidence for a separate, more axisymmetric inner bulge component.

In summary, the Galactic bulge is predominantly a peanut-shaped bar that
formed spontaneously from a disk, and there is no sign that the Galaxy
contains a significant merger-made, classical bulge. So, from a galaxy
formation point of view, the Milky Way is a “pure-disk” galaxy.

###  2.4 Pattern Speed of the Milky Way Bar

Bar pattern rotation speed is one of the most important parameters of the bar
dynamics, as it determines the orbital structure of stars. It can be measured
independently from stellar kinematics and gas kinematics, respectively.

####  2.4.1 Measurement with Stellar Kinematics

Debattista et al. (2002) applied a modified version of the Tremaine-Weinberg
continuity formalism (Tremaine & Weinberg 1984) for use with line-of-sight
velocities to a small sample of OH/IR stars in the inner Galaxy. They obtained
the first direct measurement of the Galactic bar pattern speed of $\Omega_{\rm
p}=(59\pm 5)\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$. Gaia now provides some of the
first absolute proper motions within the bulge, and the near-infrared VVV
multi-epoch catalogue can complement Gaia in highly extincted low-latitude
regions. Sanders et al. (2019a) and Clarke et al. (2019) analysed the
kinematics of the Galactic bar/bulge using proper motions from the VVV
Infrared Astrometric Catalogue (VIRAC) and Gaia DR2. The latest data with
proper motions have enabled more accurate measurement of the bar pattern speed
than before.

Sanders et al. (2019b) extended the revised Tremaine-Weinberg continuity
formalism for use with proper motions, and derived the pattern speed of the
Milky Way’s bar/bulge. They measured $\Omega_{\rm p}=(41\pm 3)\;{\rm
km~{}s^{-1}}{\rm kpc}^{-1}$, which puts the corotation radius of the Galactic
bar at $(5.7\pm 0.4)\;{\rm kpc}$. They experimented the addition of data on
the near or far side of the bar, and suggested a systematic uncertainty of
$5-10\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$ in their measurement. Clarke et al.
(2019) compared their stellar kinematical data to the made-to-measure barred
dynamical models in Portail et al. (2017a), and found that a model of the
barred bulge with a pattern speed of $37.5\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$
is able to match most of the observed features. These values also agree nicely
with the bar pattern speed of $\sim 39-40\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$
for the S10 $N$-body bar model (Shen 2014) designed to matched the full BRAVA
kinematics, and the made-to-measure models based on the mock data created from
the same $N$-body model (Long et al. 2013).

####  2.4.2 Measurement with Gas Kinematics

Non-circular gas kinematics was one of the first hints for the existence of a
Galactic bar (e.g., de Vaucouleurs 1964). In fact, the features in the
asymmetric gas flow pattern may be used to infer the properties of the
Galactic bar, especially its pattern rotation speed. As distances to
individual gas clouds are difficult to measure accurately, motions and
distribution of atomic and molecular gas are conventionally presented in the
Galactic $l-v$ diagram of HI or CO gas, i.e. the plot showing how gas emission
line intensity distributes in the Galactic longitude ($l$) and line-of-sight
velocity ($v$) space (e.g., Burton & Liszt 1993; Dame et al. 2001). Most
features in the $l-v$ diagram representing the dense gas distribution are
driven mainly by the large-scale non-axisymmetric structures such as the
Galactic bar and spiral arms. Thus $l-v$ diagram must be interpreted through
careful gas dynamical models including the bar and spiral arms due to the
large distance uncertainty of gas clouds, and it in turn can provide important
constraints on the properties of the bar and spiral arms by matching up the
simulated gas features with the observed ones.

Many hydrodynamic models of the gas flow have followed the above approach to
infer the pattern rotation speed of the Galactic bar once the Galactic bar
potential is constrained by star counts. The early models were able to
reproduce some of the prominent features in the $l-v$ diagram, but tend to
give a relatively high bar pattern speed in the range of $\Omega_{\rm
p}=50-60\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$ (e.g., Fux 1999; Englmaier &
Gerhard 1999; Bissantz et al. 2003; Rodriguez-Fernandez & Combes 2008; Baba et
al. 2010). However, the bar pattern speed derived from gas dynamics may have
some degeneracies with the properties of the bar potential such as the bar
size; a more slowly-rotating longer bar might also match to the gas features
in the $l-v$ diagram well. Li et al. (2016) modelled the Milky Way gas flow
pattern with a basic bar potential constrained by the density of bulge RCGs
(Portail et al. 2015a; Wegg & Gerhard 2013). They found that a lower bar
pattern speed may provide an even better match to the gas $l-v$ diagram than
previous high pattern speed hydrodynamical simulations, reproducing features
like the shape and kinematics of the Central Molecular Zone, Bania’s clumps,
the connecting arm, the Near and Far 3 kpc arms, the Molecular Ring, and the
spiral arm tangent points. Sormani et al. (2015) also found a lower pattern
speed of $\Omega_{\rm p}=40\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$ after
experimenting a range of parameters of a rigidly rotating bar potential with
only a monopole and a quadrupole components.

A drawback of the $l-v$ diagram is that it contains only the information of
line-of-sight velocities, and does not constrain the tangential motions of
gas. This could be further improved by considering the latest BeSSeL results
(Reid et al. 2019), which measures the 3D velocity and position of nearly 200
high-mass star-forming regions (HMSFRs) with high-precision VLBI data (§ 3).
The peculiar motions of the HMSFRs are generally small ($\sim 10\;{\rm
km~{}s^{-1}}$) except in two regions; the first is a segment of the Perseus
arm that is probably in a disrupting phase (Baba et al. 2018) and the other
region is around the bar end. The large-scale dynamics of the Galactic bar and
spiral arms might be the origin for these peculiar motions. A successful
dynamical model should not only reproduce the main features in the $l-v$
diagram, but also explain the peculiar motions of these observed HMSFRs. The
preliminary result in Li et al. (2021) seems to prefer a bar pattern rotation
speed of $\sim 37-40\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$, and a pattern speed of
spiral arms of $\sim 23\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$ which is less
constrained by this gas model.

In summary, the most recent independent measurements of the Galactic bar
pattern speed using stellar and gas kinematics appear to converge to $\sim
35-40\;{\rm km~{}s^{-1}}{\rm kpc}^{-1}$. This $\Omega_{\rm p}$ value
corresponds to a corotation radius $R_{\rm CR}\sim 6\;{\rm kpc}$. With a bar
half-length of $R_{\rm b}\sim 5\;{\rm kpc}$ (Wegg et al. 2015), we have the
dimensionless $\mathcal{R}\equiv R_{\rm CR}/R_{\rm b}\sim 1.2$, which would
put the Milky Way bar into the conventional “fast bar”
($1.0\leq\mathcal{R}\leq 1.4$) category (Debattista & Sellwood 2000).

##  3 The Spiral Structure of the Milky Way

The BeSSeL Survey is a National Radio Astronomy Observatory (NRAO) key science
project. Its aim is to determine accurate distances of HMSFRs in the bar and
spiral arms of the Milky Way by measuring the trigonometric parallaxes of the
methanol and water masers with which they are associated. This large survey
was undertaken by an international team of 22 astronomers from 12 countries
using NRAO’s Very Long Baseline Array (VLBA) and achieved parallax accuracies
of order $\pm$ 10 $\mu$as (Reid et al. 2014). The survey lasted about 15
years, starting with a pilot VLBI parallax measurement of W3(OH) in the
Perseus arm of the Milky Way (Xu et al. 2006a). They collected candidate water
and methanol masers with flux densities above 1 Jy from existing interstellar
maser catalogs (Brand et al. 1994; Fontani et al. 2010; Caswell et al. 2010,
2011). Additional surveys of maser candidates were carried out by the project
team, particularly in the outer Galaxy where masers are sparse and distant.
For maser candidates with uncertain absolute positions, VLA snapshot images
were made to locate them to better than 0.1 arcsec (Hu et al. 2016). They
searched near these masers for extragalactic background sources of
milliarcsecond size, to serve as fixed reference points: most of these came
from existing calibrator catalogs (Petrov et al. 2008, 2011). To increase the
number of useful background sources in certain sky regions, they investigated
the small-scale structures of more than 2000 potential reference sources from
the NVSS and CORNISH surveys. Through more VLA snapshots and a VLBA survey
they identified additional suitable background objects (Xu et al. 2006b; Immer
et al. 2011). In total about 200 maser sources associated with HMSFRs in the
bar and spiral arms of the Milky Way have had their trigonometric parallax
measured in the BeSSeL project (Reid et al. 2019).

Distance uncertainties increase linearly with distance. For most of the masers
in the project the parallax measurements have less than 10% error, owing to
multiple spots in the maser sources and multiple background sources. For
parallax measurements of methanol masers, many spots in the maser sources and
more than one background sources near the HMSFRs have been found.
G041.22-0.19, for example, consists of 25 maser spots and has four nearby
background sources. There are 100 fitting parallaxes for the HMSFR (Wu et al.
2019) as shown in Figure 6. This improves the accuracy of the parallax
measurement but also brings complexity. A unique ‘fake quasar’ method to
overcome the problem of signal propagation through the ionosphere from
different background sources have developed (Reid et al. 2017). Sanna et al.
(2017) have exceptionally measured the parallax of HMSFR G007.47+00.05 as
0.049 $\pm$ 0.006 mas, corresponding to a distance of 20.4 kpc with accuracy
12%. The greatest distance measurements in the BeSSeL project are crucial to
define the farthest segment of the Scutum-Centaurus spiral arm in the Milky
Way.

Combining observations from the Japanese VERA project and the European VLBI
Network, 199 trigonometric parallaxes and proper motions for water and
methanol masers associated with HMSFRs have been employed to map the Milky
Way, covering an area in the Galactic longitude from -2∘ to 240∘. Fitting log-
periodic spirals to the locations of the masers and using well-established
tangencies in the $4^{th}$ quadrant of the Galactic plane (Appendix in Reid et
al. 2019), a new model of the spiral arm structure in the Milky Way has been
established. It clearly shows four arms with some extra arm segments and
spurs, as well as the Galactic bar and 3-kpc arm. Considering the compositions
in spiral arms of external spiral galaxies, such as giant HII regions, young
OB stars, and young star clusters, filaments, the conceptual image of the
Milky Way have been built and shown in the top panel of Figure 1. It is
currently the most scientifically accurate visualization of what the Milky Way
looks like.

Figure 6: The left (right) panel shows the East (North) parallax signature,
with proper motion removed, for 6.7-GHz methanol maser G041.22-0.19 which is
characterized by 4 background quasars and 25 maser spots, for 100 quasar-maser
pairs. The final parallax, 0.113 $\pm$ 0.022 mas, is determined with the ‘fake
quasar’ method (Reid et al. 2017) and is shown as the thick solid line. Red,
yellow, blue and green dashed lines denote individual fitting results for the
four background quasars (Wu et al. 2019).

###  3.1 Major Arms

Figure 7: The conceptual image overlaying the outlines of the four spiral arms
of the Milky Way. The Galactocentric coordinate system is divided into four
quadrants, as indicated by yellow dashed lines. Quadrant numbers are indicated
in four corners. The Galactic center (red asterisk) is at (0, 0) and the Sun
(red Sun symbol) is at (0, 8.15) kpc. The outlines of four arms are Norma-
Outer arm (blue); Scutum-Centaurus-OSC arm (yellow); Sagittarius-Carina arm
(green); and Perseus arm (white). The dotted lines are the widths of the four
arms, defined as enclosing 90% of their distance indicators (Reid et al.
2019).

Figure 7 shows a diagram overlaying the outlines of the four spiral arms on
the conceptual image of the Milky Way. To represent the structure of the Milky
Way, we have used the Galactocentric coordinate system with four quadrants.
The Galactocentric azimuth $\beta$ is defined as 0 towards the Sun and
increases clockwise. The elliptical bar in the center of the Milky Way extends
from its nearer end in quadrant 2 into quadrant 4. Using red clump giant (RCG)
star surveys, Wegg et al. (2015) found that the bar has semi-major and semi-
minor axes of about 5 and 1.5 kpc and is oriented at about 30∘ to the line of
sight (see also Rattenbury et al. 2007; Cao et al. 2013). The 3-kpc arm
appears as a ring around the central bar (van Woerden et al. 1957; Dame &
Thaddeus 2008). The Norma-outer and the Scutum-Centaurus-OSC (Outer Scutum
Centaurus) arms appear to start from the near end of the bar. The Norma-outer
arm lies inside the Scutum-Centaurus-OSC arm. The Norma arm starts from near
the end of the bar at $(x,\;y)$ = (2, 3) kpc and extends into the $3^{rd}$
quadrant, passing counterclockwise through the $4^{th}$ quadrant before
wrapping around the far end of the bar and becoming the Outer arm in the
$1^{st}$ quadrant. The Scutum arm originates near $\beta$ = 90∘ in the
$2^{nd}$ quadrant, and winds counterclockwise into the $3^{rd}$ quadrant as
the Centaurus arm, which extends into the $1^{st}$ quadrant where it becomes
the OSC arm. The Sagittarius-Carina arm and the Perseus arm both begin close
to the far end of the bar, with the Sagittarius-Carina arm lying within the
Perseus arm. The Sagittarius arm passes through the $4^{th}$, $1^{st}$ and
$2^{nd}$ quadrants and becomes the Carina arm in the $3^{rd}$ quadrant before
terminating in the 4th quadrant. The Perseus arm winds through the $4^{th}$,
$1^{st}$ and $2^{nd}$ quadrants and appears to stop in the $3^{rd}$ quadrant.
There are many spurs between the main arms in this picture of the Milky Way.
Such spurs are common in spiral galaxies. Recently, Ragan et al. (2014)
proposed that the spurs in the Milky Way may be giant molecular filaments. It
is worth noting that the Spitzer/GLIMPSE survey using mid-infrared star counts
(Benjamin et al. 2005) reported only two major stellar arms, the Perseus arm
and the Scutum-Centaurus arm. A plausible reason to explain this discrepancy
from BeSSeL could be that the other two arms contain excess gas but few old
stars to be detected as stellar enhancement in GLIMPSE.

VLBI parallax and proper motion measurements use one of the most sophisticated
instrumental system and the phase calibration in astronomy. Especially, there
are strict restrictions on the observed targets which must be strong and
compact. Only about 300 masers in the HMSFRs have been measured with VLBI
astrometry. Fortunately, there are various kinds of young objects associated
the HMSFRs, such as HII regions, giant molecular clouds (GMCs), massive
outflows as well as maser with weak intensity. Reid et al. (2017) have
developed a Bayesian distance calculator and used longitude-latitude-velocity
values of these young objects to re-estimate their distances, refining the
standard kinematic values. 2607 young objects have been collected from several
surveys (Dame et al. 2001; Valdettaro et al. 2001; Anderson et al. 2012;
Pestalozzi et al. 2005; Sun et al. 2015; Green et al. 2017). We have overlaid
these 2607 young objects and 199 masers by parallax measurement (Reid et al.
2019) on the conceptual image of the Milky Way shown in Figure 8. It is
obvious that young objects clearly delineate the spiral arms in the Milky Way.

Figure 8: A conceptual picture overlaid with the 2607 young objects (Dame et
al. 2001; Valdettaro et al. 2001; Anderson et al. 2012; Pestalozzi et al.
2005; Sun et al. 2015; Green et al. 2017) and 199 masers (Reid et al. 2019)
shown as yellow points.

###  3.2 The Local Arm

Previously, the local arm was supposed to be a short fragment similar to
smaller appendages seen branching off spiral arms in other galaxies and called
the Orion or Local spur (van de Hulst et al. 1954; Georgelin & Georgelin
1976). Recently, more than 30 methanol (6.7-GHz) and water (22-GHz) masers in
high-mass star-forming regions around the Sun have been measured their
parallax and proper motions with the distance accuracy of better than $\pm$10%
and even 3%, the best parallax measurement in the BeSSeL project. The accurate
locations of interstellar masers in HMSFRs have been shown that the Local arm
appears to be an orphan segment between the Sagittarius and Perseus arms that
wraps around less than a quarter of the Milky Way. The segment has a length of
$\sim 6\;{\rm kpc}$ and the width of $\sim 1\;{\rm kpc}$ with a pitch angle
from 10.1${}^{\circ}\pm$ 2.7∘ to 11.6${}^{\circ}\pm$ 1.8∘. These results
reveal that the Local arm is larger than previously thought, and both its
pitch angle and star formation rate are comparable to those of the Galaxy’s
major spiral arms. The Local arm is reasonably referred to as the fifth
feature in the Milky Way. The “spur” interpretation is definitely incorrect
(Xu et al. 2013, 2016; Reid et al. 2019; VERA Collaboration et al. 2020).

To understand the form of the Local arm between the Sagittarius and Perseus
arms, the stellar density of a specific population of stars with about 1 Gyr
of age between 90${}^{\circ}\leq l\leq 270^{\circ}$ have been mapped using the
Gaia DR2 (Miyachi et al. 2019). The 1 Gyr population have been employed
because they are significantly evolved objects than the gas in HMSFRs tracing
the Local arm. Miyachi et al. (2019) have carried out an interesting
investigation to compare both the stellar density and gas distribution along
the Local arm. They found a marginally significant arm-like stellar
overdensity close to the Local arm, identified with the HMSFRs especially in
the region of 90${}^{\circ}\leq l\leq 190^{\circ}$. They have concluded the
Local arm as the arm segment associated with not only the gas and star-forming
clouds, but also a significant stellar overdensity. Additionally they found
that the pitch angle of the stellar arm is slightly larger than the gas-
defined arm, and also there is an offset between HMSFR-defined and stellar
arm. The offset and different pitch angles between the stellar and HMSFR-
defined spiral arms are consistent with the expectation that star formation
lags the gas compression in a spiral density wave lasting longer than the
typical star formation timescale of $\sim 10^{7}-10^{8}$ years.

##  4 Summary and Outlook

Our home Galaxy is the closest galaxy that we can study in exquisite detail.
Yet understanding the structure and kinematics of our Milky Way bulge is not a
trivial task, mostly because of our disadvantageous vantage point in the disk
and severe dust extinction. Despite these challenges we have made giant leaps
in understanding the Galactic structure in the past decade. The BeSSeL survey
has drawn a picture of the most reliable spiral arm structure of the Milky Way
to date. Careful analysis and modelling of extensive datasets on the inner
Galaxy reveal more details of the Milky Way bar/bulge. To our current best
knowledge, the Milky Way contains a long strong bar, four major spiral arms,
and a local arm that may be longer than previously thought. The Galactic bar
transitions smoothly from a central peanut-shaped structure to an extended
thin part that ends around $R\sim 5\;{\rm kpc}$. Most of the boxy Galactic
bulge that we observe is probably just the centrally thickened, peanut-shaped
bar viewed nearly end-on.

Although we have some new findings, we are also left with many more unanswered
questions and puzzles. About two thirds of spiral galaxies are barred, so in
this aspect our barred Milky Way is certainly in the majority. Our Galaxy
possesses four clearly-defined major spiral arms and an additional smaller
Local arm, which are not the most common form of spiral structure. In this
sense our Milky Way is probably a normal, but not a typical spiral galaxy.

The origin of grand-design spirals in galaxies is still actively debated in
the community, and the Galaxy’s configuration of the four plus one arms may
pose an even bigger challenge for theorists. The standard Lin-Shu quasi-steady
theory argues that gravitational instabilities on the scale of the entire
galaxy form grand-design spiral-wave patterns lasting for almost the lifetime
of a galaxy. Other theories propose that more short-lived spirals re-emerge
many times over billions of years, but the detailed mechanism, such as a
recurrent cycle of groove modes (Sellwood & Carlberg 2019), or tidally
induced, is still not completely settled. More comprehensive reviews on spiral
structure may be found in Sellwood (2014), Shu (2016), and Sellwood & Carlberg
(2019). The next generation of radio telescope arrays capable of VLBI, such as
the Square Kilometer Array in South Africa/Australia and the Next Generation
Very Large Array in North America, will detect even fainter radio emissions
from much more distant stars. These planned arrays will map out more
accurately the large-scale spiral structure and the interface region where the
bar ends in unprecedented detail. The more accurate characterization of spiral
structure, coupled with the improved phase space structures by future Gaia
releases, may hopefully provide more clues to distinguish competing theories
of how the Galaxy’s spiral structure formed (e.g. Sellwood et al. 2019).

The Galactic bar/bulge also contains crucial information about the formation
of evolutionary history of the Milky Way. There are still many open questions
to be answered in more sophisticated chemo-dynamical models of better data.
For example, how many distinct metallicity components are there in the
Galactic bulge? How do they vary spatially, and how do they correlate with
kinematics? How is the early inner Galaxy (thick disk, old and younger thin
disks) gradually mapped into the presently-observed bulge structure? How does
the outer bulge/bar transition into the inner Galactic halo? Ongoing and
upcoming large surveys promise to shed new light on these questions about the
Milky Way bar/bulge. Parallaxes and proper motions of about 20 million bulge
stars (Robin et al. 2005) will be further improved by future Gaia data
releases. The Blanco Dark Energy Camera (DECam) Bulge survey is a Vera Rubin
Observatory (LSST) pathfinder imaging survey of the relatively less reddened
Galactic bulge (Rich et al. 2020; Johnson et al. 2020). Optical photometry in
SDSS $u$ \+ Pan-STARRS $grizy$ bands can provide a large color baseline to
investigate the age and metallicity distributions of the major structures of
the Galactic bulge. These data will be more powerful when combined with other
surveys such as APOGEE, VVV, Gaia-ESO, and GIBS. With the large influx of data
and the improvement in more sophisticated chemo-dynamical models, greater
progress is expected in putting together all the pieces of the Milky Way
bar/bulge puzzle.

###### Acknowledgements.

We thank Shude Mao, Zhi Li, Zhao-Yu Li, and Iulia Simion for helpful
discussions and comments. The research presented here is partially supported
by the National Key R&D Program of China under grant No. 2018YFA0404501; by
the National Natural Science Foundation of China under grant Nos. 11773052,
11761131016, 11333003; by the “111” Project of the Ministry of Education under
grant No. B20019, and by the MOE Key Lab for Particle Physics, Astrophysics
and Cosmology. This work made use of the Gravity Supercomputer at the
Department of Astronomy, Shanghai Jiao Tong University, and the facilities of
the Center for High Performance Computing at Shanghai Astronomical
Observatory. X-W Zheng gratefully acknowledges support from National Natural
Science Foundation of China (under grants Nos. 10073004, 19673006, 10133020,
10673024, 11073054, 1113308) and the Research Priority Program of Nanjing
University and help from Z-Q Zhu (Nanjing University of Arts), P-F Chen
(Nanjing University), and X-B-N Ji (Nanjing University).

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