# The spiral structure in the Solar neighborhood

L.G. Hou 1,2

###### Abstract

The spiral structure in the Solar neighborhood is an important issue in
astronomy. In the past few years, there is significant progress in
observation. The distances for a large number of good spiral tracers, i.e.
giant molecular clouds, high-mass star-formation region masers, H ii regions,
O-type stars and young open clusters, have been accurately estimated, making
it possible to depict the detailed properties of nearby spiral arms. In this
work, we first give an overview about the research status for the Galaxy’s
spiral structure based on different types of tracers. Then the objects with
distance uncertainties better than 15% and $<$0.5 kpc are collected and
combined together to depict the spiral structure in the Solar neighborhood.
Five segments related with the Perseus, Local, Sagittarius-Carina, Scutum-
Centaurus and Norma Arms are traced. With the large dataset, the parameters of
the nearby arm segments are fitted and updated. Besides the dominant spiral
arms, some substructures probably related to arm spurs or feathers are also
noticed and discussed.

##  1 Keywords:

H ii regions – Galaxy: structure – stars: early-type – stars: massive – masers

##  2 Introduction

As observers deeply embedded in the Galactic disk, mapping the spiral
structure of the Milky Way and understanding its formation and evolution have
long been difficult issues in astronomy. Superpositions of multiple structures
along the same observed line of sight have to be solved to trace the
distribution of matters in our Galaxy. Additionally, the widespread dust in
the interstellar medium causes extinction, making the situation more complex.
However, because we live in the Milky Way, the positions and kinematics for a
large number of objects could be measured with high accuracy, making the Milky
Way as the only galaxy in the universe that we can investigate in detail.

Spiral structure is one of the fundamental characteristics of the Milky Way.
It has considerable influences on some other research fields, such as the
kinematics of nearby stars (e.g. Williams et al., 2013; Hunt et al., 2019;
Trick et al., 2021), the Galactic electron-density distribution (Taylor &
Cordes, 1993; Yao et al., 2017, Han et al. 2021), the Galactic dust
distribution and extinction map (Drimmel & Spergel, 2001; Hottier et al.,
2020), and the large-scale magnetic field of the Milky Way (e.g. Han, 2017).
There have been quite a few reviews about the global properties of Galaxy’s
spiral structure, Foster & Cooper (2010), Xu et al. (2018b) and Shen & Zheng
(2020) reviewed previous efforts. Although, disagreements remain in some
details, a general consensus that a global spiral pattern exists in the
Galactic disk has been achieved. In this work, we focus on the Solar
neighborhood, where the spiral structure can be better understood, because the
distances of a large number of nearby objects can be measured accurately.
Significant progress has been made in the past few years by taking advantage
of the astrometry measurements in radio to optical bands, which enables us to
reliably delineate the nearby spiral structure in unprecedented detail.

Morgan et al. (1952, 1953) first delineated three arm segments in the Solar
neighborhood with a sample of aggregates of high-luminosity O-A stars in the
1950s. The three segments are now known to be related to the Sagittarius-
Carina, Local and Perseus Arms. At that time, these structures were also
studied by using different methods (e.g. Thackeray, 1956; Bok, 1964; Bok et
al., 1970; Georgelin & Georgelin, 1971), such as, mapping the distribution of
H ii regions (Courtès et al., 1970), analyzing multiple structures shown in
the H i 21 cm line surveys (van de Hulst et al., 1954) or implied in the
observational data of other interstellar absorption lines toward background
stars (Münch, 1953). In the 1970s, Georgelin & Georgelin (1976) proposed the
famous model of the Galaxy’s spiral structure consisting of four major spiral
arm segments. The Sun was placed in the inter-arm region between the Perseus
Arm and the Sagittarius Arm. Then, the picture of Galaxy’s spiral structure
was extended by taking advantage of more observational data of different types
of spiral tracers e.g., H ii regions (e.g. Downes et al., 1980; Caswell &
Haynes, 1987; Russeil, 2003; Paladini et al., 2004), molecular clouds (e.g.
Cohen et al., 1980, 1985; Hou et al., 2009; Lépine et al., 2011), neutral
atomic gas (Simonson, 1970; Burton, 1973; Levine et al., 2006; Koo et al.,
2017), high-mass star-formation region (HMSFR) masers (e.g. Xu et al., 2006;
Reid et al., 2009), OB stars (e.g. Miller, 1972; Stothers & Frogel, 1974; de
Zeeuw et al., 1999; Wright, 2020), open clusters (e.g. Becker, 1964; Becker &
Fenkart, 1970; Janes et al., 1988; Dias & Lépine, 2005) and cepheids (e.g.
Fernie, 1968; Majaess et al., 2009). These great efforts enhanced our
understanding of the global properties of Galaxy’s spiral structure. For the
spiral structure in the Solar neighborhood, Xu et al. (2013) first found that
many HMSFR masers with accurate VLBI parallax measurements (Xu et al., 2006)
are situated in the Local Arm, indicating that the Local Arm is probably a
major arm segment, rather than an inter-arm spur or a branch as has been
suggested for a long time. The existence of the Local Arm also challenges the
formation mechanism of Galaxy’s spiral structure (Xu et al., 2016), since it
would be difficult to explain its existence according to the standard density-
wave theory (Yuan, 1969; Shu, 2016), owing to the narrow space between the
Sagittarius Arm and Perseus Arm.

In the past few years, there have been significant progress in observations by
taking advantage of the VLBI observations in radio band (Reid et al., 2019;
VERA Collaboration et al., 2020) and Gaia astrometry measurements in optical
band (Gaia Collaboration et al., 2016). Accurate parallaxes and proper motions
have been obtained for a large number of HMSFR masers (e.g. Reid et al.,
2019), H ii regions (e.g. Hou et al. 2021), O-type stars (e.g. Xu et al.,
2021), young open clusters (OCs, e.g. Dias et al., 2021) and evolved stars
(e.g. Khoperskov et al., 2020). Additionally, many giant molecular clouds
(GMCs) have had accurately determined distances based on the multi-wavelength
survey data from optical to infrared bands or the astrometric data of
foreground/background stars (Yan et al., 2019; Chen et al., 2020). By
combining the available data of different types of tracers together, it is now
possible to reliably map the detailed spiral structure within about 5 kpc of
the Sun.

In this work, we first give an overview about the observational status for
each type of spiral tracer, the available dataset of these objects with
accurate distances are collected. Then, we combine them together to give a
detailed description of the spiral structure in the Solar neighborhood.
Conclusions and discussions follow in the last section.

##  3 An overview of spiral tracers

Young objects (HMSFR masers, H ii regions, massive OB stars and young open
clusters etc.) and GMCs are known as good tracers for the Galaxy’s spiral
structure (hereafter gas arms). In addition, the spiral structure is imprinted
by the distribution of old and evolved stars (hereafter stellar arms). The gas
arms and stellar arms in a galaxy are not necessarily coincident with each
other. Discovering a large number of spiral tracers widely spread through the
Galactic disk, and measuring their distances as accurately as possible are the
key to settle the disputes on the spiral structure of our Milky Way Galaxy. In
the following, the observational status about GMCs, HMSFR masers, H ii
regions, OB stars, young OCs and evolved stars are discussed, respectively.

###  3.1 Giant molecular clouds

Giant molecular clouds are the vast assemblies of molecular gas with masses
from $\sim$10${}^{3}M_{\odot}$ to $\sim$10${}^{7}M_{\odot}$ (e.g. Murray,
2011). They are believed to primarily form in spiral arms (Dobbs & Baba, 2014)
and are the nurseries of most young stars in a galaxy. In the Milky Way, GMCs
have long been known as good tracers of spiral arms (e.g., Myers et al., 1986;
Grabelsky et al., 1988; Hou & Han, 2014). From the wealthy dataset of Galactic
CO surveys (see Heyer & Dame, 2015, for a review), a large number of isolated
molecular clouds have been identified by different methods (e.g. García et
al., 2014; Rice et al., 2016; Miville-Deschênes et al., 2017; Yan et al.,
2020a; Duarte-Cabral et al., 2021). For the majority of them, only kinematic
distances are known, which depend on the adopted Galaxy rotation curve, the
solution of the kinematic distance ambiguity, and deviation from the
hypothetic circular rotation. For instance, Duarte-Cabral et al. (2021)
compiled a large catalogue of 10,663 molecular clouds in the inner Galaxy.
They estimated the kinematic distances for 10,300 clouds after solving the
distance ambiguities through different methods. In addition to determining the
distances of molecular clouds and then mapping their distribution in the
Galactic disk, the other two methods have been used to reveal the Galaxy
spiral structure with CO sruveys: (1) Deconvolution of the survey data cube
(e.g. Pohl, Englmaier, & Bissantz, 2008; Nakanishi & Sofue, 2016); (2)
Modelling the observed longitude-velocity ($l-v$) maps of CO (e.g. Bissantz,
Englmaier, & Gerhard, 2003; Rodriguez-Fernandez & Combes, 2008; Baba, Saitoh,
& Wada, 2010; Pettitt et al., 2014, 2015; Li et al., 2021). A detailed review
about these two methods can be found in Xu et al. (2018b). As discussed in Xu
et al. (2018b), although there have been many efforts, the spiral structure
traced by molecular gas is still unclear, primarily due to the large
uncertainties of distances. There have been noticeable progress in the past
few years, as accurate distances were estimated for a large number of
molecular clouds.

With the CO data of the Milky Way Imaging Scroll Painting
survey111http://www.radioast.nsdc.cn/mwisp.php, the Gaia DR2 parallax and
G-band extinction (Gaia Collaboration et al., 2018), Yan et al. (2019)
proposed a background-eliminated extinction-parallax method to estimate the
distances of molecular clouds. The distance uncertainties of 11 clouds are
$\lesssim 10\%$. With the same method, Yan et al. (2020a) determined the
distances for 28 local molecular clouds ($d<1.5$ kpc, here $d$ is the distance
to the Sun) in the first Galactic quadrant. The distances for 76 molecular
clouds were measured in the second Galactic quadrant by Yan et al. (2020b).
Based on a sample of over 32 million stars with colour excesses and Gaia
distances, Chen et al. (2019b) constructed new three-dimensional dust
reddening maps of the Milky Way. With the maps and the sample of stars, Chen
et al. (2020) identified 567 dust/molecular clouds, and estimated their
distances by using a dust model fitting algorithm. The typical distance
uncertainty is less than 5%. These clouds are within $\sim 3$ kpc of the Sun.
Based on the near-infrared photometry data from the Two Micron All Sky Survey
and the Vista Variables in the Via Lactea Survey, Chen et al. (2019a) tracked
the extinction of red clump stars versus distance profiles of the sightlines
towards a sample of molecular clouds from Rice et al. (2016). Distances of 169
GMCs in the fourth Galactic quadrant were obtained.

We collected the data of GMCs from above references. 475 GMCs with masses
$>10^{4}M_{\odot}$ were obtained. To reliably depict the local spiral
structure, only the GMCs with distance uncertainties better than 15% were
adopted. For the distant clouds, we also required that their distance
uncertainties are $<$0.5 kpc. In total, 427 GMCs with masses from
$10^{4}M_{\odot}$ to 2.45$\times 10^{6}M_{\odot}$ were left. Their projected
distributions on the Galactic disk are shown in Fig. 1a. According to the
trigonometric parallax data of HMSFR masers (see Sect. 3.2), Reid et al.
(2019) obtained an updated model of Galaxy’s spiral arms, which is plotted in
Fig. 1 to make a comparison with the GMC distribution. It is shown that most
of these GMCs are distributed within about 3 kpc of the Sun, in the Perseus,
Local and Sagittarius-Carina Arms. Some distant GMCs in the fourth Galactic
quadrant are probably associated with the Centaurus Arm and the Norma Arm.
Along spiral arms, the distribution of GMCs presents some substructures,
especially in the regions within about 2 kpc of the Sun. The accuracies of
distances ensure that they are probably true features, but their nature (arm
spurs or feathers) and properties have not been well studied.

###  3.2 High-mass star-forming region masers

The early stage of massive star formation is accompanied by the maser emission
from molecular species such as OH, CH3OH and H2O (Fish, 2007). The maser spots
are compact and bright, hence are optimal targets for radio interferometric
observations. The trigonometric annual parallax measurement with Very Long
Baseline Interferometry (VLBI) is the most accurate method for deriving the
distances of astronomical objects. In 2006, a pioneer research on measuring
the trigonometric parallax of molecular masers was made by Xu et al. (2006),
who found a distance of W3(OH) in the Perseus Arm to be 1.95$\pm$0.04 kpc.
This work opened a new era to accurately reveal the Galaxy’s spiral structure
through VLBI measurements. Since then, nearly 200 HMSFRs have had measured
trigonometric parallaxes (typical accuracy is about $\pm$ 0.02 mas) and proper
motions, primarily by the Bar And Spiral Structure Legacy (BeSSeL) Survey
using the VLBA (Reid et al., 2019) and the Japanese VLBI Exploration of Radio
Astrometry (VERA) project (VERA Collaboration et al., 2020). Some sources were
observed by the European VLBI Network and the Australian Long Baseline Array
(e.g. Rygl et al., 2010; Krishnan et al., 2017). Based on the data of 199
HMSFRs, parameters of spiral arms in about one third of the Galactic disk were
updated by Reid et al. (2019), which is adopted in Fig. 1 to make a comparison
with the data distribution.

To depict the local spiral arms with high confidence, only the HMSFRs (Reid et
al., 2019; VERA Collaboration et al., 2020) with uncertainties of
trigonometric distances better than 15% were kept as for GMCs. For the distant
sources, we also required that their distance uncertainties are $<$0.5 kpc.
Then, 111 HMSFRs remain. Their distribution is given in Fig. 1b. These HMSFRs
are located in six arm segments, i.e. the Outer, Perseus, Local, Sagittarius,
Scutum and Norma Arms. Some of the HMSFRs are probably related with spur-like
structures in the inter-arm regions (Reid et al., 2019). A prominent one is
the spur branching the Sagittarius Arm and the Local Arm near $l\sim
50^{\circ}$ (see Fig. 1), which is firstly identified by Xu et al. (2016).

As shown in Fig. 1b, the HMSFRs with parallax measurements are distributed in
the regions covering about one-third of the entire Galactic disk. There is a
lack of observational data for many Galaxy areas, especially in the longitude
range of $\sim 240^{\circ}-360^{\circ}$. Other spiral tracers (e.g. GMCs, H ii
regions, massive OB stars, and young OCs) could be good complementary data,
which can help us to better depict the properties of spiral arms in the Solar
neighborhood.

Figure 1: Distributions of (a) GMCs, (b) HMSFR masers, (c) H ii regions, (d)
O-type stars and (e) young OCs in the Solar neighborhood. All of the plotted
objects have distance uncertainties better than 15% and $<$0.5 kpc as
determined by trigonometric or photometric method. The symbol sizes of GMCs
are proportional to their masses. For HMSFR masers, H ii regions and O-type
stars, an equal size of the dots is adopted. The symbol sizes of young OCs are
proportional to the number of cluster member stars. The position uncertainty
for each data point is shown by an underlying gray line segment. The thick
gray curved lines indicate the best fitted spiral arm model given by Reid et
al. (2019), the dotted lines denote the arm widths enclosing 90% of the HMSFR
masers. The black dashed lines indicate the four spurs or spur-like structures
proposed in literature (see Sect. 4.3). In each plot: the segments of spiral
arms are labelled; the Sun is at (0.0, 8.15) kpc (Reid et al., 2019), while
the Galactic center is at (0.0, 0.0) kpc; the Galactic long bar is indicated
by a shaded ellipse (Wegg, Gerhard, & Portail, 2015).

###  3.3 H ii regions

H ii regions are the regions of ionized gas surrounding recently formed O- or
early B-type stars or star clusters. They have been widely detected in the
Galactic disk, from the Galactic center (GC) region (Shahzamanian et al.,
2019) to the far outer Galaxy (Galactocentric distances $>$16 kpc, Anderson et
al., 2015). As indicators of early evolutionary stage of massive stars, H ii
regions have long been known as one of the primary tracers of spiral arms, and
helped us to construct the commonly used picture of Galaxy’s spiral structure
(e.g., Georgelin & Georgelin, 1976; Caswell & Haynes, 1987; Russeil, 2003; Hou
et al., 2009; Hou & Han, 2014). However, for the majority of known H ii
regions, only kinematic distances are available, which sometimes have large
uncertainties. It is currently the major obstacle for using H ii regions to
accurately delineate the spiral arms. There are about 400 H ii regions with
measured spectra-photometric (Russeil, 2003; Moisés et al., 2011; Foster &
Brunt, 2015) or trigonometric distances (e.g. Xu et al., 2006; Honma et al.,
2012). They are distributed within about 5 kpc of the Sun (Hou & Han, 2014).
The sample size and the accuracies of distances have yet to be improved.

In a recent work (Hou et al. 2021), we carried out a cross-match between the
WISE H ii regions (Anderson et al., 2014) and the known O- or early B-type
stars (Chen et al., 2019a; Xu et al., 2021). The ionizing stars of 315 H ii
regions were identified. The trigonometric parallaxes for these OB stars from
the Gaia Early Data Release 3 (Gaia EDR3, Gaia Collaboration et al., 2020)
were used to estimate the distances of H ii regions. In combination with the H
ii regions with known spectra-photometric/trigonometric distances, we obtain a
sample of 448 H ii regions with accurately determined distances, i.e. distance
uncertainties are better than 15% and less than 0.5 kpc. Their distribution in
the Galactic disk resembles GMCs and HMSFR masers as presented in Fig. 1c.

These H ii regions are scattered primarily in the Perseus, Local, Sagittarius-
Carina and Scutum-Centaurus Arms. The data distribution in the Local Arm and
Centaurus Arm deviate from the modelled spiral arms given by Reid et al.
(2019) in the 3rd and 4th Galactic quadrants, where the HMSFRs with
trigonometric measurements are largely absent. Hence, the extension of the
Local Arm and the position of the Centaurus Arm given by Reid et al. (2019)
need to be updated. In these arm segments, we also noticed that the H ii
regions are not uniformly distributed, but present some substructures. The
Sagittarius-Carina Arm is not continuous in the direction of
$l\sim$315${}^{\circ}-340^{\circ}$. Similar property is found for the Perseus
Arm in the longitude range of $\sim$150${}^{\circ}-160^{\circ}$. These
properties are consistent with the features illustrated by GMCs (Fig. 1a).
Although the number of H ii regions with accurate distances have been
increased largely, there is still a lack of accurate distances for many
Galactic H ii regions. From Gaia EDR3 or their future data release, it is
expected to identify more ionising stars and determine the distances of H ii
regions as accurately as possible.

###  3.4 OB stars

The massive and bright O- and early B-type (OB) stars are born in dense
molecular clouds. Many of them are not randomly distributed, but concentrated
in loose groups, named as “aggregates” (Morgan et al., 1953) or OB
associations (de Zeeuw et al., 1999; Wright, 2020). In the early 1950s,
substantial progress on tracing the arm segments in the Solar neighborhood was
first made by Morgan et al. (1952, 1953). Three segments of spiral arms (i.e.,
the Sagittarius, Local and Perseus Arms) appeared in the distribution of their
twenty-seven aggregates of O-A stars and additional eight distant stars. After
that, some follow-up studies identified more OB stars or OB associations, and
determined their spectra-photometric distances (e.g., Walborn, 1971; Miller,
1972; Stothers & Frogel, 1974; Reed & Reed, 2000). However, the picture of
Morgan did not expand significantly. With the Hipparcos catalog, de Zeeuw et
al. (1999) estimated the trigonometric distances for some OB associations
within $\sim$1 kpc from the Sun, primarily in the Local Arm. At present, the
known OB associations are limited within about $\sim$2 kpc from the Sun
(Wright, 2020). To extend the nearby arm segments traced by OB stars or OB
associations, higher accuracies of astrometry measurements than the Hipparcos
(typical parallax error $\sim$1 mas, de Zeeuw et al., 1999) are needed.

The Gaia satellite (Gaia Collaboration et al., 2016), launched in 2013, will
ultimately achieve parallax accuracy comparable to that of VLBI for
approximately $10^{9}$ stars. Many OB stars with accurate distances can be
derived from Gaia. By taking advantage of the Gaia data release 2, Xu et al.
(2018a) depicted the spiral structure within $\sim$3 kpc of the Sun. About
2,800 O-B2 stars with formal parallax uncertainties better than 10% were
extracted from the Catalog of Galactic OB stars (Reed, 2003). The spiral
structure demonstrated by the Gaia OB stars agrees well with that illustrated
by the VLBI HMSFR masers. These OB stars also extend the arm segments traced
by HMSFR masers into the fourth Galactic quadrant. Chen et al. (2019a)
identified 6,858 candidates of O- and early B-type stars. Together with the
known spectroscopically confirmed O-B2 stars from literature, a sample of
14,880 OB stars/candidates with Gaia DR2 parallax uncertainties better than
20% was obtained, and used to delineate the arm segments in the Solar
neighborhood. Recently, Gaia published its Early Data Release 3, the parallax
accuracies have been improved significantly, to be 0.02$-$0.07 mas for
$G<$17\. In a recent work, Xu et al. (2021) compiled the largest sample of
spectroscopically confirmed O-B2 stars (Skiff, 2014) available to date with
astrometric measurements of Gaia EDR3, including 14,414 O-B2 stars. 9,750 of
them have parallax uncertainties better than 10%. With this sample, the spiral
structure within $\sim$5 kpc of the Sun are delineated in detail.

In this work, the sample consisting of about 1,090 O-type stars given by Xu et
al. (2021) is adopted. Their distribution in the Galactic disk is shown in
Fig. 1d. As discussed in Xu et al. (2021), the distribution of O-type stars in
spiral arms are clumped. The Sagittarius-Carina Arm traced by O-type stars
seems to be not continuous in the direction of
$l\sim$315${}^{\circ}-340^{\circ}$. A gap of O-type stars in the range of
$l\sim$150${}^{\circ}-160^{\circ}$ in the Perseus Arm is also noticed. These
properties are consistent with the results shown by using GMCs and H ii
regions.

###  3.5 Young open clusters

An open cluster is a group of stars that formed in a giant molecular cloud. In
comparison to individual stars, it is possible to estimate more accurate
values of distance, proper motions and radial velocity for an OC, as it has
many member stars. In our Galaxy, star formation occurs mainly in spiral arms.
Hence, the majority of young OCs are believed to be borned in spiral arms, and
too young to migrate far from their birth locations. It is accepted that young
OCs (e.g. $<$20 Myr) can be used as good tracers for the nearby spiral arm
segments. In comparison, older OCs have more scattered distribution.

Becker (1963, 1964) first used 156 OCs to study the spiral structure in the
Solar neighborhood. They suggested that the distribution of those clusters
with earliest spectral type between O and B2 follows three spiral arm
segments. In comparison, the distribution of the clusters with earliest
spectral type between B3 and F does not present arm-like structures and seems
to be random. The picture was extended by Becker & Fenkart (1970) and Fenkart
& Binggeli (1979). Meanwhile, a different point of view raised by Janes &
Adler (1982) and Lynga (1982) with a large sample of about 400 open clusters.
They suggested that the observed nonuniform distribution of OCs is affected by
the interstellar obscuration, and dominated by the locations of dust clouds
rather than by the spiral structure. Janes et al. (1988) mentioned that the
young clusters define three complexes, but their association to a spiral
structure is not obvious. After that, the number of Galactic open clusters
gradually increased (e.g., see Mermilliod, 1995; Dias et al., 2002; Kharchenko
et al., 2013; Schmeja et al., 2014; Scholz et al., 2015). Meanwhile, the
spiral structure of the Milky Way was better uncovered by multi-wavelength
observations (e.g., Georgelin & Georgelin, 1976; Caswell & Haynes, 1987; Dame,
Hartmann, & Thaddeus, 2001; Russeil, 2003), especially in radio band, where
the dust obscuration has neglectable influence on the results. There has been
a general consensus that the nonuniform distribution of nearby OCs is related
to spiral arms (e.g. Dias & Lépine, 2005; Carraro et al., 2005; Moitinho,
2006; Vazquez, 2008; Moitinho, 2010; Camargo et al., 2013; Bobylev & Bajkova,
2014; Dias et al., 2019)

Before the data release of Gaia, there have been more than 3,000 known OCs
(e.g. see, Dias et al., 2002; Kharchenko et al., 2013; Dias et al., 2014;
Schmeja et al., 2014; Scholz et al., 2015). Many of them have determined mean
proper motions and membership probabilities (Sampedro et al., 2017; Dias,
Monteiro, & Assafin, 2018). Since the publication of Gaia DR2 (Gaia
Collaboration et al., 2018), on the one hand, the parameters of known OCs have
been updated (Cantat-Gaudin et al., 2018; Soubiran et al., 2018; Bossini et
al., 2019; Monteiro & Dias, 2019; Cantat-Gaudin & Anders, 2020; Cantat-Gaudin
et al., 2020; Tarricq et al., 2021; Dias et al., 2021). On the other hand, a
large number of new OCs and candidates have been identified (e.g. see Castro-
Ginard et al., 2018; Cantat-Gaudin et al., 2019; Castro-Ginard et al., 2019;
Sim et al., 2019; Liu & Pang, 2019; Hao et al., 2020; Castro-Ginard et al.,
2020; Ferreira et al., 2020; He et al., 2020; Hunt & Reffert, 2021; Ferreira
et al., 2021). With OCs, the nearby spiral arms were studied by Cantat-Gaudin
et al. (2018), Dias et al. (2019), Cantat-Gaudin et al. (2020), Tarricq et al.
(2021), and Ferreira et al. (2021) in the past few years. Especially, Monteiro
et al. (2021) studied the spiral arms traced by young OCs with the updated OC
catalogue of Dias et al. (2021), and determined the spiral pattern rotation
speed of the Galaxy, the corotation radius and the statistic properties of OC
parameters. Poggio et al. (2021) studied the spiral structure in the Solar
neighborhood with samples of young upper main sequence stars, classical
Cepheids and open clusters. The open clusters used by Poggio et al. (2021) is
from Cantat-Gaudin et al. (2020). Hao et al. (2021) compiled a catalogue of
more than 3,700 OCs from the references above, and re-calculated the
parameters (parallaxes, mean proper motions, radial velocities) based on the
latest Gaia EDR3 (Gaia Collaboration et al., 2020). The ages of these OCs were
either collected from references or estimated by their analysis.

In this work, we adopted the OC sample provided by Hao et al. (2021), in which
the OC parameters are based on the latest Gaia EDR3. There are 627 young OCs
(ages $<$ 20 Myr) in their catalogue. The distribution of young OCs in the
Galactic disk is shown in Fig. 1e. The distribution of young OCs resembles
that of GMCs, HMSFR masers, H ii regions and O-type stars. When weighted the
OCs with their number of member stars, one can notice that the OCs with more
member stars are more inclined to be located in spiral arms.

###  3.6 Evolved stars

As the velocity dispersion of gas is smaller than that of the old stars, the
gas response to any perturbations in the stellar disk is highly amplified
(Dobbs & Baba, 2014), making the gas arms easier to identify than the stellar
arms traced by old and evolved stars. For our Milky Way, unlike the gas arms
well depicted by GMCs, HMSFR masers, H ii regions, young OB stars or young
OCs, the spiral arms traced by old stars are still not clear. The properties
of stellar arms are important to better constrain the formation and evolution
of gas arms.

It is commonly suggested that the spiral structure traced by old stars is
dominated by two major spiral arms (the Scutum-Centaurus Arm and Perseus Arm)
based on analyzing the arm tangencies (Churchwell et al., 2009). In
observations, spiral arm tangencies are indicated by the local maxima in the
integrated number count of old stars or in the integrated emission in the
near-infrared and/or far-infrared bands against the Galactic longitude, and
have only been clearly identified for the Scutum-Centaurus Arm (Drimmel, 2000;
Drimmel & Spergel, 2001; Churchwell et al., 2009). Clear indications of
tangencies corresponding to the stellar Sagittarius-Carina Arm and Norma Arm
have not been found from observational data. As the Sun is located inside the
Perseus Arm, the observed line of sight do not penetrate its tangency. The
method of analyzing tangency points cannot be applied to this arm. However,
the Perseus Arm is also suggested to be a major stellar arm based on symmetry.
Indeed, many grand-design spiral galaxies with two well defined spiral arms
are observed in the universe (e.g. Willett et al., 2013). In comparison, arm
tangencies for the gaseous Sagittarius-Carina Arm, Scutum-Centaurus Arm and
Norma Arm could be identified from the wealthy survey data of radio
recombination lines, H ii regions, CO lines, dense molecular clumps and H i
21-cm line etc. (see Hou & Han, 2015).

Figure 2: Distributions of the combined dataset of GMCs (yellow circles),
HMSFR masers (blue dots), H ii regions (red dots), O-type stars (green dots)
and young OCs (yellow dots) are overlaid on a new concept map of the Milky
Way, which is credited by: Xing-Wu Zheng & Mark Reid BeSSeL/NJU/CFA based on
the spiral arm model of Reid et al. (2019).

By taking advantage of the data quality and large sky coverage of Gaia, it is
possible to map the nearby spiral structure traced by evolved stars. Miyachi
et al. (2019) studied the surface density distribution of stars aged $\sim$1
Gyr, and identified a marginal arm-like overdensity in the longitude range of
$90^{\circ}\leqslant l\leqslant 190^{\circ}$. The overdensity of stars is
close to the Local Arm defined by HMSFRs. By analyzing the Gaia DR2 data,
Kounkel & Covey (2019) identified a number of clusters, associations, and
moving groups distributed within $\sim$1 kpc of the Sun, many of them appear
to be filamentary or string-like. The youngest strings ($<$100 Myr) are
orthogonal to the Local Arm. The older ones are suggested to be the remnants
of several other arm-like structures which cannot be traced by dust and gas
any more. With a new method of analyzing the six-dimensional phase-space data
of Gaia DR2 sources, Khoperskov et al. (2020) identified six prominent stellar
density structures in the guiding coordinate space222The “guiding coordinate
space” is defined as (please see Khoperskov et al., 2020, for a detail):
$X_{g}=-R_{g}sin(\phi)$, $Y_{g}=-R_{g}cos(\phi)$, here, $R_{g}=L_{z}/V_{\rm
LSR}$ is the guiding radius, $L_{z}=R\times V_{\phi}$ is the instantaneous
angular momentum of the star, $R$ is the Galactocentric distance, $\phi$ is
the azimuthal angle around the Galactic center clockwise from the direction
towards the Sun, $V_{\phi}$ is the azimuthal velocity in the Galactic plane.,
corresponding to a physical spatial coverage of about 5 kpc from the Sun. Four
of these structures were suggested to correspond to the Scutum-Centaurus,
Sagittarius, Local, and Perseus Arms, while the remaining two may be
associated with the main resonances of the Milky Way bar and the outer
Lindblad resonance beyond the Solar circle. While Hunt et al. (2020) presented
a different point of view. They suggested that the stellar density structures
identified by Khoperskov et al. (2020) are known kinematic moving groups,
rather than coherent structure in physical space such as spiral arms. In
addition, it has also been shown that very different bar and spiral arm models
can be tuned to explain the observed features of Gaia data (e.g. Hunt et al.,
2019; Monari et al., 2019; Eilers et al., 2020; Khoperskov et al., 2020; Chiba
et al., 2021; Trick et al., 2021), making the situation more difficult to
handle.

In the past few years, progress in mapping the stellar arms in the Solar
neighborhood have been made, but there are no conclusive observational
results. As the properties of nearby stellar arms are not clear, we do not
incorporate them into our analysis/discussions in the following. But we
emphasise that determination of the properties of stellar arms in our Galaxy
definitely deserves more attention.

Figure 3: Upper: Distributions of the combined dataset of GMCs, HMSFR masers,
H ii regions, O-type stars and young OCs in the Galactic disk. For all the
plotted sources, their distance uncertainties are better than 15% and smaller
than 0.5 kpc. The positional uncertainty for each data point is shown by an
underlying gray line segment. The curved solid lines indicate the best fitted
spiral arm model given by this work (Table 1). The shaded areas around spiral
arms denote the fitted arm widths. The four dashed lines are the spurs or
spur-like structures proposed in literature. Lower: similar to the upper
panel, but a “density” distribution is calculated according to the
distribution of the sources.
Figure 4: Best fitted spiral arm model give by this work (Table 1) are
overlaid on the $l-v$ diagram of 12CO (1$-$0) of Dame, Hartmann, & Thaddeus
(2001). The spiral arm segments are indicated by different colors. To convert
the position of spiral arms into the $l-v$ diagram, the fitted “universal”
form of Galaxy rotation curve given by Reid et al. (2019) was adopted. The
distance of the Sun to the GC, $R_{0}$ is taken as 8.15 kpc. The circular
orbital speed at the Sun $\Theta_{0}$ is 236 km s-1 (Reid et al., 2019).

##  4 Properties of spiral structure in the Solar neighborhood

In order to better reveal the properties of spiral structure in the Solar
neighborhood, we combine the data of good tracers of gas arms, i.e. GMCs,
HMSFR masers, H ii regions, O-type stars and young OCs. It is probably the
most wide spread dataset of spiral tracers with accurate distances available
to date. Especially, the data distributions of different types of tracers are
complementary to each other in the sky coverage. As shown in Fig. 1 and Fig.
2, although some substructures seem to exist in spiral arms or inter-arm
regions, the distributions of these objects are in general follow the dominant
spiral arms identified by previous works (e.g. Georgelin & Georgelin, 1976;
Russeil, 2003; Hou & Han, 2014; Reid et al., 2019). Five segments of spiral
arms are delineated by the combined dataset. They are related to the Perseus,
Local, Sagittarius-Carina, Scutum-Centaurus and Norma Arms from outer Galaxy
to the GC direction. Additionally, there are about 30 sources possibly
scattered in the Outer Arm defined by HMSFR masers. However, the aggregation
of sources is not obvious. We will not discuss the Outer Arm in this work.

###  4.1 Fitting model to tracer distributions

From the combined dataset of spiral tracers (Fig. 1 and Fig. 2), some
noticeable features are the deviations of tracer distributions from the
modelled spiral arms given by Reid et al. (2019) in the 3rd and 4th Galactic
quadrants, where the HMSFRs with trigonometric measurements are largely
absent. For instance, many O-type stars and young OCs in the longitude range
of $l\sim 210^{\circ}-260^{\circ}$ deviate from the modelled Perseus Arm
towards the GC direction. Similar feature is found for the Local Arm in the
longitude range of $l\sim 260^{\circ}-280^{\circ}$. In the 4th quadrant, many
GMCs, H ii regions and O-type stars near $l\sim 300^{\circ}-350^{\circ}$
deviate slightly from the modelled Centaurus Arm of Reid et al. (2019) towards
the anti-GC direction. Hence, with the combined dataset, it would be helpful
to update the parameters of spiral arms in the Solar neighborhood.

The spiral arms observed in spiral galaxies (e.g. Seigar & James, 1998; Yu et
al., 2018) and that predicted by the density-wave theory (e.g. Lin & Shu,
1964; Shu, 2016) are approximately in the form of logarithmic, which is
characterized by a constant pitch angle. A simple and pure logarithmic form of
spiral arm was commonly adopted in previous works about the Galaxy’s spiral
structure (e.g. Russeil, 2003; Hou et al., 2009; Vallée, 2008; Reid et al.,
2009). On the other hand, it is found that the spiral arms in galaxies do not
follow logarithmic spirals perfectly, but seem to be kinked in nature (e.g.
Kennicutt, 1981; Kendall, Kennicutt, & Clarke, 2011; Honig & Reid, 2015; Díaz-
García et al., 2019, also see the Whirlpool Galaxy M 51). The observed spiral
arms can be better described by segments of logarithmic form with different
pitch angles. In theories, tidal interactions can result in noticeable kinks
along spiral arms in a galaxy (Dobbs & Baba, 2014). In simulation, D’Onghia,
Vogelsberger, & Hernquist (2013) found that the perturbers can produce
segments, and these segments are joined at kinks to form spiral arm. For our
Milky Way Galaxy, signs of kinked spiral arms were also noticed (e.g. Taylor &
Cordes, 1993; Hou & Han, 2014), as some of the spiral arms cannot be well
fitted by pure logarithmic spirals (e.g. the Sagittarius-Carina Arm). With
pure logarithmic spirals, it is also difficult to reproduce the observed $l-v$
maps of CO and HI for the outer Milky Way (e.g. Pettitt et al., 2014).
Following Reid et al. (2019), in this work we adopt a form of kinked
logarithmic spiral to fit an arm, which do not necessarily have a constant
pitch angle.

We allow one or two “kinks” in an arm, which means that two or more segments
with different pitch angles are used to describe a single spiral arm. For the
$i$th spiral arm, the form is described as:

$\ln(R/R_{i,kink})=-(\beta-\beta_{i,kink})\tan\psi_{i},$ (1)

here, $R$ is the Galactocentric radius at a Galactocentric azimuth angle
$\beta$. Following Reid et al. (2019), $\beta$ is defined as $0^{\circ}$
toward the Sun and increases in the direction of Galactic rotation.
$R_{i,kink}$ and $\beta_{i,kink}$ are the corresponding values of $R$ and
$\beta$ at the “kink” position for the $i$th arm. $\psi_{i}$ is the pitch
angle, which may have an abrupt change at the “kink” position. To be
consistent with Reid et al. (2019) and compare the results with their models,
a Markov chain Monte Carlo (MCMC) approach is adopted in this work to estimate
the arm parameters. The best-fitted arm parameters are listed in Table 1, and
the model is shown in Fig. 3. We also compare it with the observed $l-v$
diagram of CO (Dame, Hartmann, & Thaddeus, 2001) as given in Fig. 4. In the
fitting with the combined dataset, an equal weight is adopted, although the
sky coverage and sample size for different types of tracers are not the same.
Different treatments of weighting parameters were tested, e.g., scaling
according to the sample size of different types of tracers, but the
differences of the fitted arm positions were found to be small.

In comparison with the best-fitted model of Reid et al. (2019), the extension
of the Perseus Arm obtained in this work spirals slightly inward in the third
Galactic quadrant. In this work, the Local Arm is best fit with two segments
having different pitch angles, and spirals inward to the inner Galaxy regions
in the third to fourth Galactic quadrants to match the observational data. The
Centaurus Arm in the fourth quadrant is also fit with two segments in this
work. Their positions are slightly different from those of Reid et al. (2019)
near $l\sim 300^{\circ}-350^{\circ}$ but match the distributions of the
collected GMCs, H ii regions, O-type stars and young OCs. For the Sagittarius-
Carina Arm and the Norma Arm, our fitted arm positions are in general
consistent with that of Reid et al. (2019).

To evaluate that how well do the different types of tracers fit the spiral
arms, we calculate the percentages of tracers falling into our best fitted
spiral arms. The arm widths given in Table 1 were adopted to denote the spiral
arm regions. In the Norma Arm, the known HMSFR masers, H ii regions, O-type
stars and young OCs are still rare. This arm was not used in the calculation.
Additionally, the Outer Arm was also omitted. The percentages of tracers
falling into spiral arms are estimated to be 44%, 53%, 58%, 65% and 53% for
the GMCs, HMSFR masers, H ii regions, O-type stars and young OCs,
respectively. It seems that the GMCs are less confined to the spiral arms than
the other types of tracers. In comparison, if the objects are randomly
distributed in the Solar neighborhood, about 33% of them are expected to be in
the spiral arms.

###  4.2 Spiral arms in the Solar neighborhood

By taking advantage of the combined dataset of different types of tracers,
segments of spiral arms in the Solar neighborhood have been delineated and
fitted. Now we discuss their properties in detail.

Perseus Arm: The Perseus Arm is a dominant arm in our Galaxy as indicated by
high-mass star-formation activity (HMSFR masers, H ii regions, O-type stars),
young OCs, molecular gas and H i gas (e.g. Morgan et al., 1953; Caswell &
Haynes, 1987; Russeil, 2003; Hou & Han, 2014; Reid et al., 2019).
Additionally, the Perseus Arm has been suggested as one of the two dominant
stellar arms of the Milky Way (Drimmel, 2000; Drimmel & Spergel, 2001;
Churchwell et al., 2009). As shown in Fig. 3, different types of spiral
tracers (GMCs, HMSFR masers, H ii regions, O-type stars and young OCs) are
mixed together. Their distributions are in general consistent with each other.
The depicted Perseus Arm is as long as $\sim$12 kpc, starts near (X,Y) = (4.5,
8) kpc, and extends to the third Galactic quadrant near (X,Y) = ($-$6, 9) kpc.
In this arm, the spiral tracers are not evenly distributed but tend to
cluster. There are two obvious aggregation areas of sources, one is in the
longitude range of $l\sim 100^{\circ}-150^{\circ}$, the other is in $l\sim
170^{\circ}-190^{\circ}$, indicating the active star-formation areas in the
Perseus Arm. Outside these two regions, some sites of GMCs or star-formation
are scattered, and interspersed with regions showing low star-formation
activity and/or low number density of GMCs. Outside the segment shown in Fig.
3, the extension of the Perseus Arm to the first or fourth Galactic quadrant
could be explored in the $l-v$ diagram of CO and H i survey data, but have not
been accurately depicted (Xu et al., 2018b). Reid et al. (2019) has suggested
that the Perseus Arm may be not a dominant arm as measured by high-mass star-
formation activity over most of its length. More spiral tracers with accurate
distances are needed in order to reliably trace this arm to distant Galaxy
regions.

Local Arm: The Local Arm was thought to be a “spur” or secondary spiral
feature for a long time (e.g. Georgelin & Georgelin, 1976; Amaral & Lepine,
1997; Russeil, 2003), until the density of HMSFRs in the Local Arm was found
to be comparable to that of the Sagittarius Arm and Persues Arm (Xu et al.,
2013, 2016). The Local Arm traced by HMSFR masers stretches for $>$6 kpc,
which is larger and more prominent than previously thought. Hence, it is
suggested to be a dominant arm segment. As shown in Fig. 3, there are a large
number of spiral tracers (GMCs, HMSFR masers, H ii regions, O-type stars and
young OCs) located in this arm, which present complex substructures. There are
several areas where sources are accumulated. One is near (X,Y) = (1.5, 7.7)
kpc in the first Galactic quadrant, another is near (X,Y) = ($-$2, 8.2) kpc in
the fourth quadrant. A filament-like structure appears in the region from
(X,Y) = (2, 7.5) kpc to (X,Y) = (0.8, 9) kpc, and spirals outward toward the
anti-GC direction with respect to the fitted arm center. Interestingly, a
substructure near $l\sim 100^{\circ}-150^{\circ}$ and with $d\sim 0.6$ kpc is
indicated by many GMCs, but without associated HMSFR masers, H ii regions,
O-type stars or young OCs, at least shown by the collected dataset. For the
majority of sources in this arm, their distance uncertainties are less than
10%, hence, these substructures are believed to be true features. In general,
the depicted Local Arm could be as long as $\sim$9 kpc, starts near (X,Y) =
(4.5, 6) kpc, and extends to the third and even fourth quadrant near (X,Y) =
($-$3, 8) kpc. Outside the delineated segment, the extension of the Local Arm
is still not clear. The Local Arm seems to gradually spiral inward in the
fourth Galactic quadrant, becoming very close to the Carina Arm. It is
indicating that the Local Arm is possibly an arm branch locating between the
Perseus Arm and the Sagittarius-Carina Arm. More observational data are needed
to uncover its nature.

Sagittarius-Carina Arm: This arm can be clearly traced by GMCs (Grabelsky et
al., 1988) and massive star-formation regions (Russeil, 2003; Urquhart et al.,
2014; Hou & Han, 2014). There are a large number of sources in this arm. The
Sagittarius-Carina Arm in Fig. 3 starts near (X,Y) = (4.5, 4) kpc, extends to
the fourth quadrant near (X,Y) = ($-$7, 5) kpc, as long as $\sim$19 kpc. It is
found that this arm cannot be well fitted by a single pitch angle model,
especially in the longitude range of 20${}^{\circ}-40^{\circ}$ (e.g. Taylor &
Cordes, 1993; Russeil, 2003; Hou & Han, 2014; Reid et al., 2019). Three major
aggregation areas of sources are noticed. One is near $l\sim 30^{\circ}$,
showing an elongated structure, which is probably a true feature as it is not
only traced by HMSFR masers, but also by H ii regions, O-type stars or young
OCs. The other two areas are near $l\sim 340^{\circ}-360^{\circ}$ and close to
the tangent region of the Carina Arm ($l\sim 280^{\circ}-290^{\circ}$). The
distribution of sources in this arm is well consistent with the model given by
Reid et al. (2019). Outside the long segment traced in Fig. 3, the extension
of the Sagittarius-Carina Arm could be well delineated by the distribution of
GMCs or H ii regions with kinematic distances, or indicated by the features
shown in the $l-v$ diagrams of CO and H i.

Scutum-Centaurus Arm: Similar to the Sagittarius-Carina Arm, the Scutum-
Centaurus Arm has also been traced by many GMCs and massive star-formation
regions. In addition, it is also suggested to be one of the two dominant
stellar spiral arms of the Milky Way, as the Centaurus Arm tangent was clearly
shown by the evolved stars surveyed by Spitzer (Drimmel, 2000; Drimmel &
Spergel, 2001; Churchwell et al., 2009). The collected GMCs, H ii regions,
O-type stars and young OCs enrich the sample of spiral tracers in this arm,
especially in the fourth Galactic quadrant. As shown in Fig. 3, the spiral
tracers in this arm seem to be more evenly distributed than that of the
Perseus Arm, Local Arm and Sagittarius-Carina Arm. The traced segment of the
Scutum-Centaurus Arm starts near (X,Y) = (2.5, 4) kpc, and extends to the
fourth Galactic quadrant near (X,Y) = ($-$5, 4.5) kpc, as long as $\sim$8 kpc.

Norma Arm: This arm is distant ($\gtrsim 4$ kpc) from the Sun, and most likely
starts near the near end of the Galactic bar. Previously, the Normal Arm has
not been clearly traced by GMCs or massive star-formation regions. Mainly
because the majority of spiral tracers possibly associated with this arm only
have kinematic distances. With the collected dataset, it seems that only a
segment of the Norma Arm can be roughly traced by GMCs in the fourth Galactic
quadrant. The number of HMSFR masers, H ii regions, O-type stars or young OCs
related to this arm is still very limited.

Table 1: Parameters of the best-fitted model of spiral arms (see Eq. 1) with the combined dataset of GMCs, HMSFR masers, H ii regions, O-type stars and young OCs. For the $i$th spiral arm, $\beta$ Range in column (2) gives the range of the arm segment as shown in Fig. 3, $\beta$ is the Galactocentric azimuth angle, which is defined as 0∘ toward the Sun and increases in the Galactic rotation direction. $\beta_{kink}$ and $R_{kink}$ in column (3) and (4) are the corresponding values of $\beta$ and $R$ at the “kink” position, here $R$ is the Galactocentric radius. The pitch angle is $\psi_{<}$ for $\beta<\beta_{kink}$, and $\psi_{>}$ for $\beta>\beta_{kink}$. The fitted arm width is listed in column (7). The Sagittarius-Carina Arm is consist of three segments, hence are divided into two parts and listed below separately. Arm |  $\beta$ Range |  $\beta_{kink}$ |  $R_{kink}$ |  $\psi_{<}$ |  $\psi_{>}$ |  Width
---|---|---|---|---|---|---
|  (deg) |  (deg) |  (kpc) |  (deg) |  (deg) |  (kpc)
(1) |  (2) |  (3) |  (4) |  (5) |  (6) |  (7)
Perseus |  $-28\to 28$ |  32.7 |  9.57 |  3.9 |  19.9 |  0.26
Local |  $-22\to 39$ |  $-$2.0 |  8.46 |  4.4 |  12.6 |  0.23
Sagittarius-Carina 1 |  $-57\to 17.5$ |  $-$22.8 |  7.92 |  11.9 |  22.2 |  0.33
Sagittarius-Carina 2 |  $17.5\to 48$ |  17.5 |  5.95 |  21.3 |  0.2 |  0.25
Scutum-Centaurus |  $-50\to 41$ |  $-$26.3 |  6.47 |  $-$0.5 |  16.5 |  0.25
Norma |  $-38\to 18$ |  18.0 |  4.5 |  1.3 |  19.0 |  0.07

###  4.3 Substructures in the spiral arms or inter-arm regions

Besides the extended structure of major spiral arms which probably wrap fully
around the Milky Way, substructures named as branches, spurs and features are
often observed in spiral galaxies (Elmegreen, 1980; Dobbs & Bonnell, 2006). As
discussed in La Vigne, Vogel, & Ostriker (2006) and Dobbs & Baba (2014), there
are no formal definitions of these different types of substructures in
observations and/or numerical simulations. Different definitions have been
adopted (Chakrabarti, Laughlin, & Shu, 2003; Dobbs & Bonnell, 2006). The
initial definitions based on observations are as follows: (1) arm branches are
in general the structures locating between two major spiral arms, and/or where
one arm bifurcates into two, branches may extend from one arm to another
(Elmegreen, 1980; La Vigne, Vogel, & Ostriker, 2006; Dobbs & Baba, 2014). (2)
Spurs are shorter features than branches, and indicated by strings of star
formation sites in the inter-arm regions. They jut out from spiral arms into
the inter-arm regions at larger pitch angles than the arm itself (Weaver,
1970; Elmegreen, 1980). Two or more spurs are commonly found to be close or
parallel to one another. (3) Feathers are also short features, but indicated
by thin dust lanes or extinction features that cut across spiral arms and have
large pitch angles. Outside the luminous arms, these extinction features
become mostly undetectable (Lynds, 1970). Arm branches, spurs and features are
typically extend away from the trailing side of spiral arms (e.g. M 51, Dobbs
& Baba, 2014).

As shown in Fig. 3, the objects in spiral arms are not uniformly distributed,
resulting in the patchy and/or bifurcate appearance of spiral arms.
Additionally, about 40% of the collected sources distribute in the inter-arm
regions, also present some structural features. These substructures may be
related to arm branches, spurs and/or feathers as found in some nearby face-on
spiral galaxies (e.g. M 51, M 101, Dobbs & Baba, 2014; Xu et al., 2018b). Our
knowledge about these substructures in our Galaxy is very limited.

In our Galaxy, several spurs and/or spur-like structures have been classified
from observations. In the direction of $l\sim 90^{\circ}-210^{\circ}$, a
structural feature named as Orion spur (e.g. Fig.1 of Humphreys, 1970;
Schmidt-Kaler, 1975; Kolesnik & Vedenicheva, 1979) or Cepheus spur (Pantaleoni
González et al., 2021) was discussed. This feature is suggested to be located
between the Local Arm and the Perseus Arm, which may even extend to the first
Galactic quadrant (Aasi et al., 2016). However, the name of Orion spur was
also used to indicate the Local Arm in some literature (Amaral & Lepine, 1997;
Carraro, 2014; Eker et al., 2014), which brings up a question: if the Orion
spur discussed in the early days (e.g. Humphreys, 1970) exists or not? It will
be helpful to reinvestigate this question with modern observational data.
Recently, Xu et al. (2016) identified a spur near the direction of $l\sim
50^{\circ}$ traced by five HMSFRs with VLBI parallax measurements, bridging
the Local Arm to the Sagittarius Arm and having a pitch angle of $\sim$18∘
($\sim$13∘ given by a recent analysis of Reid et al., 2019). The existence of
this spur is also supported by the CO features shown in the $l-v$ diagram. By
analyzing the distribution and peculiar motions of HMSFR G352.630$-$1.067 and
five O-type stars, a possible spur-like structure is proposed by Chen et al.
(2019), which extends outward from the Sagittarius Arm. Reid et al. (2019)
mentioned that the Norma Arm in the first Galactic quadrant displays a spur-
like structure, which starts at (X, Y) = (3, 2) kpc near the end of the
Galactic bar and extends to about (X, Y) = (2, 5) kpc at Galactic azimuth
angle of $\sim 18^{\circ}$. This structure has a large pitch angle of $\sim
20^{\circ}$. In addition, a spur-like structure bridging the Scutum Arm and
the Sagittarius Arm is also mentioned in Reid et al. (2019), which is
indicated by the distribution and proper motions of six HMSFRs and has a large
pitch angle of $\sim 20^{\circ}$. These proposed spurs or spur-like structures
are plotted in Fig. 1 and Fig. 3. It seems that some GMCs, H ii regions,
O-type stars and young OCs are coincident with these structures in positions.

Except the Orion spur mentioned in some early literature, the known spurs or
spur-like structures identified in the past few years are nearly all based on
the astrometric data of HMSFR masers. In comparison to HMSFR masers, the GMCs,
H ii regions and especially O-type stars and young OCs with accurate distances
have covered a much wider Galactic range. Hence, it is expected that more
substructures could be identified. To identify the substructures in the inter-
arm regions or spiral arms, radial velocities and/or proper motions for the
sources would be helpful, which are still not available for many of them.
Additionally, the properties of these substructures will help us to better
understand the formation mechanisms of Galaxy’s spiral structure. As the
formation of these features is different for different spiral arm models
(Dobbs & Baba, 2014).

###  4.4 Formation mechanisms of Galaxy’s spiral structure

Besides accurately mapping the spiral structure, understanding its formation
mechanism is another difficult issue. Different mechanisms have been proposed,
e.g., the quasi-stationary density wave theory (Lin & Shu, 1964, 1966),
localized instabilities, perturbations, or noise-induced kinematic spirals
(Sellwood & Carlberg, 1984), dynamically tidal interactions (Toomre & Toomre,
1972), or a combination of some of them (Dobbs & Baba, 2014). Although many
efforts have been dedicated to elaborate plausible hypotheses concerning the
origin of the dominant spiral arms of the Galaxy, it is still not conclusive
for now. One way is to analyse the kinematic properties of stars in the
vicinity of the Sun (e.g. Williams et al., 2013; Faure et al., 2014; Liu et
al., 2017; Kawata et al., 2018). However, it has been shown that very
different bar and spiral arm models can be tuned to look like the local Gaia
data (Hunt et al., 2019), or convincingly explain all observed features at
once (e.g. Monari et al., 2019; Eilers et al., 2020; Khoperskov et al., 2020;
Chiba et al., 2021; Trick et al., 2021). The other method is comparing the
relative positions of gas arms and stellar arms (e.g. Roberts, 1969; Shu,
2016; Dobbs & Pringle, 2010; Dobbs & Baba, 2014; Hou & Han, 2015; Monguió et
al., 2015; He et al., 2021), which can be used to verify the predictions of
different theories. Observational evidence for the spatial offsets between the
gas arms and stellar arms have been noticed for the tangent regions (e.g. Hou
& Han, 2015). However, for other regions in the Galactic disk, it is not clear
whether the systematic spatial offsets or age pattern exist or not (Monguió et
al., 2015; Vallée, 2018; He et al., 2021). More tests based on observations
are needed.

In addition, the properties of the Local Arm make the situation more complex.
Its existence induces some challenge to the density wave theory applied to our
Galaxy (Xu et al., 2013, 2016). Before 2017, no specific mechanism for the
origin of the Local Arm has been proposed. Lépine et al. (2017) first
interpreted the Local Arm as an outcome of the spiral corotation resonance,
which traps arm tracers and the Sun inside it (also see Michtchenko et al.,
2018). Their modelled corotation zone looks consistent with the banana-like
structure of the Local Arm shown by the distributions of GMCs, H ii regions,
O-type stars and young OCs in Fig. 3. In the context of other mechanisms, e.g.
localized instabilities, perturbations, or noise-induced kinematic spirals,
the properties of the Local Arm may be easily interpreted. The Milky Way has
been suggested to be quite different from a pure grand design spiral, but
probably resemble a multi-armed galaxy M 101, due to the existence of the
Local Arm and the many possible spurs noticed from observational data (Xu et
al., 2018b). Typically, the localized instabilities are associated with
flocculent or multi-armed galaxies (Dobbs & Baba, 2014).

##  5 Conclusions and Discussions

In this work, the spiral structure in the Solar neighborhood are discussed
based on the largest dataset available to date, which consists of different
types of good spiral tracers. They are GMCs, HMSFR masers, H ii regions,
O-type stars and young OCs. All the collected data have accurate distances
with uncertainties $<$15% and $<$0.5 kpc. With the dataset, we update the
parameters of spiral arm segments in the Solar neighborhood, and discuss their
properties. The spiral structure traced by GMCs, HMSFR masers, H ii regions,
O-type stars and young OCs are in general consistent with each other. Five
segments of dominant spiral arms in the Solar neighborhood are depicted, they
are the Perseus, Local, Sagittarius-Carina, Scutum-Centaurus and Norma Arms.
However, the extensions of these arm segments to distant Galaxy regions have
not been reliably traced. In the spiral arms and inter-arm regions, the
distributions of spiral tracers present complex substructures, which are
probably true features as the distance uncertainties of the tracers are small.
At least five spurs or spur-like features have been identified in the
literature by taking advantage of the astrometric data of HMSFR masers, but
more substructures remain to be uncovered with the updated dataset of
different types of good spiral tracers. In comparison to the gas arms traced
by GMCs and star-formation activity, the properties of stellar arms indicated
by evolved stars are still inconclusive.

There is significant progress in understanding the Galaxy’s spiral structure
in the past few years, which is heavily dependent on the developments of
astrometric observations by the VLBI in radio band and the Gaia satellite in
optical band. The VLBI observations have the advantage to measure the spiral
tracers in distant Galaxy regions with high accuracies (as high as 0.006 mas,
typically about $\pm$0.2 mas, Reid et al., 2019), and almost not affected by
dust extinction. BeSSeL is planned to extend to the southern sky (Reid et al.,
2019), which will provide parallax and proper motion measurements for many
HMSFRs in the third and fourth Galactic quadrants, where the data of such kind
of measurements are largely absent at present. In the near future, the SKA is
expected to open a new era for the trigonometric measurements of a large
number of HMSFRs and hence for the investigations on the Galaxy’s global
spiral structure. On the other hand, the Gaia EDR3 has been released in the
end of 2020, the parallax uncertainties have been significantly improved to be
0.02$-$0.03 mas for $G$ band magnitude less than 15, and 0.07 mas for $G$ =
17. The full Gaia DR3 is expected in 2022. Gaia is still committing itself to
improve the accuracies of parallaxes and proper motions for a large number of
stars. Although the stars measured by Gaia suffered from the dust extinction,
so that distant objects cannot be measured, the Gaia data have the advantage
to reveal the detailed structures/substructures and kinematic properties in
the Solar neighborhood, at least for the regions within about 5 kpc of the
Sun. In the Solar neighborhood, the segments of dominant spiral arms have been
well traced as discussed in the main text. However, the properties of
substructures in the spiral arms or inter-arm regions, and the properties of
stellar arms traced by evolved stars are still far from conclusive, which may
be deserving of more attention.

## Acknowledgments

The author thanks the anonymous referees for constructive comments and
suggestions that significantly improved this work, and Prof. Y. Xu for helpful
suggestions. The author also would like to thank Dr. C. J. Hao for kindly
providing the data of young OCs, and Dr. X. Y. Gao for carefully reading the
manuscript. This work is supported by the National Key R&D Program of China
(NO. 2017YFA0402701) and the National Natural Science Foundation (NNSF) of
China No. 11988101, 11933011, 11833009. L.G.H thanks the support from the
Youth Innovation Promotion Association CAS. This work has made use of data
from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC, https://www.
cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been
provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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