TRIGONOMETRIC PARALLAXES TO STAR-FORMING REGIONS WITHIN 4 kpc OF THE GALACTIC CENTER

The so-called Galactic Molecular Ring (GMR) is a ridge of intense emission which dominates the appearance of extended CO gas in the longitude–velocity (ℓ − v) diagram of our Galaxy (e.g., Dame et al. 2001). This prominent feature marks a region of enhanced molecular density roughly halfway between the Sun and the Galactic center, at Galactocentric radii (R) between 4 and 6 kpc, which has been shown to likely trace gas emission from the inner spiral arms (e.g., Dobbs & Burkert 2012). Toward the Galactic center, the inner edge of the GMR would coincide with the Scutum-Centaurus arm, which we have recently located at an average Galactocentric radius of about 5 kpc (Sato et al. 2013). Hereafter, we will refer to the region from the inner edge of the GMR to the Galactic center as the inner Milky Way.

As part of the Bar and Spiral Structure Legacy (BeSSeL) Survey,⁴ we started a detailed study of the gas distribution and velocity field in the inner Milky Way, via trigonometric parallaxes and proper motions of masers in high-mass star-forming regions (HMSFRs). In this paper, we constrain some structures located in between the GMR and the Central Molecular Zone (CMZ; e.g., Morris & Serabyn 1996) in the first Galactic quadrant. These structures include the Connecting arm (e.g., Fux 1999; Marshall et al. 2008), the near and far 3 kpc arms (e.g., Dame & Thaddeus 2008), and the Norma arm as it is traced toward the Galactic center (e.g., Bronfman et al. 2000). The Connecting arm has received little discussion in the literature (e.g., Fux 1999 for a short summary; see also Rodriguez-Fernandez & Combes 2008 and references therein). It has been suggested to possibly appear similar to dust lanes observed in optical images of external galaxies along the extent of their bars, roughly connecting the nuclear ring with the inner tips of the spiral arms (e.g., see the Hubble Space Telescope composite view of the prototypical barred spiral galaxy NGC 1300, or that of NGC 1097). These dust lanes, often observed offset toward the leading edges of the bar structure in barred spirals, have been identified as tracers of shocks (e.g., Roberts et al. 1979; Athanassoula 1992b). In the following discussion, we will assume a general picture of the inner Galaxy as depicted in Churchwell et al. (2009), which accounts for the presence of two bar-like components: the boxy-bulge (i.e., the Galactic bar) and the long bar.

In this paper, we present trigonometric parallax measurements of 22 GHz H₂O and 12 GHz CH₃OH masers obtained with the Very Long Baseline Array (VLBA) for four sites of massive star formation located in the inner Galaxy.

We conducted multi-epoch VLBA (program BR145)⁵ observations of the 6₁₆ − 5₂₃ H₂O (rest frequency 22.235079 GHz) and the 2₀ − 3₋₁E CH₃OH (rest frequency 12.178597 GHz) maser emission toward the four HMSFRs listed in Table 1. In order to measure trigonometric parallaxes and proper motions, we switched rapidly between a maser target and three or four extragalactic continuum sources. These calibrators were selected from our survey (Immer et al. 2011) and included ICRF sources (Fey et al. 2004) with accurate positions (±2 mas). We placed four geodetic-like blocks throughout each 7 hr track, in order to measure and remove atmospheric delays for each antenna. Details about the observational strategy can be found in Reid et al. (2009a; see also Sato et al. 2010). Observation and source information are summarized in Tables 1 and 2.

Table 2. Source Information

Source	R.A. (J2000)	Decl. (J2000)	θsep	P.A.	HPBW	Fpeak	Image rms	VLSR
	(h m s)	(° ' '')	(°)	(°)	mas × mas at °	(Jy beam−1)	(Jy beam−1)	(km s−1)
G010.62−00.38	18 10 28.5629	−19 55 48.738			1.2 × 0.6 at − 18	42.94	0.05	−2.8
J1808−1822	18 08 55.5154	−18 22 53.396	1.6	−13	1.2 × 0.6 at − 20	0.011	0.001
J1821−2110	18 21 05.4692	−21 10 45.262	2.8	+117	1.3 × 0.6 at − 13	0.016	0.001
J1751−1950a	17 51 41.3438	−19 50 47.506	4.4	−90	1.2 × 0.8 at + 44	0.049	0.002
J1809−1520	18 09 10.2094	−15 20 09.699	4.6	−4	1.2 × 0.6 at − 23	0.013	0.001
G010.47+00.02	18 08 38.2302	−19 51 50.253			1.3 × 0.4 at − 171	22.55	0.04	+89.9
J1808−1822	18 08 55.5154	−18 22 53.396	1.5	+4	1.0 × 0.4 at − 120	0.006	0.001
J1751−1950a	17 51 41.3438	−19 50 47.506	3.2	−90	1.3 × 0.4 at − 98	0.009	0.001
J1821−2110	18 21 05.4692	−21 10 45.262	4.0	+66	1.2 × 0.4 at − 94	0.006	0.001
G012.02−00.03	18 12 01.8455	−18 31 55.759			2.3 × 1.1 at − 07	2.37	0.01	+108.8
J1808−1822	18 08 55.5154	−18 22 53.396	0.8	−78	4.8 × 1.9 at − 92	0.039	0.001
J1809−1520	18 09 10.2094	−15 20 09.699	3.3	−12	3.3 × 1.8 at + 69	0.039	0.001
J1825−1718a	18 25 36.5323	−17 18 49.848	3.4	+70	4.8 × 1.9 at − 84	0.174	0.001
J1751−1950a	17 51 41.3438	−19 50 47.506	5.0	−106	5.2 × 2.0 at − 76	0.068	0.001
G023.70−00.19	18 35 12.3645	−08 17 39.396			2.9 × 1.3 at − 52	3.99	0.02	+77.5
J1825−0737a	18 25 37.6096	−07 37 30.013	2.5	−74	3.3 × 1.8 at + 38	0.315	0.003
J1846−0651a	18 46 06.3002	−06 51 27.748	3.1	+63	3.3 × 1.8 at + 22	0.043	0.001
J1821−0502a	18 21 11.8094	−05 02 20.087	4.8	−47	3.2 × 1.8 at + 117	0.190	0.002

Notes. Positions and source properties for the target maser and the QSO calibrators from the first epoch data. The peak position of the phase-reference maser channels No. 138, 70, 128, and 131 (for sources from the top to the bottom, respectively) were calibrated with the ICRF sources and are accurate to within ±2 mas. For calibrators, we report positions used at the VLBA correlator. Angular offsets (θ_sep) and position angles (P.A.) east of north relative to the maser source are indicated in Columns 4 and 5. Columns 6–8 give the natural restoring beam sizes (HPBW), the peak intensities (F_peak), and image rms noise of the phase-reference maser channels (at V_LSR), K-band, and U-band background sources. ^aSources belonging to the ICRF catalog.

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Four adjacent intermediate frequency (IF) bands, each 8 MHz wide, were recorded in dual circular polarization; each band was correlated to produce 256 spectral channels. The channel width of 31.25 kHz corresponds to a spectral resolution of 0.42 and 0.77 km s⁻¹ for the H₂O and CH₃OH maser transitions, respectively. The third IF band was centered about the LSR velocity (V_LSR) of the strongest maser feature detected in our preparatory survey, as reported in Table 1 (under program BR145A). The data were processed with the VLBA DiFX software correlator in Socorro (Deller et al. 2007) using an averaging time of about 1 s, which limited the instantaneous field of view of the interferometer to about 3'' and 5'' for the H₂O and CH₃OH maser observations, respectively. Data were reduced with the NRAO Astronomical Image Processing System (AIPS) following the procedure described in Reid et al. (2009a), using a ParselTongue scripting interface (Kettenis et al. 2006). Total-power spectra of the 22.2 and 12.2 GHz maser emission toward G010.47+00.02, G010.62–00.38, G012.02–00.03, and G023.70–00.19 from the first epoch data are shown in Figure 1.

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We modeled the position offsets of compact maser spots with respect to background sources as a function of time, in order to determine their parallaxes and proper motions (e.g., Reid et al. 2009a for details). During the fitting procedure, we quantified "a posteriori" the systematic errors, via error-floors added in quadrature to the formal fitting uncertainties, for the E–W and N–S offsets. These error floors were iteratively adjusted to yield values of chi-squared per degree of freedom near unity. Results of the parallax and proper motion fitting for each maser spot and QSO used are listed in Table 3 and displayed in Figures 2–5. For each source, individual parallax measurements with multiple maser spots and QSOs were combined in a final measurement and plotted in the right panel of Figures 2–5. The formal uncertainties of the combined fits were multiplied by $\sqrt{N}$, where N is the number of maser spots, to account for the possibility of correlated position shifts among the maser spots. Details on individual parallax fittings are presented in the Appendix. In Figure 6, the Galactic locations of our sources are superposed on a schematic face-on view of the Galaxy (re-scaled for a Sun-Galactic center distance of 8.38 kpc), with a number of spatial features updated from the recent literature, such as the position of the Galactic (e.g., Gerhard 2002) and long (Benjamin et al. 2005) bars as well as the streamline model of the 3 kpc arms by Green et al. (2011).

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Table 3. Parallax and Proper Motion Fits

Maser VLSR	Δx and Δy	Background	Parallax	D	μx	μy
(km s−1)	(mas)	Source	(mas)	(kpc)	(mas yr−1)	(mas yr−1)
G010.47+00.02
+75.5	+3.6; −329.1	J1751−1950	0.116 ± 0.007		−4.029 ± 0.014	−6.515 ± 0.119
+68.0	−46.0; +68.8	J1751−1950	0.115 ± 0.007		−3.933 ± 0.012	−6.187 ± 0.146
+67.1	−66.7; +16.4	J1751−1950	0.122 ± 0.015		−3.890 ± 0.039	−6.384 ± 0.036
+67.1	−65.3; +69.4	J1751−1950	0.110 ± 0.007		−3.959 ± 0.019	−6.855 ± 0.040
+62.9	−66.7; +89.5	J1751−1950	0.125 ± 0.010		−4.044 ± 0.028	−6.729 ± 0.049
+59.5	+33.3; +57.7	J1751−1950	0.111 ± 0.007		−3.533 ± 0.018	−6.402 ± 0.056
+59.5	−92.1; −136.3	J1751−1950	0.117 ± 0.011		−3.787 ± 0.030	−6.479 ± 0.082
+75.5		Combined	0.117 ± 0.008	$8.55^{+0.63}_{-0.55}$	−4.028 ± 0.016	−6.514 ± 0.089
+68.0					−3.932 ± 0.013	−6.185 ± 0.073
+67.1					−3.890 ± 0.022	−6.385 ± 0.122
+67.1					−3.959 ± 0.022	−6.855 ± 0.122
+62.9					−4.044 ± 0.022	−6.729 ± 0.122
+59.5					−3.534 ± 0.022	−6.402 ± 0.122
+59.5					−3.788 ± 0.022	−6.480 ± 0.122
Best-value for the Secular proper motion of G010.47+00.02
			0.117 ± 0.008	$8.55^{+0.63}_{-0.55}$	−3.860 ± 0.015	−6.403 ± 0.076
G010.62−00.38
−14.2	+607.0; −605.1	J1751−1950	0.191 ± 0.034		−0.632 ± 0.084	−0.503 ± 0.122
−14.2		J1821−2110	0.200 ± 0.040
−1.1	+386.9; −247.3	J1751−1950	0.202 ± 0.034		−0.427 ± 0.084	−1.474 ± 0.084
−1.1		J1821−2110	0.216 ± 0.026
+1.0	+324.8; −194.5	J1751−1950	0.200 ± 0.030		−0.355 ± 0.075	−0.876 ± 0.053
+1.0		J1821−2110	0.213 ± 0.032
−14.2		Combined	0.202 ± 0.019	$4.95^{+0.51}_{-0.43}$	−0.632 ± 0.084	−0.503 ± 0.122
−1.1					−0.427 ± 0.084	−1.474 ± 0.084
+1.0					−0.355 ± 0.075	−0.876 ± 0.053
Best-value for the Secular proper motion of G010.62−00.38
			0.202 ± 0.019	$4.95^{+0.51}_{-0.43}$	−0.366 ± 0.081	−0.600 ± 0.055
G012.02−00.03
+108.0	+0.6; +1.0	J1808−1822	0.098 ± 0.001		−4.205 ± 0.003	−7.963 ± 0.349
+108.8	0.0; 0.0	J1808−1822	0.115 ± 0.008		−4.008 ± 0.023	−7.551 ± 0.279
+108.0		Combined	0.106 ± 0.008	$9.43^{+0.77}_{-0.66}$	−4.205 ± 0.022	−7.963 ± 0.265
+108.8					−4.008 ± 0.022	−7.551 ± 0.265
G023.70−00.19
+77.5	0.0; 0.0	J1825−0737	0.163 ± 0.038		−3.226 ± 0.096	−6.704 ± 0.224
+77.5		J1846−0651	0.187 ± 0.028		−3.100 ± 0.071	−6.237 ± 0.115
+76.7	+2.7; −21.5	J1825−0737	0.154 ± 0.034		−3.299 ± 0.084	−6.518 ± 0.256
+76.7		J1846−0651	0.173 ± 0.041		−3.171 ± 0.103	−6.046 ± 0.167
+79.0	+1.6; −2.5	J1825−0737	0.136 ± 0.041		−3.288 ± 0.103	−6.577 ± 0.231
+79.0		J1846−0651	0.161 ± 0.036		−3.159 ± 0.090	−6.104 ± 0.116
+77.5		Combined	0.161 ± 0.024	$6.21^{+1.0}_{-0.80}$	−3.164 ± 0.059	−6.474 ± 0.136
+76.7					−3.235 ± 0.059	−6.283 ± 0.136
+79.0					−3.223 ± 0.059	−6.338 ± 0.136

Notes. Columns 1 and 2 report the LSR velocity and the offset positions of the reference maser spots, respectively, with respect to the phase-reference maser channels in Table 2. Column 3 indicates the background sources whose data were used to model the relative proper motion of the maser for the parallax fit; Columns 4 and 5 report the fitted parallax and distance; Columns 6 and 7 give the fitted proper motions along the east and north directions, respectively. Combined fit used a single parallax parameter for the maser spots relative to the QSOs. Quoted uncertainties for individual parallax fits are from the formal fitting uncertainty. The Secular proper motion of G010.47+00.02 and G010.62−00.38 was obtained by the combined fit value corrected for the internal proper motions of the overall H₂O maser distribution.

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For each source, the line-of-sight velocity component (V_LSR) and the eastward and northward motions on the plane of the sky (μ_x, μ_y) give the three-dimensional velocity vector of the star-forming region as measured with respect to the equatorial heliocentric reference frame (after adding the standard solar motion to V_LSR). In previous papers, to investigate deviations from a circular rotation about the Galactic center (i.e., the peculiar motion of the HMSFR), we have moved to a reference frame rotating with the Galaxy (e.g., Reid et al. 2009b). However, for sources with Galactocentric distances R < 4 kpc, which may move along highly elliptical streamlines under the influence of the bulge/bar potential, we transform to a reference frame at rest at the Galactic center: $(U_s^{\rm GC}, V_s^{\rm GC}, W_s^{\rm GC})$. $U_s^{\rm GC}$, $V_s^{\rm GC}$, and $W_s^{\rm GC}$ are directed toward the Galactic center, in the direction of Galactic rotation and toward the North Galactic Pole, respectively, at the location of each source.⁶ In Table 4, we summarize our results together with those obtained for the other inner Galaxy sources in the literature. In this calculation, we adopted a current "best-estimate" of the Galactic parameters, R₀ = 8.38 kpc and Θ₀ = 243 km s⁻¹, from the trigonometric parallaxes measured with maser lines (Reid 2013) and the revised Hipparcos measurements of the solar motion from Schönrich et al. (2010).

Table 4. Galactic Motion of Sources in the Inner Milky Way

Source	ℓ	b	VLSR	D	R	$U_s^{\rm GC}$	$V_s^{\rm GC}$	$W_s^{\rm GC}$	Ref.	Arm
	(deg)	(deg)	(km s−1)	(kpc)	(kpc)	(km s−1)	(km s−1)	(km s−1)
G009.62+00.19	9.621	+0.196	+5.0 ± 3.1	$5.15^{+0.77}_{-0.66}$	$3.4^{+0.6}_{-0.7}$	−36.1 ± 16.7	+191.9 ± 15.1	−10.1 ± 4.1	1	Norma
G010.47+00.02	10.472	+0.027	+68.9 ± 4.5	$8.55^{+0.63}_{-0.55}$	$1.6^{+0.2}_{-0.1}$	+30.3 ± 21.5	+121.7 ± 15.8	+18.2 ± 1.8	2	Connecting
G010.62−00.38 (W31)	10.624	−0.383	−3.0 ± 2.7	$4.95^{+0.51}_{-0.43}$	$3.6^{+0.4}_{-0.4}$	−60.8 ± 14.4	+228.2 ± 6.7	+8.1 ± 1.8	2	near 3 kpc
G012.02−00.03	12.025	−0.031	+109.8 ± 2.4	$9.43^{+0.77}_{-0.66}$	$2.1^{+0.5}_{-0.3}$	+25.5 ± 32.7	+215.0 ± 26.8	+1.5 ± 5.8	2	far 3 kpc
G023.44−00.18	23.440	−0.182	+104.2 ± 4.3	$5.88^{+1.37}_{-0.93}$	$3.8^{+0.5}_{-0.4}$	+4.7 ± 42.7	+225.4 ± 18.1	+2.0 ± 3.1	3	Norma
G023.70−00.19	23.707	−0.198	+76.5 ± 10	$6.21^{+1.0}_{-0.80}$	$3.7^{+0.4}_{-0.3}$	+51.4 ± 15.5	+167.1 ± 12.0	+4.6 ± 2.6	2	Norma

Notes. Proper motion of sources that belong to the inner Milky Way with respect to a reference frame joined with the Galactic center (see Section 3). For converting the heliocentric measurements to the Galactic center reference frame, we considered the best estimates of R₀ = 8.38 kpc and Θ₀ = 243 km s⁻¹ given in Reid (2013) and the updated values of the solar motion in Schönrich et al. (2010). Column 4 gives the LSR velocity of the regions assumed in the calculation, as inferred from the CS (2–1) line survey by Bronfman et al. (1996) with the exception of G010.62−00.38 and G023.70−00.19 (see the Appendix). Columns 5 and 6 report the heliocentric and projected Galactocentric distance of each source, respectively. Columns 7–9 give the velocity components toward the Galactic center, in the direction of Galactic rotation, and toward the North Galactic Pole, respectively. Column 10 lists the reference papers for the trigonometric parallax measurements: (1) Sanna et al. (2009); (2) this work; (3) Brunthaler et al. (2009). Last column lists the Galactic arms associated with the HMSFRs as presented in Section 3.1.

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3.1. Individual Sources

It is possible to associate each of the present HMSFRs to prominent large-scale features in CO and H i longitude–velocity diagrams of the inner Galaxy (|ℓ| < 30°). In Figure 7, we present a longitude–velocity diagram of extended gas emission from the Galactic CO survey by Dame et al. (2001) with a number of structures relevant for discussing the inner few kiloparsecs of the Galactic center. The near and far 3 kpc arms appear as outlined by Dame & Thaddeus (2008), as parallel lanes within the range of longitudes where they can be followed clearly in CO (−12° < ℓ < +13°). Note that the far 3 kpc arm shows only weakly in Figure 7 (see Dame & Thaddeus 2008 for a detailed analysis). In the first quadrant, the line-of-sight velocity pattern of the near side of the Connecting arm, indicated in Figure 7 following the analysis by Fux (1999, e.g., his Figure 1 and Section 6.1), passes through the peak of the terminal velocity curve at positive longitudes. While crossing the ℓ − v pattern of the far 3 kpc arm at a Galactic longitude near 10°, this feature is better isolated at negative latitudes in both H i and CO (e.g., Figure 4 of Marshall et al. 2008). An approximate locus for the Norma/4 kpc arm in the ℓ − v diagram is obtained by assuming a logarithmic spiral with the following constraints: (1) an expanding motion fixed at ℓ = 0° of −29.3 km s⁻¹, as obtained from CO spectra in absorption toward the Galactic center (first noted by Kerr 1967 in H i; see also Greaves & Williams 1994 for CS absorption lines); (2) a southern tangent at a Galactic longitude of −325 (e.g., Bronfman 2008, his Figure 2); (3) a northern tangent near 25° (e.g., Table 1 of Englmaier & Gerhard 1999, their "inner Scutum tangent"). The HMSFRs are not expected to follow the lines in Figure 7 to any better than the 3–9 km s⁻¹ velocity dispersion of the molecular cloud population (e.g., Combes 1991, their Section 3.2.1). Similarly, velocity dispersions measured from hydrogen profiles show characteristic broadening by ∼7 km s⁻¹, which may be regarded as an upper limit due to the presence of blending features (e.g., Burton 1974).

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In the following, we present our results for each source and list the associated arms in the last column of Table 4. Note that we also include two sources from previous measurements that are of interest for a general discussion (G009.62+00.19 and G023.44−00.18).

G009.62+00.19. According to Sanna et al. (2009), on the basis of a CO latitude-velocity analysis, this HMSFR is associated with gas along the Norma Arm at a distance of $5.15^{+0.77}_{-0.66}$ kpc from the Sun, which corresponds to a Galactocentric radius of 3.4 kpc for R₀ = 8.38 kpc. On the one hand, the near 3 kpc arm has an LSR velocity blueshifted by 15–20 km s⁻¹ at the same longitude. The brightest CO emission from the near 3 kpc arm lies below the Galactic plane at Galactic longitudes greater than ≈6° and is offset by about 05 in latitude, with respect to the midplane of the Galaxy, at the Galactic longitude of the maser site (Figure 8; see also Figure 3 of Dame & Thaddeus 2008). On the other hand, at ℓ ≈ 95 the Norma arm peaks at velocities between 0 and 10 km s⁻¹ centered at about zero latitude, in agreement with the Galactic location and LSR velocity of G009.62+00.19 (Figure 8). We also note that the star-forming region appears to expand from the Galactic center at a velocity of about 36 km s⁻¹, close to the Norma value of ≈30 km s⁻¹ at zero longitude⁷ (Table 4).

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G010.47+00.02. At a parallax distance of $8.55^{+0.63}_{-0.55}$ kpc from the Sun, our measurement translates to a Galactocentric radius of 1.6 kpc, assuming R₀ = 8.38 kpc. The LSR velocity of large-scale emission associated with G010.47+00.02 (∼70 km s⁻¹) falls in the ℓ − v locus of the Connecting arm in the first quadrant, about 20 km s⁻¹ lower than a close by ℓ − v feature associated with the far 3 kpc arm (Figure 7). At the longitude of the source, the far 3 kpc arm shows a bump of faint emission below the Galactic plane (Figure 8; see also Figure 3 of Dame & Thaddeus 2008), whereas G010.47+00.02 lies close to zero latitude, a few tens of parsec above the Galactic plane. On the other hand, by comparing the velocity profile of the Connecting arm at ℓ ∼ 105 with the latitude-velocity maps of Bitran et al. (1997; our Figure 8), one can clearly see a strong CO feature centered at zero latitude at the LSR velocity of G010.47+00.02. Therefore, we associate G010.47+00.02 with gas condensations belonging to the Connecting arm.

G010.62−00.38. The combined parallax measurement for G010.62−00.38 is 0.202 ± 0.019 mas, which corresponds to a distance of $4.95^{+0.51}_{-0.43}$ kpc from the Sun and a Galactocentric radius of 3.6 kpc (for R₀ = 8.38 kpc). This prominent site of star formation has a combination of slightly negative LSR velocity (−3 km s⁻¹) and negative Galactic latitude, which associates the star-forming region with a bright CO feature belonging to the near 3 kpc arm (Figure 8, lower panel). In this range of longitudes, the Norma and near 3 kpc arms are clearly separated by about 20 km s⁻¹ at different distances below the Galactic plane (Figure 8). G010.62−00.38 belongs to the W31 star-forming complex that has been long thought to have an intrinsic, large, non-circular motion of several tens of km s⁻¹. While hydrogen recombination lines from the large-scale H ii complex show velocities near zero, which could be associated with either nearby or very distant gas, absorption features from different molecules/transitions have been detected up to velocities of about 50 km s⁻¹ (see discussion in, e.g., Wilson 1974; Caswell et al. 1975; Fish et al. 2003). Along nearly circular orbits, the terminal velocity at ℓ ≈ 10° would be in excess of three times the absorption cutoff assuming a IAU Galactic rotation speed, which would locate G010.62−00.38 on the near side of the tangent point (e.g., Fish et al. 2003, their Figure 1). While this argument has been questioned on the basis of a general deficiency of CO and H i gas within a Galactocentric radius of about 3 kpc (e.g., Figure 6 of Corbel & Eikenberry 2004), the current parallax distance of 5 kpc from the Sun indeed places W31 on the near edge of the Galactic gas hole, assuming the W31 cluster of H ii regions is physically related (cf. Corbel & Eikenberry 2004, their Figure 8). The observed absorption cutoff is due to the radial expansion of G010.62−00.38 from the Galactic center (∼60 km s⁻¹), as inferred from its full-space kinematics (Table 4).

G012.02−00.03. We measured a combined trigonometric parallax of 0.106 ± 0.008 mas for this source, corresponding to a distance of $9.43^{+0.77}_{-0.66}$ kpc from the Sun and a Galactocentric radius of 2.1 kpc (for R₀ = 8.38 kpc). In Figure 7, the ℓ − v position of G012.02−00.03 is associated with the locus of the far 3 kpc arm in the first Galactic quadrant, which lies close to zero latitude at the longitude of our source (Dame & Thaddeus 2008, their Figure 3). For ℓ ≈ 12°, the current parallax measurement locates the far 3 kpc arm at almost half the distance to the Galactic center of the near 3 kpc arm at a similar longitudes (Figure 6), which has a direct implication for interpreting the nature of the 3 kpc feature of our Galaxy (see Section 4.1).

G023.44−00.18. Brunthaler et al. (2009) measured this massive star-forming region to be at a heliocentric distance of $5.88^{+1.37}_{-0.93}$ kpc, or a Galactocentric radius of 3.8 kpc for R₀ = 8.38 kpc, in the general direction of the northern Norma tangent in the first Galactic quadrant (Figure 7). According to Dame et al. (1986, their Figure 10(b)), at the longitude of the source, velocities in excess of +100 km s⁻¹ are expected for the inner regions of the Norma arm, whereas material in the Scutum arm would show LSR velocities which are more than 30 km s⁻¹ below that of G023.44−00.18. Therefore, we associate G023.44−00.18 as belonging to the Norma arm near its tangent.

G023.70–00.19. The distance to this star formation site is $6.21^{+1.0}_{-0.80}$ kpc, which corresponds to a Galactocentric radius of 3.7 kpc (for R₀ = 8.38 kpc). This measurement locates G023.70−00.19 only a few hundred parsecs away from G023.44−00.18 in a similar direction below the Galactic plane, which argues for an association with the Norma arm. As shown in Figure 7, its LSR velocity of about +77 km s⁻¹ associates the star-forming region to gas emission at the low-longitude edge of a "gas hole" near ℓ ∼ 25°. According to Cohen et al. (1980, their Figure 2), molecular gas at velocities between 70–90 km s⁻¹ and Galactic longitudes between 23° and 25° is associated with the Norma arm. At a similar longitude, gas belonging to the nearby Scutum arm shows LSR velocities less than +60 km s⁻¹ that involves CO emission below the gas hole. Therefore, we associate G023.70–00.19 with gas condensations in the Norma arm.

Together with the two previous measurements listed in Table 4, the HMSFRs presented here sample the inner regions of the Milky Way at Galactic longitudes from +96 to +237 and Galactocentric radii between 1.6 and 3.8 kpc. In the inner Galaxy, the mass distribution of the Galactic (nested) bar(s) provides non-axisymmetric gravitational perturbations on gas and stellar orbits, whereas a nearly flat rotation curve is generally measured between Galactocentric radii of about 4–13 kpc (e.g., Reid et al. 2009b; Honma et al. 2012). Under the influence of a bar potential, highly non-circular streamlines of gas and stellar orbits are indeed expected as for the families of periodic orbits, x₁, x₂, and x₃ (e.g., Contopoulos & Papayannopoulos 1980; van Albada & Sanders 1982; Athanassoula 1992a); these streamlines would appear on ℓ − v diagrams as parallelogram-shaped features (e.g., Binney et al. 1991; Bureau & Athanassoula 1999). A comparison of the measured LSR velocities with those expected for circular orbits (e.g., Englmaier & Gerhard 1999) at the longitudes and Galactocentric distances of our sample shows, in general, differences of several tens of km s⁻¹ (e.g., Sanna et al. 2009). From Table 4, a weighted average of the rotation speed of HMSFRs in the inner Milky Way differs by about −40 ± 5 km s⁻¹ from the rotation speed at the solar circle of Θ₀ = 243 km s⁻¹ (Reid 2013). This value is significantly lower than the average peculiar motion derived for HMSFRs at Galactocentric radii greater than 4 kpc, which lag Galactic rotation by less than 10 km s⁻¹ (e.g., Xu et al. 2013). We note that this result does not depend sensitively on the value of Θ₀ assumed in the calculation. Evidence for a substantially flat rotation curve which drops inward at small Galactocentric radii are commonly observed for barred galaxies with rotation velocities comparable to the Milky Way (e.g., Sofue et al. 1999).

Moving from the star-forming region closest to the Galactic center (G010.47+00.02) to the one farthest from the center (G023.44−00.18), we start to fix the positions of the major arm-like features of the inner Milky Way on a coherent face-on view (Figure 6). In the following, we describe these constraints in brief. Within about 3 kpc of the Galactic center and outside the CMZ, three CO features pointed out on the ℓ − v diagram of Figure 7 dominate the gas kinematics, the near and far 3 kpc arms (yellow lines), and the Connecting arm (green line). The Connecting arm, as fixed by the position of G010.47+00.02 at $R=1.6^{+0.2}_{-0.1}$ kpc, apparently runs along the far edge of the long bar, probably closer to the Galactic center than the far 3 kpc arm, constrained at a similar longitude by the position of G012.02−00.03 at $R=2.1^{+0.5}_{-0.3}$ kpc. The distance measurement to G010.62−00.38 further constrains the position of the near side of the 3 kpc arm at a Galactocentric radius ($R=3.6^{+0.4}_{-0.4}$ kpc) almost twice that of G012.02−00.03. Despite early claims that the near 3 kpc arm was deficient in star formation activity (e.g., Lockman 1980), at the position of our sources the CO velocity-integrated maps show local peaks of emission (Figure 3 of Dame & Thaddeus 2008), which pinpoint enhanced star formation such as in the prominent W31 complex. This is also in agreement with the recent detection of several, massive, star formation sites from the Methanol Multibeam Survey that are associated in longitude, latitude, and velocity with the brightest CO emission along the 3 kpc arms (cf. Figure 2 of Green et al. 2009 and Figure 3 of Dame & Thaddeus 2008).

In the first Galactic quadrant, outward of 3 kpc from the Galactic center but within the GMR, an annulus of less than 2 kpc in radius encompasses the northern Scutum-Centaurus, Norma, and near 3 kpc arm tangents (Figure 6). This is evident, for instance, in the Galactic Ring Survey of extended ¹³CO emission along the Galactic plane, with prominent concentrations at ℓ ∼ 31° and 23° (Jackson et al. 2006, their Figure 1). While interarm distances are expected to decrease as the arms converge to the end of the (long) bar at a Galactocentric azimuth near 45° (i.e., the angle between the Sun and the source as viewed from the Galactic center, β), our distance measurements for G009.62+00.19 and G010.62−00.38 show that the Norma and near 3 kpc arms nearly overlap at a Galactic longitude of 10° (β ∼ 14°) on a face-on view of the Milky Way (Figure 6). On the other hand, a b–v analysis of the CO emission from the arms at this longitude reveals that their gas distributions do not mix, with the near 3 kpc arm passing under (at lower Galactic latitudes) the Norma arm (Figure 8).

4.1. Topics on the Inner Arm Features

This work was partially funded by the ERC Advanced Investigator Grant GLOSTAR (247078). This work made use of the Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Programme and operated under license.

Facility: VLBA - Very Long Baseline Array

Maser spots for parallax fitting were selected according to the following criteria: (1) spots persisting over one year that belong to isolated features, in order to avoid emission blended between different maser centers; (2) compact maser spots, unresolved by the VLBA beam or slightly resolved but with a stable, deconvolved, position angle; (3) strong maser spots (∼1–10 Jy beam⁻¹) with typical signal-to-noise ratios of more than a hundred.

G010.62−00.38. For the purposes of a maser reference position, we employed three spots at the LSR velocities of −14.2, −1.1, and +1.0 km s⁻¹ from the H₂O maser distribution measured within the field of view of the VLBA. Among the calibrators observed in K band, the two stronger QSOs in Table 2, J1821−2110 and J1751−1950, served as a background reference position and their images from the first epoch data are shown in Figure 9. The angular separation on the plane of the sky (θ_sep) between the background QSOs and the target maser is reported in Table 2. The ICRF J1751−1950 was detected at each epoch above a 5σ level; at the third epoch, the peak intensity of J1821−2110 fell below a 3σ level due to poor phase stability between the maser and the calibrator (because of poor weather conditions) and was not used. Due to the lack of the third epoch data, parallax fitting with the calibrator J1821−2110 results in a higher correlation between the parallax sinusoid and the (linear) proper motion component from each maser spot. Since we expect no detectable proper motion for the extragalactic sources, parallax fitting with J1821−2110 was constrained with proper motions determined from J1751−1950 for each spot. The error-floors determined by combining the measurements of the three maser spots with respect to the two QSOs were ±0.05 mas in the E–W direction and ±0.07 mas in the N–S direction. Since water maser cloudlets have typical proper motions of tens of km s⁻¹, determining a secular proper motion for the HMSFR requires to correct for maser velocity components. We estimated this contribution from the average proper motion of all maser features (80) determined as in Sanna et al. (2010) with respect to the reference spot at +1.1 km s⁻¹, used for the parallax fitting and with the more accurate proper motion measurement. The average, internal, velocity components are −0.01 ± 0.03 mas yr⁻¹ toward the east and +0.28  ±  0.02 mas yr⁻¹ toward the north, where we report the standard error of the mean. Thus, the secular proper motion of the HMSFR is estimated to be −0.366 ± 0.081 mas yr⁻¹ and −0.600 ± 0.055 mas yr⁻¹ in the east and north directions, respectively. We explicitly note that these small uncertainties may still be affected by a further uncertainty of several tenth of mas yr⁻¹, due to the complexity of G010.62−00.38 as a cluster of young stellar objects (e.g., Liu et al. 2011). At our measured distance, these values correspond to −8.6 ± 1.9 km s⁻¹ and −14.1 ± 1.3 km s⁻¹ eastward and northward, respectively. Completing the kinematic information, we assume an LSR velocity of −3.0 ± 2.7 km s⁻¹ for the HMSFR G010.62−00.38, obtained from the large-scale rest velocity of the CS (1−0) and NH₃ (1,1) line emission (Anglada et al. 1996).

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G010.47+00.02. As a maser reference position, we combined the positions of seven spots associated with seven distinct maser cloudlets spread over a region of about 0.4 arcsec in size (Table 3). Imaging of the calibrators for G010.47+00.02 was optimized by setting an elevation cutoff of 25° for each antenna. Among the set of calibrators observed in combination with G010.47+00.02, only the ICRF calibrator J1751−1950, at an angular offset of 3° from the target maser (Table 2), had a distinct peak of emission at all epochs and has been used as a background reference position in the parallax measurement (Figure 9). The error-floors determined from the simultaneous fitting of these seven maser spots were ±0.01 mas and ±0.09 mas toward the E–W and N–S directions, respectively. As for G010.62−00.38, we estimated the secular proper motion of the star-forming region by subtracting the relative motion of all measured maser features (11) with respect to the reference spot at +68.0 km s⁻¹ (Table 3). The average internal velocity components are +0.073 ± 0.006 mas yr⁻¹ toward the east and −0.22 ± 0.08 mas yr⁻¹ toward the north, where we report the standard error of the mean. Thus, the total motion of the whole source is estimated to be −3.860 ± 0.015 mas yr⁻¹ and −6.403 ± 0.076 mas yr⁻¹ in the east and north directions, respectively. At our measured distance, these values correspond to −156.4 ± 0.6 km s⁻¹ and −259.5 ± 3.1 km s⁻¹ eastward and northward, respectively.

G012.02−00.03. The 12.2 GHz methanol maser from G012.02−00.03 consists of a single spectral feature persisting during the four observing epochs with emission extended over an area of a few mas (squared). The brightness distribution is centrally peaked and we employed the peak positions of two velocity channels, at +108.0 and +108.8 km s⁻¹, as maser reference positions. While the U-band calibrators were easily detected at all epochs, only the closer QSO J1808–1822 (see Table 2) had a stable spatial morphology (deconvolved size) suitable for an accurate parallax measurement. The error-floors from these combined measurements were ±0.01 mas and ±0.19 mas toward the E–W and N–S directions, respectively. Methanol masers move with typical velocities of only a few km s⁻¹ that are very close to the systemic velocity of the molecular cloud core they are associated with. Therefore, we will neglect their contribution for computing the secular proper motion of G012.02−00.03. By averaging the proper motion inferred from the two maser spots, we obtain Galactic velocity components of −183.6 ± 1.0 km s⁻¹ and −346.7 ± 11.8 km s⁻¹ eastward and northward, respectively.

G023.70−0.19. For the parallax measurement of G023.70–00.19 we made use of three maser spots, two of them are associated with the peak position of the 12.2 GHz methanol maser emission (at +77.5 and +79.0 km s⁻¹) and a third spot is associated with an isolated maser cloudlets at about 21 mas to the south of the peak emission (at +76.7 km s⁻¹). Only measurements with the two closer calibrators (see Table 2), J1825−0737 and J1846−0651, gave individual error-floors in the E-W direction smaller than 0.1 mas for each maser spot and were used in the parallax estimate. These final error-floors were ±0.06 mas and ±0.15 mas toward the E–W and N–S directions, respectively. By averaging the proper motion inferred from the three maser spots, we obtain Galactic velocity components of −94.4 ± 2.0 km s⁻¹ and −187.4 ± 4.0 km s⁻¹ eastward and northward, respectively. Toward the maser position, CS (2−1) line emission shows an LSR velocity of +68.3 km s⁻¹ (Bronfman et al. 1996), about ten km s⁻¹ slower than the peak velocity of the H110α line at the same position (Sewilo et al. 2004, +76.5 km s⁻¹). In order to resolve the near/far kinematic distance ambiguity, Sewilo et al. observed the H₂CO (1₁₀ − 1₁₁) line in absorption against the H ii region up to velocities of +86 km s⁻¹, with an H₂CO absorption component at the same velocity of the CS line. Following these evidence, we assume a central LSR velocity for the HMSFR G023.70–00.19 of +76.5 ± 10 km s⁻¹, that better matches the 12 GHz CH₃OH maser velocities of Figure 1, which usually trace more quiescent gas dynamics close to the systemic velocity of the region (<5–10 km s⁻¹).