Cloud-Cloud Collision in the Galactic Center Arc

We performed a search of cloud-cloud collision (CCC) sites in the Sagittarius A molecular cloud (SgrAMC) based on the survey observations using the Nobeyama 45-m telescope in the C$^{32}$S $J=1-0$ and SiO $v=0~J=2-1$ emission lines. We found candidates being abundant in shocked molecular gas in the Galactic Center Arc (GCA). One of them, M0.014-0.054, is located in the mapping area of our previous ALMA mosaic observation. We explored the structure and kinematics of M0.014-0.054 in the C$^{32}$S $J=2-1$, C$^{34}$S $J=2-1$, SiO $v=0~J=2-1$, H$^{13}$CO$^+ J=1-0$, and SO $N,J=2,2-1,1$ emission lines and fainter emission lines. M0.014-0.054 is likely formed by the CCC between the vertical molecular filaments (VP) of the GCA, and other molecular filaments along Galactic longitude. The bridging features between these colliding filaments on the PV diagram are found, which are the characteristics expected in CCC sites. We also found continuum compact objects in M0.014-0.054, which have no counterpart in the H42$\alpha$ recombination line. They are detected in the SO emission line, and would be"Hot Molecular Core (HMC)"s. Because the LTE mass of one HMC is larger than the virial mass, it is bound gravitationally. This is also detected in the CCS emission line. The embedded star would be too young to ionize the surrounding molecular cloud. The VP is traced by poloidal magnetic field. Because the strength of the magnetic field is estimated to be $\sim m$Gauss using the CF method, the VP is supported against fragmentation. The star formation in the HMC of M0.014-0.054 is likely induced by the CCC between the stable filaments, which may be a common mechanism in the SgrAMC.


Introduction
The Galactic center region is the nucleus of the nearest spiral galaxy. The Central Molecular Zone (CMZ) (Morris & Serabyn 1996) is a large molecular cloud reservoir in the galaxy, which extends along the galactic plane up to l ∼ ±1 • . The mass of the CMZ is estimated to be ∼ 5 × 10 7 M (e.g. Morris & Serabyn 1996;Tsuboi, Handa & Ukita 1999). The molecular clouds in the CMZ are much denser, warmer, and more turbulent than those in the Galactic disk region. The CMZ is recognized to be a laboratory for peculiar phenomena, which will be found in central molecular cloud reservoirs of normal external galaxies by future telescopes. Young and luminous star clusters which contain over several ten OB stars, for example Arches cluster and Quintuplet cluster, have been found in the CMZ by IR observations (e.g. Genzel et al. 1996;Figer et al. 1999;Figer et al. 2002). They are as luminous as those which are nearly hard to be found in the Galactic disk region. These star clusters presumably have been formed in the cradle molecular clouds in the CMZ.
The star formation would be influenced by external factors, such as interactions with SNRs and/or cloud-cloud collisions(CCC) because they are crowded in the region (e.g. Morris 1993;Hasegawa et al. 1994;Hasegawa et al. 2008). However, it is difficult to demonstrate observationally how the cradle molecular clouds produce such massive clusters because almost these clusters have already lost the surrounding molecular materials. The Galactic Center 50 kms −1 molecular cloud (50MC) is an exception, which has still abundant molecular gas and several compact HII regions. In the previous observations, we have found a half-shell structure filled with shocked molecular gas, which would be made by CCC (Tsuboi et al. 2011, Tsuboi et al. 2015. As known widely, the dense molecular clouds in the CMZ seem to exist as molecular ridges along the galactic plane, which are bundles of the molecular filaments (Bally et al. 1987;Oka et al. 1998;Tsuboi, Handa & Ukita 1999). The molecular filaments would collide each other, where star formation would be activated. It is an open issue whether CCCs usually induce star formation in the CMZ or not.
First, we searched CCC sites based on the survey observations for the Sagittarius A molecular cloud complex (SgrAMC) with the Nobeyama 45-m telescope (Tsuboi, Handa & Ukita 1999;Tsuboi et al. 2011). The SgrAMC is one of most conspicuous molecular cloud complexes in the CMZ. One of the candidates, M0.014-0.054 near the 50MC, is located serendipitously in the mosaic observation area using ALMA of the 50MC although the observation itself had other science objective ). Then we looked for the signs of CCCs and induced star formation in the ALMA data.
Throughout this paper, we adopt 8 kpc as the distance to the Galactic center (e.g. Boehle et al. 2016).
Then, 1 corresponds to about 0.04 pc at the distance.

Search for the Cloud-Cloud Collision Candidates
We searched the CCC candidates in the SgrAMC based on the existing survey observations with the Nobeyama 45-m telescope in the C 32 S J = 1−0 (48.990957 GHz) and SiO v = 0,J = 2−1 (86.846995 GHz) emission lines (C 32 S; Tsuboi, Handa & Ukita 1999, SiO;Tsuboi et al. 2011). These surveys have the highest angular resolutions among single dish observations. The C 32 S emission line is a tracer of medium dense molecular cloud, n(H 2 ) cl ∼ 10 4 cm −3 . Because this emission line is moderately optically thick, τ ∼ 0.5 − 3, in the SgrAMC (e.g. Tsuboi, Handa & Ukita 1999), this emission shows mainly the location of the medium dense molecular cloud. On the other hand, the SiO emission line is a famous tracer of strong C-shock wave (∆V > 30 km s −1 ) which propagated in the region within 10 5 yr (e.g. Gusdorf et al. 2008, Jiménez-Serra et al. 2008. Because the emission line is often detected in the CCC sites, the detection indicates the CCC candidates. Center Arc (GCA) in the 20-cm continuum emission for comparison (Yusef-Zadeh, Morris, & Chance 1984). The molecular cloud is identified as two curved ridges along the GCA (e.g. Serabyn & Güsten 1987). Moreover, a large molecular cloud connecting with the curved ridges is located apparently in the "continuum gap" between the GCA and Sagittarius A east SNR. This cloud extends vertically north, l ∼ −0.02 • , b ∼ 0.05 • , and south, l ∼ 0.03 • , b ∼ −0.12 • . We call it the "Vertical Part (VP)" here. M0.014-0.054 is identified as a strong compact feature which is apparently located on the VP in the C 32 S integrated intensity map. Figure 1b  (Yusef-Zadeh, Morris, & Chance 1984). The contour levels are (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, and  4 the same area and velocity range as in Figure 1a. Almost all molecular clouds in the area become faint or disappear in the SiO map. This shows that no strong C-shock wave propagated in the area except for several compact components including M0.014-0.054. M0.014-0.054 extends roughly east and west. The east-west extent of M0.014-0.054 seems to correspond with the width of the VP seen in the C 32 S emission line. M0.014-0.054 is more prominent in the SiO emission line than in the C 32 S emission line. This shows that shocked molecular gas originated by the C-shock wave within 10 5 yr is abundant in M0.014-0.054. This suggests that the object would be made by some historical event including cloud-cloud collision. In addition, Figure 1d shows the continuum emission map at 330 MHz (LaRosa et al. 2000).
Well-known continuum features, "threads" are identified (yellow arrows). There is also a emission extending from the Sagittarius A east SNR to east, which crosses "threads" and reaches up to l ∼ 0.10 • , b ∼ −0.06 • . Because M0.014-0.054 is adjacent to these continuum features, this would be associated physically with them.

ALMA Observation
We have performed the observation of a 330 × 330 area covering the 50MC in the C 32 S J = 2 − 1 and a 52 pointing mosaic of the 7-m array (ACA). Additionally, the single-dish data has been obtained by Total Power Array. The red broken line square in Figure 1c indicates the mapping area. It is fortunate that M0.014-0.054 is located in the mapping area of the ALMA observation by chance.
The molecular emission lines used for imaging here are summarized in Table 1.
The C 34 S and H 13 CO + emission lines are tracers of dense molecular cloud, n(H 2 ) cl ∼ 10 5 cm −3 . These emission lines are thought to be optically thin even in the SgrAMC. The optical thickness of the C 34 S emission line will be demonstrated to be thin for the typical case in the subsection 4.4.
That of the H 13 CO + emission line is estimated to be τ < 0.2 based on the observed mean temperature ratio, T B (H 12 CO + )/T B ( H 13 CO + ) ∼ 7 (e.g. Armijos-Abendaño et al. 2015). As mentioned previously, the SiO emission line is a well-known tracer of strong C-shock wave, while the CH 3 OH molecules are enhanced even by mild C-shock (∆V ∼ 10 km s −1 e.g. Hartquist et al. 1995). The C 2 H and .328624 dense regions exposed to UV radiation † 6 c-C 3 H 2 emission lines are well-known tracers of photodissociation regions (PDRs). The abundance of both radicals was found to increase close to the dissociation front (e.g. Jansen et al. 1995;Fuente, Rodriguez-Franco, & Martin-Pintado 1996). The HN 13 C and HC 15 N emission lines have critical densities in the environment of the SgrAMC as high as n(H 2 ) cl ∼ 10 6 cm −3 and n(H 2 ) cl ∼ 10 7 cm −3 , respectively. These intensities can vary widely by their path length, abundance, and isotope ratio.
The SO and 34 SO emission lines are usually emitted from "Hot Molecular Core (HMC)"s where the molecular cloud is heated up to 100 K by newborn stars. The H42α recombination line and continuum emission at 86 GHz are simultaneously observed. The H42α recombination line traces ionized gas.
The continuum emission at 86 GHz is usually emitted by ionized gas. However, there is a possibility that the emission is originated by warm dust or non-thermal mechanism in the Galactic center region.
In addition, the CCS emission line is partly in the observation frequency range. The CCS molecule is abundant in the early stage of star formation but decreases with increasing time (e.g. Hirahara et al. 1992).
Although the area around M0.014-0.054 is less dense comparing to the 50MC ), the C 32 S and C 34 S emission lines are significantly resolved out only by the interferometer observations when they have been processed in the same procedure mentioned above. This is because the molecular cloud is widely extended in the area. The combining with the single-dish data, Total Power Array data, is required to recover the missing flux. We performed the procedure using the CASA task "FEATHER". We present the detailed description of the procedure and the full results in other papers .      In the PV diagrams, there are two compact components with V LSR ∼ 20 km s −1 adjoining the extended feature mentioned above. In order to clarify the angular extension of these components, the integrated intensity maps with V LSR = 10 to 35 km s −1 are shown in Figures 3c and 4c. These features are resolved into two molecular filaments which are almost parallel to each other in the maps. The two components in the PV diagrams are thought to be a part of the molecular filament bundle, which will be discussed in the following subsection.
In addition, a faint feature is also identified around the angular offset of M0.014-0.054 and velocity of V LSR ∼ −50 km s −1 in the C 34 S J = 2 − 1 emission line (see Figure 4b). The feature is the contamination by the CH 3 CHO J Ka,Kc = 5 −2,4 − 4 −2,3 E emission line (96.425620 GHz) because this feature is not detected in Figure 3b.

"Molecular Filament Bundle"
Another molecular cloud ridge extends roughly east and west over this area (see Figures 5a and 5b).
The western and eastern parts of this structure are seen in the negative and positiveLSR velocities, respectively. We call this structure "Molecular Filament Bundle" (MFB). Figure  is given by where T ex and f are the excitation temperature and beam-filling factor of the emission line, respectively. The isotope abundance ratio of 32 S and 34 S in the molecular cloud is assumed to be equal to the natural abundance ratio of 22.35 1 .
The mean line intensity ratio in M0.014-0.054 is calculated to be R ∼ 9.4. Therefore the mean optical thickness of the C 32 S emission line toward M0.014-0.054 is estimated to be τ ∼ 2.1 assuming The correction factor for the optical thickness of the C 32 S emission line is τ 1−e −τ ∼ 2.4. The corrected integrated intensity of the object in the CS J = 2 − 1 emission line is given by The total number of the H 2 molecules in the object is given by where N LTE (H 2 ) is the LTE molecular column density. Here the Einstein A coefficient of the CS The excitation temperature of the CS J = 2 − 1 emission line is assumed to be T ex = 80 K (T K = 80 K in Ao et al. 2013). The fractional abundance of the CS molecule is assumed to be X(CS) = N (CS) N (H 2 ) = 1 × 10 −8 , which is usually used for molecular clouds in the disk region. The LTE molecular cloud mass is given by where µ is the mean molecular weight per H 2 molecule: µ = 2.8 in amu = 2.4 × 10 −57 M . The integrated intensity of the whole of M0.014-0.054 in the C 32 S emission line is object Although the mean optical thickness of the C 32 S emission line is fairly high in M0.014-0.054, that of the C 34 S emission line is estimated to be as small as τ ∼ 2.1 22.35 ∼ 0.09. We can estimate the molecular cloud mass using the C 34 S emission line data without the correction for the opti- Typical error of these masses is estimated to be ∼ 30 %.
The LTE molecular cloud mass is consistent with that from the C 32 S emission line observation. These are summarized in Table 2.
Using the same procedure and the C 32 S emission line data, the LTE molecular cloud masses of , respectively. These are also summarized in Table 2. The "Bridge" features are identified in these PV diagrams of Figures 6 and 7, which are connecting between M0.014-0.054 on the VP and the MFB (arrows, also see a red arrow in Figure 3b).
The "Bridge"s also correspond to the faint features seen in Figures 6c and 6e. They contain shocked molecular gas made by hard C-shock wave. Recent hydrodynamical simulation studies have shown that such connecting features in PV diagrams are reproduced as a characteristic feature of a CCC (e.g. , Haworth et al. 2015b). Therefore the "Bridge" features support the scenario that the MFB and VP collided each other and made the "Bridge" with the intermediate velocity between those of the MFB and VP, which should be caused by the momentum exchange of the molecular cloud in them. Especially, the feature around the angular offset of −60 is more prominent than that around the angular offset of −80 around in these emission lines. SiO molecules have been known to be taken in the mantle of interstellar dusts within 10 5 years and disappear from interstellar gas as mentioned previously. If the CCC was occurs once in such past, the difference between the"Bridge"s may be made by the elapsed time from the collision.
However, if the MFB and VP collided with the proper motion velocity of V = 40 × tan φ km/s before 10 5 yr, one molecular cloud is now separating from another molecular cloud by ∆d ∼ 4.1 × tan φ pc. The separation is corresponding to the angular separation of ∆θ ∼ 0.03 • × tan φ at the distance of 8 kpc, which can be easily distinguished in this observation although φ is unknown.
However, such large angular separations are not observed in the "Bridge"s connecting two clouds. There are at least two possibilities to explain it. As will be mentioned in Section 7, mGauss magnetic fields run along these filaments. In this case, the molecular cloud can move along the filaments but cannot move crossing them. Therefore, the molecular cloud in the Bridge would be fixed around the collision area by the magnetic field which are probably tangled by the collision. On the other hand, in the assumption of LTE and optically thin condition (e.g. Mezger & Henderson 1967). Therefore, the ratio at 86 GHz of ionized gas with up to T e < ∼ 1 × 10 4 K is estimated to be larger than unity, T B (H42α)/T B,cont > 1. The mean brightness temperatures of the H42α recombination line are expected to beT B (H42α) > 0.030 K in the object A andT B (H42α) > 0.020 K in the object B, respectively. Figure 8b shows the integrated intensity map with the velocity range of −25 to 0 km s −1 of the H42α recombination line. The velocity width is as large as that of the recombination line from the ionized gas at T e ∼ 1 × 10 4 K. The upper limits of the mean brightness temperatures in the H42α recombination line are 5σ = 0.019 K at the object A and 5σ = 0.019 K at the object B, respectively.
The integration areas are the same as those mentioned above. The objects A and B are not detected in the map. There is no ionized gas in the objects A and B of M0.014-0.054 above the detection limit of our observation. In the cases of the objects C, D, and E, we cannot exclude the existence of ionized gas by this procedure because of their weak intensities. However, the low T B [C 2 H]/T B [c-C 3 H 2 ] ratios suggest that the objects C, D, and E have no ionized gas as will be discussed in Subsection 6.4.
There are two possibilities to explain the situation that the ionized gas does not exist although the mm-wave continuum is detected. One possibility is that these continuum emissions are made by the low frequency extension of the dust emission shown in the JCMT map of Figure 2l. As mentioned previously, the continuum emissions of the objects A and B at 86 GHz correspond to "Double peaks" of the 850 µm dust emission withT B ∼ 0.3 K (see Figure 2l). If the dust β is ∼ 2, the 20 mean brightness temperatures at 86 GHz of the objects A and B are consistent with the dust emission at the low frequency. In addition, the objects C, D, and E also have the corresponding components in the 850 µm dust emission (see Figure 2l). Another possibility is that this emission is an artifact by contamination from other molecular emission lines. If so, the appearance of the 86 GHz continuum emission in Figure 8a should resemble those in the other molecular emission lines. However, they do not always resemble that of the 86 GHz continuum emission. Therefore, the second possibility seems unlikely. These will be discussed in the followings. These suggest that the object B has a hollow structure in these molecules. The objects A and B would be HMCs despite some different structures. The appearances in these emission lines resemble those in the HC 15 N emission line which is shown in Figure 9e. Chemical models of HMCs suggest that the HC 15 N emission line is enhanced in HMCs with the age of > ∼ 10 5 years (e.g. see Figure 11 in Stéphan et al. 2018). Therefore star formation activity may have fairly advanced in the HMCs. In addition, faint features in the SO, 34 SO and HC 15 N emission lines are also detected around the objects C, D, and E. This may suggest that these objects are in the similar evolutional stage to the objects A and B. respectively. Although the emissions of the HCOOH and CH 3 CHO emission lines are very weak, they are also centered in the object A. The association with the other objects is marginal. Figure   10c shows the wide field peak intensity map of the whole area in the HCOOH emission line. The emissions of HCOOH are identified only on several spots in the 50MC except for in M0.014-0.054.
These spots seem to correspond to HMCs identified by Miyawaki et al (2020). The concentration to HMCs of the HCOOH emission should be remarkable. The HCOOH emission line may be a good tracer of HMCs. Although the distribution in the CH 3 CHO emission line is not clear in the 50MC because of the contamination of the C 34 S emission line, the similar concentration might be seen.

Physical Properties of Hot Molecular Cores
the virial mass of the object A is estimated to be M vir = 5.0 × 10 3 M . It is difficult to estimate the virial mass of the object B using this formula since the shape of the C 34 S image is not spherical (see Figure 9b). Because the CCC is ongoing around the object A as mentioned previously, the observed velocity width may be widened, and the derived viral mass should be on the upper limit. Therefore, the virial parameter of the object A is estimated to be M vir /M LTE < ∼ 1. Although the fractional abundance of the CS molecule and the excitation temperature of the CS emission line have large ambiguity, the object A could be bound gravitationally. These masses are also summarized in Table 2.
The flux density at 850 µm in the object A is S ν ∼ 240 Jy (see Figure 2l). Because the beam size of JCMT is not sufficiently small to resolve the structure seen in the map and there are other components in the line-of-sight (see Figures 3 and 4), the flux density should be the upper limit.

HOCO + Ion
The HOCO + emission line has been detected toward the molecular clouds in the CMZ including the 50MC (e.g. Minh et al. 1991). Figure   There are some possibilities of the formation of the HOCO + ion which could make the distributions mentioned above. An ion-molecule reaction; HCO + + OH → HOCO + + H, might be possible (e.g. Fontani, et al. 2018) because OH radical should be abundant and the gas kinetic temperature is high in the Sgr A region. Because CO molecule is also abundant in the region, the reaction consuming the HOCO + ion, is also expected in the region (e.g. Sakai et al. 2008). In this case, the distribution of the HOCO + emission line would resemble that of the H 13 CO + emission line.
The HOCO + ion may be formed by the protonated reaction of CO 2 molecule. H + 3 ion is 27 abundant by the abundant cosmic ray in the Sgr A region (e.g. Oka et al. 2019). CO 2 molecules are evaporated extensively from the dust mantle by high gas kinetic temperature in M0.014-0.054 (T K 80 K in Ao et al. 2013). Therefore an ion-molecule reaction forming the HOCO + ion, is also expected in the region (e.g. Sakai et al. 2008). In this case, it is not necessary that the distribution of the HOCO + emission line resemble that of the H 13 CO + emission line. Note that these reactions are not mutually exclusive and other reactions forming and destroying HOCO + ion are also possible. SNR. This suggests that the physical interaction between the 50MC and Sgr A East SNR forms the HOCO + ions or at least assists the formation. There are two possibilities explaining the scenario.
The first one may be concerned in shock chemistry by the SNR. However, it is hard to specify the mechanism of the formation immediately. In the second one, abundant OH radicals made by cosmic ray of the SNR may form the ions through the reaction mentioned above (also see Tielens 2013).
On the other hands, the formation scenario of the features observed in M0.014-0.054 is not concerned probably in SNRs because there is no known SNR around it. However, the low frequency continuum emission associated with the south edge of M0.014-0.054 is seen. This is identified more clearly at 330 MHz as mentioned in Sec.2 (see Figure 1d). A possibility explaining the continuum emission would be that the CCC between the VP and MFB accelerates cosmic ray. The strong magnetic field (see Section 7) and large collision velocity (see Section 5) may enable such acceleration around M0.014-0.054 although it has not been observed in the disk region. The accelerated cosmic ray would increase the abundance of OH radicals simultaneously (also see Tielens 2013). Therefore the HOCO + ions would be formed through second scenario mentioned above.

CH3OH and SiO Molecules
As mentioned previously, the C-type shock wave propagating in the molecular cloud enhances the abundances of the CH 3 OH and SiO molecules.  Figure 9g is smaller than that in Figure 9h although the intensity in the former is larger than that in the latter. The difference between the two CH 3 OH maps is similar to that between the maps of the 28 SiO and 29 SiO emission lines, which are the major and minor isotopes (see Figures 9i and 9j). These would be explained by that the CH 3 OH (96.741 GHz) and 28 SiO emission lines are fairly optically thick around the object A but the CH 3 OH (97.583 GHz) and 29 SiO emission lines are optically thin. Figure   9h and 9j would indicate faithfully the abundance enhancements of these molecules. Therefore, we conclude that the shocked molecular gas is enhanced strongly in the object A although it is somewhat enhanced in other components. This is consistent with the detection of the Class-I methanol maser only in the object A as mentioned above.

Embedded Stars in the "Hot Molecular Core"s
The C 2 H and c-C 3 H 2 molecules would fairly survive even in the molecular clouds exposed to UV radiation than others (e.g. Cuadrado et al. 2015). Figures 11a and 11b   1.47 ± 0.04, respectively(see Figure 11c). The ratios in the objects C, and E are about ∼ 1.5. These are located on the intensity ridge of the molecular cloud in M0.014-0.054 (see Figure 11a and 11b).
The ratio of the object D is slightly higher than the others.
Although the photodissociation potential of the C 2 H molecule, 4.9 eV (C 2 H → C 2 + H), is similar to that of the c-C 3 H 2 molecule, 4.4 eV (c-C 3 H 2 → C 3 H + H), the ionization potential of the C 2 H molecule, 11.4 eV, is fairly higher than that of the c-C 3 H 2 molecule, 9.  The same velocity range as in other panels cannot be set because this emission line is at the edge of the observation frequency range. The faint mission is centered in the object A. The emission in the object B is not centered in it but traces the southern limb of the object. The faint emission is probably associated with the objects C, D and E. The objects A and B are detected in the dust continuum emission but not detected in the recombination line as shown in Subsection 6.1. The star formation activities had started and the surfaces of the embedded stars had been heated at least to several 100 K.
However, the existence of CCS molecules suggests that the chemical evolution by the star formation activity in the object A is still in the early stage (e.g. Hirahara et al. 1992).
On the other hand, the molecular emission lines including the CCS emission line are not centered in the object B. The observed features suggest that CCS molecules are still remained in the hollow structure of the molecular cloud around the embedded star. The star would emit soft UV radiation enough to dissociate the surrounding molecular cloud. This means that the chemical evolution in the object B is advanced comparing with that in the object A. If the star has already been in the main sequence stage, it may be a less massive star than B1 because it does not emit vast Lyman continuum emission enough to ionize the surrounding gas. In addition, if the faint features seen around the objects C, D, and E in the molecular emission lines including the CCS emission line are the remnants of the cradle molecular clouds, the chemical evolutions in these objects may be more advanced comparing with that in the object B.
7 Magnetic Field in the "Vertical Part"

Direction of the Magnetic Field
We used polarization data at 350µm with the Caltech Submillimeter Observatory 10-m telescope (CSO) to obtain the direction of the magnetic field, φ int , in the VP (Table 4 in Chuss et al. 2003).  Table 4 in Chuss et al. 2003), whic are overlaid on integrated intensity maps around the "Vertical Part" and M0.014-0.054 in the C 32 S J = 2 − 1 emission line with the velocity ranges of VLSR = −150 to 150 km s −1 (pseudo color) and VLSR = −40 to 10 km s −1 (contours), respectively.
The first contour and contour interval are both 25 K km s −1 .

33
The well-ordered B vectors suggest that the magnetic filed lines run along the filaments of the VP.
Such poloidal magnetic field (or perpendicular to the Galactic plane) has been usually observed in the non-thermal structures in the Galactic center region (e.g. Yusef-Zadeh, Morris, & Chance 1984, Tsuboi et al. 1986). Meanwhile the magnetic field in the Galactic center molecular clouds has been unveiled to be mainly troidal (or parallel to the Galactic plane) by IR observations (e.g. Nishiyama et al. 2010). The poloidal magnetic field in the molecular cloud is an unique case in the Galactic center region.

Strength of the Magnetic Field
The Chandrasekhar-Fermi method is used to estimate the magnetic field strength from the direction fluctuation of the magnetic filed line and internal gas kinematics (Chandrasekhar & Fermi 1953).
The magnetic field strength on the plane of sight is given by where ρ, δv, and δφ are gas density, velocity dispersion, and direction fluctuation of the magnetic field, respectively. This is converted to the following formula for molecular clouds (Crutcher et al. 2004); where ∆φ int [degree] is the direction fluctuation of the magnetic field, the n(H 2 )[cm −3 ] is the molecular gas density, which can be estimated by the critical density of the observed molecular line, and ∆v int [km s −1 ] is the FWHM velocity width of the line profile integrated in the area. The relation between the observed fluctuation, ∆φ obs , and ∆φ int , is given by where φ err is the mean error of the observation. The ∆φ obs is calculated from the observed magnetic field directions (Chuss et al. 2003) as the standard deviation. The intrinsic fluctuation of the direction of the magnetic field is estimated to be ∆φ int ∼ 9 deg in the VP (Chuss et al. 2003). The FWHM velocity width of the C 34 S emission line is derived to be ∆v int = 13.8 ± 0.8 km s −1 by Gaussianfit. The emission line is optically thin in the VP as mentioned previously. The sound velocity of C 34 S molecules is estimated to be c s,C34S = k B T K µ C34S m H 0.1 km s −1 at T K = 80 K where µ C34S is the molecular weight of a C 34 S molecule, µ C34S = 46, and m H is the mass of a Hydrogen atom. The broadening of the FWHM velocity width by the sound velocity is negligible. The effective critical density of the C 34 S emission line is assumed to be n(H 2 ) ∼ 5 × 10 4 cm −3 at T K = 80 K. Consequently, the magnetic field strength in the VP is estimated to be B ⊥ ∼ 3mGauss.
The Chandrasekhar-Fermi method is not valid when the magnetic field line is significantly fluctuated by the external perturbations such as HII regions and/or SNRs because the fluctuation of the magnetic field is assumed to be originated only by Alfvèn wave in the method. Because the CMZ is generally filled with the external perturbations, the magnetic field must suffer from such perturbations in varying degrees. The estimated value of the magnetic field strength should have large ambiguity.

Stability of Molecular Cloud Filaments
The critical mass per unit length of molecular filaments is given by where σ tot is the total velocity dispersion which is given by σ tot = σ 2 nonth + c 2 s + 1 2 V 2 A for a magnetized molecular cloud filament (e.g. Fiege & Pudritz 2000, Arzoumanian et al. 2013. When the LTE mass per unit length of the filament is larger than this limit, the filament can fragment into molecular cores along the axis of the filament (e.g. Inutsuka & Miyama 1997). In the case of the VP, the velocity dispersion of the nonthermal motion is calculated to be σ nonth = ∆v 2 int −c 2 s,C34S 8ln2 = 5.9 ± 0.3 km s −1 .
The sound velocity in the VP is estimated to be c s = k B T K µm H 0.5 km s −1 at T K = 80 K where µ is the mean molecular weight, µ = 2.8. While the Alfvèn velocity is estimated to be V A = 1300B √ n(H 2 ) 17 km s −1 at the magnetic field strength of B ∼ 3 mGauss and the molecular gas density of n(H 2 ) ∼ 5 × 10 4 cm −3 as mentioned in the previous subsection. The sound velocity is much smaller than the Alfvèn velocity and the velocity dispersion of the nonthermal motion. Therefore, the critical mass per unit length of the VP is estimated to be M line,crit = 2σ 2 tot G ∼ 8 × 10 4 M pc −1 . Because the magnetic field strength is not observed in the MFB, the critical mass per unit length cannot be derived. However, the lower limit can be estimated when the magnetic field is ignored. In the case of the MFB, the velocity dispersion of the nonthermal motion is calculated to be σ nonth = 5.1 ± 0.3 km s −1 . The critical mass per unit length of the MFB is M line,crit > ∼ 1 × 10 4 M pc −1 . On the other hands, the LTE mass per unit length of the VP is given by where M LTE is the LTE molecular cloud mass estimated in Subsection 4.4, M LTE ∼ 4 × 10 4 ( Tex 80 )M , L is the the length of the VP, L ∼ 8 pc, and n is the number of the observed filaments, n ∼ 3 (see Figures 3a and 4a). Therefore, the LTE mass per unit length of the VP is estimated to be M line,LTE ∼ 2 × 10 3 ( Tex 80 ) M pc −1 . Using the same procedure, the LTE mass per unit length of the MFB is estimated to be M line,LTE ∼ 3 × 10 3 (  the VP and MFB are perpendicular to the Galactic plane and parallel to it, respectively. Although the magnetic field in the MFB is not observed, it is expected that this is parallel to the Galactic plane because the magnetic field in the neighboring molecular clouds is usually along the Galactic plane (e.g. Nishiyama et al. 2010). The molecular clouds in them are thought to be along the magnetic fields. The molecular clouds in the VP are considered to be confined around the Galactic plane by the gravity although the molecular clouds in the MFB are considered to be able to move along the magnetic fields. b Schematic display of the VP and MFB after the collision. The viewpoints of the left and right panels are along the MFB and VP, respectively. The collision velocity should be larger than ∆ > ∼ 40 km s −1 because the SiO molecules seem to be abundant in the colliding area, which are confined in the tangled magnetic field there.
In the VP, the molecular clouds should converge kinematically along the magnetic fields and form massive molecular cloud cores around the collision area.
Successively, they form high mass protostars in their insides and evolve into HMCs. On the other hand, the molecular clouds in the MFB can move from the colliding area along the magnetic field because there is no confined molecular cloud like in the VP. Therefore the molecular clouds around the colliding area would become less dense than those in the VP and cannot form high mass protostars in their insides.
are not known, these LTE masses per unit length are the upper limits. Both the LTE masses per unit length of the VP and MFB are much smaller than their critical masses per unit length, respectively.
The filaments are stable for the fragmentation along the filaments. The star formation activity in the VP and MFB cannot start without any external trigger. In this observation, we found the evidences of the CCC including the "Bridge"s between the VP and MFB, and also found the evidences of the star formation including HMCs in M0.014-0.054, which is located at the intersection between the colliding filaments. Even for stable molecular filaments, the CCC is presumably make a role in the star formation as the external trigger (see also Figure 1 in Inoue &Fukui 2013). Although there are still many issues in massive star formation, the star formation induced by CCC would be a promising mechanism in the SgrAMC. Based on the observation results and discussion mentioned above, we would like to depict the spatial structure of the CCC between the VP and MFB and infer the possible scenario. As mentioned in the previous section, the VP and MFB, except for the colliding area, are stable molecular filaments against gravitational fragmentation, which are approximately perpendicular to the Galactic plane and parallel to it, respectively. The stabilities are secured by the strong magnetic field and/or large velocity dispersion in the filaments. Figure 14a shows the schematic display of the VP and MFB before the collision. The viewpoint of the panel is along the MFB. The directions of the magnetic fields observed by CSO is considered to indicates the large scale structure of the magnetic fields in the VP because the effective angular resolution is as large as FWHM 2 + Grid 2 ∼ 27 (Chuss et al. 2003). The magnetic field in the VP is approximately perpendicular to the Galactic plane (see Figure 13). The molecular filaments depicted in the CS emission line are along the magnetic field. Note that it has not been clear how the vertical magnetic field are originated and how molecular clouds are took into the VP. On the other hand, those in the MFB are not observed although the molecular filaments are approximately parallel to the Galactic plane (see Figure 5). However, because the magnetic field along the Galactic plane is observed in the neighboring molecular clouds (e.g. Nishiyama et al. 2010), such magnetic field may exist also in the MFB. Molecular clouds can generally move along the magnetic fields even if they have B ∼mGauss in the MFB. On the other hand, those in the VP may not be such case. As mentioned above, the molecular clouds in the VP would be distributed perpendicular to the Galactic plane. It is impossible that they orbit in Kepler motion keeping this distribution. The portions obeying the Kepler motion don't feel the gravity although the portions departing from it feel the gravity. If the molecular cloud near the the Galactic plane moves along the magnetic field, it must push up other clouds captured around the Galactic plane by the gravity. Therefore, the molecular clouds in the VP are confined around the Galactic plane by the gravity. Figure 14b shows the schematic display of the VP and MFB after the collision. The viewpoint of the left panel is along the MFB, which is the same as that in Figure 14a. While, that of the right panel is perpendicular to the Galactic plane, which is along the VP. The collision velocity should be larger than ∆ > ∼ 40 km s −1 because the SiO emission line is enhanced around the expected colliding area. The molecular filaments in the VP are seen to get tangled up around M0.014-0.054 although they are lined up perpendicular to the Galactic plane in the farther area from it (see Figures 2 and 3).
This probably shows that the magnetic field in the VP got tangled up in the colliding area because the filaments trace the magnetic field. In the VP, the molecular clouds should converge kinematically along the magnetic fields because the magnetic fields are deformed as shown in Figure 14b (C.f. Inoue &Fukui 2013), and form massive molecular cloud cores around the collision area. Because the shocked molecular gas made by the collision cannot expand crossing the filaments, this should be confined around the colliding area. The molecular cloud cores were massive enough to be bound gravitationally as mentioned in Subsection 6.2. Therefore, they form high mass protostars in their insides and evolve into HMCs. On the other hand, the molecular clouds in the MFB can escape from the colliding area along the magnetic field because there is no confined molecular cloud like in the VP as shown the right panel of Figure 14b. Therefore the molecular clouds around the colliding area would become less dense than those in the VP and cannot form high mass protostars in their insides.
This scenario explains that the HMCs are observed only in the VP.