STRUCTURAL VARIATION OF MOLECULAR GAS IN THE SAGITTARIUS ARM AND INTERARM REGIONS

Observations of the ¹²CO J = 1–0 (rest frequency of 115.271 GHz) and ¹³CO J = 1–0 (110.201 GHz) transitions were carried out in 2002–2003 (Period 1) and 2005–2006 (Period 2) using the NRO 45 m telescope. The observing parameters are summarized in Table 1. The half-power beam width (HPBW) of the telescope at 115 GHz was 15''. At the distances of the near- and far-side Sgr arm and the tangent point, this corresponds to 0.22, 0.65, and 0.49 pc, respectively. The main-beam efficiency (η_MB) was ≃ 0.4 (see Table 1). The forward spillover and scattering efficiency (Kutner & Ulich 1981) at 115 GHz was measured using the moon in 2003 November, η_moon = 0.69 ± 0.03.

Table 1. Parameters of the Observations and Reduced Maps

	Period 1	Period 2
	(2002 Nov–2003 May)	(2005 Dec–2006 Mar)
	13CO J = 1–0	12CO J = 1–0	13CO J = 1–0
Grid spacing	137 (PSW)	Nyquist (OTF)	Nyquist (OTF)
Area (Δl × Δb)	03 × 05	08 × 08	08 × 08a
Bandwidth	32 MHz (87.0 km s−1)	512 MHz (1330 km s−1)	32 MHz (87.0 km s−1)
	...	...	512 MHz (1390 km s−1)
Frequency resolution	37.8 kHz (0.10 km s−1)	1 MHz (2.6 km s−1)	62.5 kHz (0.17 km s−1)
	...	...	1 MHz (2.7 km s−1)
Main-beam efficiency	0.46 ± 0.03	0.39 ± 0.03	0.45 ± 0.03
System noise temperature (DSB)	300–600 K	350–450 K	300–400 K
Map grid	685	6''	6''
Effective HPBW	20''	17''	17''
rms noise (TMB)	0.57 K (at 0.2 km s−1)	0.44 K (at 2.6 km s−1)	0.62 K (at 0.2 km s−1)
	...	...	0.16 K (at 2.6 km s−1)

Note. ^aExcept for the area observed in Period 1.

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We used the 25-BEam Array Receiver System (BEARS; Sunada et al. 2000). The front end consists of a 5 × 5 focal-plane array of double-sideband (DSB), superconductor–insulator–superconductor (SIS) mixer receivers with a beam separation of 411 (Yamaguchi et al. 2000). We adopted the chopper-wheel method, switching between a room-temperature load and the sky, for primary intensity calibrations. This corrects for atmospheric attenuation and antenna losses, and converts the intensity scale to the antenna temperature in DSB [T*_A(DSB)]. The back end was a set of 1024-channel digital autocorrelation spectrometers (Sorai et al. 2000). It was used in the wide-band and high-resolution modes (bandwidth of 512 and 32 MHz, respectively: Table 1).

In Period 1, we mapped the ¹³CO line in a 03 × 05 region (3743 ≲ l ≲ 3780, −052 ≲ b ≲ +002) using the position-switch (PSW) observing method. The spectrometer was mainly used in the high-resolution mode. The grid spacing was chosen to be 137, one-third of the beam separation of BEARS. An emission-free reference (off) position was taken at (l, b) ≈ (375, −15) for three 20 s on-source integrations. The total number of observed points was about 13,500, and the typical integration time per point was 80 s. We also mapped the same area at a sparse spatial sampling using the wide-band mode to determine the spectral baseline range.

In Period 2, we employed the On-The-Fly (OTF) mapping technique (Sawada et al. 2008) to map the ¹²CO and ¹³CO lines in a 08 × 08 region (3735 ⩽ l ⩽ 3815, −050 ⩽ b ⩽ +030). The size of the map (08) corresponds to 40, 130, and 90 pc at the distances of the near- and far-side Sgr arm and the tangent point, respectively. The wide-band mode of the spectrometer was used to observe the ¹²CO line, while the ¹³CO data were taken with both modes. The sampling interval along the scan rows was set to be 3'', and the separation between the scan rows was 5''. An off position was observed before every scan, whose duration was typically 40 s. The off position (l, b) ≈ (380, −17) had been confirmed to be emission-free in ¹²CO J = 1–0: i.e., <0.07 K in T*_A(DSB), which corresponds to ≲ 0.15 K in single sideband (SSB). Scans were made in two orthogonal directions, i.e., along l and b, in order to minimize scanning artifact (systematic errors along the scan direction) in the data reduction process (see Section 3.2).

The pointing of the telescope was calibrated by observing SiO J = 1–0 maser (42.821 and 43.122 GHz) sources OH39.7+1.5 and R Aql with another SIS receiver at 40 GHz band (S40) every 1–2 hr. The pointing accuracy was typically 6'' (Period 1) and 7'' (Period 2).

Since BEARS is a DSB receiver system, we need to correct the observed intensity scale to that of an SSB receiver. The scaling factors to convert T*_A(DSB) to T*_A(SSB) were derived by observing a calibrator with S100, the single-beam SIS receiver equipped with an SSB filter, and with every beam of BEARS. We used the factors provided by the observatory in Period 1, and measured them ourselves by observing W51 in Period 2. Based on multiple measurements, the reproducibility of the factors in Period 2 was 4% (¹²CO) and 9% (¹³CO).

The ¹³CO PSW data were reduced with the NEWSTAR reduction package developed at NRO (Ikeda et al. 2001). During the data reduction, it turned out that there was weak emission of T*_A ≃ 0.3 K and v_LSR ≃ 42 km s⁻¹ at the off position for the outer four receiver beams. We successfully corrected this error for three out of the four beams by removing Gaussian profiles from the off data. For the remaining one beam, we could not remove the influence; therefore we have excluded the beam from the further reduction process. Due to an aberration originating in the beam-transfer optics of the telescope, the beams of BEARS were not exactly aligned on a regular 411 grid on the sky. Therefore, after flagging out bad data, the data were resampled onto a 685 grid using a convolution with a Gaussian whose FWHM was 137. As a result the effective spatial resolution became 20''. Linear baselines were fitted and subtracted. Baseline ranges were taken at v_LSR ≃ 30 and 100 km s⁻¹, which had been confirmed to be emission free using the wide-band data. Resultant spectra have typical rms noise of 0.4 K at a resolution of 20'' × 20'' × 0.10 km s⁻¹.

The reduction of the OTF data was made with the NOSTAR reduction package (Sawada et al. 2008). Bad data were flagged, and linear (high-resolution) or parabolic (wide-band) baselines were fitted and subtracted. The data were mapped onto a square grid of 6'' separation by spatial convolution with a Gaussian-tapered Jinc function J₁(πr/a)/(πr/a) · exp [ − (r/b)²], where J₁ is the first-order Bessel function, a = 1.55, b = 2.52, and r is the distance from the grid point to the observed position divided by the grid spacing (Mangum et al. 2007). As a result the effective spatial resolution was 17''. The scanning artifact was reduced by combining the maps made from the longitudinal and latitudinal scans using the PLAIT method (Emerson & Gräve 1988). Since the ¹³CO high-resolution data do not cover sufficient emission-free velocity ranges for baseline subtraction, we used the wide-band data as a reference to determine the spectral baseline. That is, the difference between the high-resolution and wide-band spectra was linearly fitted for each spatial grid, and the regression was added to the high-resolution data. The final data set has an rms noise level of 0.18 K (¹²CO wide band), 0.074 K (¹³CO wide band), and 0.29 K (¹³CO high resolution), at a resolution of 17'' × 17'' × 2.6 km s⁻¹ (wide band) and 17'' × 17'' × 0.2 km s⁻¹ (high resolution).

We checked the relative intensity calibration between Periods 1 and 2. The Period 1 map was resampled onto the same grid as the Period 2 map, and the correlation of the intensities was examined in the region in which the maps overlap. The results are consistent and we found the relation T*_A(Period 1) = (1.048  ±  0.001) · T_A*(Period 2) for the pixels which were brighter than 1 K in both maps. The difference of ≈5% is within the uncertainties of η_MB and the scaling factors converting T*_A(DSB) into T*_A(SSB). Thus, we combined the maps from two periods.

Hereafter, the line intensities are shown in the main-beam temperature [T_MB ≡ T*_A(SSB)/η_MB] scale (for the ¹³CO data, we adopted the value in Period 2, i.e., η_MB = 0.45). The T_MB is appropriate for the brightness temperature of compact structures, whereas the brightness of spatially extended emission may be overestimated (Appendix B).

The ¹²CO J = 3–2 data (T. Sawada et al. in preparation) are compared with the J = 1–0 lines. The observations of the J = 3–2 line were made with the Atacama Submillimeter Telescope Experiment (ASTE) 10 m telescope at Pampa la Bola, Chile (Ezawa et al. 2004; Kohno 2005) in 2005 September. The region of 3743 ≲ l ≲ 3780, −052 ≲ b ≲ +002 (a part of the 45 m field of view, see Figure 2) was mapped using the OTF technique. The HPBW and η_MB of the telescope were 22'' and 0.6, respectively. The data were reduced with NOSTAR and the reduced data cube has an effective resolution of 24'' × 24'' × 0.87 km s⁻¹. Details will be described in a forthcoming paper. The peak intensity maps of the three lines are presented in Figure 2.

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Figures 3 and 4 show the velocity channel maps of the ¹²CO and ¹³CO lines, respectively, which cover the velocity range v_LSR = 10–100 km s⁻¹ with an interval of 5 km s⁻¹.

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The distribution of the emission in the channel maps significantly changes with the velocity. At the lowest velocity (10–25 km s⁻¹) in Figure 3, low brightness ¹²CO emission originating in the solar neighborhood is widespread in the field of view. Beyond 25 km s⁻¹, the widespread emission vanishes. Instead, bright (T_MB ≳ 10 K) and spatially confined structures begin to dominate at ≳ 35 km s⁻¹. These structures have sharp boundaries and form clumps (e.g., at l ≃ 375, b ≃ −01, v_LSR = 52.5 km s⁻¹) and filaments (e.g., at the top of the panel at 47.5 km s⁻¹). Beyond ≳ 60 km s⁻¹, the bright structures become less prominent. Though they remain up to 62.5 km s⁻¹ (at the bottom of the panel), low brightness extended emission starts to spread over the field. At the tangent velocity (75–90 km s⁻¹), the low brightness (≃ 4 K) emission almost fills the field of view, except a lump of ≃ 10 K emission at the top-right corner of the field. The high surface-filling factor at the tangent velocity can be attributed partly to the velocity crowding effect; nevertheless, the lack of bright structures is a distinct difference from the velocity range of 40–60 km s⁻¹ (Section 4.2).

The ¹³CO channel maps (Figure 4) show similar characteristics as those seen in the ¹²CO maps: the bright (≳ 4 K), compact structures dominate at 40–65 km s⁻¹, whereas the emission of 1–2 K is widespread at 75–90 km s⁻¹. The ¹³CO maps have, in general, higher brightness contrast than those of the ¹²CO line, likely due to the lower optical depth. One of the most extreme cases is the 62.5 km s⁻¹ channel. The bright (≳ 4 K) clumps seen in the ¹³CO map are not very prominent in ¹²CO, implying that the gas in the foreground with low excitation temperature obscures the bright ¹²CO line of the clumps.

Anderson & Bania (2009) compiled catalogs of H ii regions in the first Galactic quadrant and determined the distances to them, resolving the near–far distance ambiguity using the H i emission/absorption method and the H i self-absorption method. Their catalog contains 10 H ii regions situated in our field of view (Table 2). Figures 5 and 6 show the peak brightness maps around the H ii regions in ¹²CO and ¹³CO, respectively. Nine of them are associated with the bright (>10 K in ¹²CO and/or >4 K in ¹³CO) clumps or filaments within a few parsec. In particular, five ultracompact H ii regions (whose names begin with "U") are all tightly associated with the molecular clumps. This is consistent with Anderson et al. (2009). One exception is C37.67 + 0.13 at the tangent velocity. The ¹²CO around this object appears weak and extended, probably due to the self-absorption. The ¹³CO line is rather faint (≈4 K) in comparison with the other regions.

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Our sufficient (≲ 1 pc) spatial resolution reveals that the spatial structure of molecular gas varies with the radial velocity and thus with respect to the Galactic structure. We classify the structures into the following two components, the B component and the D component. The B component is bright (T_MB > 10 K in ¹²CO; >4 K in ¹³CO) and spatially confined emission. It appears as clumps and filaments in the channel maps, whose typical size and mass are 1'–3' (3–8 pc at 9 kpc) and 10³–10⁴ M_☉, respectively. The D component is diffuse (i.e., spatially extended) and fainter (T_MB ≃ 4 K in ¹²CO and ≃ 1 K in ¹³CO) emission. The former is seen in the velocity range of ≃ 40–60 km s⁻¹, while the latter dominates the solar neighborhood (10–25 km s⁻¹) and at the tangent velocity (75–90 km s⁻¹). The emission in the range 60–65 km s⁻¹ is in-between—possibly a transition between or the mixture of them.

A number of studies have been performed in order to investigate the distribution and physical conditions of the gas in the Milky Way. Most of them started from the decomposition of emission into individual, discrete molecular clouds/clumps and determined their properties (see Section 1). For example, Scoville et al. (1987) identified 1427 clouds and 255 hot cloud cores from the Massachusetts-Stony Brook Survey data. Among them 19 and 1 are in our field of view, respectively. Their only hot cloud core is at (l, b, v) = (3755, −010, 53 km s⁻¹) and is a prototype of the B component in our classification. Our higher-resolution and Nyquist-sampled maps reveal a number of comparable structures (e.g., Figure 2). We also find a significant extended molecular emission. The previous studies might have missed a considerable amount of emission because of the cloud identification, i.e., the assumption that the molecular gas forms discrete objects. The emission below the cloud boundary threshold can be inevitably excluded from such analyses. The D component has a typical intensity (≃ 4 K) comparable to the boundary used by Scoville et al. (1987) and Solomon et al. (1987). Thus, a significant fraction of emission would have been overlooked in their work. In our data, 62% and 48% of the ¹²CO emission is below 4 K in the velocity ranges of 40–60 and 75–90 km s⁻¹, respectively. Though the B component emission will easily be identified as clouds/clumps, it only accounts for a small fraction of the total gas mass (Section 4.3). In the following, we address the characteristics of the gas in a quantitative fashion by using the crude observed line brightness, rather than extracting clouds.

There is clear variation of spatial structure of the gas with the radial velocity. Here we use histograms of the brightness temperatures, or the BDFs, which visualize the spatial structure of the gas without separating structures into arbitrary clouds. Figures 7 and 8 present the BDFs of ¹²CO and ¹³CO, respectively. The data with the 6'' × 6'' × 1.25 km s⁻¹ grid are divided into 5 km s⁻¹ velocity channels, and the number of l–b–v pixels in each 1 K (¹²CO) and 0.4 K (¹³CO) brightness bin is plotted (normalized by the total number of pixels in each velocity channel). In each panel the brightness distribution index (BDI) is also shown, which we introduce in the following subsection in order to quantify the characteristics of BDF.

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The BDF clearly reflects the amount of the two components of molecular gas described above. The ¹²CO BDF in the v_LSR = 35–40 km s⁻¹ channel (Figure 7) shows a sharp peak in the 0–1 K brightness bin. This corresponds to the fact that a large portion of the field of view is almost emission free (Figure 3). The high-brightness tail represents the B component in the right-hand side of the field (the most prominent structure is at l = 37°23', b = −0°14'). As the velocity goes up to v_LSR ≈ 55 km s⁻¹, the high-brightness tail is even more populated, and the peak brightness also increases. It corresponds to the B component structures in the velocity channel maps, with increased numbers (i.e., surface-filling factors) and peak brightness. The peak of the BDF at ≃ 0 K is still prominent, reflecting the relatively small surface-filling factor of the CO emission. At ≈60 km s⁻¹, the 0 K peak starts to drop, and another remarkable component, the shoulder at ≈4 K, emerges. It reflects the D component, which fills the bottom half of the field. At ≈75 km s⁻¹, the high-brightness tail truncates, while the 4 K shoulder still exists. At the tangent velocity (75–90 km s⁻¹), the 0 K peak is no longer prominent and the 4 K shoulder turns into a peak. This transition is obvious in the channel maps, in which the D component fills almost the whole field of view. Beyond 95 km s⁻¹, the 0 K peak reappears since the surface-filling factor of the D component decreases. The BDF, with a 4 K shoulder and truncation toward high brightness, is similar to that at 65–75 km s⁻¹.

The ¹³CO BDF shows a similar trend—high-brightness (≳ 4 K) tail at 40–65 km s⁻¹, truncation beyond 65 km s⁻¹, and a shoulder at ≈1 K at the tangent velocity. The ¹³CO BDF has, in general, a more prominent 0 K peak and sharper truncation toward the high-brightness tail, which come from the higher brightness contrast in the ¹³CO channel maps (Section 4.1).

We suggest that the difference of the BDF between the Sgr arm (40–60 km s⁻¹) and the interarm region (75–90 km s⁻¹) is due to a change of gas properties. There are, however, a couple of potential issues that we should consider, which might cause apparent variation between the velocity components: (1) distance from us (i.e., linear resolution) and (2) velocity crowding.

In order to test (1), we convolve the maps with a Gaussian to degrade the resolution by a factor of three (equivalent to HPBW = 51'') and see how the spatial resolution affects the map's appearance and thus the BDF. The BDFs from the convolved maps (crosses in Figures 7 and 8) confirm the features discussed above. This implies that a near–far distance ambiguity up to a factor of ≈3 (Section 2) does not affect the result.

As for (2), the line-of-sight path length in a 10 km s⁻¹ bin for the tangent component is ≈2.5 times larger than those for the near- and far-side Sgr arm (Section 2). This increases the (l, b, v)-volume filling factor of the emitting region in the tangent component, which may have turned the 4 K shoulder in the ¹²CO BDF into the peak seen at the tangent velocity. The absence of bright (≳ 10 K) ¹²CO emission may possibly be attributed to velocity crowding and self-absorption. However, the optically thin ¹³CO emission also lacks bright (≳ 4 K) structures at this velocity. This supports that the BDF in the interarm region differs intrinsically from that in the Sgr arm.

The BDFs clearly characterize the variation of the spatial structure, showing the bright, compact clumps/filaments and more extended component of molecular gas. We introduce the BDI to characterize the BDF with one number, which can be correlated with other parameters, such as the physical conditions of the gas and star-forming activity. The BDI is defined as the flux ratio of the bright emission to the low-brightness emission:

$$\begin{eqnarray} {{\rm BDI}} &=& \log _{10} \left(\frac{\int _{T_2}^{T_3} T\cdot B(T) dT}{\int _{T_0}^{T_1} T\cdot B(T) dT} \right) \nonumber \\ &=& \log _{10} \left(\frac{\sum _{T_2<T[i]<T_3}T[i]}{\sum _{T_0<T[i]<T_1}T[i]} \right), \end{eqnarray} \tag{ 1 }$$

where the BDF is denoted as B(T); T₀, T₁, T₂, and T₃ are the brightness thresholds; and T[i] is the brightness of the ith pixel. We note that the flux is roughly proportional to the mass.

In this paper, we adopt (T₀, T₁, T₂, T₃) = (3, 5, 10, ∞) for ¹²CO and (1, 1.5, 4, ∞) for ¹³CO. These thresholds are somewhat arbitrary, but are empirically chosen so that the numerator and the denominator of Equation (1) represent the gas of the typical brightness of the B and D components that are evident in the channel maps (Section 4.2), respectively. The typical molecular gas temperature that is determined in a wider Galactic plane ¹²CO survey is ≃ 10 K (Scoville & Sanders 1987); subtracting the cosmic microwave background temperature, the average brightness temperature would be ≃ 7 K. Our choice of the thresholds represents the brightness appreciably below and above this average over the large area in the Galactic plane. The thresholds for ¹³CO are adjusted correspondingly to pick out the similar regions in the maps (Figures 3 and 4). In the following, we demonstrate the utility of the BDI to characterize the spatial structure, despite that the thresholds can be specific to the line of sight we observed. An important future work would be to revisit the choice of these parameters when more examples become available.

The BDIs for ¹²CO and ¹³CO within the 5 km s⁻¹ velocity bins are shown in Figures 7 and 8, respectively. At v_LSR ≃ 40–60 km s⁻¹ the BDIs are higher (−1.2 to −0.5 in ¹²CO, −1.2 to −0.9 in ¹³CO), while at the 80–90 km s⁻¹ BDIs are lower (−2.7 to −2.2 in ¹²CO, −3.5 to −2.9 in ¹³CO). The fraction of bright emission varies with velocity. It is also remarkable that even at the velocities with a high BDI (i.e., in spiral arm), only a small fraction of the gas is composed in the B component. That is, despite the highest ¹²CO BDI (−0.47) at 45–50 km s⁻¹, the flux of the T_MB > T₂ emission amounts to only one-third of the T₀ < T_MB < T₁ emission, or 6.6% of the total flux. The mass fraction of the B component gas is even lower at other radial velocities.

The variation of BDI as a function of radial velocity (i.e., velocity profiles of BDIs) for ¹²CO and ¹³CO is presented in Figures 9 and 10, along with the mean brightness in the field. The line brightness shows four prominent peaks at 20 km s⁻¹ (solar neighborhood), 45 km s⁻¹ (near-side Sgr arm), 65 km s⁻¹ (far-side Sgr arm), and 85 km s⁻¹ (tangent velocity). The BDI in ¹²CO is high in the velocity range 40–60 km s⁻¹ (i.e., Sgr arm), with a steep decrease beyond 60 km s⁻¹. The BDI is low at 80–90 km s⁻¹. In other velocity ranges the BDI is infinitely small because of the lack of ⩾T₂ emission. The ¹³CO BDI behaves similarly to that of ¹²CO: it is high in 40–60 km s⁻¹ with peaks at 45 and 60 km s⁻¹ (the Sgr arm) and is low in 80–90 km s⁻¹ (the interarm region). Molecular gas is extended with little brightness variation in the interarm region, and bright, compact structures emerge in spiral arms.

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The ¹²CO J = 3–2 data are available for a smaller field (Figure 2), ≈1/4 of the 45 m field of view. The BDI, the ¹²CO J = 1–0 brightness, the T_MB(¹²CO J = 3–2)/T_MB(¹²CO J = 1–0) ratio [R_3–2/1–0(¹²CO)], and the T_MB(¹³CO J = 1–0)/T_MB(¹²CO J = 1–0) ratio [R_13/12(J = 1–0)] are shown in Figure 11. The overall characteristics of the ¹²CO brightness and the BDI are similar to those in the whole 45 m field of view (Figure 9). The R_3–2/1–0(¹²CO) is the highest at the radial velocity of 40–45 km s⁻¹ and tends to decrease toward the higher velocity. It has local peaks at 40–45, 55, and 85 km s⁻¹. The first two peaks agree with those of the BDI. If we assume that the brightness peaks at ≈47 and 63 km s⁻¹ trace the near- and far-side Sgr arm, respectively, these BDI and R_3–2/1–0(¹²CO) peaks are both offset from the corresponding brightness peaks toward the lower velocity by several km s⁻¹ (discussed in Section 4.6). On the other hand, the radial velocity of the third peak coincide with that of the brightness peak. The R_13/12(J = 1–0) generally correlates with the brightness and traces the optical depth (the column density) of the gas. Thus, the ¹²CO brightness peaks correspond to the peaks of molecular gas distribution along the radial velocity.

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The sets of the ratios (R_3–2/1–0(¹²CO), R_13/12(J = 1–0)) are calculated for the two components (1) v_LSR = 40–60 km s⁻¹, T_MB(¹²CO) > 10 K and (2) v_LSR = 70–80 km s⁻¹,⁹T_MB(¹²CO) = 3–5 K. They represent the B and D components. The ratios are derived as (⩾ 0.63 ± 0.03, 0.23 ± 0.02) and (0.40 ± 0.11, 0.16 ± 0.05),¹⁰ respectively. The errors quoted are estimated from baseline uncertainties (i.e., constant offset of 1σ is assumed in all spectra over all channels, which we consider as a very conservative estimate) and the random noise.

In order to estimate qualitatively the main difference between the two components, we compare the obtained intensity ratios with simple model calculations. Here, we use the large-velocity-gradient (LVG; Goldreich & Kwan 1974; Scoville & Solomon 1974) model and adopt the one-zone assumption: i.e., the emission lines originate in a homogeneous volume of the gas. More detailed analyses of the physical conditions of the gas by using more lines will be reported in a forthcoming paper. Figure 12 shows the result of LVG calculations made with RADEX (van der Tak et al. 2007). The R_3–2/1–0(¹²CO), R_13/12(J = 1–0), and the ¹²CO J = 1–0 brightness temperature were calculated as functions of the kinetic temperature of the gas (T_k) and the column density of ¹²CO molecules per unit velocity width [N(CO)/dv]. The number density of molecular hydrogen [n(H₂)] was assumed to be 10^2.5, 10^3.0, 10^3.5, and 10^4.0 cm⁻³. The ¹²C/¹³C abundance ratio at a Galactocentric distance of 6 kpc was estimated to be 40–55 (Langer & Penzias 1993; Savage et al. 2002; Milam et al. 2005). Here, we adopted 50 for the calculation. The physical conditions which reproduce the observed intensity ratios are plotted as the filled and open squares. The T_k of the two components are estimated to be ⩾13–22 and 8–16 K if the n(H₂) is in the range of 10^2.5–10^4.0 cm⁻³ (note that R_3–2/1–0(¹²CO), and thus the derived T_k of the B component gas is a lower limit). The gas in the B component is found to be warmer than that of the D component, as expected. Although no tight constraints on the gas density can be given, the possibility of the high (n(H₂) ≳ 10⁴ cm⁻³) density of the D component is rejected because the observed brightness cannot be reproduced even if the surface-filling factor is unity.

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The H ii region catalog compiled by Anderson & Bania (2009) contains 10 samples in our field of view (Table 2: see Section 4.1). The radial velocities of these H ii regions are plotted in Figure 11. The ones in the ASTE field of view are shown in filled symbols, while the others are open. Nine H ii regions are located at the far side (circles in Figure 11, top), and they are mostly concentrated at ≈50–60 km s⁻¹. This coincides with the velocity range where the BDI and the R_3–2/1–0(¹²CO) are high.

These nine H ii regions at the far side (50–60 km s⁻¹) are most likely associated with the far-side Sgr arm (i.e., the peak of the brightness at ≈63 km s⁻¹). Thus, the H ii regions in our line of sight have radial velocities systematically lower than that of the molecular spiral arm. We note again that the radial velocities of the BDI and R_3–2/1–0(¹²CO) peaks are offset from those of the CO brightness maxima toward the lower velocity (Section 4.4). All BDI and R_3–2/1–0(¹²CO) peaks and H ii regions are offset in velocity from the spiral arm.

We identified two distinct components of the molecular gas, the B component and the D component, based on high-resolution, wide-field mapping observations of the Galactic plane. The B component emission is prominent at the velocities of the spiral arms, although its flux (mass) fraction of the total flux is small. The D component (and even fainter emission) is the majority of the molecular mass, dominating the emission both at the spiral arm and at the interarm velocities. We have introduced the BDF and the BDI to quantify the difference, and demonstrated that the BDI characterizes the structural variation of the gas along the line of sight, i.e., the BDI is high in the spiral arm velocities and low outside. The B component emission corresponds to the "warm" or "hot" clouds defined in Solomon et al. (1985) and Scoville et al. (1987). Our analysis confirms their results that the "warm" or "hot" clouds are concentrated on the l–v loci of the spiral arms and resolves them as bright clumps and filaments. The advantages of our study are the following: the high-resolution observations revealed that the D component emission is faint and spatially extended, and therefore was missed in the "cloud identification" scheme. This component comprises about half the mass in our field and is quite substantial. Our method is free from the process of cloud identification and takes into account such a component as well as bright and clumpy (the B component) emission. Furthermore, the new parameter, BDI, characterizes the gas structure and is directly comparable with other tracers of the spiral arms (e.g., H ii regions) and the physical conditions of the gas (e.g., line ratios).

Extended emission in CO J = 1–0 has been found in external galaxies, especially in their interarm regions (e.g., Adler et al. 1992; Koda et al. 2009). However, at their current resolutions even with interferometers (>100 pc), it remains unclear if these components are an ensemble of small unresolved giant molecular clouds or truly extended emission. Our results are drawn at a very high spatial resolution of ≃ 0.5 pc, and are therefore different from the extragalactic results both qualitatively and quantitatively. The relation between such small structures and kpc-scale galactic structures that we find in Figures 3 and 4 is the new finding. The Atacama Large Millimeter/Submillimeter Array will bridge the gap between these studies with its ability to produce high-fidelity images of parsec-sized structures over nearby galaxies.

The peaks of the BDI coincide in velocity with the R_3–2/1–0(¹²CO) local maxima. The B component gas, which makes the BDI high, shows a high R_3–2/1–0(¹²CO) ratio and is warm, as opposed to the D component gas. The BDI peaks also coincide with H ii regions, but are offset toward lower velocities from the maxima of the CO brightness (the near- and far-side Sgr arm). These results indicate that the distribution of the high-BDI gas and H ii regions is shifted from the molecular spiral arm by several km s⁻¹.

The offset in velocity between the high-BDI gas and molecular spiral arm implies that the high-BDI gas is located in the outer (i.e., larger Galactocentric radius; see Figure 1(b)) side of the spiral arm. If we assume the 220 km s⁻¹ flat rotation of the Galaxy, the velocity offset (several km s⁻¹) translates to ≃ 500 pc in space. The corotation radius of spiral arms in the Milky Way is likely outside the solar circle.¹¹ Therefore, the gas at a Galactocentric radius of 6 kpc revolves faster than the spiral pattern, by ≈100 km s⁻¹. Hence, the gas with high BDI and high R_3–2/1–0(¹²CO) and star-forming regions are located on the downstream side of the spiral arm (CO brightness peak) in our field of view. If we assume a pitch angle of the Sgr arm of 12° (Georgelin & Georgelin 1976), the drift timescale for the offset is ∼20 Myr. This is consistent with the timescale found in other galaxies (Egusa et al. 2009). Note that the velocity offset may partially be attributed to the effect of radiative transfer (e.g., the B component gas in the spiral arm velocity with high R_3–2/1–0(¹²CO) may be obscured by the bulk D component gas) and needs to be verified by using optically thinner lines. Nevertheless, the asymmetry of BDI, R_3–2/1–0(¹²CO), and the distribution of H ii regions with respect to the arm velocities indicate that the trend is real.

We treated the tangent-velocity gas as a prototype of the gas in the interarm region. There are, however, some caveats. First, this line of sight shows slightly more emission at the tangent velocity compared with the neighboring longitudes (e.g., Figure 3 in Dame et al. 2001). This area is a molecular-rich interarm region. Second, the BDI is higher compared with the other velocity ranges corresponding to interarm regions, i.e., between the far-side Sgr arm and the tangent velocity (70–80 km s⁻¹) and the solar neighborhood (≃ 20 km s⁻¹). The emission at the tangent velocity has been proposed, though not proven, as a special structure, a spur that extends from a spiral arm into the interarm region (e.g., Dame et al. 1986). Sakamoto et al. (1997) found that there was no enhancement of the ¹²CO J = 2–1/¹²CO J = 1–0 ratio and deduced a lower gas density than the average over a much larger region. Koda et al. (2009) performed high-resolution mapping observations of the ¹²CO J = 1–0 line in the entire disk of M51 and detected spurs in the interarm regions. The gas at our tangent velocity could be a relatively molecular-rich portion of the interarm region. Still, the clear difference of gas structure between spiral arms and interarm regions is striking. The richness of molecular gas is not the only determinant of gas structure. There is a correlation with large Galactic structure.