# On the Structure of the Sagittarius Spiral Arm in the Inner Milky Way

S. B. Bian  Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210033, China<EMAIL_ADDRESS>School of Astronomy and Space Science,
University of Science and Technology of China, Hefei 230026, China  Y. W. Wu
National Time Service Center, Key Laboratory of Precise Positioning and Timing
Technology, Chinese Academy of Sciences, Xi’an 710600, China  Y. Xu  Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210033, China;
<EMAIL_ADDRESS>School of Astronomy and Space Science, University of Science
and Technology of China, Hefei 230026, China  M. J. Reid  Center for
Astrophysics $|$ Harvard $\&$ Smithsonian, 60 Garden Street, Cambridge, MA
02138, USA  J. J. Li  Purple Mountain Observatory, Chinese Academy of
Sciences, Nanjing 210033, China<EMAIL_ADDRESS>B. Zhang  Shanghai
Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
K. M. Menten  Max-Planck-Institut f$\ddot{u}$r Radioastronomie, Auf dem Hügel
69, 53121 Bonn, Germany  L. Moscadelli  INAF-Osservatorio Astrofisico di
Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy  A. Brunthaler  Max-Planck-
Institut f$\ddot{u}$r Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany

###### Abstract

We report measurements of trigonometric parallax and proper motion for two 6.7
GHz methanol and two 22 GHz water masers located in the far portion of the
Sagittarius spiral arm as part of the BeSSeL Survey. Distances for these
sources are estimated from parallax measurements combined with 3-dimensional
kinematic distances. The distances of G033.64$-$00.22, G035.57$-$00.03,
G041.15$-$00.20, and G043.89$-$00.78 are $9.9\pm 0.5$, $10.2\pm 0.6$, $7.6\pm
0.5$, and $7.5\pm 0.3$ kpc, respectively. Based on these measurements, we
suggest that the Sagittarius arm segment beyond about 8 kpc from the Sun in
the first Galactic quadrant should be adjusted radially outward relative to
previous models. This supports the suggestion of Xu et al. (2023) that the
Sagittarius and Perseus spiral arms might merge in the first quadrant before
spiraling inward to the far end of the Galactic bar.

Interstellar masers (846), Trigonometric parallax (1713), Star forming regions
(1565), Milky Way Galaxy (1054)

##  1 Introduction

Over the last 16 years, the parallaxes and proper motions of over 200 masers
associated with high-mass star-forming regions (HMSFRs) have been measured
(Reid et al. 2019, hereafter R19; VERA Collaboration et al. 2020), which trace
the spiral arms and three-dimensional (3D) motions of their young stars. While
the nearby spiral arms of the Milky Way have been mapped in detail (e.g., Xu
et al., 2016), there are few parallax measurements for sources with distances
beyond $\approx$10 kpc. In order to extend our mapping of the Milky Way, in
this work we report parallax measurements of four distant maser sources,
G033.64$-$00.22, G035.57$-$00.03, G041.15$-$00.20, and G043.89$-$00.78,
located past the tangent point of the Sagittarius spiral arm in the first
Galactic quadrant. In addition, in order to better constrain the spiral arm
structure in distant regions, we also calculate the 3D kinematic distances for
several sources whose distances are greater than about 8 kpc. Reid (2022) has
shown 3D kinematic distances to be generally superior to parallax distances
for sources well past the Galactic center.

##  2 Observations and Data Analysis

Table 1: Positions and Brightnesses

Source | R.A. (J2000) | Dec. (J2000) | $\Delta\Theta_{\rm E}$ | $\Delta\Theta_{\rm N}$ | Brightness | $V_{\rm LSR}$ | Beam
---|---|---|---|---|---|---|---
| $\mathrm{(^{h}\;\;\;{}^{m}\;\;\;{}^{s})}$ | $(\arcdeg\;\;\;\arcmin\;\;\;\arcsec)$ | (∘) | (∘) | (Jy/beam) | (km s-1) | (mas $\times$ mas @ $\arcdeg$)
G033.64$-$00.22(M) | 18 53 32.56656 |  $+$00 31 39.1152 | … | … | 16.0 | 60.36 | 6.7 $\times$ 5.1 @ 165
J1848+0138 | 18 48 21.81041 |  $+$01 38 26.6296 |  $-$1.3 | 1.1 | 0.030 |  | 5.1 $\times$ 3.6 @ 173
J1857$-$0048 | 18 57 51.35887 |  $-$00 48 21.9369 | 1.1 |  $-$1.3 | 0.053 |  | 5.9 $\times$ 3.0 @ 3
G035.57$-$00.03(W) | 18 56 22.52577 |  $+$02 20 27.5007 | … | … | 0.9 | 48.62 | 1.6 $\times$ 0.5 @ 164
J1855+0251 | 18 55 35.43649 |  $+$02 51 19.5650 |  $-$0.2 | 0.5 | 0.115 |  | 1.4 $\times$ 0.5 @ 164
G041.15$-$00.20(M) | 19 07 14.36746 |  $+$07 13 18.0190 | … | … | 3.2 | 56.00 | 3.7 $\times$ 1.5 @ 4
J1905+0652 | 19 05 21.21029 |  $+$06 52 10.7830 |  $-$0.5 |  $-$0.4 | 0.058 |  | 4.2 $\times$ 2.4 @ 6
J1907+0907 | 19 07 41.96333 |  $+$09 07 12.3956 | 0.1 | 1.9 | 0.072 |  | 3.9 $\times$ 2.0 @ 179
G043.89$-$00.78(W) | 19 14 26.39610 |  $+$09 22 36.5926 | … | … | 8.6 | 59.18 | 1.4 $\times$ 0.4 @ 163
J1905+0952 | 19 05 39.89897 |  $+$09 52 08.4075 |  $-$2.2 | 0.5 | 0.072 |  | 1.3 $\times$ 0.6 @ 163
J1913+0932 | 19 13 24.02535 |  $+$09 32 45.3775 |  $-$0.3 | 0.2 | 0.047 |  | 1.5 $\times$ 0.7 @ 159
J1922+0841 | 19 22 18.63365 |  $+$08 41 57.3753 | 1.9 |  $-$0.7 | 0.013 |  | 1.4 $\times$ 0.6 @ 164

Note. — Source names followed by M and W in parentheses indicate methanol and
water masers. $\Delta\Theta_{\rm E}$ and $\Delta\Theta_{\rm N}$ are the
angular offsets of the QSOs relative to the maser toward the East and North.
The absolute position, peak brightness, and (naturally weighted) beam size and
position angle (PA; east of north) are listed for the first epoch. Note that
the absolute position accuracies are limited to about $\pm 1$ mas from the
assumed values for the QSOs. The local standard of rest (LSR) velocities
($V_{\rm LSR}$) of the reference maser spots are listed for G033.64$-$00.22,
G041.15$-$00.20, and G043.89$-$00.78, whereas for G035.57$-$00.03, J1855+0251
was used as the phase reference.

We conducted parallax observations of two 6.7 GHz methanol (CH3OH) and two 22
GHz water (H2O) masers over 16 epochs spanning 1.2 yr with the National Radio
Astronomy Observatory’s (NRAO’s)111NRAO is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. Very Long Baseline Array (VLBA) under program BR210. Prior to our
program, G035.57$-$00.03 had not been observed for a parallax measurement.
Parallaxes for the other three sources had been previously published by Wu et
al. (2014, 2019). These were specifically chosen for re-observation, because
previous parallax measurements (with only 4 or 5 epochs per source) were not
accurate enough to provide strong constraints on spiral structure for distant
portions of the Sagittarius arm.

Details of the observations are listed in Table 5. We scheduled the
observations to occur near the extrema of the sinusoidal parallax signatures
in R.A., since the parallax amplitudes in decl. were considerably smaller. At
each epoch, three 1.7-hr blocks of phase-referenced observations were inserted
between four 0.5-hr geodetic blocks, used for clock and atmospheric delay
calibrations (see Reid et al., 2009, for details). Four adjacent dual-
polarized intermediate-frequency (IF) bands of 16 MHz bandwidth were used for
the phase-referenced observations. The maser emissions were centered in the
third IF.

The data were correlated in Socorro, New Mexico, with the DiFX222DiFX, a
software correlator for very long baseline interferometry (VLBI), is developed
as part of the Australian Major National Research Facilities Programme by the
Swinburne University of Technology and operated under licence. software
correlator (Deller et al., 2007). The IF bands containing the masers were
correlated with 4000 and 2000 spectral channels for the 6.7 GHz CH3OH and the
22 GHz H2O masers, yielding velocity channels of 0.18 and 0.11 km s-1,
respectively.

We reduced the correlated data with the Astronomical Image Processing System
(AIPS; Greisen, 2003) and ParselTongue (Kettenis et al., 2006) scripts in four
steps as described in Reid et al. (2009). In step 1, we corrected delays and
phases for feed rotations, updated Earth’s orientation parameters, ionospheric
delays using total electron content maps, residual clock errors, tropospheric
delays determined from the geodetic calibration blocks, and updated source
positions (when necessary). In step 2, we converted correlator amplitudes to
Jansky units by applying telescope gains and system temperatures. In step 3,
for the maser data we shifted frequencies to hold LSR velocities at a desired
value for all sources and observations. In step 4, one scan on a strong
calibrator was chosen to remove delay and phase differences among all bands.
In step 5, for all but one source, a channel with strong and compact maser
emission was used as the interferometer phase reference and applied to all
maser channels and background quasi-stellar objects (QSOs). For
G035.57$-$00.03, the bright background QSO (J1855+0251) was used as the phase
reference, because the peak brightness of the H2O maser (0.9 Jy beam-1)
provided insufficient signal-to-noise ratios on individual VLBA baselines in 8
kHz spectral channels and 20 s integrations.

The AIPS task IMAGR was used to image the spectral-line emission of the masers
and continuum emission of the QSOs. The positions of the maser spots and
background QSOs were determined by fitting elliptical Gaussian brightness
distributions to the images using the AIPS task JMFIT. Table 1 lists the
positions and brightnesses from the first epoch.

Table 2: Astrometric Results

Source | $\pi$ | $\mu_{x}$ | $\mu_{y}$ | $V_{\rm LSR}$ | Dπ | Dk | Dave
---|---|---|---|---|---|---|---
| (mas) | (mas y-1) | (mas y-1) | (km s-1) | (kpc) | (kpc) | (kpc)
G019.60$-$00.23 | $0.076\pm 0.011$ | $-3.11\pm 0.16$ | $-6.36\pm 0.17$ | $41\pm 3$ | $13.2^{+2.2}_{-1.7}$ | $12.5\pm 0.8$ | $12.6\pm 0.7$
G020.08$-$00.13 | $0.066\pm 0.010$ | $-3.14\pm 0.14$ | $-6.44\pm 0.16$ | $41\pm 3$ | $15.2^{+2.7}_{-2.0}$ | $12.4\pm 0.6$ | $12.7\pm 0.6$
G032.74$-$00.07‡ | $0.126\pm 0.016$ | $-3.15\pm 0.27$ | $-6.10\pm 0.29$ | $37\pm 10$ | $7.9_{-0.9}^{+1.2}$ | $11.4\pm 1.0$ | $10.6\pm 0.8$
G033.64$-$00.22∗†‡ | $0.103\pm 0.011$ | $-3.01\pm 0.07$ | $-6.30\pm 0.08$ | ${}^{a}61\pm 3$ | $9.7^{+1.2}_{-1.0}$ | $10.0\pm 0.6$ | $9.9\pm 0.5$
G035.57$-$00.03∗ | $0.098\pm 0.008$ | $-3.02\pm 0.13$ | $-6.08\pm 0.18$ | ${}^{a}53\pm 3$ | $10.2^{+0.9}_{-0.8}$ | $10.2\pm 0.7$ | $10.2\pm 0.6$
G035.79$-$00.17 | $0.113\pm 0.013$ | $-2.96\pm 0.12$ | $-6.23\pm 0.14$ | $61\pm 5$ | $8.8_{-0.9}^{+1.2}$ | $9.6\pm 0.8$ | $9.4\pm 0.6$
G037.47$-$00.10 | $0.088\pm 0.030$ | $-2.63\pm 0.07$ | $-6.19\pm 0.15$ | $58\pm 3$ | $11.4_{-2.9}^{+5.9}$ | $9.4\pm 1.0$ | $9.6\pm 0.9$
G038.03$-$00.30 | $0.095\pm 0.022$ | $-3.01\pm 0.06$ | $-6.20\pm 0.11$ | $60\pm 3$ | $10.5_{-2.0}^{+3.2}$ | $9.2\pm 0.6$ | $9.3\pm 0.6$
G041.15$-$00.20∗† | $0.137\pm 0.011$ | $-2.74\pm 0.15$ | $-6.03\pm 0.16$ | ${}^{b}60\pm 3$ | $7.3^{+0.6}_{-0.5}$ | $8.4\pm 1.2$ | $7.6\pm 0.5$
G041.22$-$00.19 | $0.113\pm 0.022$ | $-2.82\pm 0.13$ | $-5.89\pm 0.16$ | $59\pm 5$ | $8.8^{+2.1}_{-1.4}$ | $8.5\pm 1.4$ | $8.7\pm 1.1$
G043.03$-$00.45 | $0.130\pm 0.019$ | $-3.03\pm 0.15$ | $-6.56\pm 0.20$ | $56\pm 5$ | $7.7^{+1.3}_{-1.0}$ | $8.3\pm 0.7$ | $8.2\pm 0.6$
G043.89$-$00.78∗† | $0.136\pm 0.005$ | $-3.01\pm 0.16$ | $-6.03\pm 0.18$ | ${}^{c}54\pm 3$ | $7.3^{+0.3}_{-0.3}$ | $8.3\pm 0.8$ | $7.5\pm 0.3$
G045.07+00.13 | $0.129\pm 0.007$ | $-3.21\pm 0.26$ | $-6.11\pm 0.26$ | $59\pm 5$ | $7.8^{+0.4}_{-0.4}$ | $7.7\pm 1.0$ | $7.7\pm 0.4$
G045.45+00.06 | $0.119\pm 0.017$ | $-2.34\pm 0.38$ | $-6.00\pm 0.54$ | $55\pm 7$ | $8.4^{+1.4}_{-1.1}$ | $7.6\pm 1.4$ | $8.1\pm 0.9$
G045.49+00.12 | $0.144\pm 0.024$ | $-2.62\pm 0.17$ | $-5.61\pm 0.16$ | $58\pm 3$ | $6.9^{+1.4}_{-1.0}$ | $7.0\pm 1.6$ | $6.9\pm 0.9$
G045.80$-$00.35 | $0.137\pm 0.023$ | $-2.52\pm 0.17$ | $-6.08\pm 0.27$ | $64\pm 5$ | $7.3^{+1.5}_{-1.0}$ | $6.3\pm 1.5$ | $7.0\pm 1.0$

Note. — Astrometric results are listed for the four sources discussed in this
paper and 12 other sources in the Sagittarius arm at distances greater than
about 8 kpc. Column 1 lists Galactic source names. Columns 2, 3, and 4 give
parallaxes and proper motions in the eastward ($\mu_{x}$
=$\mu_{\alpha}\cos\delta$) and northward directions ($\mu_{y}$ =
$\mu_{\delta}$ ). Column 5 lists LSR velocities. Columns 6, 7, and 8 list the
parallax distances, 3D kinematic distances, and their variance-weighted
averages. We adopted these weighted averages in column 8 as the ”final”
distance. Sources with a superscript (*) are those reported in this paper.
Their $V_{\rm LSR}$ are determined from NH${}_{3}(J,K)=(1,1)$ emission and the
references are (a) Wienen et al. (2012); (b) Pandian et al. (2012); and (c)
Olmi et al. (1993). For other sources parallaxes, proper motions, and line-of-
sight velocities are taken from Table 1 of R19 (along with their primary
references), except for G019.60$-$00.23 and G020.08$-$00.13, which are taken
from Xu et al. (2021). Sources with a superscript ($\dagger$) are those having
previously published parallaxes, and column 2 lists their weighted averages
with the parallax measurements in this paper, as described in Section 3.2.
Sources with a superscript ($\ddagger$) are those flagged as outliers in R19
but included in this paper when determining the characteristics of the
Sagittarius arm, as described in Section 4.2.

##  3 Parallax and Distance Estimates

###  3.1 Parallax and Proper Motion Fitting

We selected compact maser spots for parallax and proper motion fitting. For
the H2O masers G035.57$-$00.03 and G043.89$-$00.78, we first did the parallax
and proper motion fitting for each maser spot relative to each background
source in order to identify and remove outliers caused by the blending of
maser spots. We added “error floors” in the eastern and northern directions in
quadrature with the formal positional uncertainties from JMFIT and adjusted
them to achieve a reduced $\chi^{2}$ per degree of freedom near unity in each
coordinate. The error floors were used to capture systematic errors in
position measurements, usually owing to uncompensated atmospheric delays.

At the lower frequency of the 6.7 GHz methanol maser sources G033.64$-$00.22
and G041.15$-$00.20, ionospheric “wedges” can cause systematic positional
shifts across the sky, significantly increasing astrometric error. In order to
mitigate this issue, we used an image-position-based method to generate
positional data relative to an “artificial quasar” at the target maser
position during each epoch. Detailed descriptions of this method can be found
in Reid et al. (2017) and Zhang et al. (2019). We adopted this approach (Zhang
et al., 2019) in the parallax fits.333A phase-calibration based procedure,
MultiView (Rioja et al., 2017) and inverse MultiView (Hyland et al., 2022),
has recently been shown superior to the image-based method, but could not be
used with the observing strategy adopted in program BR210.

Because all maser spots in a source should have the same parallax, we used all
(unblended) maser spots and background sources to carry out a combined
solution, which uses a single parallax parameter but allows each maser spot to
have a different proper motion. The fitting results for the H2O and CH3OH
masers are shown in Figures 4 and 5, respectively. Tables 6 and 7 provide
detailed results of the parallax and proper motion fits. Since systematic
errors caused by propagation delays are essentially the same for all maser
spots, we multiplied the formal parallax uncertainties by the square root of
the number of spots used for the parallax fitting (Reid et al., 2009).

Individual fits for G043.89$-$00.78 with different QSOs revealed some
differences among the inferred error-floor values, suggesting different
contributions to the systematic error budget from uncompensated atmospheric
delays and/or variable unresolved QSO structure. After determining the
individual error floors, we added these in quadrature to their formal
uncertainties from JMFIT before doing a combined fit. Also, as seen in Figure
4, the decl. data for G043.89$-$00.78 show the presence of systematics in the
residuals, which might be attributed to proper-motion acceleration, possibly
owing to orbital acceleration in a long-period stellar binary. Such effects
have been seen in Very Long Baseline Interferometric data from Pleiades stars
(Melis et al., 2014). When adjustable acceleration parameters were included in
the fitting process, these systematic residuals disappeared, as shown by the
red dashed line in Figure 4. The estimated acceleration parameters are listed
in Table 6. We adopted the parallax results from this approach for
G043.89$-$00.78.

The internal motions of maser features persisting for at least five epochs
were averaged to estimate the motion of the central star. Considering typical
values of maser spot motions relative to the central star of $\sim 5$ km s-1
(Moscadelli et al., 2002) for 6.7 GHz CH3OH masers and $\sim 10$ km s-1 (Gwinn
et al., 1992) for 22 GHz H2O masers, for sources with multiple maser features
we inflated the formal uncertainties for each proper motion component of the
central star by adding $\pm 3$ km s-1 and $\pm 5$ km s-1 “error floors” in
quadrature, respectively. For sources with only one maser feature, we adopted
$\pm 5$ km s-1 and $\pm 10$ km s-1 error floors for the CH3OH and H2O masers.
We adopted an LSR velocity for the central star based on the centroid of the
NH3 molecular line emission (Wienen et al., 2012; Pandian et al., 2012; Olmi
et al., 1993).

###  3.2 Previous Measurements

Regarding G033.64$-$00.22, Reid et al. (2014) reported a parallax of 0.131
$\pm$ 0.020 mas, whereas our data yield a parallax of 0.090 $\pm$ 0.014 mas.
These two parallaxes are statistically consistent at the 1.7$\sigma$ level.
Combining these two measurements with variance weighting yields a parallax of
0.103 $\pm$ 0.011 mas.

For G041.15$-$00.20, our data yield a parallax of 0.144 $\pm$ 0.014 mas, and
combining this with the parallax of 0.125 $\pm$ 0.018 mas of Wu et al. (2019)
yields a variance-weighted average parallax of 0.137 $\pm$ 0.011 mas.

For G043.89$-$00.78, parallaxes of 0.121 $\pm$ 0.020 mas and 0.144 $\pm$ 0.014
were reported by Wu et al. (2014) and Wu et al. (2019), respectively.
Combining these with the our measured parallax of 0.137 $\pm$ 0.006 mas yields
a parallax of 0.136 $\pm$ 0.005 mas.

###  3.3 3D Kinematic Distances

The 3D kinematic distances provide an alternative method to estimate distance,
independent of parallax measurements. This technique combines likelihoods as a
function of distance for line-of-sight velocities and proper motion components
in Galactic longitude and latitude, assuming a rotation curve for the Galaxy.
Multiplying these three likelihoods yields a posteriori distance estimate,
which is generally free of the two-fold ambiguities for standard (1D)
kinematic distances using only line-of-sight velocities for sources within the
Solar circle (ie, Galactocentric radii less than $R_{0}$).

For the four sources discussed in this paper and 12 other sources in the
Sagittarius arm whose distances are greater than about 8 kpc, their 3D
kinematic distances were estimated using the proper motions, LSR velocities
and the Galactic rotation curve of Reid (2022). Table 2 lists their
trigonometric parallaxes, proper motions, LSR velocities, the 3D kinematic
distances, and a variance-weighted average 444We first convert the measured
parallax ($\pi\pm\sigma_{\pi}$) to distance ($d\pm\sigma_{d}$), where
$d=1/\pi$ and $\sigma_{d}=d^{2}\sigma_{\pi}$, and then combine the parallax-
converted distance and the 3D kinematic distance by variance weighting. of the
two distance estimates for each source. We adopted these average distances in
the following discussion.

Figure 1:  Locations of sources superposed on a CO $(l,v)$ diagram from the
Galactic Ring Survey (Jackson et al., 2006) integrated from b =
$-1{{}^{\circ}}$ to $+1{{}^{\circ}}$. Black dots with purple edges indicate
previously published sources assigned to the far portion of the Sagittarius in
the Table 1 of R19 (along with their primary references). White crosses
indicate the target for which we are performing VLBA parallax measurements
under program BL312 as described in in Section 4.2. Red triangles and squares
indicate the $(l,v)$ positions of H II regions and 6.7 GHz CH3OH masers,
estimated to be at far kinematic distances in http://astro.phys.wvu.edu/wise/
(catalog WISE Catalog of Galactic H II Regions) (Anderson et al., 2014) and
the GLOSTAR Galactic plane survey 6.7 GHz methanol maser catalogue (Nguyen et
al., 2022), respectively. Traces of the Sagittarius and Perseus arms from Reid
et al. (2016) pass through the CO (Dame et al., 2001; Jackson et al., 2006)
and H I (Stil et al., 2006) emission features that define the arms in
longitude, latitude, and velocity. The solid and dashed lines correspond to
the far and near portions of the Sagittarius arm. The width of the shaded
region corresponds to a $\pm$ 7 km s-1velocity dispersion.

##  4 Discussion

###  4.1 Spiral Arm Assignments

We now discuss the spiral arm assignments of the four sources from this paper
and the two sources reported by Xu et al. (2021). We assigned maser sources to
the spiral arms based on their locations in H I and/or CO longitude–velocity
$(l,v)$ diagrams. As shown in Figure 1, traces of the Sagittarius and Perseus
arms (Reid et al., 2016) roughly follow the 13CO ($J$= 1–0) Galactic Ring
Survey (Jackson et al., 2006) integrated from b = $-1{{}^{\circ}}$ to
$+1{{}^{\circ}}$. However, for Galactic longitudes lower than about
$30{{}^{\circ}}$, the near portion of the Sagittarius arm overlaps with the
velocities associated with the Perseus arm in $(l,v)$ plots. And, for
longitudes less than about $20{{}^{\circ}}$, it is difficult to distinguish
the far portion of the Sagittarius arm from the Perseus arm. This highlights
the need for accurate distance measurements to trace these arms in space.

The $(l,v)$ distribution of H II regions and 6.7 GHz CH3OH masers, estimated
to be at their far kinematic distances in Anderson et al. (2014) and Nguyen et
al. (2022), reasonably well follow the Sagittarius and Perseus arms, at least
down to Galactic longitudes of about $25{{}^{\circ}}$.

As is evident in Figure 1, the $(l,v)$ positions of G033.64$-$00.22,
G035.57$-$00.03, G041.15$-$00.20, and G043.89$-$00.78 indicate unambiguously
an association with the far portion of the Sagittarius arm. Figure 2 shows the
same four sources (green pentagrams) superposed on a map containing $\sim$200
maser sources listed in R19, as well as sources from Xu et al. (2021), and
Bian et al. (2022). The locations of our four sources are also consistent with
the far portion of the Sagittarius arm. Therefore, we adopt that arm
assignment for these four newly measured maser sources.

The distances for G019.60$-$00.23 and G020.08$-$00.13 are consistent with
either the Sagittarius or Perseus arms. However, the far portion of the
Sagittarius arm is favored over the Perseus arm by their $(l,v)$ positions,
since, as shown in Figure 1, their LSR velocities are $\approx 20$ km
s-1offset from those expected for the Perseus arm. Typical LSR velocity
deviations, owing to internal Virial motions, are $\approx 7$ km s-1 from the
average arm values (Reid et al., 2016). Also, at longitudes near 20∘, the
Galactic latitude of the far portion of the Sagittarius arm is
$\approx-$0${\hbox to0.0pt{.\hss}}^{\circ}$075, while that of the Perseus arm
is $\approx+$0${\hbox to0.0pt{.\hss}}^{\circ}$076 (Reid et al., 2016, 2019).
At distances of over 12 kpc, the Galactic latitudes of G019.60$-$00.23
($-$0${\hbox to0.0pt{.\hss}}^{\circ}$23) and G020.08$-$00.13 ($-$0${\hbox
to0.0pt{.\hss}}^{\circ}$13) would place them more than 200 pc below the center
of the Perseus arm. Comparing this offset to the (Gaussian $1\sigma$) vertical
dispersion of about 100 pc for the Perseus arm (see Fig. 2 of Reid et al.,
2016) also favors association with the Sagittarius over the Perseus arm.
Considering all the evidence, we confidently assign G019.60$-$00.23 and
G020.08$-$00.13 to the far portion of the Sagittarius arm.

Figure 2: Plan view of the Milky Way as seen from the north Galactic pole
following R19. The Galactic center is at (0,0) kpc and the Sun is at (0,8.15)
kpc. Solid dots indicate parallax locations of the maser sources. Distance
uncertainties are indicated by the inverse size of the symbols as given in the
legend at the lower left. Purple dots with 1$\sigma$ error bars indicate
sources described in Section 3 and listed in Table 2. Green stars indicate the
locations of the sources reported in this paper. The spiral arm models from
R19 are traced with solid lines and dotted lines enclose 90% of the sources.
The location of the kink in Sagittarius arm is marked with a ”K.” The long
Galactic bar is indicated with a shaded ellipse (Wegg et al., 2015). The pitch
angle fit for the Sagittarius arm determined in this paper is traced with a
thick purple line.

###  4.2 Structure of the Sagittarius Arm

R19 fitted log-period spiral functions to the locations of HMSFRs in the
Sagittarius arm with trigonometric parallax distances. They found that the
Sagittarius arm has a “kink” at Galactocentric azimuth $\beta\approx
24{{}^{\circ}}$ with pitch angles of 17${\hbox to0.0pt{.\hss}}^{\circ}$1 $\pm$
1${\hbox to0.0pt{.\hss}}^{\circ}$6 for $2{{}^{\circ}}<\beta<24{{}^{\circ}}$,
and 1${\hbox to0.0pt{.\hss}}^{\circ}$0 $\pm$ 2${\hbox
to0.0pt{.\hss}}^{\circ}$1 for $24{{}^{\circ}}<\beta<97{{}^{\circ}}$. Beyond
the Galactic center (i.e., $\beta>90{{}^{\circ}}$), only two sources,
G037.47$-$00.10 and G038.03$-$00.30, with parallaxes reported by Wu et al.
(2019), were used by R19 to characterize the Sagittarius arm. Our results for
G033.64$-$00.22 and G035.57$-$00.03 together with the measurements of
G019.60$-$00.23 and G020.08$-$00.13 (Xu et al., 2021) add significant weight
in determining the arm structure in this distant region. Using these six
distant sources, adopting the averaged distances given in Table 2, and the
same methodology as R19, we redetermine the characteristics of the Sagittarius
arm over an extended range. It is worth noting that, while employing the same
procedure as R19, the increased accuracy of distances in Table 2 has resulted
in two R19 outliers (G032.74-00.07 and G033.64-00.22, with $>3\sigma$
residuals), now being within the acceptable range ($<3\sigma$ residuals).

We estimate the pitch angles of the two Sagittarius arm segments to be
18${\hbox to0.0pt{.\hss}}^{\circ}$6 $\pm$ 1${\hbox to0.0pt{.\hss}}^{\circ}$4
and 1${\hbox to0.0pt{.\hss}}^{\circ}$5 $\pm$ 1${\hbox
to0.0pt{.\hss}}^{\circ}$1 for segments between azimuths of
$-2{{}^{\circ}}<\beta<22{{}^{\circ}}$ and
$22{{}^{\circ}}<\beta<132{{}^{\circ}}$, respectively. Our best-fitting
parameters are consistent with the results of R19 (17${\hbox
to0.0pt{.\hss}}^{\circ}$1 $\pm$ 1${\hbox to0.0pt{.\hss}}^{\circ}$6 and
1${\hbox to0.0pt{.\hss}}^{\circ}$0 $\pm$ 2${\hbox to0.0pt{.\hss}}^{\circ}$1
for the segments between azimuths of $2{{}^{\circ}}<\beta<24{{}^{\circ}}$ and
$24{{}^{\circ}}<\beta<97{{}^{\circ}}$, respectively). Our results, based on
more parallax data, extend the azimuth range from 97∘to 132∘ (see Table 3). In
addition, the significant decrease in the uncertainty of the pitch angle for
$\beta>22{{}^{\circ}}$ between the estimate of R19 and ours suggests that the
pitch angle is nearly constant over the azimuth range
$22{{}^{\circ}}<\beta<132{{}^{\circ}}$. We plot our extended model as the
thick purple line in Figure 2.

While our fitted pitch angles are close to those of R19, our model for the
Sagittarius arm in Fig. 2 starting near $\beta=42{{}^{\circ}}$ traces radially
outward from the R19 model, and by $\beta=132{{}^{\circ}}$ it is at $\approx
1$ kpc greater radius. Why does this occur? When the R19 model was generated,
G019.60$-$00.23 and G020.08$-$00.13 had not yet been measured, and
G032.74$-$00.07 and G033.64$-$00.22 were flagged as outliers (and not used in
their arm fitting). Thus, the pitch angle for $\beta$ $>$ 42∘ was not well
constrained. In order to build a more complete spiral arm model for the Milky
Way, for the distant portion of the Sagittarius arm they adopted a pitch angle
of $8{{}^{\circ}}$, which was closer to the average value determined for the
spiral arms in the Milky Way and extrapolated the Sagittarius arm to the far
end of the Galactic bar at approximately the same radius as that measured for
the Norma arm at the near end of the bar.

As seen in Figure 2, our updated model for the far portion of the Sagittarius
arm, based on new parallax and 3D kinematic distance measurements, approaches
the R19 model for the Perseus arm at $\beta\approx 130{{}^{\circ}}$. This
supports the suggestion (Xu et al., 2023) that the Sagittarius and Perseus arm
might merge. However, we note that the location of the Perseus arm for
azimuths greater than $\approx 90{{}^{\circ}}$ is currently not well
constrained, and the Perseus and Sagittarius arms might merge closer to the
far end of the bar, or they may not merge at all.

As can be seen in the shaded regions of Figure 1, there are dozens of 6.7 GHz
masers at $\ell\approx$ 20∘ to 35∘ that could be associated with the far
portion of the Sagittarius arm or Perseus arms. Parallax measurements for
these sources using the MultiView calibration technique (Rioja et al., 2017;
Hyland et al., 2022) could help us to test these possibilities. In fact, for
this purpose, under program BL312 (from March 2024 to March 2025), we are
measuring the parallax of eight maser sources. Six of the eight sources are in
the scope of Figure 1, shown as white crosses.

Table 3: Sagittarius Arm Fitting Results

Reference |  $l$ Tangency |  $\beta$ Range | $\beta_{\rm kink}$ | $R_{\rm kink}$ | $\psi_{<}$ | $\psi_{>}$ | Width
---|---|---|---|---|---|---|---
| (deg) | (deg) | (deg) | (kpc) | (deg) | (deg) | (kpc)
This paper | 284.4 | $-2\rightarrow 132$ | $22\pm 2$ | $6.06\pm 0.06$ | $\phantom{0}18.4\pm 1.4$ | $\phantom{0}1.7\pm 1.0$ | $0.18\pm 0.03$
R19 | 285.6 | $2\rightarrow\phantom{0}97$ | $24\pm 2$ | $6.04\pm 0.09$ | $\phantom{0}17.1\pm 1.6$ | $\phantom{0}1.0\pm 2.1$ | $0.27\pm 0.04$

Note. — Parameters estimated from fitting log-periodic spirals to the
Sagittarius arm based on data from this paper, Xu et al. (2021), and R19,
assuming the distance to the Galactic center of $R_{0}$ = 8.15 kpc. An arm
tangency prior of $283\pm 2{{}^{\circ}}$ (Bronfman et al., 2000) was used to
constrain the fit. Column 2 lists the fitted tangency. Column 3 lists the
azimuth range of the parallax data. Columns 4 and 5 list the Galactic azimuth
and radius of the arm kink, separating two arm segments. Columns 6 and 7 give
pitch angles for azimuths less and greater than $\beta_{\rm kink}$. Column 9
lists the intrinsic (Gaussian 1$\sigma$) arm width at $R_{\rm kink}$. Rows 1
and 2 give the best-fitting parameters in this paper and from R19 for
comparison.

###  4.3 Kinematics of the Sagittarius Arm

The peculiar motion components, $U_{s}$ (toward the Galactic center), $V_{s}$
(in the direction of Galactic rotation), and $W_{s}$ (toward the north
Galactic pole) listed in Table 8 for the maser sources listed in Table 2 were
calculated by adopting the distance to the Galactic center, ${R_{0}}$ = 8.15
kpc; the circular rotation speed at the Sun, $\Theta_{0}$ = 236 km s-1 the
solar motion values $U_{\odot}$= 10.6 km s-1, $V_{\odot}$= 10.7 km s-1, and
$W_{\odot}$= 7.6 km s-1; and the Galactic rotation curve from R19.

Figure 3 shows the peculiar motions components ($U_{s}$, $V_{s}$, $W_{s}$) as
a function of Galactic azimuth ($\beta$) for sources in the Sagittarius arm
based on the data from this paper and Table 1 of R19. From Figure 3, one can
see that all values are consistent with 0 $\pm$ 20 km s-1. The variance-
weighted average peculiar motion components ($\overline{U_{s}}$,
$\overline{V_{s}}$, $\overline{W_{s}}$) for the Sagittarius arm sources are
listed in Table 4. For comparison with other spiral arms, the corresponding
values for the sources in the Norma, Scutum, Local, Perseus, and Outer arms
are also listed in Table 4 (based on data in Table 1 of R19). Among these
spiral arms, the Sagittarius arm has the among the smallest $\overline{U_{s}}$
and $\overline{V_{s}}$ magnitudes, indicating near circular Galactic orbits.
However, the Sagittarius arm has the only statistically significant
$\overline{W_{s}}$ value, which comes from sources in the arm segment with
$\beta<22{{}^{\circ}}$ mostly moving toward the South Galactic Pole.

Figure 3: Plots of the peculiar motion components vs. Galactic azimuth for
sources in the Sagittarius arm based on the data from this paper and Table 1
of R19. The top, middle, and bottom panels show $U_{s}$, $V_{s}$, and $W_{s}$,
respectively, calculated by adopting model A5 and the Galactic rotation curve
from R19.  Table 4: Average Peculiar Motions of HMSFRs in Spiral Arms

Arm | N | $\overline{U_{s}}$ | $\overline{V_{s}}$ | $\overline{W_{s}}$
---|---|---|---|---
Name |  | (km s-1) | (km s-1) | (km s-1)
Norma | 14 |  $9.9$1$\pm$ | $3.2$ |  $-7.7$1$\pm$ | $1.7$ |  $0.2$1$\pm$ | $1.7$
Scutum | 40 |  $10.8$1$\pm$ | $1.3$ |  $-1.4$1$\pm$ | $1.1$ |  $-0.7$1$\pm$ | $1.0$
Sagittarius | 42 |  $2.2$1$\pm$ | $1.0$ |  $-0.8$1$\pm$ | $1.0$ |  $-3.0$1$\pm$ | $0.9$
Local | 28 |  $0.1$1$\pm$ | $1.0$ |  $-7.4$1$\pm$ | $0.9$ |  $1.7$1$\pm$ | $1.0$
Perseus | 41 |  $8.7$1$\pm$ | $0.9$ |  $-5.9$1$\pm$ | $1.1$ |  $0.1$1$\pm$ | $1.0$
Outer | 11 |  $5.7$1$\pm$ | $1.9$ |  $-6.7$1$\pm$ | $2.6$ |  $0.7$1$\pm$ | $2.4$

Note. — Variance-weighted averages of peculiar motions were calculated from
data in this paper and Table 1 of R19. Columns 1 and 2 list the arm name and
the number of sources. Columns 3, 4, and 5 list the variance-weighted average
of the peculiar motion components $U_{s}$, $V_{s}$, and $W_{s}$.

##  5 Summary

We measured the parallaxes and proper motions of four masers in HMSFRs
associated with the distant portions of the Sagittarius spiral arm. The
results for G041.15$-$00.20 and G043.89$-$00.78 at Galactic azimuth $\beta\sim
80{{}^{\circ}}$ are consistent with the previous model for the arm by R19.
However, the more distant sources, G033.64$-$00.22 and G035.57$-$00.03, as
well as G019.60$-$00.23 and G020.08$-$00.13 from Xu et al. (2021), better
constrain the structure of the Sagittarius arm beyond the Galactic center
($\beta>90{{}^{\circ}}$) and suggest that the Sagittarius arm model of R19
should be moved outward by about 1 kpc at $\beta\approx 130{{}^{\circ}}$,
where it might merge with the Perseus arm.

This work was funded by the National SKA Program of China (grant No.
2022SKA0120103), NSFC grant 11933011, 12303072, the Key Laboratory for Radio
Astronomy, the Jiangsu Funding Program for Excellent Postdoctoral Talent
(grant No. 2023ZB093), and the Natural Science Foundation of Jiangsu Province
(grant No. BK20210999).
VLBA

##  Appendix A Observations

Here, we list the details of the epochs observed in Table 5.

Table 5: Dates of VLBA Observations G033.64$-$00.22 | G035.57$-$00.03 | G041.15$-$00.20 | G043.89$-$00.78
---|---|---|---
2015 Mar 01 | 2015 Mar 08 | 2015 Mar 01 | 2015 Mar 08
2015 Mar 28 | 2015 Mar 27 | 2015 Mar 28 | 2015 Mar 27
2015 Apr 22 | 2015 Apr 20 | 2015 Apr 22 | 2015 Apr 20
2015 May 20 | 2015 May 14 | 2015 May 20 | 2015 May 14
2015 Aug 28 | 2015 Aug 29 | 2015 Aug 28 | 2015 Aug 29
2015 Sep 10 | 2015 Sep 13 | 2015 Sep 10 | 2015 Sep 13
2015 Sep 21 | 2015 Sep 28 | 2015 Sep 21 | 2015 Sep 28
2015 Oct 03 | 2015 Oct 09 | 2015 Oct 03 | 2015 Oct 09
2015 Oct 16 | 2015 Oct 24 | 2015 Oct 16 | 2015 Oct 24
2015 Oct 27 | 2015 Nov 02 | 2015 Oct 27 | 2015 Nov 02
2015 Nov 06 | 2015 Nov 13 | 2015 Nov 06 | 2015 Nov 13
2015 Nov 16 | 2015 Nov 23 | 2015 Nov 16 | 2015 Nov 23
2016 Feb 26 | 2016 Feb 25 | 2016 Feb 26 | 2016 Feb 25
2016 Mar 25 | 2016 Mar 22 | 2016 Mar 25 | 2016 Mar 22
2016 Apr 18 | 2016 Apr 16 | 2016 Apr 18 | 2016 Apr 16
2016 May 26 | 2016 May 25 | 2016 May 26 | 2016 May 25

##  Appendix B Parallax and Proper Motion Fits

Here, we list the details of the parallaxes fits with formal uncertainties and
the proper motion estimations listed in Table 6 and Table 7, respectively.

Figure 4: Parallax fitting results for the H2O masers G035.57$-$00.03 and
G043.89$-$00.78. The top panels give the eastward (solid line) and northward
(dashed line) position offsets vs. time. The middle and bottom panels display
the eastward and northward data with the fitted proper motion removed. See the
legend for the source names, the $V_{\rm LSR}$ of each maser spot, and the
background QSO(s) used for the position reference(s). The red dashed line
shows the northward position offsets when proper-motion acceleration was
included in the fitting process for G043.89$-$00.78.

Figure 5: Same as Figure 4, but for the CH3OH masers, G033.64$-$00.22 and G041.15$-$00.20. Their parallaxes are estimated using the approach of Zhang et al. (2019).  Table 6: Detailed Results of the Parallaxes  Target | Background | $V_{\rm LSR}$ | Detected | Parallax | Solved for | accx | accy
---|---|---|---|---|---|---|---
Source | Source | (km s-1) | epochs | (mas) | acceleration | (mas y-2) | (mas y-2)
H2O maser |  |  |
G035.57$-$00.03 | J1855+0251 | 48.62 | 1111 1111 1111 1111 | 0.098 $\pm$ 0.006 | No |  |
|  | 53.90 | 1111 1111 1111 1000 | 0.098 $\pm$ 0.013 | No |  |
| Combined fit |  | 0.098 $\pm$ 0.008 | No |  |
G043.89$-$00.78 | J1905+0952 | 59.18 | 1111 11111111 1111 | 0.146 $\pm$ 0.006 | No |  |
|  | 60.47 | 1111 11111111 1111 | 0.142 $\pm$ 0.006 | No |  |
| J1913+0932 | 59.18 | 1111 11111111 1111 | 0.143 $\pm$ 0.004 | No |  |
|  | 60.47 | 1111 11111111 1111 | 0.140 $\pm$ 0.004 | No |  |
| J1922+0841 | 59.18 | 1111 11111111 1111 | 0.150 $\pm$ 0.003 | No |  |
|  | 60.47 | 1111 11111111 1111 | 0.145 $\pm$ 0.005 | No |  |
| Combined fit |  | 0.145 $\pm$ 0.003 | No |  |
G043.89$-$00.78 | J1905+0952 | 59.18 | 1111 11111111 1111 | 0.153 $\pm$ 0.012 | Yes |  $-$0.12 $\pm$ 0.16 | 0.62 $\pm$ 0.12
|  | 60.47 | 1111 11111111 1111 | 0.129 $\pm$ 0.013 | Yes | 0.16 $\pm$ 0.18 | 0.48 $\pm$ 0.12
| J1913+0932 | 59.18 | 1111 11111111 1111 | 0.157 $\pm$ 0.007 | Yes |  $-$0.21 $\pm$ 0.09 | 0.73 $\pm$ 0.05
|  | 60.47 | 1111 11111111 1111 | 0.130 $\pm$ 0.009 | Yes | 0.11 $\pm$ 0.13 | 0.55 $\pm$ 0.09
| J1922+0841 | 59.18 | 1111 11111111 1111 | 0.140 $\pm$ 0.007 | Yes | 0.11 $\pm$ 0.09 | 0.43 $\pm$ 0.15
|  | 60.47 | 1111 11111111 1111 | 0.119 $\pm$ 0.010 | Yes | 0.36 $\pm$ 0.14 | 0.26 $\pm$ 0.16
| Combined fit |  | 0.137 $\pm$ 0.006 | Yes | 0.08 $\pm$ 0.06 | 0.54 $\pm$ 0.05
CH3OH maser |  |  |
G033.64$-$00.22 | J848 & J1857 | 60.36 | 1111 1111 1101 1111 | 0.081 $\pm$ 0.018 | No |  |
|  | 62.70 | 1111 1111 1101 1111 | 0.099 $\pm$ 0.019 | No |  |
Combined fit |  |  | 0.090 $\pm$ 0.014 | No |  |
G041.15$-$00.20 | J1905 & J1907 | 55.64 | 1111 1111 1111 1111 | 0.128 $\pm$ 0.026 | No |  |
|  | 55.82 | 1111 1111 1111 1111 | 0.140 $\pm$ 0.016 | No |  |
|  | 56.00 | 1111 1111 1111 1111 | 0.141 $\pm$ 0.015 | No |  |
Combined fit |  |  | 0.144 $\pm$ 0.014 | No |  |
Table 7: Detailed Results of the Proper Motions  Target | Feature | $V_{\rm LSR}$ | $\mu_{x}$ | $\mu_{y}$ | $\Delta x$ | $\Delta y$
---|---|---|---|---|---|---
Source |  | (km s-1) | (mas y-1) | (mas y-1) | (mas) | (mas)
H2O maser
G035.57$-$00.03 | 1 | 48.19$\sim$49.05 |  $-$3.11 $\pm$ 0.04 |  $-$6.26 $\pm$ 0.07 | 0 | 0
| 2 | 64.50$\sim$68.71 |  $-$3.23 $\pm$ 0.11 |  $-$6.02 $\pm$ 0.21 | 624 |  $-$1088
| 3 | 55.75$\sim$56.07 |  $-$3.17 $\pm$ 0.07 |  $-$6.16 $\pm$ 0.17 |  $-$319 |  $-$303
| 4 | 50.56$\sim$54.88 |  $-$2.45 $\pm$ 0.06 |  $-$5.93 $\pm$ 0.11 | 53 | 46
| 5 | 53.16$\sim$53.59 |  $-$3.16 $\pm$ 0.12 |  $-$6.04 $\pm$ 0.20 | 1428 | 596
| Average |  $-$3.02 $\pm$ 0.08 |  $-$6.08 $\pm$ 0.15 |  |
Enlarge 5 km s-1 Error |  $-$3.02 $\pm$ 0.13 |  $-$6.08 $\pm$ 0.18 |  |
G043.89$-$00.78 | 1 | 58.10$\sim$59.61 |  $-$2.48 $\pm$ 0.03 |  $-$6.08 $\pm$ 0.03 | 0 | 0
| 2 | 48.71$\sim$51.73 |  $-$3.42 $\pm$ 0.04 |  $-$5.02 $\pm$ 0.05 |  $-$62 |  $-$51
| 3 | 59.72$\sim$60.80 |  $-$3.09 $\pm$ 0.03 |  $-$5.81 $\pm$ 0.13 |  $-$78 |  $-$102
| 4 | 54.43$\sim$56.37 |  $-$3.03 $\pm$ 0.10 |  $-$7.22 $\pm$ 0.14 |  $-$65 |  $-$276
| Average |  $-$3.01 $\pm$ 0.05 |  $-$6.03 $\pm$ 0.09 |  |
Enlarge 5 km s-1 Error |  $-$3.01 $\pm$ 0.16 |  $-$6.03 $\pm$ 0.18 |  |
CH3OH maser
G033.64$-$00.22 | 1 | 60.18$\sim$60.54 |  $-$3.01 $\pm$ 0.03 |  $-$6.26 $\pm$ 0.05 | 0 | 0
| 2 | 62.52$\sim$63.24 |  $-$3.00 $\pm$ 0.04 |  $-$6.33 $\pm$ 0.06 |  $-$28 |  $-$2
| Average |  $-$3.01 $\pm$ 0.04 |  $-$6.30 $\pm$ 0.06 |  |
Enlarge 3 km s-1 Error |  $-$3.01 $\pm$ 0.07 |  $-$6.30 $\pm$ 0.08 |  |
G041.15$-$00.20 | 1 | 55.65$\sim$56.00 |  $-$2.74 $\pm$ 0.03 |  $-$6.03 $\pm$ 0.06 | 0 | 0
Enlarge 5 km s-1 Error |  $-$2.74 $\pm$ 0.15 |  $-$6.03 $\pm$ 0.16 |  |

##  Appendix C Peculiar Motions

Here, we list the peculiar motions of the sources located in the Sagittarius
arm in Table 8.

Table 8: Peculiar Motions

Source | $\beta$ | $U_{s}$ | $V_{s}$ | $W_{s}$ | Distance | $\mu_{x}$ | $\mu_{y}$ | $v_{\rm LSR}$
---|---|---|---|---|---|---|---|---
| (∘) | (km s-1) | (km s-1) | (km s-1) | kpc | mas y-1 | mas y-1 | km s-1
G045.49$+$00.12 | $56.0_{-8.7}^{+8.2}$ |  $-8.5$. $\pm$ | $9.2$ |  $-10.1$. $\pm$ | $5.4$ |  $-1.6$. $\pm$ | $5.6$ | $6.9^{+0.9}_{-0.9}$ |  $-2.62$. $\pm$ | $0.17$ |  $-5.61$. $\pm$ | $0.16$ |  $58$. $\pm$ | $3$
G045.80$-$00.35 | $56.9_{-9.6}^{+8.9}$ |  $1.1$. $\pm$ | $11.3$ |  $-0.3$. $\pm$ | $9.0$ |  $-12.8$. $\pm$ | $7.2$ | $7.0^{+1.0}_{-1.0}$ |  $-2.52$. $\pm$ | $0.17$ |  $-6.08$. $\pm$ | $0.27$ |  $64$. $\pm$ | $5$
G043.89$-$00.78 | $62.2_{-2.8}^{+2.8}$ |  $7.0$. $\pm$ | $6.3$ |  $-10.7$. $\pm$ | $4.4$ |  $2.3$. $\pm$ | $5.9$ | $7.5^{+0.3}_{-0.3}$ |  $-3.01$. $\pm$ | $0.16$ |  $-6.03$. $\pm$ | $0.18$ |  $54$. $\pm$ | $3$
G045.07$+$00.13 | $63.6_{-3.6}^{+3.5}$ |  $9.5$. $\pm$ | $9.4$ |  $2.0$. $\pm$ | $7.3$ |  $8.1$. $\pm$ | $9.4$ | $7.7^{+0.4}_{-0.4}$ |  $-3.21$. $\pm$ | $0.26$ |  $-6.11$. $\pm$ | $0.26$ |  $59$. $\pm$ | $5$
G041.15$-$00.20 | $64.1_{-5.1}^{+4.8}$ |  $1.5$. $\pm$ | $6.8$ |  $-14.5$. $\pm$ | $5.1$ |  $-4.9$. $\pm$ | $5.5$ | $7.6^{+0.5}_{-0.5}$ |  $-2.74$. $\pm$ | $0.15$ |  $-6.03$. $\pm$ | $0.16$ |  $60$. $\pm$ | $3$
G045.45$+$00.06 | $66.9_{-8.0}^{+7.2}$ |  $-9.3$. $\pm$ | $19.0$ |  $-2.7$. $\pm$ | $13.9$ |  $-19.8$. $\pm$ | $16.4$ | $8.1^{+0.9}_{-0.9}$ |  $-2.34$. $\pm$ | $0.38$ |  $-6.00$. $\pm$ | $0.54$ |  $55$. $\pm$ | $7$
G043.03$-$00.45 | $68.9_{-5.5}^{+5.1}$ |  $19.6$. $\pm$ | $7.7$ |  $2.4$. $\pm$ | $10.6$ |  $-6.2$. $\pm$ | $6.4$ | $8.2^{+0.6}_{-0.6}$ |  $-3.03$. $\pm$ | $0.15$ |  $-6.56$. $\pm$ | $0.20$ |  $56$. $\pm$ | $5$
G041.22$-$00.19 | $74.3_{-10.3}^{+8.8}$ |  $-9.7$. $\pm$ | $9.7$ |  $-6.2$. $\pm$ | $13.8$ |  $-1.1$. $\pm$ | $5.8$ | $8.7^{+1.1}_{-1.1}$ |  $-2.82$. $\pm$ | $0.13$ |  $-5.89$. $\pm$ | $0.16$ |  $59$. $\pm$ | $5$
G038.03$-$00.30 | $81.8_{-5.4}^{+4.9}$ |  $-0.3$. $\pm$ | $5.8$ |  $-2.3$. $\pm$ | $9.6$ |  $0.2$. $\pm$ | $3.3$ | $9.3^{+0.6}_{-0.6}$ |  $-3.01$. $\pm$ | $0.06$ |  $-6.20$. $\pm$ | $0.11$ |  $60$. $\pm$ | $3$
G035.79$-$00.17 | $84.5_{-5.7}^{+5.1}$ |  $-1.5$. $\pm$ | $7.3$ |  $-8.2$. $\pm$ | $10.2$ |  $-1.9$. $\pm$ | $5.6$ | $9.4^{+0.6}_{-0.6}$ |  $-2.96$. $\pm$ | $0.12$ |  $-6.23$. $\pm$ | $0.14$ |  $61$. $\pm$ | $5$
G037.47$-$00.10 | $84.8_{-8.0}^{+6.8}$ |  $-8.3$. $\pm$ | $7.9$ |  $-5.9$. $\pm$ | $14.1$ |  $-14.8$. $\pm$ | $4.7$ | $9.6^{+0.9}_{-0.9}$ |  $-2.63$. $\pm$ | $0.07$ |  $-6.19$. $\pm$ | $0.15$ |  $58$. $\pm$ | $3$
G033.64$-$00.22 | $91.0_{-4.5}^{+4.1}$ |  $-2.2$. $\pm$ | $4.9$ |  $-6.3$. $\pm$ | $8.8$ |  $-1.7$. $\pm$ | $3.4$ | $9.9^{+0.5}_{-0.5}$ |  $-3.01$. $\pm$ | $0.07$ |  $-6.30$. $\pm$ | $0.08$ |  $61$. $\pm$ | $3$
G035.57$-$00.03 | $91.4_{-4.9}^{+4.4}$ |  $-6.2$. $\pm$ | $7.6$ |  $-5.7$. $\pm$ | $11.8$ |  $3.3$. $\pm$ | $6.8$ | $10.2^{+0.6}_{-0.6}$ |  $-3.02$. $\pm$ | $0.13$ |  $-6.08$. $\pm$ | $0.18$ |  $53$. $\pm$ | $3$
G032.74$-$00.07 | $97.6_{-6.6}^{+5.5}$ |  $3.9$. $\pm$ | $12.9$ |  $-19.4$. $\pm$ | $20.2$ |  $8.7$. $\pm$ | $13.9$ | $10.6^{+0.8}_{-0.8}$ |  $-3.15$. $\pm$ | $0.27$ |  $-6.10$. $\pm$ | $0.29$ |  $37$. $\pm$ | $10$
G020.08$-$00.13 | $130.9_{-3.2}^{+2.6}$ |  $-7.1$. $\pm$ | $5.7$ |  $0.3$. $\pm$ | $17.9$ |  $-5.3$. $\pm$ | $8.7$ | $12.7^{+0.6}_{-0.6}$ |  $-3.14$. $\pm$ | $0.14$ |  $-6.44$. $\pm$ | $0.16$ |  $41$. $\pm$ | $3$
G019.60$-$00.23 | $131.3_{-3.9}^{+3.1}$ |  $-9.8$. $\pm$ | $6.0$ |  $-8.2$. $\pm$ | $19.8$ |  $-4.8$. $\pm$ | $9.7$ | $12.6^{+0.7}_{-0.7}$ |  $-3.11$. $\pm$ | $0.16$ |  $-6.36$. $\pm$ | $0.17$ |  $41$. $\pm$ | $3$

Note. — Peculiar motion for sources listed in Table 2. Column 1 lists the
source names nominated with Galactic coordinates. The sources are sorted in
increasing Galactic azimuth as listed in Column 2. Columns 3, 4, and 5 list
the peculiar motions toward the Galactic center, in the direction of Galactic
rotation, and toward the north Galactic pole, respectively. Columns 6–9 list
the distances, proper motions in the eastward and northward directions, and
LSR velocities, respectively. The Galactic “Univ” model and solar motions
found by R19 were used to calculate the peculiar motions.

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