Abstract

We performed Nyquist-sampled mapping observations of the central molecular zone of our Galaxy in the J = 1–0 lines of CO, 13CO, and C18O using the 45 m telescope at the Nobeyama Radio Observatory. The newly obtained data sets were an improvement by a factor of four in spatial resolution of the CO data previously obtained with the same telescope 22 years ago, providing the highest angular resolution CO atlas of this special area of the Galaxy. The data cover the area: −0|${^{\circ}_{.}}$|8 ≤ l ≤ +1|${^{\circ}_{.}}$|4 and −0|${^{\circ}_{.}}$|35 ≤ b ≤ +0|${^{\circ}_{.}}$|35 with a 15″ beamwidth. Total intensity ratios for CO J = 3–2/J = 1–0, 13CO/CO J = 1–0 and C18O/13CO J = 1–0, are 0.70 ± 0.06, 0.12 ± 0.01, and 0.14 ± 0.01, respectively. The high-resolution CO images show the fine structure of the molecular gas and enable us to identify a number of compact clouds with broad velocity widths, i.e., high-velocity compact clouds. We conducted a detailed comparison of our CO J = 1–0 data with the CO J = 3–2 data obtained with the James Clerk Maxwell Telescope to derive the distribution and kinematics of the highly excited gas. Three, out of four, of the previously identified high CO J = 3–2/J = 1–0 ratio areas at l = +1|${^{\circ}_{.}}$|3, 0|${^{\circ}_{.}}$|0, and −0|${^{\circ}_{.}}$|4 were confirmed with a higher spatial resolution. In addition to these, we identified several very compact, high CO J = 3–2/J = 1–0 spots with broad velocity widths for the first time. These are candidates for accelerated gas in the vicinity of invisible, point-like massive objects.

1 Introduction

The central few hundred parsecs of the Galaxy is characterized by a strong concentration of molecular gas, namely, the central molecular zone (CMZ; Morris & Serabyn 1996). The temperature and density of the molecular gas in the CMZ are higher than those in the Galactic disk, showing highly complex distribution and kinematics as well as a remarkable variety of peculiar features; e.g., Bania’s Clump 2 (Bania 1977), the l = +1|${^{\circ}_{.}}$|3 complex (also referred to as the l = +1|${^{\circ}_{.}}$|5 complex; Bally et al. 1988; Oka et al. 2001), the 200-pc expanding molecular ring (EMR; Kaifu et al. 1972; Scoville 1972), and a number of expanding shells/arcs (e.g., Tsuboi et al. 1997; Oka et al. 2001).

High-velocity compact clouds (HVCC) constitute a category of peculiar clouds with compact appearances (d ≲ 5 pc) and extremely broad velocity widths (ΔV ≳ 50 km s−1) found in the CMZ (e.g., Oka et al. 1998b, hererafter Oka+98). To date, approximately 80 HVCCs have been identified by eye (Nagai 2008). Most HVCCs have no counterpart in other wavelengths, although some of them are associated with high CO J = 3–2/J = 1–0 intensity ratio spots (Oka et al. 2007, 2012). The origin of HVCCs has remained unknown since they were discovered.

An energetic HVCC, CO 0.02–0.02, may deserve special mention (Oka et al. 1999). This HVCC is located approximately 5′ Galactic-east from the Galactic nucleus, Sgr A*, and is characterized by extremely large kinetic energy (1051.5–51.9 erg) and short expansion time (105.5–5.7 yr). The association of an emission cavity and a group of infrared point-like sources in the cavity suggest that CO 0.02–0.02 may have been accelerated, heated, and compressed in a series of supernovae that occurred within the last 105.5–5.7 yr (Oka et al. 2008). This also suggests that a young (10–30 Myr) massive compact cluster was responsible for the acceleration of the CO 0.02–0.02.

Another prominent HVCC is CO–0.40–0.22, which was found at 60 pc Galactic-west in the projected distance from the nucleus (Oka et al. 2016). This cloud has a compact appearance (d ≃ 3 pc) and extremely broad velocity width (ΔV ≃ 100 km s−1), being characterized by a very high CO J = 3–2/J = 1–0 intensity ratio and a remarkably isolated appearance in the HCN J = 4–3 line intensity maps. The kinematic structure of CO–0.40–0.22 can be attributed to a sudden powerful gravitational impact upon the molecular cloud caused by an invisible compact object with a mass of ∼105M. Its compactness and the absence of a counterpart at other wavelengths suggest that this massive object is an intermediate-mass black hole (IMBH). The detection of a point-like continuum source near the center of CO–0.40–0.22 supports the IMBH hypothesis (Oka et al. 2017), while the other interpretations such as explosion or cloud-to-cloud collision can not be ruled out.

These HVCCs were found in the spatially undersampled CO J = 1–0 data set, of which the virtual angular resolution is 60″ (Oka+98). This suggested that we were overlooking a large number of HVCCs, especially small (d ≲ 1 pc) ones such as HCN–0.009–0.044 and HCN–0.085–0.094 (Takekawa et al. 2017a). The complete detection of HVCCs in the CMZ would require Nyquist-sampled, high-resolution CO images to be captured as an absolute essentiality. In this study, we conducted on-the-fly mapping observations of the CMZ in the J = 1–0 lines of CO, 13CO, and C18O again using the 45 m telescope at the Nobeyama Radio Observatory (NRO). These data sets enabled us to identify a number of “overlooked” HVCCs.

This paper presents these data sets in the form of velocity-integrated maps, velocity channel maps, and longitude–velocity maps to provide the highest angular resolution CO atlas of this special area in our Galaxy. This atlas is expected to be useful for all researchers interested in this area. The CO J = 1–0 data were compared with the fully sampled CO J = 3–2 data to investigate the distribution and kinematics of the highly excited gas. Four examples of new HVCC candidates with high R3–2/1–0 are described in comparative detail. The identification of HVCCs from the new data sets will be discussed in forthcoming papers.

2 Observations

2.1 NRO 45 m telescope + BEARS

CO J = 1–0 (νrest = 115.271202 GHz; hereafter, all line frequencies are rest frequencies) line observations of the CMZ were performed using the 45 m NRO telescope during the period from 2011 January 19 to 29. We mapped the area as roughly −0|${^{\circ}_{.}}$|8 ≤ l ≤ +1|${^{\circ}_{.}}$|4  and −0|${^{\circ}_{.}}$|35 ≤ b ≤ +0|${^{\circ}_{.}}$|35, covering the bulk of the CMZ, in the on-the-fly (OTF) mapping mode.

We used the 5 × 5 focal-plane array SIS receiver BEARS (25-BEam Array Receiver System; Sunada et al. 2000; Yamaguchi et al. 2000). The typical system noise temperature of BEARS was approximately 800 K. The full width half-maximum beam size (FWHM) was 15″ at 115 GHz. We used the digital auto-correlator spectrometer AC45 in the wide-bandwidth mode, which covers an instantaneous bandwidth of 500 MHz with a 0.5-MHz resolution. At 115 GHz these settings correspond to a 1300 km s−1 velocity coverage and a 1.3 km s−1 velocity resolution, respectively. The pointing accuracy was checked and corrected every 1.5 hr by observing the SiO maser source VX-Sgr at 43 GHz. The pointing accuracy was maintained within 2″. Intensity calibration of the antenna temperature was accomplished by the standard chopper-wheel method.

The data were reduced on the NOSTAR reduction package. We subtracted baselines of the spectra by fitting the linear lines, or if necessary, the lowest degree polynomials that produce straight baselines in emission-free velocity ranges. Less than 1% of spectra needed non-linear baseline subtraction. The data were smoothed with a Gaussian function with 15″ FWHM. The final map was obtained with a 7|${^{\prime\prime}_{.}}$|5 × 7|${^{\prime\prime}_{.}}$|5 × 2 km s−1 grid and rms noise of |$\Delta T^{*}_{{\rm A}} = 1\:$|K (1σ).

2.2 NRO 45 m telescope + FOREST

Observations of the 13CO J = 1–0 (110.201354 GHz) and C18O J = 1–0 (109.782176 GHz) lines were performed using the 45 m NRO telescope during the periods 2016 January 26–31, February 1–15, and March 9–23. These two lines were observed simultaneously. We mapped the area as roughly −1|${^{\circ}_{.}}$|4 ≤ l ≤ +1|${^{\circ}_{.}}$|4 and −0|${^{\circ}_{.}}$|35 ≤ b ≤ +0|${^{\circ}_{.}}$|35 in the OTF mapping mode. In this paper, we present the data covering −0|${^{\circ}_{.}}$|8 ≤ l ≤ +1|${^{\circ}_{.}}$|4, and −0|${^{\circ}_{.}}$|35 ≤ b ≤ +0|${^{\circ}_{.}}$|35 in accordance with the CO J = 1–0 data coverage.

We used the FOur-beam REceiver System for the 45 m telescope (FOREST) receiver (Minamidani et al. 2016). The typical system noise temperature of the FOREST was 150–300 K. The FWHM beam size wss 15″ at 110 GHz. The pointing accuracy was checked and corrected every 1.5 hr by observing the SiO maser source VX-Sgr at 43 GHz. This accuracy was maintained within 3″. Calibration of the antenna temperature was accomplished by the chopper-wheel method. We used the highly flexible FX-type correlator SAM45 in the 1 GHz bandwidth, 244.14 kHz spectral resolution mode. At 110 GHz these settings correspond to a 2700 km s−1 velocity coverage and a 0.67 km s−1 velocity resolution, respectively.

The data were reduced on the NOSTAR reduction package. We subtracted the baselines from the spectra by fitting the linear lines, or if necessary, the lowest degree polynomials that produce straight baselines in emission-free velocity ranges. The highest degree polynomial is 6, but this holds for only a few exceptional cases (less than 1%). The data were smoothed with a Bessel–Gauss function with 15″ FWHM, and resampled on a 7|${^{\prime\prime}_{.}}$|5 × 7|${^{\prime\prime}_{.}}$|5 × 2 km s−1 grid to obtain the final maps. The rms noise of the final maps is approximately |$\Delta T^{*}_{{\rm A}} = 0.2\:$|K (1σ).

2.3 James Clerk Maxwell Telescope

CO J = 3–2 (345.795990 GHz) line observations toward the CMZ were performed with the James Clerk Maxwell Telescope (JCMT) by the JCMT Galactic Plane Survey (JPS) team during the periods 2013 July to September, 2014 July, and 2015 March to June (14 hours in total; Parsons et al. 2018). The data presented in this paper cover the area −0|${^{\circ}_{.}}$|8 ≤ l ≤ +1|${^{\circ}_{.}}$|4 and −0|${^{\circ}_{.}}$|25 ≤ b ≤ 0|${^{\circ}_{.}}$|25. The JPS team used the Heterodyne Array Receiver Program (HARP) (Buckle et al. 2009), which is a single sideband (SSB) array receiver with 4 × 4 SIS mixers with a 30″ spacing between receptors. The typical system noise temperature and FWHM beam size of the HARP were 100–200 K and 14″ at 345 GHz. The average pointing error of HARP is typically 3″. The JPS team used the digital autocorrelation spectrometer Auto Correlation Spectral Imaging System (ACSIS) as a receiver backend with bandwidth and resolution of 1000 MHz and 976.56 kHz, respectively, which correspond to velocity coverage and resolution of 869 km s−1 and 0.847 km s−1, respectively, at 345 GHz. The data were reduced with the Starlink software package. The data were smoothed with a Gaussian function with FWHM = 15″ and resampled on a 7|${^{\prime\prime}_{.}}$|5 × 7|${^{\prime\prime}_{.}}$|5 × 2 km s−1 grid to obtain the final map. The rms noise of the map is approximately |$\Delta T_{\mathrm{A}}^* = 0.3\:$|K.

3 Data

All CO data presented in this paper are in units of the radiation temperature (⁠|$T_{\mathrm{R}}^*$|⁠; Kutner & Ulich 1981) scale, which reproduces the intrinsic brightness temperature (TB) when the source is spatially extended. We determined the |$T_{\mathrm{R}}^*$| scale of the CO J = 1–0 data by comparing these data with the previous CO J = 1–0 data (Oka et al. 1998b), of which the intensity scale was calibrated to |$T_{\mathrm{R}}^*$| of the Harvard-Smithsonian Center for Astrophysics survey (Dame et al. 1987). We multiplied the 13CO J = 1–0 and C18O J = 1–0 data by the same scaling factor that was calculated by comparing the 13CO J = 1–0 spectrum of Sgr B2 with that taken with the single-beam SIS receiver S100 (Oka et al. 1998b). The resultant ηfss values were 0.71 and 0.53 for CO and 13CO|$/$|C18O J = 1–0 lines, respectively. These NRO 45 m data are available to the public.1 The CO J = 3–2 antenna temperatures (⁠|$T_{\mathrm{A}}^*$|⁠) were converted to |$T_{\mathrm{R}}^*$| by dividing by ηfss = 0.71 (Parsons et al. 2018). By comparing the sums of the integrated intensity of CO J = 3–2 (⁠|$\sum ^{}_{} \int T_{\mathrm{R}}^* dV$|⁠), we noticed that the |$T_{\mathrm{R}}^*$| scale of JCMT is smaller than that of ASTE by a factor of 1.107. Thus, we additionally multiplied |$T_{\mathrm{R}}^*$| by 1.107 to ensure consistency with the previous analyses (Oka et al. 2012).

3.1 Integrated intensity maps

Figure 1 shows images of the CO J =1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2 line emissions integrated over the velocity range VLSR = −220 to +220 km s−1. The Nyquist sampled CO images show the detailed spatial structure of the CMZ. The spatial extent of the CO J = 1–0 and CO J = 3–2 lines are similar, whereas that of the 13CO J = 1–0 line is narrower, delineating the distribution of high column density clouds, such as the Sgr A, B, and C complexes. In other words, the less-intense CO J = 1–0 and CO J = 3–2 emissions trace the low column density peripheries of the three major complexes. The l = +1|${^{\circ}_{.}}$|3 complex is not prominent in the 13CO J = 1–0 line. In the C18O J = 1–0 image, all the features visible in the other three images are faint except for the intense emission from Sgr B2 (M) and B2 (N).

Integration intensity ($\int T_{\mathrm{R}}^* dV$) maps of (a) CO J = 1–0, (b) 13CO J = 1–0, (c) C18O J = 1–0, and (d) CO J = 3–2 line emission. The emission was integrated over velocities between VLSR = −220 and +220 km s−1. The half power beamwidths are 15″ and 14″, for the J = 1–0 lines and the J = 3–2 line of CO, respectively. All 13CO J = 1–0 and C18O J = 1–0 spectra used in this figure were processed by third-order polynomial baseline subtractions. The CO J = 3–2 data have a narrower coverage in Galactic latitude, $-{0{^{\circ}_{.}}25} \le {\it b} \le {0{^{\circ}_{.}}25}$ than the others. (Color online)
Fig. 1.

Integration intensity (⁠|$\int T_{\mathrm{R}}^* dV$|⁠) maps of (a) CO J = 1–0, (b) 13CO J = 1–0, (c) C18O J = 1–0, and (d) CO J = 3–2 line emission. The emission was integrated over velocities between VLSR = −220 and +220 km s−1. The half power beamwidths are 15″ and 14″, for the J = 1–0 lines and the J = 3–2 line of CO, respectively. All 13CO J = 1–0 and C18O J = 1–0 spectra used in this figure were processed by third-order polynomial baseline subtractions. The CO J = 3–2 data have a narrower coverage in Galactic latitude, |$-{0{^{\circ}_{.}}25} \le {\it b} \le {0{^{\circ}_{.}}25}$| than the others. (Color online)

3.2 Moment maps

We also present the moment maps of CO J = 1–0 in figure 2. Figure 2a shows a map of intensity-weighted Local Standard of Rest (LSR) velocity (average velocity), |$\langle {V_{\rm LSR}}\rangle \equiv \int V_{\rm LSR}T_{\rm R}^* dV/\int T_{\rm R}^* dV$|⁠. The average velocity ranges from VLSR = −197 km s−1 to +205 km s−1. The general trend, especially in the midplane where strong emission from the CMZ gas dominates, is a velocity gradient from right (VLSR ∼ −100 km s−1) to left (VLSR ∼ +100 km s−1) due to the Galactic rotation. The positive velocity component (VLSR ≥ +100 km s−1) in the upper right corresponds to the negative-longitude end of the 200 pc EMR in the positive velocity side. The positive high-velocity (VLSR ≥ +150 km s−1) component in the upper center to left is the Polar arc (Bally et al. 1988). The negative velocity component (VLSR ≤ −100 km s−1) in the lower center corresponds to the negative velocity side of the 200 pc EMR.

Moment maps obtained from the CO J = 1–0 data set. Data with $T_{\rm R}^* \ge 5.19\:$K (5σ) are used. (a) Map of intensity-weighted LSR velocity (〈VLSR〉). (b) Map of velocity dispersion (σV). (Color online)
Fig. 2.

Moment maps obtained from the CO J = 1–0 data set. Data with |$T_{\rm R}^* \ge 5.19\:$|K (5σ) are used. (a) Map of intensity-weighted LSR velocity (〈VLSR〉). (b) Map of velocity dispersion (σV). (Color online)

Figure 2b shows a map of velocity dispersion, |$\sigma _{\rm V} \equiv \sqrt{\int \left(V_{\rm LSR}- \langle {V_{\rm LSR}}\rangle \right)^2 T_{\rm R}^* dV/\int T_{\rm R}^* dV}$|⁠. The CMZ gas generally shows velocity dispersions of σV = 30 km s−1 to 40 km s−1. The upper part of the Polar arc shows somewhat narrower velocity dispersions (σV < 20 km s−1). Areas of very large velocity dispersions (σV ≥ 80 km s−1) are due to superpositions of unrelated large-scale features with different velocities. HVCCs do not affect the σV map since they generally have low CO J = 1–0 intensities (⁠|$T_{\rm R}^* < 5\:$|K).

3.3 Velocity channel maps

Figure 3 shows CO J = 1–0 velocity channel maps integrated over 10 km s−1 widths. The Nyquist sampled CO images with a 15″ resolution precisely delineate the parsec-scale structure of molecular gas in the CMZ. The main components of the CMZ, the Sgr A-C complexes, are characterized by intense CO emission with rather sharp boundaries. The bulk of these complexes belong to the 120-pc ring (Sofue 1995), whereas several giant molecular clouds, e.g., M–0.02–0.07 and M–0.13–0.08, are located adjacent to the Galactic nucleus (e.g., Takekawa et al. 2017b). The l = +1|${^{\circ}_{.}}$|3 complex has a low-intensity, fluffy morphology. At both of the high-velocity ends, the 200 pc EMR (Kaifu et al. 1972; Scoville 1972) appears as aggregations of misty clouds. The low-intensity emission spread over the maps in velocities VLSR = −60 km s−1 to +20 km s−1 is from the less-dense molecular gas in the Galactic disk. A number of spotty emission features continuous in velocity are likely to be HVCCs.

Fig. 3.

Velocity channel maps of the CO J = 1–0 line emission integrated over 10 km s−1 widths. The numbers indicate the velocity range in units of km s−1. (Color online)

3.4 Longitude–velocity maps

Figure 4 shows the CO J = 1–0 longitude–velocity (lV) maps in intervals of 1′. The intense, broad-velocity-width CO emission originates from the four cloud complexes, which are roughly aligned from the upper left to the lower right in each of the lV maps. Another broad-velocity-width feature is the 200-pc EMR seen as two straight lines at both velocity ends in the lV maps at b = −8′ to −4′. These lines correspond to the two facing sides of a parallelogram, which is considered to be a lV pattern of the non-self-intersecting, innermost x1 orbit (Binney et al. 1991). The narrow-velocity- width, straight lines in the velocity range between −60 km s−1 and +20 km s−1 are due to spiral arms in the Galactic disk (e.g., the 3 kpc, 4.5 kpc, local, and +20 km s−1 arms). In addition to these, a number of broad-velocity-width features with small spatial sizes are visible. These features, except for the circumnuclear disk at l ∼ −0|${^{\circ}_{.}}$|05, should be categorized as HVCCs, which are peculiar clouds characterized by their compact appearance (d < 10 pc) and unusually large velocity width (ΔV > 50 km s−1).

4 Analyses

4.1 Total molecular mass

The total molecular mass in the CMZ was calculated by various techniques to be (2–6) × 107M (e.g., Oka et al. 1998a, and references therein). Here we try to calculate it by using the CO total integrated intensities. Molecular mass estimation from the opaque 12CO J = 1–0 lines is due to the CO-to-H2 conversion technique;
(1)
where DGC is the distance to the Galactic center (8.5 kpc is recommended by the International Astronomical Union, IAU) and XCO is the CO-to-H2 conversion ratio [|$\sim 1.0\times 10^{20}\:{\rm cm^{-2}(K\:{\rm km}\:{\rm s}^{-1})^{-1}}$| at GC; Arimoto et al. 1996].
Mass estimates from optically thin molecular lines may be more reliable if the fractional abundances of molecules are precisely determined. From 13CO J = 1–0 line intensity, assuming the local thermodynamical equilibrium, we obtained
(2)
where [13CO]|$/$|[H2] is the abundance ratio (∼1.0 × 10−6 at Sgr B2; Lis & Goldsmith 1989) and Tex is the excitation temperature (∼21.4 K; see subsection 4.4). Using the C18O J = 1–0 line,
(3)
where [C18O]/[H2] is the abundance ratio ([13CO]/[C18O] = 4.95 at GC; Langer & Penzias 1990). These molecular mass estimates are reasonably within the range of previously obtained values.

4.2 Total intensity ratios

The total intensity ratios were calculated by |$\langle {R_{\rm i/j}}\rangle \equiv \sum \int T_{\mathrm{R}}^{*}({\rm i}) dV/\sum \int T_{\mathrm{R}}^{*}({\rm j}) dV$|⁠, excluding the velocity range severely contaminated by gas in the Galactic disk, [8.18(l/°) − 55.3] km s−1VLSR ≤ 20.0 km s−1. We obtained 〈R3–2/1–0〉 = 0.70 ± 0.06, 〈R13/12〉 = 0.12 ± 0.01, and 〈R18/13〉 = 0.14 ± 0.01 for the CMZ gas, where the subscripts 3–2, 1–0, 12, 13, and 18 mean CO J = 3–2, CO J = 1–0, CO J = 1–0, 13CO J = 1–0, and C18O J = 1–0, respectively. The uncertainties of the ratios were estimated by using the uncertainties of telescope beam efficiencies (6.0% for NRO 45 m; 6.4% for JCMT).

The 〈R3–2/1–0〉 value in the CMZ, 0.70, is comparable with those in the CMZs in nearby galaxies (the average value ∼0.6; Mauersberger et al. 1999). It is higher than that in the spiral arms (0.4–0.5; Oka et al. 2007, 2012) or the average value of cold giant molecular clouds (GMCs) in the Galactic disk (0.4; Sanders et al. 1993). Such enhancements in R3–2/1–0 were found in several nearby galaxies, e.g., M 33 (Miura et al. 2012), M 51 (Vlahakis et al. 2013), and M 83 (Muraoka et al. 2007). Detailed analyses of the physical conditions based on these CO multi-line data sets will be presented in forthcoming papers.

4.3 High 13CO J = 1–0/CO J = 1–0 ratio gas

Here we attempt to extract the distribution/kinematics of high column density components such as dense cores by using the 13CO J = 1–0/J = 1–0 intensity ratio (R13/12). Figure 5 shows the spatial and lV distributions of CO-opaque gas. We employed the threshold R13/12 ≥ 0.2, which corresponds to τ12 ≥ 5.3 if we assume the [12CO]|$/$|[13CO] = 24 (Langer & Penzias 1990) and the local thermodynamic equilibrium (LTE) condition. The several narrow horizontal lines of intense 13CO emission in figure 5b represent low-density opaque gas in the Galactic spiral arms.

(a) Map of 13CO J = 1–0 emission ($\int T_{\rm R}^{*}\, dV$) integrated over velocities VLSR between −220 km s−1 and +220 km s−1 for data with R13/12 ≥ 0.2. Data severely contaminated by the disk gas have been excluded from the velocity integration. (b) Longitude–velocity map of 13CO J = 1–0 emission integrated over the observed latitudes ($\sum T_{\rm R}^{*}$) for data with R13/12 ≥ 0.2. The shaded region shows the l–V area excluded from the velocity integration, [8.18(l/°) − 55.3] km s−1≤VLSR ≤ 20.0 km s−1. (Color online)
Fig. 5.

(a) Map of 13CO J = 1–0 emission (⁠|$\int T_{\rm R}^{*}\, dV$|⁠) integrated over velocities VLSR between −220 km s−1 and +220 km s−1 for data with R13/12 ≥ 0.2. Data severely contaminated by the disk gas have been excluded from the velocity integration. (b) Longitude–velocity map of 13CO J = 1–0 emission integrated over the observed latitudes (⁠|$\sum T_{\rm R}^{*}$|⁠) for data with R13/12 ≥ 0.2. The shaded region shows the lV area excluded from the velocity integration, [8.18(l/°) − 55.3] km s−1VLSR ≤ 20.0 km s−1. (Color online)

The chain of intense 13CO clumps from (l, b, VLSR) ≃ (−0|${^{\circ}_{.}}$|8, −0|${^{\circ}_{.}}$|1, −140 km s−1) to (0|${^{\circ}_{.}}$|7, 0|${^{\circ}_{.}}$|0, +80 km s−1) is the Sofue’s Galactic Center Arm I (GCA; Sofue 1995). Another GCA (GCA II) is also visible as a chain from (l, b, VLSR) ≃ (−0|${^{\circ}_{.}}$|5, −0|${^{\circ}_{.}}$|2, −60 km s−1) to (1|${^{\circ}_{.}}$|1, −0|${^{\circ}_{.}}$|1, +90 km s−1). The low-velocity parts of the GCAs are absent from figure 5a because they were excluded from velocity integration to avoid contamination by the disk gas.

The positive longitude end of GCA I is defined by the most intense 13CO clump at (l, b, VLSR) ≃ (0|${^{\circ}_{.}}$|7, 0|${^{\circ}_{.}}$|0, +60 km s−1), the Sgr B2 cloud. Two appendages, which may be unrelated to GCA I, are associated with the Sgr B2 cloud. The first appears at (l, b, VLSR) ≃ (0|${^{\circ}_{.}}$|7, −0|${^{\circ}_{.}}$|15, +30 km s−1) and the other appears at (l, b, VLSR) ≃ (0|${^{\circ}_{.}}$|8, −0|${^{\circ}_{.}}$|2, +40 km s−1). The latter shows a roughly expanding shell morphology and kinematics. The physical relation between the two appendages and to the Sgr B2 main cloud is currently uncertain. The narrow horizontal line in figure 5(b) at (l, VLSR) ≃ (0|${^{\circ}_{.}}$|9, +45 km s−1) might be representing one of the very minor spiral arms in the Galactic disk behind the CMZ.

The intense clump at (l, b, VLSR) ≃ (0°, 0°, +50 km s−1) is M–0.02–0.07 (the +50 km s−1 molecular cloud), a GMC near the Galactic nucleus. Another GMC near the nucleus (M–0.13–0.08; the +20 km s−1 molecular cloud) is less intense in figure 5. The steep velocity gradient of the M–0.02–0.07 and M–0.13–0.08 system suggests that these GMCs do not belong to GCA II. We notice a compact broad-velocity-width feature at (l, b, VLSR) ≃ (0|${^{\circ}_{.}}$|006, −0|${^{\circ}_{.}}$|114, +40 km s−1), the relation of which to M–0.02–0.07 is also unknown.

The 200-pc EMR is also visible in figure 5b as two faint, loose strings at both of the high-velocity ends. To summarize, high-R13/12 gas features show rather narrow velocity widths (ΔV ≤ 20 km s−1) except for the compact broad-velocity-width feature near M–0.02–0.07.

4.4 LTE analyses

Assuming the LTE condition, we calculated the 12CO J = 1–0 optical depth (τ12) and CO excitation temperature from 12CO and 13CO J = 1–0 intensities at each data pixel with |$T_{\rm R}^*(^{13}{\rm CO}) \ge 1.08\:$|K (5σ). The calculation procedures were presented in subsection 4.2 of Oka+98.

Figure 6 shows the frequency distribution of τ12. This is the same histogram as figure 7 of Oka+98, while the data resolutions were improved by a factor of 4 spatially, and by a factor of 2.5 in velocity. The basic behavior of the frequency distribution is the same as the previous low-resolution data. Most of the data have optical depths between ∼2 and 8, having a sharp peak at 3. These values are slightly lower than those in Oka+98. The τ12 frequency distribution for the local arm (defined by −10 km s−1VLSR ≤ +20 km s−1) has a peak at 5, contributing a half of the total frequency at τ12 ≥ 10. Thus, the bulk of molecular gas in the CMZ has moderate optical depth.

Frequency distribution of the 12CO optical depth. The data with at least 5 σ 13CO detection are used for the analysis. The gray area shows the contributions of the local arm emission, VLSR = −10 to +20 km s−1.
Fig. 6.

Frequency distribution of the 12CO optical depth. The data with at least 5 σ 13CO detection are used for the analysis. The gray area shows the contributions of the local arm emission, VLSR = −10 to +20 km s−1.

The frequency distribution of the excitation temperature (Tex) is shown in figure 7 (same as figure 8 of Oka+98). Again, the basic behavior is the same as that of the previous low-resolution distribution. The Tex frequency distribution has two prominent peaks at Tex ≃ 7 and 16 K; the latter is higher than that of the previous low-resolution data (13 K). The high-temperature wing is more prominent in the new one. Half of the low-temperature component is attributable to the local arm, and most of the rest may be attributable to the other component in the Galactic disk. We calculated the average Tex by subtracting the double of the local arm contribution from the Tex frequency distribution and averaging it at Tex ≥ 8 K, to be 〈Tex〉 = 21.4 K. The standard deviation of the subtracted frequency distribution is 6.0 K.

Frequency distribution of the excitation temperature. The data with at least 5 σ 13CO detection are used for the analysis. The gray area shows the contributions of the local arm emission, VLSR = −10 to +20 km s−1.
Fig. 7.

Frequency distribution of the excitation temperature. The data with at least 5 σ 13CO detection are used for the analysis. The gray area shows the contributions of the local arm emission, VLSR = −10 to +20 km s−1.

4.5 High CO J = 3–2/J = 1–0 ratio gas

The CO J = 3–2/J = 1–0 intensity ratio (R3–2/1–0) is sensitive to the density and temperature, and is thus a good indicator of the excitation of molecular gas. Figure 8 shows the spatial and lV distributions of R3–2/1–0 gas, which is a high-resolution, enlarged version of figure 8 in Oka et al. (2012). We employed the threshold R3–2/1–0 ≥ 1.5. One-zone LVG calculations indicate that R3–2/1–0 ≥ 1.5 corresponds to n(H2) ≥ 103.6 cm−3 and Tk ≥ 48 K when NCO/dV = 1017 cm−2 (km s−1)−1 (figure 4 in Oka et al. 2007). High-R3–2/1–0 regions/spots previously pointed out (Oka et al. 2007, 2012, 2016) are visible at a higher spatial resolution. These images are useful to extract highly excited gas, and thereby to search for “active” regions, where high mechanical or photonic energy is input into, in the CMZ.

(a) Map of CO J = 3–2 emission ($\int T_{\rm R}^{*}\, dV$) integrated over velocities VLSR between −220 km s−1 and +200 km s−1 for data with R3–2/1–0 ≥ 1.5. Data severely contaminated by the disk gas were excluded from the velocity integration. (b) Longitude–velocity map of CO J = 3–2 emission integrated over the observed latitudes ($\sum T_{\rm R}^{*}$) for data with R3–2/1–0 ≥ 1.5. The shaded region shows the l–V area excluded from the velocity integration, [8.18(l/°) − 55.3] km s−1 ≤ VLSR ≤ 20.0 km s−1. (Color online)
Fig. 8.

(a) Map of CO J = 3–2 emission (⁠|$\int T_{\rm R}^{*}\, dV$|⁠) integrated over velocities VLSR between −220 km s−1 and +200 km s−1 for data with R3–2/1–0 ≥ 1.5. Data severely contaminated by the disk gas were excluded from the velocity integration. (b) Longitude–velocity map of CO J = 3–2 emission integrated over the observed latitudes (⁠|$\sum T_{\rm R}^{*}$|⁠) for data with R3–2/1–0 ≥ 1.5. The shaded region shows the lV area excluded from the velocity integration, [8.18(l/°) − 55.3] km s−1VLSR ≤ 20.0 km s−1. (Color online)

Again we see several horizontal lines in figure 8b in the velocity range severely contaminated by gas in the Galactic disk. High R3–2/1–0 in this velocity range does not necessarily mean high excitation; instead, it is most likely the result of efficient CO J = 1–0 absorption against the CMZ by low-density gas in the Galactic disk (Oka et al. 2007, 2012). The spatial and lV distributions of high-R3–2/1–0 gas in the CMZ (figure 8) significantly differ from those of opaque gas (figure 5). They are roughly anti-correlated in the lV space. This means that high-R3–2/1–0 gas avoids the center of GCAs. Most of the high-R3–2/1–0 gas is confined to forms of compact clumps with broad velocity widths.

A group of these clumps is found at (l, b, VLSR) ≃ (1|${^{\circ}_{.}}$|2, 0|${^{\circ}_{.}}$|1, +150 km s−1). This corresponds to the northern half of the l = +1|${^{\circ}_{.}}$|3 region (Oka et al. 2012), which contains several expanding shells (e.g., Oka et al. 2001). The southern half of this region appears less intense in figure 8a, being consistent with the findings of previous work conducted at lower resolution.

Another group of excited gas clumps is found in the Sgr A region, (l, b) ≃ (0°, 0°). The negative velocity half of the circumnuclear disk (CND) and its negative longitude extension (NLE; Oka et al. 2011) are prominent. Two small spots adjacent and to the east of the CND are the positive velocity part of the CND and the negative high-velocity clump C1 (Oka et al. 2011), respectively. Another clump at (l, b, VLSR) ≃ (0|${^{\circ}_{.}}$|02, −0|${^{\circ}_{.}}$|02, +110 km s−1) is a well-known HVCC CO 0.02–0.02 (Oka et al. 1999).

HVCC CO–0.40–0.22 stands out at (l, b) ≃ (−0|${^{\circ}_{.}}$|4, −0|${^{\circ}_{.}}$|2) in figure 8a, showing a more compact appearance than that in the previous lower resolution image. This compactness of the excited gas distribution supports the idea that CO–0.40–0.22 has been accelerated by an invisible, massive point-like object (Oka et al. 2016, 2017).

In addition to these features, we identified several high-R3–2/1–0 spots. Some of them have very compact appearances and broad velocity widths. These are candidates for gas clumps accelerated by point-like massive objects. We briefly discuss four of them in the next subsection. In total, 15 high-R3–2/1–0 spots are visible in figure 8a and these are listed in table 1. Many of these high-R3–2/1–0 spots are poorly understood. Therefore, they would need to be studied intensively in the near future.

Table 1.

Prominent high-R3–2/1–0 spots.

IDl (°)b (°)V  LSR (km s−1)Δl (°)Δb (°)ΔV (km s−1)R  3–2/1–0*Comments
T1−0.55−0.07−740.030.02121.933
T2−0.54−0.12−640.020.0181.436
T3−0.440.11−1400.030.02541.4
T4−0.40−0.22−800.040.04461.6CO–0.40–0.22
T5−0.31−0.06470.010.02461.348, 49, 50
T6−0.260.02−920.020.03541.855
T7−0.170.02490.010.02101.4
T8−0.08−0.05−850.050.03732.764, CND
T90.02−0.021100.010.03761.6CO 0.02–0.02
T100.85−0.18760.010.02211.4131
T110.880.15750.010.03161.4135
T120.89−0.07480.020.03281.4134
T130.98−0.13500.060.03582.1138
T141.210.101580.040.07801.4l = +1|${^{\circ}_{.}}$|3 region
T151.38−0.201270.030.02411.4
IDl (°)b (°)V  LSR (km s−1)Δl (°)Δb (°)ΔV (km s−1)R  3–2/1–0*Comments
T1−0.55−0.07−740.030.02121.933
T2−0.54−0.12−640.020.0181.436
T3−0.440.11−1400.030.02541.4
T4−0.40−0.22−800.040.04461.6CO–0.40–0.22
T5−0.31−0.06470.010.02461.348, 49, 50
T6−0.260.02−920.020.03541.855
T7−0.170.02490.010.02101.4
T8−0.08−0.05−850.050.03732.764, CND
T90.02−0.021100.010.03761.6CO 0.02–0.02
T100.85−0.18760.010.02211.4131
T110.880.15750.010.03161.4135
T120.89−0.07480.020.03281.4134
T130.98−0.13500.060.03582.1138
T141.210.101580.040.07801.4l = +1|${^{\circ}_{.}}$|3 region
T151.38−0.201270.030.02411.4

*Calculated at each listed coordinate by intensities weighted by a FWHM = 36″, 36″, 10 km s−1 three-dimensional Gaussian. The resultant R3–2/1–0 contains an 8.8% uncertainty.

The numbers correspond to those in table 1 in Oka et al. (2012).

Table 1.

Prominent high-R3–2/1–0 spots.

IDl (°)b (°)V  LSR (km s−1)Δl (°)Δb (°)ΔV (km s−1)R  3–2/1–0*Comments
T1−0.55−0.07−740.030.02121.933
T2−0.54−0.12−640.020.0181.436
T3−0.440.11−1400.030.02541.4
T4−0.40−0.22−800.040.04461.6CO–0.40–0.22
T5−0.31−0.06470.010.02461.348, 49, 50
T6−0.260.02−920.020.03541.855
T7−0.170.02490.010.02101.4
T8−0.08−0.05−850.050.03732.764, CND
T90.02−0.021100.010.03761.6CO 0.02–0.02
T100.85−0.18760.010.02211.4131
T110.880.15750.010.03161.4135
T120.89−0.07480.020.03281.4134
T130.98−0.13500.060.03582.1138
T141.210.101580.040.07801.4l = +1|${^{\circ}_{.}}$|3 region
T151.38−0.201270.030.02411.4
IDl (°)b (°)V  LSR (km s−1)Δl (°)Δb (°)ΔV (km s−1)R  3–2/1–0*Comments
T1−0.55−0.07−740.030.02121.933
T2−0.54−0.12−640.020.0181.436
T3−0.440.11−1400.030.02541.4
T4−0.40−0.22−800.040.04461.6CO–0.40–0.22
T5−0.31−0.06470.010.02461.348, 49, 50
T6−0.260.02−920.020.03541.855
T7−0.170.02490.010.02101.4
T8−0.08−0.05−850.050.03732.764, CND
T90.02−0.021100.010.03761.6CO 0.02–0.02
T100.85−0.18760.010.02211.4131
T110.880.15750.010.03161.4135
T120.89−0.07480.020.03281.4134
T130.98−0.13500.060.03582.1138
T141.210.101580.040.07801.4l = +1|${^{\circ}_{.}}$|3 region
T151.38−0.201270.030.02411.4

*Calculated at each listed coordinate by intensities weighted by a FWHM = 36″, 36″, 10 km s−1 three-dimensional Gaussian. The resultant R3–2/1–0 contains an 8.8% uncertainty.

The numbers correspond to those in table 1 in Oka et al. (2012).

We also noticed two spatially extended, high-R3–2/1–0 gas components with moderate velocity widths at (l, VLSR) ∼ (0|${^{\circ}_{.}}$|9, +60 km s−1) and (−0|${^{\circ}_{.}}$|5, −70 km s−1). The latitudinal extents of these components are ambiguous. The morphology and kinematics suggest that they have been excited by large-scale shocks, such as cloud-to-cloud collisions, or are generated by CO J = 1–0 absorption by the low-density gas in their foreground.

4.6 High CO J = 3–2/J = 1–0 ratio spots

Here we present four examples of high-R3–2/1–0 spots from table 1 with several comments on their morphology and kinematics. Detailed studies based on quantitative analyses will be presented in forthcoming papers.

4.6.1 T3.

This high-R3–2/1–0 spot appears at (l, b, VLSR) ≃ (−0|${^{\circ}_{.}}$|44, 0|${^{\circ}_{.}}$|11, −140 km s−1) (figure 9). The entity shows up as a protrusion from a larger cloud in the west having an angular size of Δl × Δb ≃ 0|${^{\circ}_{.}}$|01 × 0|${^{\circ}_{.}}$|03. It seems to consist of two velocity components at VLSR ≃ −140 and −110 km s−1. These components and the eastern edge of the western cloud display a rough expanding shell resembling kinematics with an expansion velocity of 25 km s−1. However, as is often the case with expanding shells in the CMZ, there is neither a radio nor an X-ray counterpart associated with this shell.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T3 (table 1) The velocity range for integration is −190 to −90 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over the latitudes of the V-integrated maps. The lower and upper bounds of the color scale are shown in the bottom left of each panel. (Color online)
Fig. 9.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T3 (table 1) The velocity range for integration is −190 to −90 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over the latitudes of the V-integrated maps. The lower and upper bounds of the color scale are shown in the bottom left of each panel. (Color online)

4.6.2 T6.

This feature appears at (l, b, VLSR) ≃ (−0|${^{\circ}_{.}}$|26, 0|${^{\circ}_{.}}$|02, −92 km s−1) at the eastern edge of a larger cloud (figure 10). The CO J = 3–2 map shows the corresponding clump has an angular size of Δl × Δb ≃ 0|${^{\circ}_{.}}$|01 × 0|${^{\circ}_{.}}$|01 and that it is on the edge of a shell-like structure with an angular diameter of |${0{^{\circ}_{.}}05}$|⁠. The 13CO J = 1–0 velocity integrated emission also traces the shell yet the T6 clump is not prominent. The expanding velocity of the shell is approximately 15 km s−1. The velocity width of the T6 clump exceeds 50 km s−1, which cannot be explained solely by the expanding shell. Another small expanding shell with an angular diameter of 0|${^{\circ}_{.}}$|02 and expanding velocity of ∼40 km s−1 seems to be associated with T6, to the west thereof. This situation is similar to that of the l = −1|${^{\circ}_{.}}$|2 region (Tsujimoto et al. 2018), in that counterparts in other wavelengths are absent.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T6. The velocity range for integration is −142 to −42 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over latitudes of the V-integrated maps. (Color online)
Fig. 10.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T6. The velocity range for integration is −142 to −42 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over latitudes of the V-integrated maps. (Color online)

4.6.3 T7.

This feature appears in a slightly crowded region, (l, b, VLSR) ≃ (−0|${^{\circ}_{.}}$|17, 0|${^{\circ}_{.}}$|02, 49 km s−1) (figure 11). The corresponding clump has a central velocity of VLSR ≃ 65 km s−1. The angular size of this clump is Δl × Δb ≃ 0|${^{\circ}_{.}}$|02 × 0|${^{\circ}_{.}}$|02 and the velocity width is approximately 40 km s−1. A larger cloud, which has velocities approximating VLSR ∼ 15 km s−1, is visible in the south, although its physical relation to the T7 clump is ambiguous. Because high-velocity wing emission arises on both velocity sides of the T7 clump, the driving source may be located inside of T7. The negative velocity wing has a high R3–2/1–0 exceeding 1.5. This feature has no counterpart in other wavelengths.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T7. The velocity range for integration is −1 to 99 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over latitudes of the V-integrated maps. (Color online)
Fig. 11.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T7. The velocity range for integration is −1 to 99 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over latitudes of the V-integrated maps. (Color online)

4.6.4 T15.

This spot appears at (l, b, VLSR) ≃ (1|${^{\circ}_{.}}$|38, −0|${^{\circ}_{.}}$|20, 127 km s−1) near the eastern edge of our mapping area (figure 12). The location corresponds to the southeastern edge of the l = +1|${^{\circ}_{.}}$|3 cloud complex (e.g., as discussed by Oka et al. 2012). The corresponding clump has a size of Δl × Δb ≃ 0|${^{\circ}_{.}}$|03 × 0|${^{\circ}_{.}}$|02 and an apparent positive high-velocity wing. The 13CO map shows an associated 0|${^{\circ}_{.}}$|05 angular diameter shell located in the northwestern part of the T15 clump. The CO J = 3–2 map shows another small shell with an angular diameter of 0|${^{\circ}_{.}}$|02 in the southeast. In the CO J = 3–2 lV map, the high-velocity wing shows a sharp western boundary. This can be interpreted as the expanding shell with a central velocity of ∼150 km s−1, which is inconsistent with the observed northwestern shell. Again we suggest the presence of a driving source inside the T15 clump, although counterparts in other wavelengths are not associated with this feature.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T15. The velocity range for integration is 77 to 177 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over latitudes of the V-integrated maps. (Color online)
Fig. 12.

(a)–(d) Velocity-integrated maps of CO J = 1–0, 13CO J = 1–0, C18O J = 1–0, and CO J = 3–2, respectively. The maps are centered at the high-R3–2/1–0 spot T15. The velocity range for integration is 77 to 177 km s−1. (e) Longitude–velocity map of CO J = 3–2 emission integrated over latitudes of the V-integrated maps. (Color online)

5 Summary

We performed Nyquist-sampled mapping observations of the Galactic CMZ in the J = 1–0 lines of CO, 13CO, and C18O using the two focal-plane array SIS receivers, BEARS and FOREST, with which the 45 m NRO telescope is equipped. The spatial resolution of these new data sets was improved by a factor of 4 compared to the previous survey data (Oka et al. 1998b, 2012). The major results from these observations and analyses are summarized as follows.

  1. The full data set of CO J = 1–0 emission was presented in the form of velocity channel maps and longitude–velocity maps. The velocity-integrated maps of CO, 13CO, and C18O emissions were also presented.

  2. Total intensity ratios for the CMZ gas are 〈R3–2/1–0〉 = 0.70 ± 0.06, 〈R13/12〉 = 0.12 ± 0.01, and 〈R18/13〉 = 0.14 ± 0.01.

  3. Most of CO-opaque (τ12 ≥ 5.3) gas in the CMZ follows the Galactic Center Arms I and II (Sofue 1995).

  4. CO J = 1–0 data were compared with CO J = 3–2 data obtained with the JCMT. The existence of the previously identified, three high-R3–2/1–0 ratio areas at l = +1|${^{\circ}_{.}}$|3, 0|${^{\circ}_{.}}$|0, and −0|${^{\circ}_{.}}$|4 was confirmed with the spatial resolution improved by a factor of 4.

  5. Several very compact high CO J = 3–2/CO J = 1–0 ratio spots with broad velocity widths were newly identified. Some of them are candidates for accelerated gas in the vicinity of invisible, point-like massive objects. Four examples of the high-ratio spots were discussed in more detail.

Acknowledgments

The results in this paper are based on observations at the Nobeyama Radio Observatory (NRO) and James Clerk Maxwell Telescope (JCMT). The Nobeyama 45 m radio telescope is operated by the Nobeyama Radio Observatory, a division of the National Astronomical Observatory of Japan.

The James Clerk Maxwell Telescope is operated by the East Asian Observatory on behalf of The National Astronomical Observatory of Japan, the Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, the National Astronomical Observatories of China, and the Chinese Academy of Sciences (Grant No. XDB09000000), with additional funding support from the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada.

We are grateful to the Nobeyama Radio Observatory staff and all the members of the James Clerk Maxwell Telescope team for operation of the telescope. T.O. acknowledges support from Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (B) No. 15H03643. S.T. acknowledges support from JSPS Grant-in-Aid for Research Fellows No. 15J04405.

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