Article Title

Giant molecular clouds (GMCs) are the vast assemblies of molecular gas with masses from $\sim$10${}^{3}M_{\odot}$ to $\sim$10${}^{7}M_{\odot}$ (e.g. murr11). They are expected to form in spiral arms (db14) and the nurseries of most young stars in a galaxy. In the Milky Way, the GMCs have long been known as good tracers of spiral arms (e.g., mdt+86; gcbt88; hh14). From the rich data set of Galactic CO surveys (see hd15, for a review), a large number of isolated molecular clouds has been identified by different methods (e.g. gbn+14; rgb+16; mme17; yys+20). But for the majority of them, only kinematic distances are available, which depends on e.g., the adopted Galaxy rotation curve, the solution of the kinematic distance ambiguity, and the influence of non-circular rotation. Based on the kinematic distances, the spiral arm properties traced by GMCs can not be reliably derived (xhw18). In the past few years, significant progresses have been made, as accurate distances were estimated for a large number of molecular clouds.

With the CO observational data of the Milky Way Imaging Scroll Painting (MWISP) survey¹¹1http://www.radioast.nsdc.cn/mwisp.php, the Gaia DR2 parallax and G-band extinction (dr2), yys+19 proposed a background-eliminated extinction-parallax method to estimate the distances of molecular clouds. 11 clouds in the third Galactic quadrant ($210^{\circ}<l<218^{\circ}$) were presented with distance uncertainties $\lesssim 10\%$. With the same method, yys+20 determined distances for 28 local molecular clouds ($<1.5$ kpc) in the first Galactic quadrant ($26^{\circ}<l\leqslant 49^{\circ}$), yys+21 measured the distances for 76 molecular clouds in the second Galactic quadrant ($104^{\circ}<l<151^{\circ}$). Based on a sample of over 32 million stars with estimates of colour excesses and Gaia distances, chy+19 constructed new 3D dust reddening maps of the Milky Way. With the maps and the sample of stars, (cly+20) 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, chh19 tracked the extinction of red clump stars versus distance profiles of the sightlines towards a sample of molecular clouds from rgb+16. Distances of 169 GMCs in the fourth Galactic quadrant were obtained.

We collected the available GMCs from above references. There are 475 GMCs with masses $>10^{4}M_{\odot}$. To depict the nearby spiral arms with high confidence, only the GMCs with distance uncertanties better than 15% were adopted. For the distant clouds (e.g. $>5$ kpc), we also required that their distance uncertanties are $<$0.5 kpc, approximately the widths of Galactic spiral arms (rmb+19). Finally, 427 GMCs with masses from $10^{4}M_{\odot}$ to 24.5$\times 10^{5}M_{\odot}$ were left. Their projected distributions on the Galactic plane are shown in Fig. 3a. The updated model of Galaxy spiral arms given by rmb+19 according to their trigonometric parallax data of high-mass star-formation masers (see Sect. 3.2) are overplotted to make a comparison. Most of these GMCs are distributed in the regions within about 3 kpc of the Sun, located in segments of the Perseus Arm, the Local Arm and the Sagittarius-Carina Arm. Some distant GMCs in the fourth Galactic quadrant are roughly coincide with the Centaurus Arm and the Crux Arm. In total, about 78% of these GMCs are located in the spiral arms defined by HMSFR masers. Along the segments of spiral arms shown in Fig. 3a, the distribution of GMCs seems to present some elongated substructures, especially in the regions within about 2 kpc of the Sun in the Local Arm. Their parameters and nature (e.g. spurs, feathers) have not been well studied. The existence of these substructures also indicates that, to get a reliable estimates of the spiral arm parameters, the adopted spiral tracers should span a wide longitude range.

The early stage of massive star formation is accompanied by the maser emission from molecular species of e.g. OH, CH₃OH and H₂O. As the maser spots are compact and bright, they are optimal targets for radio interferometric observations. The trigonometric annual parallax measurement with Very Long Baseline Interferometry (VLBI) is the most accurate and reliable method for the distance determination of astronomical objects.

In 2006, a pioneering research on measuring the trigonometric parallax of molecular masers for the HMSFR W3(OH) in the Perseus Arm was given by xrzm06, who found a distance of 1.95$\pm$0.04 kpc (xrzm06; hbm+06), and opened a new era to accurately revealing the Galactic spiral structure through VLBI measurements. Since then, nearly 200 HMSFR masers have had accurately measured trigonometric parallaxes and proper motions (typical accuracy is about $\pm$ 0.02 mas), primarily by the Bar And Spiral Structure Legacy (BeSSeL) Survey using the VLBA (rmb+19) and the Japanese VLBI Exploration of Radio Astrometry (VERA) project (VERA), some sources were observed by the European VLBI Network (EVN) and the Australian Long Baseline Array (LBA) through the 6.7 GHz mathenal masers (e.g. rbr+10; ker+17). Based on the data of 199 HMSFR masers, parameters of spiral arms in about a third of the entire Galactic disk had been updated and demonstrated by rmb+19.

At present, there are more than 200 HMSFR masers (rmb+19; VERA) having trigonometric parallax measuremnts. To depict the nearby spiral arms with high confidence, only the HMSFR masers with distance uncertanties better than 15% were kept as what we did for GMCs. For the distant sources (e.g. $>5$ kpc), we also required that their distance uncertanties are $<$0.5 kpc. Then, 111 HMSFR masers are left, and their distribution is given in Fig. 3b. These HMSFRs are located in six spiral arm segments, i.e. the Outer Arm, the Perseus Arm, the Local Arm, the Sagittarius Arm, the Scutum Arm and the Norma Arm. Some of the HMSFRs are probably related with spur-like structures in the inter arm regions (rmb+19). A prominent one is the spur branching the Sagittarius Arm and the Local Arm near $l\sim 50^{\circ}$ identified by xrd+16.

As shown in Fig. 3b, the available HMSFR masers with trigonometric parallax measuremnts 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, OB stars) could be good complementary data to the HMSFR masers to better constrain the properties of spiral arms in the vicinity of the Sun.

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 Centre (GC) region (e.g. ssn+19) to the far outer Galactic disk (Galactocentric distances $D>$16 kpc, aaj+15). As indicators of early evolutionary stage of massive stars, H ii regoins have long been known as one of the primary tracers of spiral arms, and help us to construct the commonly used picture of Galaxy spiral structure (e.g., gg76; ch87; rus03; hhs09; hh14). But for the majority of known H ii regions, only kinematic distances are available, which sometimes have large uncertainties. It is currently a main obstacle for using H ii regions to accurately delineate the spiral arms. There are about 400 H ii regions with measured spectra-photometric distances (rus03; mdf+11; fb15) or trigonometric parallax distances (e.g. xrzm06; honm12). They are distributed within about 5 kpc of the Sun (xhw18). The sample size and also the accuray of the spectra-photometric/trigonometric distance 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/candicates (wise) and known O- or early B-type stars (chh19; xhb+21). The exciting stars of 315 H ii regions were identified. The trigonometric parallaxes for these OB stars from the Gaia Early Data Release 3 (Gaia EDR3 edr3) were used to estimated the distances of H ii regions. Most of these H ii regions ($\gtrsim$75%) do not have spectra-photometric/trigonometric distances before. In combination with the H ii regions with known spectra-photometric/trigonometric distances, we have 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 distributions in the Galactic plane are given in Fig. 3c.

The distribution of these H ii regions resembles those of GMCs and HMSFR masers, also extends the nearby spiral arms in some Galaxy regions. These H ii regions are primarily scattered in the Perseus Arm, Local Arm, Sagittarius-Carina Arm and Scutum-Centaurus Arm. Similar to GMCs, about 77% of these H ii regions are located in the spiral arms defined by HMSFR masers. While, the extension of the Local Arm and the position of the Centaurus Arm seems to be updated. In some spiral arm segments, we also noticed that the H ii regions are not uniformly distributed, but present some substructures. Especially, the Sagittarius-Carina Arm seems to be not continuus 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}$. Same indications are also shown in the GMC data (Fig. 3a).

Although the number of H ii regions with accurate distance estimations have been increased a lot. There are still a lack of distance information for many nearby or distant H ii regions. From Gaia EDR3 or their future data release, it is expected to identify more central exciting stars of H ii regions, and determine their distances as accurately as possible, which will help us to better delineate the spiral arms in our Galaxy.

The massive and bright O- and early B-type (OB) stars were born in dense molecular clouds. It has been found that many of them are not randomly distributed, but concentrated in loose groups, e.g. “aggregates” (mor53) or OB associations (dhb+99; wri20). They are young objects and believed to be good tracers of Galaxy spiral arms. In fact, in the early 1950s, a substantial progress about tracing the arm segments in the solar neighborhood was first made by mor52; mor53 with high-luminosity O-A stars. Three segments of spiral arms (i.e., the Sagittarius Arm, Local Arm and Perseus Arm) in the longitude range of $330^{\circ}\lesssim l\lesssim 210^{\circ}$ appeared in the projected distribution of their twenty-seven aggregates of O-A stars and eight distant stars. After that, some follow-up studies identified more OB stars or OB associations, and determined their spectrophometric distances (e.g., wal71; mil72; sf74; rr00), but the picture of Morgan did not expanded significantly. With the Hipparcos catalog, dhb+99 determined the trigonometric distances for some OB associations within $\sim$1 kpc from the Sun, which are primarily located in the Local Arm. At present, the known OB associations are limited within about $\sim$2 kpc from the Sun (wri20). To extend the arm segments, one need to identify more OB stars or OB associations. Higher accuracy of astrometry measurements than the Hipparcos (typical parallax errors $\sim$1 mas, dhb+99) are desired, which will improve the spectrophotometric distances (sd19), and accuratly derive the distances of spiral arm tracers.

The Gaia satellite (gaia), 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. xbr+18 depicted the spiral structure within $\sim$3 kpc of the Sun with the Gaia data release 2. About 2800 O-B2 stars with formal parallax uncertainties better than 10% were extracted from the Catalog of ree03. The spiral structure demonstrated by the Gaia OB stars agrees well with that illustrated by VLBI masers. These OB stars also extend the spiral arm segments traced by HMSFR masers into the fourth Galactic quadrant. Then, chh19 identified 6858 candidates of O- and early B-type stars, together with the known spectroscopically confirmed O-B2 stars from the literature, a sample of 14880 OB stars/candicates with Gaia DR2 parallax uncertainties better than 20% was used to delineate the nearby arm segments. Recently, Gaia published its Early Data Release 3, the parallax accuracies of which have been improved significantly, to be 0.02$-$0.07 mas for $G<$17. In a recent work, xhb+21 compiled the largest sample of spectroscopically confirmed O-B2 stars (skiff14) available to date with astrometric measurements by GAIA EDR3, including 14414 O-B2 stars. 9750 of them have parallax uncertainties better than 10%. With this sample of O-B2 stars, the spiral structure within $\sim$5 kpc of the Sun are delineated clearly in detail.

The sample of about 1090 O-type stars given by xhb+21 is adopted. Their distribution in the Galactic plane is shown in Fig. 3d. About 81% of these O-type stars are located in the spiral arms defined by HMSFR masers. However, the extension of the Local Arm and the position of the Centaurus Arm seems to be updated, which are also shown by the H ii region data (Fig. 3c). As discussed in xhb+21, the distribution of O-type stars in spiral arms are clumped. Consistent with the results shown by GMCs and H ii regions, the Sagittarius-Carina Arm traced by O-type stars seems to be not continuus in the direction of $l\sim$315${}^{\circ}-340^{\circ}$. There is also a gap of spiral tracers in the longitude range of $\sim$150${}^{\circ}-160^{\circ}$ in the Perseus Arm.

The spiral structure traced by GMCs, HMSFR masers, H ii regions and young OB stars reflect the response of gas to the stellar disc. As the velocity dispersion of gas is smaller than that of the old stars, the gas response to any perturbations in the stellar disc is highly amplified (db14), making the gas arms are easier to be identified than the stellar arms traced by old stars. For our Milky Way, the spiral arms traced by older objects are still not clear. The properties of stellar arms are important for us to better constrain the formation and evolution of gas arms.

Unlike the gas arms traced by gas or young stars, it is now commonly suggested that the spiral structure traced by old stars is probably dominated by two spiral arms (the Scutum-Centaurus Arm and Perseus Arm) based on analyzing the observed arm tangencies (cbm+09). Spiral arm tangency indicated by the local maxima in the integrated number counts of old stars or in the integrated emissions against the Galactic longitudes in the near-infrared and/or far-infrared bands has only been clearly identifed for the Scutum-Centaurus Arm (dri00; ds01; cbm+09). Such tangencies coresponding to the stellar Sagittarius-Carina Arm and Norma Arm have not been found from observations. As the Sun is located inside the Perseus Arm, whose tangencies are thus not observable. But the Perseus Arm is also suggested to be a major stellar arm based on symmetry. In comparison, arm tangencies for the gaseous Sagittarius-Carina Arm, Scutum-Centaurus Arm and Norma Arm could be identified from the survey data of e.g. radio recombination lines, H ii regions, CO lines, dense molecular clumps and also H i 21-cm line (hh15).

The high quality and sky coverage of the Gaia data make it possible to map the structure in the disc traced by older stars, at least for the Galaxy regions within several kpc from the Sun. msk+19 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 DR data, kc19 identified a number of clusters, associations, and moving groups within 1 kpc of the Sun, and many of them appear to be filamentary or string-like. The youngest strings ($<$100 Myr) are orthogonal to the Local Arm. The older ones appear to be remnants of several other arm-like structures that cannot be presently traced by dust and gas. With a new method to analyzing the 6D phase-space data pf Gaia DR2 sources, kgd+20 identified six prominent stellar density structures in the guiding space, corresponding to a physical space coverage within about 5 kpc from the Sun. Four of these structures were suggested to be corresponding to the Scutum-Centaurus Arm, Sagittarius Arm, Local Arm, and Perseus Arm. The remaining two are associated with the main resonances of the Milky Way bar and the outer Lindblad resonance beyond the solar circle. hjp+20 presented a different point of view, they suggested that the stellar density structures identified by kgd+20 are known kinematic moving groups, and not coherent structure in physical space such as spiral arms.

In the past few years, some progresses in mapping the structure in the disc traced by older stars have been made. But there is still no conclusive observational results. In addition, it has also been shown that very different bar and spiral arm models can be tuned to look like the local Gaia data (hbb+19) or convincingly explain all observed features at once (e.g. mfs+19; ehr+20; kgd+20; cfs+21; tfh+21).

The spiral tracers collected in this work all have accurate determined distances, and distributed in a wide range of Galactic regions (within $\sim$5 kpc of the Sun). Although there are many substructures, the distributions of sources are in general follow the dominant spiral arms. With the dataset, we can update the parameters of the arm segments. In this section, we fit the data to give a better description of the major arm segments.

A logarithmic spiral arm model is adopted to fit the data distributions. For the $i$th arm, its logarithmic form is:

here, $R$ is the Galactocentric radius at a Galactocentric azimuth angle $\beta$. Follow rmb+19, $\beta$ 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. The fitting results are shown in Fig. 2 and the arm parameters are listed in Table 1.

Besides the tracers located in the major spiral arms (Norma Arm, Scutum-Centaurus Arm, Sagittarius–Carina Arm, Local Arm and Perseus Arm), there are some sources (about 20% in the present dataset) distributed in the inter arm regions. The presented substructures may be related with giant molecular clouds, arm branches, spurs and/or feathers as found in some nearby face-on spiral galaxies (e.g. M 51, M 101, db14; xhw18). Our knowledge about the substructures in our Galaxy is very limited.

In our Galaxy, several spur or spur-like structures have been classified in observations. In addition to pointing away and being traceable between heliocentric distances of 0.3 and 1.5 kpc, the Orion Spur protrudes from this major feature between $l\sim 210^{\circ}$ and $l\sim 220^{\circ}$. xrd+16 identified a spur near the direction of $l\sim 50^{\circ}$ traced by five HMSFRs with VLBI parallax measurements, which bridging the Local Arm to the Sagittarius Arm and having a pitch angle of $\sim$18^∘ ($\sim$13^∘ given by a recent analysis of rmb+19). The existence of this spur is also supported by the CO features shown in the longitude-velocity ($l-V$) diagram. By analyzing the distributions and peculiar motions of HMSFR G352.630$-$1.067 and five O-type stars, a possible spur-like structure is proposed by clz+19, which extending outward from the Sagittarius Arm and close to the GC direction. rmb+19 mentioned that the Norma Arm in the first quadrant displays a spur-like structure, which starting at (X, Y) = (3,2) kpc near the end of the Galaxy bar and extending to about (2,5) kpc at Galactic azimuth 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 mentioned in rmb+19, which is indicated by the distributions and proper motions of six HMSFRs and also has a large pitch angle of $\sim 20^{\circ}$. These four proposed spur or spur-like structures are plotted in Fig. 2. It seems that some GMCs, H ii regions and O-type stars are coincident with these structures in positions.

These four known spur or spur-like structures all are identified with the data of HMSFR masers, as discussed in Sect.2.2, there is a lack of HMSFR data in large Galaxy area. While, the data of GMCs, H ii regions and especially O-type stars cover a larger sky, as the complement of radial velocity data, it is expected that more substrcutures could be identified. To identify more substructures, 6D information are necessary, which are still not available for many sources. In the spiral arms, there are possible some substructures, to be continuued.

Besides accurately mapping the spiral structure, understanding their formation mechnisim is another difficult issue. Different mechanisms have been proposed to interprete the observed properties of spiral tracers, e.g., the quasi-stationary density wave theory (ls64; ls66), localized instabilities, perturbations, or noise induced kinematic spirals (sc84), dynamically tidal interactions (tt72), or a combination of some of them (db14). Although many efforts have been dedicated to elaborate plausible hypotheses concerning the origin of the main spiral arms of the Galaxy, it is still not conclusive for now. One way is to analysis the kinematic properties of stars in the vicinity of the Sun (e.g. wsb13; fsf14; lws+17; kbc18). It has been shown that very different bar and spiral arm models can be tuned to look like the local Gaia data (hbb+19) or convincingly explain all observed features at once (e.g. mfs+19; ehr+20; kgd+20; cfs+21; tfh+21). The other method is through comparing the relative positions of gas arms and stellar arms (e.g. rob69; shu16; dp10; db14; hh15; mgf15; hxh21), which can be used to verify the predictions of different theories. Observational evidences for the position offsets between the gas arms and stellar arms have been noticed for the arm tangent regions (hh15). For other regions in the Galactic disc, it is still not conclusive whether the spatial offsets or age pattern exist or not (mgf15; val18; hxh21), which is important for understanding the dynamic nature of Galaxy’s dominant spiral arms, more tests based on observations would be necessary.

The properties of the Local Arm make the sitution more complex. Its existence post some challenge to the density wave theory to our Galaxy (xlr+13; xrd+16). Before 2017, no specific mechanism for the origin of the Local Arm has been proposed. lmb+17 first interpreted the Local Arm as an outcome of the spiral corotation resonance, which traps arm tracers and the Sun inside it (also see mlb+18). Their modeled corotation zones seems well consisitent with the banana-like structure of the Local Arm shown in Fig. 2.

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