Temperature and Density in the Foot Points of the Molecular Loops in the Galactic Center; Analysis of Multi-J Transitions of 12CO(J=1-0, 3-2, 4-3, 7-6), 13CO(J=1-0) and C18O(J=1-0)
Kazufumi Torii, Natsuko Kudo, Motosuji Fujishita, Tokuichi Kawase, Takeshi Okuda, Hiroaki Yamamoto, Akiko Kawamura, Norikazu Mizuno, Toshikazu Onishi, Mami Machida, Kunio Takahashi, Satoshi Nozawa, Ryoji Matsumoto, Juergen Ott, Kunihiko Tanaka, Nobuyuki Yamaguchi, Hajime Ezawa, Juergen Stutzki, Frank Bertoldi, Bon-Chul Koo, Leonardo Bronfman, Michael Burton, Arnold Benz, Hideo Ogawa, Yasuo Fukui
aa r X i v : . [ a s t r o - ph . GA ] M a y Temperature and Density in the Foot Points of theMolecular Loops in the Galactic Center; Analysis ofMulti-J Transitions of CO( J =1–0, 3–2, 4–3, 7–6), CO( J =1–0) and C O( J =1–0) Kazufumi
Torii , Natsuko
Kudo , Motosuji
Fujishita , Tokuichi
Kawase , Takeshi
Okuda , Hiroaki
Yamamoto , Akiko
Kawamura , Norikazu
Mizuno , Toshikazu
Onishi , Mami
Machida , Kunio
Takahashi , Satoshi
Nozawa , Ryoji
Matsumoto , J¨urgen
Ott , Kunihiko
Tanaka , Nobuyuki
Yamaguchi , Hajime
Ezawa , J¨urgen
Stutzki , Frank
Bertoldi , Bon-Chul
Koo , Leonardo
Bronfman , Michael
Burton , Arnold O.
Benz , Hideo
Ogawa , and Yasuo Fukui Department of Astrophysics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602 National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 Department of Physical Science, Osaka prefecture University, Sakai, Osaka 599-8531 Japan Agency for Marine-Earth Science and Technology, Kanazawa-ku, Yokohama, Kanagawa236-0001, Japan Department of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512 Faculty of Science, Chiba University, Inage-ku, Chiba 263-8522 National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville Road, Socorro, NM 87801,USA Institute of Science and Technology, Keio University, 4-14-1 Hiyoshi, Yokohama, Kanagawa223-8522 Open Technologies Research Laboratory, 6-1-21 Hon-komagame, Bunkyo, Tokyo 113-0021 Nobeyama Radio Observatory, National Astronomical Observatory of Japan, Minamimaki,Minamisaku, Nagano 384-1305 KOSMA, I. Physikalisches Institut, Universit¨at zu K¨oln, Z¨ulpicher Stra βe
77, 50937 K¨oln,Germany Radioastronomisches Institut der Universit¨at Bonn, Auf dem H¨ugel 71, 53121 Bonn, Germany Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea Departmento de Astronom´ıa, Universidad de Chile, Casilla 36-D, Santiago, Chile School of Physics, University of New South Wales, Sydney 2052, NSW, Australia Institute of Astronomy, ETH Zurich, 8093 Zurich, [email protected], [email protected] Received 2010 March 12; accepted 2010 March 17)
Abstract
Fukui et al. (2006) discovered two molecular loops in the Galactic center and ar-gued that the foot points of the molecular loops, two bright spots at both loops ends,represent the gas accumulated by the falling motion along the loops, subsequent tomagnetic flotation by the Parker instability. We have carried out sensitive CO obser-vations of the foot points toward l =356 ◦ at a few pc resolution in the six rotationaltransitions of CO; CO( J =1–0, 3–2, 4–3, 7–6), CO( J =1–0) and C O( J =1–0).The high resolution image of CO ( J =3–2) has revealed the detailed distribution ofthe high excitation gas including U shapes, the outer boundary of which shows sharpintensity jumps accompanying strong velocity gradients. An analysis of the multi-JCO transitions shows that the temperature is in a range from 30–100 K and densityis around 10 –10 cm − , confirming that the foot points have high temperature anddensity although there is no prominent radiative heating source such as high massstars in or around the loops. We argue that the high temperature is likely due to theshock heating under C-shock condition caused by the magnetic flotation. We madea comparison of the gas distribution with theoretical numerical simulations and notethat the U shape is consistent with numerical simulations. We also find that the regionof highest temperature of ∼
100 K or higher inside the U shape corresponds to thespur having an upward flow, additionally heated up either by magnetic reconnectionor bouncing in the interaction with the narrow neck at the bottom of the U shape.We note these new findings further reinforce the magnetic floatation interpretation.
Key words:
ISM: clouds—ISM: magnetic fields— magnetic loops— Radio lines:ISM
1. Introduction
The central molecular zone (hereafter CMZ, Morris & Serabyn 1996) is located in theinner 300 pc of the Galactic center and contains the Sgr A and Sgr B2 molecular clouds, twooutstanding features in the CMZ (e.g., Scoville, Solomon & Penzias 1975; Fukui et al. 1977;G¨usten & Henkel 1983). The molecular gas in the CMZ is characterized by high kinetictemperature from 30 K to 300 K (e.g., Rodr´ıguez-Fern´andez et al. 2001; H¨uttemeister et al.1993; Martin et al. 2004; Oka et al. 2005; Nagai et al. 2007), and high density around 10 cm − (e.g., Tsuboi, Handa & Ukita 1999). The molecular gas in the CMZ also shows violent motionswith an rms velocity dispersion of 15–30 km s − , much larger than those of the typical molecularclouds of few km s − outside the central kpc (Morris & Serabyn 1996; G¨usten & Philipp 2004).It has been suggested that supernova explosions may be responsible for these properties, but2he total star formation efficiency is too small to account for the required abundance of OBstars (Morris & Serabyn 1996). The origin of these two peculiar properties, high temperaturesand violent motions, has been puzzling since its discovery in the 1970’s. It is important tounderstand the physical properties of the molecular gas to understand star formation in theGalactic center and, consequently, the evolution of the Galaxy.There are several molecular features with very broad velocity widths outside the CMZincluding Clumps 1 and 2 (Bania 1977) and the l = 5 . ◦ cloud (Bitran et al. 1997). These cloudsare located outside the CMZ, perhaps distributed in the central 1 kpc, but they have not yetbeen given as much attention as in the CMZ.Recently, Fukui et al. (2006; hereafter F06) discovered loop-like molecular features,hereafter loops 1 and 2, toward l =355 ◦ –359 ◦ outside the CMZ (Figure 1) and showed that thetwo loops each have two foot points on the both ends; the foot points are bright molecularcondensations and show velocity widths as large as ∼
50 km s − . F06 suggested that thetwo loops are formed by magnetic flotation driven by the Parker instability and showed thatnumerical magneto-hydrodynamics (MHD) calculations reproduce the loops successfully. Thisdiscovery is the first observational verification of the Parker’s instability in the Galactic scale40 years after the prediction by Parker (1966). In the scenario of F06, the two foot points areinterpreted as the accumulated gas formed by the down-falling motion by the stellar gravity.Details of such a signature has already been shown by numerical simulations by Matsumoto etal. (1988). F06 argues that the relatively strong magnetic field of 150 µ G, which is eventuallya result of the strong gravitation in the inner 1 kpc of the Galaxy, makes it possible to createthe loops throughout the Galactic center.Subsequently, Torii et al. (2009) made a detailed analysis of the NANTEN CO( J =1–0) and CO( J =1–0) datasets and revealed further details including helical distributions inloops 1 and 2 as well as associated H I and dust features. Fujishita et al. (2009) presented thediscovery of loop 3, another magnetically floated loop, in the same direction with loops 1 and 2in a positive velocity range. Machida et al. (2009) presented a three-dimensional global MHDsimulations of the central 2-kpc magnetized gas disk, and Takahashi et al. (2009) detailed two-dimensional local MHD simulations of the magnetic loops. These follow-up works offer furthersupports for the magnetic flotation picture.In the magnetic flotation picture, the floated gas falls back down to the galactic planealong the loop driven by stellar gravity, and then collides with the nuclear gas disk. If thefalling speed exceeds the sound speed, shocks must occur, leading to violent gas motions withenhanced density and kinetic temperature caused by compression and heating by the shocks.This is a conversion of the magnetic energy into the kinetic and thermal energy of the gas, andthe magnetic flotation may provide an interpretation of physical conditions and kinematics ofthe central molecular gas. In order to test this scenario, it is important to reveal the distributionof temperature and density of the loop, in particular, in the foot points.3n this paper, we present and discuss the results of pc-scale observations in six rotationaltransitions of CO ( J =1–0, 3–2, 4–3, 7–6), CO( J =1–0) and C O( J =1–0) toward two of thefoot points with the ASTE, Mopra, NANTEN2 mm/sub-mm telescopes. We adopt a distanceof 8.5 kpc to the Galactic center. Details of the observations are given in section 2 and theresults are given in section 3. An analysis of the line radiative transfer is given in section 4, adiscussion is in section 5, and the conclusions are presented in section 6.
2. Observations
We observed CO( J =1–0), CO( J =1–0) and C O( J =1–0) emission lines with theMopra 22 m telescope and the CO( J =3–2) line with the ASTE 10m telescope. In additionwe observed the CO( J =4–3, 7–6) lines with the NANTEN2 4m telescope. The CO( J =3–2) observing areas were selected using the NANTEN CO( J =1–0) dataset (Figure 1). Weproduced a complete view of the foot points of the loops in CO( J =3–2) at a 40 ′′ grid with a 22 ′′ beam size. The Mopra observations were limited to a subset of the area obtained with ASTE,but covered the brightest features associated with the foot points. NANTEN2 observationswere carried out toward four small regions centered on J =3–2 features identified in the ASTEresults (Figure 2). The details of these observations are as follows (see also Tables 1, 2 and 3). Observations of CO( J =1–0), CO( J =1–0), and C O( J =1–0) were carried out byusing the 22m ATNF Mopra mm telescope in Australia, during September 2007 and August2008. On-the-fly (OTF) mode was used, with a unit field of 4 ′ × ′ and we scanned in both lon-gitudinal and latitudinal directions separately to minimize scanning effects. The telescope hada half-power beamwidth (HPBW) of 33 ′′ at 100 GHz, which corresponds to 1.4 pc. The typicalsystem noise temperature, T sys , was 500 K in the single side band (SSB). The Mopra telescopewas also equipped with backend system ”MOPS”, providing 4096 channels across 137.5 MHz ineach of the two orthogonal polarizations. The effective velocity resolution was 0.088 km s − andthe velocity coverage was 360 km s − at 115 GHz. MOPS enabled simultaneous observationsof CO( J =1–0), CO( J =1–0), and C O( J =1–0). The pointing accuracy was checked every1 hour to keep within 7 ′′ by observations of the 86 HGz SiO maser from AH Sco [R.A. (2000)= 17 h m . s
16, Dec. (2000) = − ◦ ′ . ′′ T ∗ a scale and the baseline fitting was done with the livedata task in AIPS++. The spectrawere gridded to a 15 ′′ spacing, and smoothed with a 36 ′′ HPBW Gaussian function. We alsosmooth the channels in velocity to a 0.86 km s − interval for CO( J =1–0) and CO( J =1–0)and a 2.0 km s − for C O( J =1–0). The spectra were converted into a T mb scale by dividingby ”extended beam” efficiency 0.55 (Ladd et al. 2005). For comparison of CO( J =1–0) withother excitation lines, the spectra were spatially smoothed with a 38 ′′ Gaussian function beam,equivalent to the beam size of NANTEN2 at 460 GHz. We finally achieved the rms noise levels4n the CO( J =1–0), CO( J =1–0), and C O( J =1–0) spectra of 0.13 K, 0.06 K, and 0.03 K,respectively (see also Table 1). Observations of the CO( J =3–2) line were made using the ASTE (AtacamaSubmillimeter Telescope Experiment) 10m sub-mm telescope of NAOJ at Pampa La Bola atan altitude of 4800 m in Chile (Kohno 2005; Ezawa et al. 2004, 2008) for 7 days in Augustand September 2006. The HPBW was 22 ′′ at 345 GHz. We used a position switching modeto cover the region shown in Figure 1, in 1399 points, with a 40 ′′ grid spacing. ASTE wasequipped with 345 GHz SIS receiver SC 345 providing a typical system noise temperature of190–300 K at 345 GHz for an elevation angle of 30–80 degrees in the double-side band (DSB).For checking the system stability and the absolute intensity calibration, M17SW [R.A. (1950)=18 h m . s
0, Dec. (1950) = − ◦ ′ . ′′
0] was observed every 2–3 hours, the absolute temper-ature of which was assumed to be 69.6K (Wang et al. 1994), and we adopt a beam efficiency of0.6 at 345 GHz. The spectrometer comprises four digital back-end systems (autocorrelators)with 2048 channels. The total frequency bandwidth is 512 MHz, corresponding to a velocitycoverage of 450 km s − with a velocity resolution of 0.43 km s − at 345GHz. We smoothedthe data in velocity to a 0.86 km s − resolution to improve the noise level and smoothed inspace to a 38 ′′ beam size for comparison with other excitation lines. The telescope pointingwas measured to be accurate to within 2 ′′ by radio observations of Jupiter and W Aql [R.A.(2000) = 19 h m . s
21, Dec. (2000) = − ◦ ′ . ′′ ∼ T mb . We used the NANTEN2 4m sub-mm telescope at 4800 m altitude at Pampa La Bola inChile to observe the four regions in the foot points (Figure 2). These regions are chosen basedon the results of CO( J =3–2) (see Section 3). Observations of the CO( J =4–3) transition at460 GHz and the CO( J =7–6) transition at 810 GHz were made in June 2006 and December2007. The HPBW in 460 GHz and 810 GHz were measured to be 38 ′′ and 22 ′′ , respectively.The telescope was equipped with a dual-channel 460/810 GHz receiver. DSB receiver noisetemperatures were ∼
250 K at 460 GHz and ∼
750 K at 810 GHz. The spectrometer was anacousto-optical spectrometer (AOS) with a bandwidth of 1 GHz of 2048 channels and thevelocity resolution was 0.37 km s − at 460 GHz and 0.21 km s − at 806 GHz, respectively. Weused the OTF mode with equatorial (J2000.0) coordinates and scanned in both RA and Decdirections for a 2 ′ × ′ unit field. Main beam efficiencies at 460 GHz and 810 GHz were 0.5and 0.45, respectively. The raw data were calibrated into T ∗ A scale and then converted to T mb scale by dividing by the main beam efficiency. The typical rms noise fluctuations were ∼ ∼ − . For comparisonof CO( J =7–6) with other lines, the spectra were smoothed to 38 ′′ .5 . Results Figure 2 shows the integrated intensity distribution that includes the two foot pointsof loops 1 and 2 (Figure 2a) and part of the top of loop 1 (Figure 2b) in CO( J =3–2) at a22 ′′ ∼ −
180 km s − to −
40 km s − . The foot points are generally elongatedvertically to the plane and the most prominent feature ranges from l = 356 . ◦ to 356.25 ◦ and b = 0 . ◦ to 1.0 ◦ . The rest of the distribution is extended with a few local maxima, e.g., toward( l , b )=(356.17 ◦ , 0.75 ◦ ), (356.13 ◦ , 0.78 ◦ ) and (356.25 ◦ , 1.10 ◦ ). We have chosen four peaks in thefoot points, A–D, and a peak in the loop top as listed in Table 3 for a multi-J transition analysisin section 4. We note the emission is stronger in the eastern half of the distribution and thatthe eastern boundary shows a sharp intensity decrease perhaps barely resolved with the presentresolution. Figures 3a and 4a show the distribution of CO( J =1–0) and CO( J =1–0) in thesame velocity range at a 2 pc resolution with a spatial coverage limited to the bright part of CO( J =3–2) and these distributions are generally similar to the CO( J =3–2) distribution.Figures 3b and 4b show the different velocity range, −
70 to −
10 km s − , which exhibit a ”Ushape” (see section 3.2). Figures 5–7 show the CO( J =3–2) velocity distribution of the foot points in two ways,i.e., position-velocity diagrams and velocity-channel distributions every 10 km s − , and Figures8 and 9 show the labels and auxiliary lines superposed on the velocity distributions in order toshow the components discussed below.Figures 5a and 5b are latitude-velocity and longitude-velocity distributions of CO( J =3–2), respectively. The main part of the foot points, hereafter ”main component”, isdistributed in a velocity range from v = −
150 km s − to −
40 km s − (Figure 8). The nature ofthe weaker emission for velocities greater than −
40 km s − was not yet discussed in F06, whilethe very narrow velocity feature at ∼
10 km s − is likely foreground outside the Galactic center.Examination of line intensity ratios like that of CO( J =3–2) to ( J =1–0) indicates that mostof the emission seen in Figure 5 probably located in the Galactic center, as suggested by theirhigh excitation (see section 4). We call the low velocity feature at −
30 km s − to 0 km s − the”subcomponent” hereafter.We note that the subcomponent is probably linked to the main component of the footpoints, as suggested by the connecting broad emission at b = 0 . ◦ and by a few additional broademission components at b = 0 . ◦ , 0.94 ◦ and 1.0 ◦ (Figures 5 and 8). The subcomponent showsa velocity gradient from b = 0 . ◦ to 0.90 ◦ in the opposite sense to that of the main componentand forms a ”U shape” in the v - b diagram with the main component and the broad emission6t b = 0 . ◦ . Figure 6 shows the six latitude-velocity diagrams of the foot points every 0.03 ◦ in l . The main component and the subcomponent are clearly seen and appear linked at b = 1 . ◦ (a), b = 0 . ◦ (d,e) and b = 0 . ◦ (d,e,f). Below b = 0 . ◦ we also find another U shape in the v - b diagram and name it U shape 2 which is distributed in b = 0 . ◦ –0.8 ◦ and v = − −
10 kms − (Figures 5 and 8). A protrusion toward the galactic plane is seen in l = 356 . ◦ –356.20 ◦ and b = 0 . ◦ –0.8 ◦ at v = − −
50 km s − . In summary the distribution of the molecular gasconsists of two U shapes and a protrusion as indicated in Figures 7 and 9.Figure 7 shows the velocity channel distributions of the main components in CO( J =3–2). The main component appears in every panel from −
120 to −
40 km s − and subcomponentfrom −
30 km s − to 0 km s − . We recognize the intense part delineates a U shape in the bottomof the foot points as seen in panels from −
70 km s − to −
10 km s − (see also Figure 9). ThisU shape is also seen in CO( J =1–0) (Figures 3b and 4b around b =0.8 ◦ ).Peaks A–D are seen over a broad velocity range. Peak A is seen in two panels in Figure7 from −
110 to −
90 km s − , peak B in four panels from −
80 to −
40 km s − , peak C in fourpanels from −
100 to −
60 km s − , peak D in four panels from −
80 to −
40 km s − . The mostintense region in the foot point is peak C, which is connected to the bottom of the U shape,and peak D corresponds to the protrusion and shows a sharp inverse-triangle like shape. PeakD also seems to be connected to the component at l =356.06 ◦ and b =0.76 ◦ at v = −
10 km s − .These configure the another U shape. Peak B corresponds to one of the broad features shownin Figures 5 and 8. Other two broad features can be seen at l = 356 . ◦ and b = 0 . ◦ to 1.10 ◦ at velocity from −
60 to −
20 km s − and at l = 356 . ◦ and b = 0 . ◦ to 0.80 ◦ (Figure 9). Thesetwo features were not observed except in CO( J =3–2) emission. A general trend in Figure 7is that the peaks A, C and D show sharp intensity decreases toward the east and south withweaker ”tails” toward the north. Figure 10 shows the line profile of peak C where the COpeak velocity changes by ∼
10 km s − every ∼
20 pc with a decrease of the peak intensity by afactor of 4 toward the plane. Such a trend is not clearly seen for peak B, embedded in spatiallyextended emission in the panels from −
70 to −
60 km s − . We show the line spectra obtained at the four peaks A–D as well as at the peak positionat the top of the loop in Figure 11. All the spectra are smoothed to a 38 ′′ Gaussian beam forcomparison with the CO( J =4–3) profiles and are smoothed to 0.86 km s − resolution. Onlythe C O( J =1–0) spectra were smoothed to 2.0 km s − resolution to obtain better signal-noiseratios. The CO( J =1–0, 3–2, 4–3) and CO ( J =1–0) transitions are clearly detected whilethe CO ( J =7–6) transition is not detected, with an upper limit of 0.76 K. The line widths ofall the spectra are broad with velocity extents of more than 20–40 km s − .We investigate the intensity ratios, R j/i , in order to reveal the excitation condition ofthe gas. Here R j/i stands for an intensity ratio of emissions from lien i to line j . CO( J =1–7), CO( J =3–2), CO( J =4–3), CO( J =7–6), CO( J =1–0) and C O( J =1–0) for i and j are represented as 1–0, 3–2, 4–3, 7–6, 13 and 18, respectively. We show three histograms ofline intensity ratios in the four velocity ranges of − −
40 km s − (white), − −
20 km s − (red), − − (orange) and 0–20 km s − (green) and the combinations of these velocityranges (black) in Figure 12. Figure 12a shows R − / − ; this indicates that the loop emissionis characterized by high ratios peaked at 0.6 with a range from 0.3 to 0.95 at a 90 % peaklevel, somewhat smaller than R − / − of 0.9 in CMZ estimated by Oka et al. (2007). Thelocal emission has a narrow linewidths mostly in a range from 0 to 20 km s − is peaked at 0.2with a 90 % range of 0.1 to 0.6. The other two show peaks near 0.6 while the − − component shows another peak at 0.3 similar to the local clouds. The other two histograms, R − / , (Figure 12b) and R − / (Figure 12c), also indicate that the loop component and thecomponents in a range from −
40 to 0 km s − show ratios distinct from the local componentfrom 0 to 20 km s − . Figure 13 shows a histogram of the CO optical depth estimated bytaking ratio R − / with assumption of the abundance ratio [ C]/[ C]. Riquelme et al. (2010)estimated [ C]/[ C] in the loops as ∼ C]/[ C] ∼
53 estimated by Wilson & Rood (1994). Figure 13 indicatesthat the gas in the loops tends to show smaller optical depths peaked at around 3–4, while thelocal component of −
20 km s − is peaked at around 6–10. This estimate is similar to the opticaldepth derived in the CMZ by Oka et al. (1998). We summarize that the loop component is bestcharacterized by high excitation conditions as indicated by the high ratio of the CO( J =3–2)to CO( J =1–0) line intensities and the smaller CO optical depth.Figure 14 show the distributions of the ratio R − / − in velocity channel distributions.Generally speaking, the ratio is correlated with the CO( J =3–2) intensity and the ratio be-comes higher than 0.7 when the CO( J =3–2) intensity is higher than ∼
44 K km s − . Themost notable enhanced ratio, corresponding to peak B (broad emission), is found in Figure14 at ( l, b ) ∼ (356 . ◦ , . ◦ ) for velocity range of − −
10 km s − , where the highest ratiois around 2.0. The secondary enhancement is seen at ( l, b ) ∼ (356 . ◦ , . ◦ –0 . ◦ ) and velocityrange of − −
60 km s − , showing a ratio around 1.0 and corresponding to peak D.Figure 15 shows v - b diagrams of the R − / − and is generally consistent with Figure14. The most enhanced component around peak B shown in Figure 14 is found toward thebroad feature at b ∼ ◦ –0.95 ◦ for longitude range of 356.17 ◦ –356.20 ◦ . In addition, a highratio feature with a very narrow velocity width of 1–2 km s − is seen at v ∼ −
80 km s − and l = 356 . ◦ with a weak velocity gradient from b = 0 . ◦ to 1.05 ◦ and another similar feature isseen at v ∼ −
30 km s − and l = 356 . ◦ from b = 0 . ◦ to 0.95 ◦ . These narrow features aresmeared out in Figure 14. 8 . Data analysis We identified clumps in the following way in the CO( J =3–2) integrated intensitydistributions shown in Figure 2; 1) Find local peaks that have the integrated intensity strongerthan half of that in peak C, because peak C shows the maximum integrated intensity levelin the foot point. 2) Draw a contour at two thirds of the peak integrated intensity level andidentify it as a clump unless it contains other local peaks, 3) If there are other peaks insidethe contour, draw another contour with interval of 10 σ and find a contour which has no otherpeaks inside, and 4) If we find multiple peaks with an isolated contour when we perform theoperation (3), we should identify these all peaks as local peaks and repeat operations (2) and(3). In this way, we identified six clumps in the foot point. Then, we derived physicalproperties of the clumps. The results are summarized in Table 5. The radii of the clumps, r , are ∼ V , at the peakpositions are ∼ − . We estimate the clump masses in two ways; the mass estimatedfrom r and ∆ V by assuming virial equilibrium, M vir , and the mass estimated from CO byassuming the local thermodynamic equilibrium (LTE). M vir is calculated as follows by assuminguniform density distribution; M vir = 209 r pc ! (cid:18) ∆ V km s − (cid:19) M ⊙ (1) CO column densities are calculated by assuming the LTE condition to estimate the molecularmass. The optical depth of CO, τ ( CO), was calculated using following equation; τ ( CO) = − ln " − T ∗ R ( CO)5 . × ( J ( T ex ) − . (2)where, T ∗ R ( CO) and T ex are the radiation temperature and the excitation temperature of CO, respectively. J ( T ) is defined as J ( T ) = 1 / [exp(5 . /T ) − N ( CO) was estimatedfrom: N ( CO) = 2 . × τ ( CO)∆
V T ex − exp( − . /T ex ) (cm − ) . (3)In this study, we assume uniform T ex of 40 K as discussed in the next subsection. We assumetwo abundance ratios [H ]/[ CO] = 10 , the value of Sgr B2 (Lis & Goldsmith 1989), and5 × , the average value of local clouds (Dickman 1978), to convert N ( CO) into N (H ). M CO of each clump is estimated by using M CO = 2 . m H X h D Ω N (H ) i M ⊙ . (4)while M vir is in the order of ∼ –10 M ⊙ , M CO is only in the order of 10 M ⊙ . It means thatthe dynamical state of the molecular gas is considerably different from the virial equilibrium.9f we assume the uniform velocity dispersion of 20 km s − as a lower limit for the turbulentvelocity, the kinetic energy of each clumps is estimated to ∼ erg. We applied the large velocity gradient (LVG) analysis (Goldreich & Kwan 1974; Scoville& Solomon 1974) to estimate the physical parameters of the molecular gas toward the loop footpoints and the loop top by adopting a spherically symmetric uniform model having a radialvelocity gradient dv/dr . We calculate level populations of CO, CO and C O molecularrotational states and line intensities under these assumptions. The LVG model requires threeindependent parameters to calculate emission line intensities; kinetic temperature, T k , densityof molecular hydrogen, n (H ), and X (CO) / ( dv/dr ). X (CO) / ( dv/dr ) is the abundance ratio ofCO to H divided by the velocity gradient in the cloud. We use the abundance ratios [ C]/[ C] ∼
53 and [ O]/[ O] ∼
327 (Wilson & Rood 1994) and the molecular abundance [ CO]/[H ] ∼ − as a typical value for the inner Galaxy (i.e. Frerking, Langer & Wilson 1982; Leung,Herbst & Huebner 1984; Blake et al. 1987). We estimate the mean velocity gradient within thefoot point as ∼ − pc − (Table 5) and X (CO) / ( dv/dr ) to be 1 . × − for CO.In order to solve for the temperatures and densities which reproduce the observed lineintensity ratio, we calculate chi-square defined as below; χ = N − X i =1 N X j = i +1 " { R obs ( i, j ) − R LVG ( i, j ) } σ ( i, j ) (5)where N is the number of transitions of the observed molecule. i and j refer to differentmolecular transitions, R obs ( i,j ) is the observed line intensity ratio from transition i to transition j and R LVG ( i, j ) is the ratio between transitions i and j estimated from the LVG calculations.The standard deviation σ ( i, j ) for R obs ( i, j ) is estimated by considering the noise level of theobservations and the calibration error. We assume that the error of calibration from T ∗ a to T mb is uniformly 10 % for all observations. Because we use the same calibration factor for thespectra obtained with Mopra, the relative calibration error has no effect when we take a ratiobetween intensities obtained with Mopra; i.e., CO( J =1–0), CO( J =1–0) and C O( J =1–0).In order to reduce the error, we use the average line intensities over 10 km s − bins exceptfor C O, because C O has already been smoothed to be 2.0 km s − velocity resolution asdiscussed in section 3.3 and Figure 11, further smoothing did not give a better noise level. Thedegree of freedom, ν , is defined as follows; ν = N (6)The data used here are derived from the line profiles in Figure 11 and the ratios are estimatedfor peaks A–D and the loop top with all transitions. Therefore, the degree of freedom is givenas 15 for N= 6. The intensities of all transitions used here are listed in Table 4. Because wecould not detect any emissions of CO( J =7–6), we use the 1 σ noise levels for calculations as10pper limit. Since χ is weighted by σ , this assumption does not affect the results.Figure 16 shows the loci of constant R j/i for the five R j/i ’s as a function of density andtemperature. We find R − / − is sensitive to a large density range from 10 cm − to 10 cm − while R − / − is sensitive to higher density above 10 cm − . We also note that R − / isnearly orthogonal to R − / − for density lower than 10 cm − , making the combination usefulin obtaining solutions.Figures 17a–17e and Table 6 show the results of fitting the data obtained with a χ minimization approach to find the best solution of temperature and density. Each thick locussurrounding the cross indicates the χ of 25.0, which corresponds to the 5% confidence level of χ distribution with 15 degree of freedom. The crosses denote the lowest point of χ . Threeintensity ratios, R − / − , R − / − and R − / , are also shown by thin lines. The −
75 kms − and −
15 km s − components at peak B do not have any solutions with 5% confidencelevel. Another presentation of the results is found in Figure 18 for the five peaks along withthe CO( J =3–2) line profiles. An error bar in the figure is defined as 5% confidence levelof χ distribution. The density is in the range from 10 to 10 cm − and the temperature isfrom ∼ R − / − values in Figures 14 and15, the broad emission connecting different sides of the U shape (peak B) shows the highesttemperature, 100 K or higher, amongst the five peaks.
5. Discussion
There are no candidates for protostars identified by IRAS in the observed regions. The10 GHz radio continuum emission observed by Handa et al. (1987) gives an upper limit of 0.1K. This 10 GHz flux density is equivalent to 10 . FUV photons s − , assuming 220 square arcminutes as the area of the foot point and 8000 K electron temperature. That corresponds toa single B3 star or a star of later spectral type (Kurtz, Churchwell & Wood 1994; Panagia1973; Mezger & Henderson 1967). Only one ultra compact H II region (UCH II ) is identified at( l , b ) ∼ (356.25 ◦ , 0.7 ◦ ) at a velocity of +120 km s − from H α recombination line observations(Caswell & Haynes 1987; Lockman 1989). So, the UCH II is not associated with the foot point.Here, there is no indication of significant formation of massive stars. Some other mechanismfor heating the molecular gas is required, in particular, towards peaks B and C.The magnetic flotation model presented by F06 is able to offer another explanation toheat the gas by shocks. F06 suggested that loops 1 and 2 are created by magnetic buoyancydriven by the Parker instability. The floated gas falls down to the Galactic plane along themagnetic loop, and the accumulated gas forms a massive cloud in the foot point of the loop.In this case, if the fall down velocity of the gas exceeds the speed of sound, shock fronts areformed in the foot point (Matsumoto et al. 1988). The magnetic field is estimated to be 150 µ G in the loops under the assumption of energy equipartition, and the velocity of the gas isestimated to be similar to the Alfv´en speed, ∼
24 km s − (F06).11he structure of shock waves in molecular clouds is an important subject. Draine,Roberge, & Dalgarno (1983) made such calculations including the effects of ion-neutral stream-ing driven by the magnetic field. They found that shock waves in molecular clouds are usuallyC-type shock waves, mediated by the dissipation accompanying ion-neutral streaming, and inwhich all of the hydrodynamic variables are continuous. In the foot point of the loops, C-typeshock seems to be a viable model because they occur with a strong magnetic field and at amoderate shock speed. The limiting shock speed for C-type shocks not dissociating the H molecules is estimated to be 45 km s − (Draine, Roberge, & Dalgarno 1983). The Alfv´enspeed 24 km s − estimated by F06 and the velocity dispersion of the clumps shown in Table 5are both within this range and hence we adopt C-type shock as the heating mechanism for theloops. Draine, Roberge, & Dalgarno (1983) show that the neutral gas temperature is in a range100–1000 K for a density of 10 cm − , B of 100 µ G and shock speed of 20–40 km s − . Theseparameters are consistent with density of 10 –10 cm − , magnetic field of 150 µ G and a fallingspeed of 24 km s − (F06). Such high temperature is consistent with the present estimate oftemperature higher than 30–40 K, since the high temperature layer should be thin like 10 –10 cm, ∼ R − / − is formed not to-ward the bottom of the foot points but well above the foot points apparently separated fromthe strongly shocked layer in the bottom of the U shape. It is interesting to compare theseresults with the solar foot points for which a number of observations have been accumulated12n magnetic activity.Isobe, Tripathi & Archontis (2007) argued that anti-parallel field lines are produced inthe foot point when multiple loops rose. This causes magnetic reconnection that can lead to ajet-like structure rising upward. Or, alternatively, in the U shaped region the field lines becomecompressed to reduce the falling gas flux, leading to gas bouncing at the narrow neck (Kudoh& Shibata 1999). We present a schematic figure of these scenarios in Figure 19. Numericalsimulations in the solar case suggest that the initial condition may determine which processbecomes dominant, either reconnection or bouncing. The basic physics is common to the spursin Galactic loops as already discussed by Matsumoto et al. (1988) and Takahashi et al. (2009).We shall make a crude estimate of the energies concerned, both the magnetic and grav-itational energies released. Here we assume the concerned volume of the U shape as a cylinderwith a radius of 10 pc and a height of 30 pc. Gravitational energy is released by the gas fallingdown along the loop that can lead to shock heating of the U shape. The heights of the topsof loops 1 and 2 and the U shape from the galactic plane are estimated as ∼
200 pc, ∼ ∼
130 pc, respectively, at a distance to the Galactic center of 8.5 kpc, and the totalmolecular mass in the U shape is estimated as ∼ × M ⊙ . Potential energies from theU shape to the tops of loops 1 and 2 divided by the time scale of 10 years (Machida et al.2009; Takahashi et al. 2009) at the galacto-centric radius of 670 pc are derived as 0 . × erg s − and 1 . × erg s − , respectively, by using the modified Miyamoto-Nagai potential(Miyamoto & Nagai 1975; Sofue 1996). If the reconnection takes place, we need to take intoaccount the additional magnetic energy release. We use the magnetic field strength and Alfv´enspeed of 150 µ G and 24 km s − , respectively, estimated by F06. According to the scenariogiven above, the field lines move parallel to the galactic plane and inflow into the U shape. Ifwe roughly assume the inflow speed to be 10% of the Alfv´en speed, the total magnetic energyaccumulated into the cylinder is estimated to ∼ × erg in ∼ years. This energy iscomparable to the magnetic energy of ∼ ergs for a typical single loop given by Machidaet al. (2009). In ∼ years after the magnetic reconnection occurs, the maximum availablepower of the reconnection is derived as ∼ . × erg s − . Thus, the total available energyinjected to the U shape is 1 . × –2 . × erg s − by summing up both the magnetic andgravitational energies. The cooling power in peak B is estimated to be ∼ . × erg s − for kinetic temperature of 100 K and density of 4 × cm − for a uniform sphere with ∼ ∼ . × erg s − for 40 K and4 × cm − (Goldsmith & Langer 1978). These values correspond to nearly comparable to,or ∼
20% of, the maximum available power. We therefore infer that the reconnection is able toexplain the heating of the warm gas in the U shape, while obviously we require more detailedmodel simulations and direct measurements of the magnetic field to reach a firm conclusion onthe physical processes related to the heating mechanism.13 . Conclusions
We have made detailed high-resolution observations of the foot points of the molecularloops 1 and 2 (Fukui et al. 2006) in six rotational transitions of the interstellar CO molecule.The main conclusions are summarized below;1) The foot points have sharp intensity gradients toward the south and east, as is con-sistent with the shock formation at the bottom of the foot points (Figure 2b). The foot pointshave several major peaks having 10 –10 M ⊙ gas in each. The foot points are characterized bytwo U shapes both in space and velocity and the protrusion (Figures 5–8). We suggest that theU shape may be formed by merging of two down flows between two loops as derived in MHDnumerical simulations.2) Toward five selected peaks of CO( J =3–2), peaks A–D and peak top (Figures 2–4),we have carried out a multi-line LVG analysis of line radiation transfer and derived the moleculartemperature and density. The four peaks in the foot point show rather high temperatures of ∼ cm − to 10 cm − (Figures 17 and 18). Among the four peaks,the peak toward the central region of the foot point, peak B, shows the highest temperature of ∼
100 K or more.3) We compared the results with calculations of C-shocks by Draine, Roberge, &Dalgarno (1983) and find that the derived temperature and density are roughly consistentwith theoretical estimates for magnetic field around 100 µ G, suggesting that shock heating isa viable explanation for the high temperature over the foot point. In addition, by comparingtheoretical work on the solar activity, we argue that the warmest region in the central part ofthe foot point may be additionally heated up either by magnetic reconnection or by upwardflowing gas bounced by the narrow neck in the foot point.We thank all the members of the NANTEN2 consortium, ASTE team, and Mopra stafffor the operation and persistent effors to improve the telescopes.The Mopra telescope is funded by the Commonwealth of Australia as a National Facilitymanaged by CSIRO as part of the Australia Telescope. UNSW-MOPS spectrometer usedwas funded by the Australian Research council with the support of the Universities of NewSouth Wales, Sydney and Macquarie, together with the CSIRO. The ASTE project is drivenby Nobeyama Radio Observatory (NRO), a division of National Astronomical Observatoryof Japan (NAOJ), in collaboration with University of Chile, and Japanese institutes includ-ing University of Tokyo, Nagoya University, Osaka Prefecture University, Ibaraki University,and Hokkaido Univsersity. Observations with ASTE were in part carried out remotely fromJapan by using NTT’s GEMnet2 and its partner R&E (Research and Education) networks,which are based on AccessNova collaboration of University of Chile, NTT Laboratories, andNAOJ. NANTE2 project is based on a mutual agreement between Nagoya Univerisity andthe University of Chile and includes member universities, Nagoya, Osaka Prefecture, Cologne,14onn, Seoul National, Chile, New South Wales, Macquarie, Sydney and Zurich.@This work was financially supported in part by a Grant-in-Aid for Scientific Research(KAKENHI) from the Ministry of Education, Culture, Sports, Science and Technology of Japan(Nos. 15071203 and 18026004) and from JSPS (Nos. 14102003, 20244014, and 18684003). Thiswork is also financially supported in part by core-to-core program of a Grant-in-Aid for ScientificResearch from the Ministry of Education, Culture, Sports, Science and Technology of Japan(No. 17004).This work was also supported by the Global COE Program of Nagoya University gQuestfor Fundamental Principles in the Universe (QFPU)h from JSPS and MEXT of Japan.LB acknowledges support from Center of Excellence in Astrophysics and AssociatedTechnologies (PFB 06) and by FONDAP Center for Astrophysics 15010003.15 eferences
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Table 3: Observed areas of On-the-fly observationstransition coord. reference position map size grid N map region( ′ ) ( ′′ ) CO, COand C O( J =1–0) galactic 356.222 ◦ , 0.845 ◦ ◦ , 1.333 ◦ CO( J =4–3) CO( J =7–6) Equatorial(J2000.0) 17 h m . s − ◦ ′ . ′′
76 2 15 1 top17 h m . s − ◦ ′ . ′′
44 2 15 1 peak A17 h m . s − ◦ ′ . ′′
02 2 15 1 peak B17 h m . s − ◦ ′ . ′′
49 2 10 1 peak C17 h m . s − ◦ ′ . ′′
85 2 15 1 peak D
Note. - Column (2) : Coordinate system of observations. Column (4) : Size of the unit square of OTF scan.Column (5) : Grid intervals of the out put data. Column (6) : Number of maps that were observed witheach reference position. able 4: 10 km s − average intensity of the peaks.Peak V lsr
10 km s − average intensity (K)(km s − ) CO(1–0) CO(3–2) CO(4–3) CO(1–0) C O(1–0)A −
110 3.31 3.31 2.29 0.21 — −
100 5.26 5.49 4.00 0.63 0.05 −
90 4.27 3.41 2.24 0.51 — −
80 2.40 1.44 0.71 0.20 — −
68 2.06 1.23 0.61 0.14 — −
58 2.43 1.88 0.90 0.21 —B −
105 2.39 1.39 0.54 0.15 — −
95 4.75 3.77 1.31 0.36 — −
85 6.56 6.00 3.10 0.52 — −
75 4.52 5.76 3.54 0.40 — −
65 5.24 7.10 4.81 0.33 — −
55 2.84 5.48 3.62 0.15 — −
45 0.87 1.94 1.45 0.08 — −
35 0.82 1.51 0.67 0.14 — −
25 1.62 2.50 1.85 0.20 — −
15 2.58 3.42 2.44 0.39 — − −
95 8.90 6.21 4.41 0.53 0.04 −
85 10.33 9.50 7.89 0.92 0.08 −
75 8.22 7.54 6.05 0.69 0.06 −
65 6.75 5.62 4.08 0.54 0.04 −
55 5.34 3.19 1.87 0.42 — −
45 4.45 1.84 0.94 0.38 —D −
68 6.61 5.83 4.02 0.50 — −
58 10.95 10.65 8.10 0.99 0.10 −
48 5.42 4.75 3.19 0.47 — −
38 2.77 1.02 0.77 0.29 —TOP −
80 3.35 1.36 1.00 0.24 — −
70 4.83 2.84 2.28 0.50 — −
60 6.23 4.46 4.06 0.69 — −
50 2.09 1.66 1.32 0.13 —
Note. ”—” stands for non-detection above 3 σ . Column (2) indicates Center velocity forcalculations. able 5: Physical properties of the clumps. l b ∆V r M vir M CO region( ◦ ) ( ◦ ) (km s − ) (pc) ( × M ⊙ ) ( × M ⊙ )356.124 0.780 26.0 4.6 65.0 1.2 † / 2.5 ‡ † / 1.4 ‡ peak B356.174 0.708 19.2 2.8 21.6 0.6 † / 1.2 ‡ peak D356.187 0.988 33.1 2.4 55.0 0.4 † / 0.8 ‡ † / 7.4 ‡ peak C356.254 1.113 38.2 3.9 118.9 1.5 † / 3.0 ‡ peak A † [H ]/[ CO]= 5 × (Dickman 1978) was used for estimation. ‡ [H ]/[ CO]= 10 (Lis & Goldsmith 1989) was used for estimation.Note. - Column (1, 2) : Peak position of the clump. Column (3) : Intensity weightedvelocity dispersion (FWHM). Column (4) : Radius of the clumps. Column (5) : Clumpmass derived with assumption of Virial equilibrium. M vir = 209 r (∆ V ) . Column (6) :Clump mass derived by using CO( J =1–0) with LTE assumption. able 6: LVG results for X(CO)/(dv/dr) = 1.1 × − .Peak V lsr n(H ) (cm − ) T k (K) min. χ (km s − ) χ <
25 min. χ χ <
25 min. χ A −
110 10 . –10 . . −
100 10 . –10 . . −
90 10 . –10 . . −
80 10 . –10 . . −
68 10 . –10 . . >
20 32 3.35 −
58 10 . –10 . . −
105 10 . –10 . . >
20 33 3.34 −
95 10 . –10 . . −
85 10 . –10 . . −
75 — — — — 30.52 −
65 10 . –10 . . −
55 10 . –10 . . >
97 128 22.55 −
45 10 . –10 . . >
60 98 19.68 −
35 10 . –10 . . −
25 10 . –10 . . −
15 — — — — 30.36 − . –10 . .
28 - 37 31 19.24C −
95 10 . –10 . . −
85 10 . –10 . . −
75 10 . –10 . . −
65 10 . –10 . . −
55 10 . –10 . . −
45 10 . –10 . . −
68 10 . –10 . . −
58 10 . –10 . . −
48 10 . –10 . . −
38 10 . –10 . . −
80 10 . –10 . . >
18 37 12.88 −
70 10 . –10 . . −
60 10 . –10 . . − > . . >
22 42 4.67
Note. - ”—” stands for no-solution above 5% confidence level of χ distribution. Column(3): Number density, n (H ) cm − , for that χ is less than 25. (4) : Number density, n (H )cm − , at the point that minimum χ is found. (5) : Kinetic temperature, T k K, for that χ is less than 25. (6) : Kinetic temperature, T k K, at the point that minimum χ is found. (7): minimum χ CO( J =1–0) obtained byNANTEN 4m telescope (Fukui et al. 2006). Yellow boxes in each image show the observedregion in CO( J =3–2) by ASTE. (a) Loop 1 : The integration range in velocity is from − −
90 km s − . Contours are illustrated from 7 K km s − (white) with an interval of 50 K kms − . (b) Loop 2 : The integration range in velocity is from −
90 to −
40 km s − . Contour levelsare the same as that in (a). (c) Schematic image of loops 1 and 2. The foot points and tops ofthe loops are depicted by circles and dashed boxes.22ig. 2: Integrated intensity distributions of CO( J =3–2) emissions at the top and foot pointof the loops. (a) Top of the loop1. Integration range is from −
180 to −
40 km s − . Contoursare plotted every 40 K km s − from 15 K km s − . (b) Foot point of the loops. Integration rangeand contour levels are the same as that in (a). The dotted box shows the observing region of CO( J =1–0) emissions and CO( J =1–0) emissions, that are shown in Figures 3 and 4. Thesmall boxes show the observed reigons of CO( J =4–3, 7–6) emissions.23ig. 3: Integrated intensity distribution of CO( J =1–0) emissions at the foot point of theloops. Integration ranges are from −
180 to −
40 km s − (a) and from −
70 to −
10 km s − (b).Contours are plotted every 30 K km s − from 2 K km s − . The labeled clumps are discussedin the text. 24ig. 4: Integrated intensity distribution of CO( J =1–0) emissions at the foot point of theloops. Integration ranges are from −
180 to −
40 km s − (a) and from −
70 to −
10 km s − (b).Contours are plotted every 5 K km s − from 2 K km s − .Fig. 5: (a) Velocity - galactic latitude diagram of the footpoint of the loops in CO( J =3–2)averaged from 356.03 ◦ to 356.27 ◦ in galactic longitude. Contours are plotted every 0.2 K. (b)Galactic longitude-velocity diagram of the footpoint of the loops in CO( J =3–2) averagedfrom 0.63 ◦ to 1.27 ◦ in galactic latitude. Contours are plotted every 0.2 K.25ig. 6: (a–f) Longitude channel maps of CO( J =3–2) averaged over successive 100 ′′ intervals.Contours are plotted every 1 K from 0.5 K. The figure in the left side is the integrated intensitydistributions which is the same as the image shown in figure 2. Solid lines in the figure showthe integration ranges of figures (a)–(f). 26ig. 7: Velocity channel maps of CO( J =3–2) integrated over successive 10 km s − . Contoursare illustrated every 10 K km s − from 4 K km s − .27ig. 8: Positions of main component, subcomponent and broad emission regions are superposedon the CO( J =3–2) figure shown in Figure 5.28ig. 9: Positions of main component, subcomponent and broad emissions are superposed onthe velocity channel maps shown in Figure 7. Velocity range is from −
70 to −
10 km s − .29ig. 10: (a) Peak velocity map around peak C estimated with CO( J =3–2) is shown in thecolor image. Contours show the integrated intensity levels of CO( J =3–2) integrated from −
140 to −
40 km s − and are plotted every 60 K km s − . (b) CO( J =3–2) and CO( J =1–0)spectra of the four points on the red arrow in figure (a). The order of the spectra is the directionof the red arrow, from peak C to the left-bottom of the peak C.30ig. 11: Observed CO spectra at the peak of each of the clumps shown in Figures 3 and 4.The C O( J =1–0) spectra intensity scale have been multiplied by two for clearly. The verticaldashed lines are drawn with 20 km s − intervals from −
120 km s − . The gray scale boxes showthe regions where the LVG calculations was carried out (Figure 18).31ig. 12: Intensity weighted frequency distributions of the CO intensity ratio. The data weresmoothed to a 60 ′′ spatial resolutions with a gaussian function and smoothed to a 2 km s − velocity resolution. The white lines show the contributions of the loops ( −
140 km s − to − − ), and the red, orange and green lines show the contributions of the local componentswith a interval of 20 km s − from −
40 km s − . (a) R − / − = CO( J =3–2)/ CO( J =1–0).(b) R − / = CO( J =1–0)/ CO( J =1–0). (c) R − / = CO( J =1–0)/ CO( J =3–2).Fig. 13: Histogram of the CO( J =1–0) optical depth in the foot point of the loops. The dataare smoothed to a 5 km s − resolutions. The white line shows the contributions of the loops( −
140 km s − to −
30 km s − ), and the red, orange and green lines show the contributions ofthe local components, same as in Figure 12. 32ig. 14: Velocity channel maps of the CO( J =3–2)/ CO( J =1–0) intensity ratio integratedover successive 10 km s − channels. Contours are CO( J =3–2) and illustrated every 10 K kms − from 4 K km s − . 33ig. 15: Longitude channel maps of the CO( J =3–2)/ CO( J =1–0) intensity ratio averagedfor successive 45 ′′ with an interval of 120 ′′ . Contours are the averaged intensity of CO( J =3–2)and are plotted every 1 K from 0.5 K. 34ig. 16: Intensity ratio distributions in the density-temperature space calculated from theLVG model for X(CO)/(dv/dr) of 1.1 × − . R − / − , R − / − , R − / − , R − / and R − / stand for the intensity ratio of CO( J =3–2)/ CO( J =1–0), CO( J =4–3)/ CO( J =1–0), CO( J =7–6)/ CO( J =1–0), CO( J =1–0)/ CO( J =1–0) and CO( J =1–0)/C O( J =1–0), respectively. 35ig. 17a: LVG results of peak A. Values shown at left-top of the figures show the centervelocity of the calculated velocity range. Crosses denote the lowest point of chi-square χ .Contours surrounding the cross indicate χ = 25.0 which correspond to 5% confidence level of χ distribution with 15 degree of freedom. Thin lines show the typical intensity ratios; R − / − (solid lines), R − / − (dashed lines) and R − / (dotted lines).36ig. 17b: LVG results of peak B. Details are the same in Figure 17a.37ig. 17c: LVG results of peak C. Details are the same in Figure 17a.Fig. 17d: LVG results of peak D. Details are the same in Figure 17a.38ig. 17e: LVG results of peak top. Details are the same in Figure 17a.39ig. 18: LVG results for X(CO)/(dv/dr) of 1.1 × − for the five spectra at the peaks. Thehorizontal axis of all figures is LSR velocity. The top row shows the CO( J =3–2) spectra atthe peaks A-D, and the peak in the loop top. The second and third rows show the numberdensity, n (H ) cm − and the kinetic temperature, T k K, respectively. Circles show the lowestpoint of χ , and the error range is defined as a 5% confidence level of χ distribution with 15degree of freedom, that corresponds to χ =25.0. The minimum χ2