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

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 χ² 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. ¹⁰

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 B1 and B2, respectively. Tables B1 and B2 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 B1, 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 B1. The estimated acceleration parameters are listed in Table B1. 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 ∼5 km s⁻¹(Moscadelli et al. 2002) for 6.7 GHz CH₃OH masers and ∼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 ±3 and ±5 km s⁻¹ "error floors" in quadrature, respectively. For sources with only one maser feature, we adopted ±5 and ±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 (Olmi et al. 1993; Pandian et al. 2012; Wienen et al. 2012).

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

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

For G043.89−00.78, parallaxes of 0.121 ± 0.020 mas and 0.144 ± 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 ± 0.006 mas yields a parallax of 0.136 ± 0.005 mas.

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 (i.e., Galactocentric radii less than R₀).

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 ¹¹ of the two distance estimates for each source. We adopted these average distances in the following discussion.

Table 2. Astrometric Results

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

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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° to +1°. However, for Galactic longitudes lower than about 30°, 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°, 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.

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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°.

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 ∼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.

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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 ≈20 km s⁻¹offset from those expected for the Perseus arm. Typical LSR velocity deviations, owing to internal Virial motions, are ≈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 ≈ − 0075, while that of the Perseus arm is ≈ + 0076 (Reid et al. 2016, 2019). At distances of over 12 kpc, the Galactic latitudes of G019.60−00.23 (−023) and G020.08−00.13 (−013) would place them more than 200 pc below the center of the Perseus arm. Comparing this offset to the (Gaussian 1σ) vertical dispersion of about 100 pc for the Perseus arm (see Figure 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.

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 β ≈ 24° with pitch angles of 171 ± 16 for 2° < β < 24°, and 10 ± 21 for 24° < β < 97°. Beyond the Galactic center (i.e., β > 90°), 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 >3σ residuals), now being within the acceptable range (<3σ residuals).

We estimate the pitch angles of the two Sagittarius arm segments to be 186 ± 14 and 15 ± 11 for segments between azimuths of −2° < β < 22° and 22° < β < 132°, respectively. Our best-fitting parameters are consistent with the results of R19 (171 ± 16 and 10 ± 21 for the segments between azimuths of 2° < β < 24° and 24° < β < 97°, 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 β > 22° between the estimate of R19 and ours suggests that the pitch angle is nearly constant over the azimuth range 22° < β < 132°. 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 Figure 2 starting near β = 42° traces radially outward from the R19 model, and by β = 132° it is at ≈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 β > 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°, 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 β ≈ 130°. 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 ≈90° 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 ℓ ≈ 20°–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 2024 to 2025 March), 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.

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 C1 for the maser sources listed in Table 2 were calculated by adopting the distance to the Galactic center, R₀ = 8.15 kpc; the circular rotation speed at the Sun, Θ₀ = 236 km s⁻¹ the solar motion values U_⊙ = 10.6 km s⁻¹, V_⊙ = 10.7 km s⁻¹, and W_⊙ = 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 (β) 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 ± 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 β < 22° mostly moving toward the South Galactic Pole.

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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 ± 3.2	−7.7 ± 1.7	0.2 ± 1.7
Scutum	40	10.8 ± 1.3	−1.4 ± 1.1	−0.7 ± 1.0
Sagittarius	42	2.2 ± 1.0	−0.8 ± 1.0	−3.0 ± 0.9
Local	28	0.1 ± 1.0	−7.4 ± 0.9	1.7 ± 1.0
Perseus	41	8.7 ± 0.9	−5.9 ± 1.1	0.1 ± 1.0
Outer	11	5.7 ± 1.9	−6.7 ± 2.6	0.7 ± 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 .

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