Cloud-Cloud Collision in the Galactic Center Arc

Figures 2a, 2b, 2c, 2d, and 2e show the integrated intensity maps with ALMA of M0.014-0.054 and the VP in the C³²S, C³⁴S, H¹³CO⁺, SiO, and CH₃OH (blended lines around 96.741 GHz) emission lines, respectively. Note that the data for the C³²S and C³⁴S maps are not combined with the single-dish data. The velocity range of each map is $V_{\mathrm{LSR}}=-25$ to $0$ km s^-1. The velocity range was determined from Figures 1b and 1c.

M0.014-0.054 and the VP are clearly detected in the map of the C³²S emission line. The VP is resolved into the bundles of the molecular filaments extending roughly from north to south. M0.014-0.054 is extended roughly from west to east and over the filaments. The filaments line up nearly at a right angle to M0.014-0.054 in the far distance area. However, they become disordered and tangled in the vicinity of M0.014-0.054. The positions of the peaks in the C³²S emission line do not correspond to those in the maps of the other emission lines which will be mentioned in the following part. This is probably because the C³²S emission line is partially optically thick in the region. M0.014-0.054 is also clearly detected in the maps of the C³⁴S and H¹³CO⁺ emission lines. They resemble each other very well. These show that dense molecular cloud with $n({\mathrm{H}}_{2})_{\mathrm{cl}}\sim 10^{5}$ cm^-3 is abundant in M0.014-0.054. In contrast, the molecular filaments in the C³⁴S and H¹³CO⁺ emission lines are fainter than those in the C³²S emission line, suggesting that this shows that the molecular cloud in the filaments is less dense than that in M0.014-0.054.

M0.014-0.054 is clearly detected in the maps of the SiO and CH₃OH emission lines. The detection in the SiO emission line shows that a strong C-shock wave ($\Delta V>30$ km s^-1) propagated within $10^{5}$ yr over the entire M0.014-0.054. Although the molecular filaments of the VP are also detected in the maps of these emission lines, they are faint on the whole. For example, the prominent parts are located around $l\sim 0^{\circ}.010,~{}b\sim-0^{\circ}.060$, $l\sim 0^{\circ}.015,~{}b\sim-0^{\circ}.087$, and $l\sim 0^{\circ}.025,~{}b\sim-0^{\circ}.035$ in the maps of the C³²S and H¹³CO⁺ emission lines. However, they almost disappear in the SiO emission line.

The C₂H (87.317 GHz) and c-C₃H₂ emission lines show a similar distribution in M0.014-0.054 (see Figures 2f and 2g). The other C₂H (87.329 GHz) emission line is also detected although this line is fainter. The VP almost disappears in the c-C₃H₂ emission line. It has been reported that the $N$[C₂H]/$N$[c-C₃H₂] column density ratio increases by the UV radiation ($\sim 32$ at the PDR edge; Cuadrado et al. (2015), up to $\sim 80$ at planetary nebulae; Schmidt, Zack, & Ziurys (2018)). Because the VP is less dense than M0.014-0.054, even the interior of the VP should have the high ratio. The c-C₃H₂ and HN¹³C emission lines show a similar distribution in M0.014-0.054 but the latter is faint (see Figures 2g and 2h). The HC¹⁵N and SO emission lines show a similar distribution (see Figures 2i and 2j). M0.014-0.054 is identified as a faint extended feature with a single compact peak in the maps of the HC¹⁵N and SO emission lines. The peak of the feature is located in the vicinity of strongest peaks in the other emission lines except for the C³²S emission line. The filaments of the VP disappears in the HC¹⁵N and SO emission lines.

The structures mentioned above including M0.014-0.054 and the filaments of the VP have no ionized gas counterparts which appears in the H42$\alpha$ recombination line (see Figure 2k). However, two distinct components in M0.014-0.054, are identified in the continuum emission at 86 GHz (see Figure 2l). The east one corresponds to the peak in the SO emission line. As mentioned previously, the SO emission line is a tracer of HMCs. Then the peaks would involve HMCs. The map of the 850 $\mu$m continuum with JCMT (Pierce-Price et al., 2000) is shown for comparison. The whole of M0.014-0.054 is also detected in the 850 $\mu$m continuum although the VP is not identified. Two peaks detected at 850 $\mu$m are associated with the peaks detected at 86 GHz.

Figures 3a and 4a show the integrated intensity maps with $V_{\mathrm{LSR}}=-25$ to $0$ km s^-1 in the C³²S $J=2-1$ and C³⁴S $J=2-1$ emission lines, respectively. Because the data of these maps are combined with the single-dish data, the mapping areas become narrow slightly. The appearances of the VP in these emission lines resemble each other very well. Figures 3b and 4b show the PV diagrams along the VP in the C³²S $J=2-1$ and C³⁴S $J=2-1$ emission lines, respectively. The sampling areas are shown as the rectangles in Figures 3a and 4a. In the PV diagrams, the VP is identified as a long feature with $V_{\mathrm{LSR}}\sim-30$ to $0$ km s^-1. There is no clear velocity gradient in the feature. The appearance and velocity gradient are consistent with those of the corresponding feature shown in Figure 1b. On the other hand, M0.014-0.054 is identified as a compact curved feature on the filaments of the VP (Figures 3b and 4b). This feature suggests that M0.014-0.054 had been affected by any external interaction (e.g. Haworth et al. (2015), Haworth et al. (2015b)). Additionally, a large extended feature with $V_{\mathrm{LSR}}\sim 30$ to $80$ km s^-1 is also identified. The appearances and kinematics of these features are consistent with those of the corresponding features shown in Figure 1b.

In the PV diagrams, there are two compact components with $V_{\mathrm{LSR}}\sim 20$ km s^-1 adjoining the extended feature mentioned above. In order to clarify the angular extension of these components, the integrated intensity maps with $V_{\mathrm{LSR}}=10$ 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 $V_{\mathrm{LSR}}\sim-50$ km s^-1 in the C³⁴S $J=2-1$ emission line (see Figure 4b). The feature is the contamination by the CH₃CHO $J_{K_{a},K_{c}}=5_{-2,4}-4_{-2,3}E$ emission line ($96.425620$ GHz) because this feature is not detected in Figure 3b.

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 5a and 5b show the integrated intensity maps around the MFB with $V_{\mathrm{LSR}}=-40$ to $10$ km s^-1 (pseudo color) and $V_{\mathrm{LSR}}=10$ to $35$ km s^-1 (contours) in the C³²S $J=2-1$ and C³⁴S $J=2-1$ emission lines, respectively. The MFB would be extended over the mapping area. The MFB is almost along the Galactic longitude but curved slightly. The MFB is resolved into the bundle of a few thin molecular filaments in these maps. The width of the MFB is changed periodically from $\sim 40\arcsec$ around $l\sim-0^{\circ}.035$ and $l\sim 0^{\circ}.005$ to $\sim 20\arcsec$ around $l\sim-0^{\circ}.050$ and $l\sim-0^{\circ}.025$. These filaments are seem to be twisted each other. The appearance of the MFB is similar to each other in both the emission lines. M0.014-0.054 is located around the apparent intersection of the MFB and VP. There is shocked molecular gas abundantly in M0.014-0.054 as shown in Section 4.1. Although the velocity of M0.014-0.054 is similar to that of the VP, it is $V_{\mathrm{LSR}}\sim 40$ km s^-1 different from that of the MFB. As will be discussed in detail later, M0.014-0.054 is connected to the MFB by the ”Bridge” on the PV diagram and a collisionally excited maser spot is also located in M0.014-0.054. These features demonstrate that the MFB and VP collided each other within $10^{5}$ years and M0.014-0.054 was made in the interaction by the CCC consequently. In addition, M0.014-0.054 is resolved into a series of compact features in these figures. The strongest feature (labeled A) and second one (labeled B) in the CS emission line maps are centered at $l\sim 0.021^{\circ},b\sim-0.051^{\circ}$ (the left circle) and $l\sim 0.014^{\circ},b\sim-0.052^{\circ}$ (the right circle), respectively.

The derivation of molecular cloud mass should suffer from the optical thickness of the observed emission line. The ratio of the observed brightness temperatures of the C³²S and C³⁴S emission lines is given by

where $T\mathrm{{}_{ex}}$ and $f$ are the excitation temperature and beam-filling factor of the emission line, respectively. The isotope abundance ratio of ³²S and ³⁴S in the molecular cloud is assumed to be equal to the natural abundance ratio of $22.35$¹¹1$https://physics.nist.gov/cgi-bin/Compositions/stand\_alone.pl$.

The mean line intensity ratio in M0.014-0.054 is calculated to be $R\sim 9.4$. Therefore the mean optical thickness of the C³²S emission line toward M0.014-0.054 is estimated to be $\tau\sim 2.1$ assuming that $T\mathrm{{}_{ex}(C^{32}S)}=T\mathrm{{}_{ex}(C^{34}S)}$ and $f(\mathrm{C^{32}S})=f(\mathrm{C^{34}S})$. The correction factor for the optical thickness of the C³²S emission line is $\frac{\tau}{1-e^{-\tau}}\sim 2.4$. The corrected integrated intensity of the object in the CS $J=2-1$ emission line is given by

The total number of the H₂ molecules in the object is given by

where $N{\mathrm{{}_{LTE}(H_{2})}}$ is the LTE molecular column density. Here the Einstein $A$ coefficient of the CS $J=2-1$ emission line is assumed to be $A_{21}=2.2\times 10^{-5}$ s^-1.

The excitation temperature of the CS $J=2-1$ emission line is assumed to be $T_{\mathrm{ex}}=80$ K ($T_{\mathrm{K}}=80$ K in Ao et al. (2013)). The fractional abundance of the CS molecule is assumed to be $X\mathrm{(CS)}=\frac{N\mathrm{(CS)}}{N\mathrm{(H_{2})}}=1\times 10^{-8}$, which is usually used for molecular clouds in the disk region. The LTE molecular cloud mass is given by

where $\mu$ is the mean molecular weight per H₂ molecule: $\mu=2.8$ in amu $=2.4\times 10^{-57}M_{\odot}$. The integrated intensity of the whole of M0.014-0.054 in the C³²S emission line is $\int_{\mathrm{object}}\int_{-40}^{10}T_{\mathrm{B}}\mathrm{(C^{32}S)}dvds=1.15\times 10^{40}\mathrm{[K~{}kms^{-1}cm^{2}]}$. The LTE molecular cloud mass is estimated to be $M_{\mathrm{C32S,LTE}}\simeq 5.3\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})[M_{\odot}]$.

Although the mean optical thickness of the C³²S emission line is fairly high in M0.014-0.054, that of the C³⁴S emission line is estimated to be as small as $\tau\sim\frac{2.1}{22.35}\sim 0.09$. We can estimate the molecular cloud mass using the C³⁴S emission line data without the correction for the optical thickness. The integrated intensity of the whole of M0.014-0.054 in the C³⁴S emission line is $\int\int_{-40}^{10}T_{\mathrm{B}}\mathrm{(C^{34}S)}dvds=1.22\times 10^{39}\mathrm{[K~{}kms^{-1}cm^{2}]}$. The LTE molecular cloud mass is estimated to be $M_{\mathrm{C34S,LTE}}\simeq 5.3\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})[M_{\odot}]$. The LTE molecular cloud mass is consistent with that from the C³²S emission line observation. These are summarized in Table 2.

Using the same procedure and the C³²S emission line data, the LTE molecular cloud masses of the VP and MFB are $M_{\mathrm{C32S,LTE}}\simeq 4.3\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})[M_{\odot}]$ and $M_{\mathrm{C32S,LTE}}\simeq 8.4\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})[M_{\odot}]$, respectively. Meanwhile, using the C³⁴S emission line data, the LTE molecular cloud masses of the VP and MFB are $M_{\mathrm{C34S,LTE}}\simeq 4.2\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})[M_{\odot}]$ and $M_{\mathrm{C34S,LTE}}\simeq 8.1\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})[M_{\odot}]$, respectively. These are also summarized in Table 2.

Figure 8a shows the continuum map at 86 GHz of M0.014-0.054. The noise level of the map is $1\sigma=0.01$ K in $T_{\mathrm{B}}$. M0.014-0.054 is detected as a series of the compact objects, A, B, C, D, and E. The eastern two objects are prominent, which correspond to “A” and “B” shown in Figures 5a and 5b. The cross in the map indicates the position, $l=0^{\circ}.02055~{}b=-0^{\circ}.05013$, of the CH₃OH $J=4_{-1}-3_{0}$ maser emission spot at 36.2 GHz in the velocity range of $V=0.0\pm 8.3$ km s^-1 (Yusef-Zadeh et al. (2013)). This is located in the object A. The mean brightness temperatures of the continuum emission in the objects A and B are $\bar{T}_{\mathrm{B,cont}}\sim 0.030\pm 0.002$ K and $\bar{T}_{\mathrm{B,cont}}\sim 0.020\pm 0.001$ K, respectively. The integration areas are shown as the circles in the map. The brightness temperature ratio of the recombination line to continuum emission is given by the formula, $T_{\mathrm{B,line}}/T_{\mathrm{B,cont}}\sim 3\times 10^{4}[T_{\mathrm{e}}/\mathrm{K}]^{-1.65}[\nu/\mathrm{GHz}]^{1.1}$ 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 $T_{\mathrm{e}}\lesssim 1\times 10^{4}$ K is estimated to be larger than unity, $T\mathrm{{}_{B}(H42\alpha)}/T_{\mathrm{B,cont}}>1$. The mean brightness temperatures of the H42$\alpha$ recombination line are expected to be $\bar{T}\mathrm{{}_{B}(H42\alpha)}>0.030$ K in the object A and $\bar{T}\mathrm{{}_{B}(H42\alpha)}>0.020$ 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 H42$\alpha$ recombination line. The velocity width is as large as that of the recombination line from the ionized gas at $T_{\mathrm{e}}\sim 1\times 10^{4}$ K. The upper limits of the mean brightness temperatures in the H42$\alpha$ recombination line are $5\sigma=0.019$ K at the object A and $5\sigma=0.019$ 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 $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂] 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 $850~{}\mu$m dust emission with $\bar{T}_{\mathrm{B}}\sim 0.3$ K (see Figure 2l). If the dust $\beta$ is $\sim 2$, the 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 $850~{}\mu$m 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.

Figures 8c and 8d show the enlarged integrated intensity maps of M0.014-0.054 in the SO and ³⁴SO emission lines with the velocity ranges of $V_{\mathrm{LSR}}=-25$ to $0$ km s^-1, respectively. As mentioned previously, the SO and ³⁴SO emission lines are good tracers of the HMC. A compact feature in the SO and ³⁴SO emission lines is located in the object A. In contrast, these emissions are associated with the object B but not centered in it. Or rather, these emissions traces the southern limb of the object. 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 HC¹⁵N emission line which is shown in Figure 9e. Chemical models of HMCs suggest that the HC¹⁵N emission line is enhanced in HMCs with the age of $\gtrsim 10^{5}$ 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, ³⁴SO and HC¹⁵N 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.

Figures 8e and 8f show the enlarged integrated intensity maps of M0.014-0.054 in the HCOOH and CH₃CHO(96.475523GHz) emission lines with the velocity ranges of $V_{\mathrm{LSR}}=-25$ to $0$ km s^-1, respectively. Although the emissions of the HCOOH and CH₃CHO 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 CH₃CHO emission line is not clear in the 50MC because of the contamination of the C³⁴S emission line, the similar concentration might be seen.

Figures 9a, 9b, 9c, and 9d show the enlarged integrated intensity maps of M0.014-0.054 in the C³²S, C³⁴S, H¹³CO⁺, and HN¹³C emission lines with the velocity ranges of $V_{\mathrm{LSR}}=-25$ to $0$ km s^-1. The image in the C³²S emission line has a ridge-like feature along the distribution of the objects A-E in the continuum map, which does not resemble the images in the other emission lines as mentioned previously. The image would suffer from large optical thickness of the C³²S emission line. The images in the C³⁴S, H¹³CO⁺ and HN¹³C emission lines resemble each other. These emissions have strong intensity peaks centered at the object A. Meanwhile, the emissions trace the southern limb of the object B rather than the continuum emission peak. There are also their emissions associated with the objects C, D, and E. These similar images would be caused by tracing the similar number density of Hydrogen molecules, $n({\mathrm{H}}_{2})\sim 10^{5}$ cm^-3. Figure 9e shows the map in the HC¹⁵N emission line with the same velocity range. The critical density of this emission line, $n({\mathrm{H}}_{2})_{\mathrm{crit}}\sim 10^{7}$ cm^-3, is higher than those of the others. This emission becomes strong at the object A, indicating that the object is filled by a very dense molecular cloud. While, although there is the emission along the south limb of the object B, it dose not centered at the object. The center part of the object B is not filled by such very dense molecular cloud.

The LTE molecular cloud masses of the objects A and B are estimated from the C³²S and C³⁴S emission line observations using the procedure shown in Section 4.4. The mean intensity ratios are calculated to be $R\sim 6.3$ in the object A and $R\sim 8.1$ in the object B, respectively. Then the optical thicknesses of the C³²S emission line are $\tau\sim 3.8$ in the object A and $\tau\sim 2.7$ in the object B, respectively. While those of the C³⁴S emission line are $\tau\sim 3.8/22.35=0.17$ in the object A and $\tau\sim 2.7/22.35=0.12$ in the object B, respectively. Because the C³²S emission line of the object is fairly thick, the LTE molecular cloud masses of the objects A and B are estimated from the C³⁴S emission line data using the optical thickness correction factors of $\frac{\tau}{1-e^{-\tau}}\sim 1.09$ and $\sim 1.06$, respectively. The integration velocity range is $V_{\mathrm{LSR}}=-40$ to $10$ km s^-1. The LTE molecular cloud masses of the objects A and B are $M_{\mathrm{LTE}}=1.3\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})M_{\odot}$ and $M_{\mathrm{LTE}}=1.2\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})M_{\odot}$, respectively. Although these masses are consistent with the LTE masses of the HMCs detected in the 50MC, $\bar{M}_{\mathrm{LTE}}\sim 8\times 10^{3}(\frac{T_{\mathrm{ex}}}{80})M_{\odot}$ (Miyawaki et al. (2020)), they are much larger than those of the molecular cloud cores detected in the 50MC, $\bar{M}_{\mathrm{LTE}}\sim 2\times 10^{2}(\frac{T_{\mathrm{ex}}}{50})M_{\odot}$ (Uehara et al. (2019)).

The mean physical radius of the object A is estimated to be $R_{\mathrm{HWHM}}=0.33$ pc as the half width at half maximum (HWHM) by 2-dimensional Gaussian fit for the C³⁴S image. The FWHM velocity width is estimated to be $V_{\mathrm{FWHM}}=8.5\pm 0.7$ km s^-1 by 1-dimensional Gaussian fit for the the C³⁴S line profile. Using the following formula for a spherical object,

the virial mass of the object A is estimated to be $M_{\mathrm{vir}}=5.0\times 10^{3}M_{\odot}$. It is difficult to estimate the virial mass of the object B using this formula since the shape of the C³⁴S 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 $M_{\mathrm{vir}}/M_{\mathrm{LTE}}\lesssim 1$. 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 $\mu$m in the object A is $S_{\nu}\sim 240$ 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. Assuming that the dust temperature is 33 K (see Fig. 3 in Etxaluze et al. (2016)) and the gas-to-dust ratio is 100, the gas mass is estimated to be $M\sim 7\times 10^{3}M_{\odot}$. This mass is consistent with the LTE molecular cloud mass and larger than the virial mass. This also indicates that the object A is bound gravitationally.

The C₂H and c-C₃H₂ 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 show the integrated intensity maps of M0.014-0.054 in the C₂H $N=1-0~{}J=3/2-1/2~{}F=2-1$ and c-C₃H₂ $J_{K_{a},K_{c}}=2_{1,2}-1_{0,1}$ emission lines. The velocity ranges are both $V_{\mathrm{LSR}}=-25$ to $0$ km s^-1. The distributions in these emission lines resembles those in the C³⁴S, H¹³CO⁺ and HN¹³C emission lines. The higher $J$ emission line, c-C₃H₂ $J_{K_{a},K_{c}}=4_{3,2}-4_{2,3}$, at $85.6564$ GHz is not detected. Other small hydrocarbon molecules, l-C₃H (97.996GHz and 98.012 GHz), C₄H (96.478 GHz), and C₅H (97.863 GHz) emission lines are not also detected. The transition of c-C₃H is not in our observation frequency range.

Figure 11c shows the ratio map of $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂] in M0.014-0.054. In addition, figures 12a and 12b show the spectra of the C₂H $N=1-0~{}J=3/2-1/2~{}F=2-1$ and c-C₃H₂ $J_{K_{a},K_{c}}=2_{1,2}-1_{0,1}$ emission lines on the objects A and B, respectively. The sampling areas are shown in Figures 11a and 11b as circles. The ratio in the object A is $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂]$=1.73\pm 0.03$. However, the ratio is seen to be inhomogeneous in the object. The ratio of the southeastern half is $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂]$=2.06\pm 0.05$ (see Figure 11c). The ratio of the northwestern half is $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂]$=1.47\pm 0.04$ (see Figure 11c). On the other hand, the ratio in the object B is $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂]$=1.53\pm 0.02$(see Figure 11c). The ratios of the southern half and northern half are $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂]$=1.31\pm 0.03$ and $=1.96\pm 0.05$. Although the integrated intensities of the emission lines in the northern half are weaker than those in the southern half, the ratio in the northern half is larger than that in the southern half. The ratios in the objects C, D, and E are $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂]$=1.40\pm 0.04$, $1.84\pm 0.04$, and $1.47\pm 0.04$, respectively(see Figure 11c). The ratios in the objects C, and E are about $\sim 1.5$. 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 C₂H molecule, 4.9 eV (C₂H $\rightarrow$ C₂ + H), is similar to that of the c-C₃H₂ molecule, 4.4 eV (c-C₃H₂ $\rightarrow$ C₃H + H), the ionization potential of the C₂H molecule, 11.4 eV, is fairly higher than that of the c-C₃H₂ molecule, 9.2 eV (van Hemert & van Dishoeck (2008)). The difference between the ionization potentials may raise the viability of C₂H molecule in the UV irradiated condition compared with that of the c-C₃H₂ molecule and increase the abundance ratio of $X$[C₂H]/$X$[c-C₃H₂]. Consequently, $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂] ratio would increase.

The high ratios measured in the southeastern half of the object A and the northern half of the object B are distinct from those in the northwestern half of the object A, the southern half of the object B, the object C and the object E. The $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂] ratios have been reported to be increased in UV irradiated regions, for example, $\sim 3$ at the Horse head PDR (Teyssier et al. (2004)). The measured high ratios may be consistent with that of the Horse head PDR. Similar UV irradiated condition is expected in both M0.014-0.054 and the Horse head PDR. Because the object B is adjacent to the object A, these are expected to be in the similar UV irradiated condition. If the UV photons with softer spectrum, for example $h\nu_{\mathrm{typ.}}\sim 4-5$ eV, are dominated in the objects, a slight difference between the photodissociation potentials of these molecules would decrease the abundance ratio between $X$[C₂H] and $X$[c-C₃H₂]. Consequently, $T_{\mathrm{B}}$[C₂H]/$T_{\mathrm{B}}$[c-C₃H₂] ratio is decreased. These suggest that the lower ratios of $\sim 1.5$ are mainly determined by the embedded stars or protostars.

Figure 11d shows the enlarged integrated intensity map of M0.014-0.054 in the CCS $N,J=7,6-6,5$ (86.181413 GHz) emission line with the velocity range of $V_{\mathrm{LSR}}=-18$ to $-8$ km s^-1. 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.

We used polarization data at $350\mu$m with the Caltech Submillimeter Observatory 10-m telescope (CSO) to obtain the direction of the magnetic field, $\phi_{\mathrm{int}}$, in the VP (Table 4 in Chuss et al. (2003)). Figure 13 shows the submillimeter polarization ($B$ vector) overlaid on the velocity integrated intensity map with the velocity ranges of $-150$ to $150$ km s^-1 (pseudo color) and $-40$ to $10$ km s^-1 (contours) in the C³²S $J=2-1$ emission line. There are two molecular cloud components on the line of sight, of which one belongs to the VP and another is seen in the velocity range of $30$ to $70$ km s^-1 (see Figures 3b and 4b). The observed polarization vectors are the sum of of the intrinsic polarization vectors originated by these components. Although the 50MC is dominant in the western half area, the VP could be identified as the bundle of filaments in the eastern half area. Therefore the observed $B$ vectors in the eastern half area are expected to be originated mainly by the VP. We consider that the observed $B$ vectors well trace the magnetic filed lines through the classical Davis-Greenstein mechanism, in which the observed $B$ vectors are thought to be parallel to the magnetic filed lines. 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.

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 $\rho$, $\delta v$, and $\delta\phi$ 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 $\Delta\phi_{\mathrm{int}}$ [degree] is the direction fluctuation of the magnetic field, the $n\mathrm{(H_{2})}$[cm^-3] is the molecular gas density, which can be estimated by the critical density of the observed molecular line, and $\Delta v_{\mathrm{int}}$[km s^-1] is the FWHM velocity width of the line profile integrated in the area. The relation between the observed fluctuation, $\Delta\phi_{\mathrm{obs}}$, and $\Delta\phi_{\mathrm{int}}$, is given by

where $\phi_{\mathrm{err}}$ is the mean error of the observation. The $\Delta\phi_{\mathrm{obs}}$ 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 $\Delta\phi_{\mathrm{int}}\sim 9$ deg in the VP (Chuss et al. (2003)). The FWHM velocity width of the C³⁴S emission line is derived to be $\Delta v_{\mathrm{int}}=13.8\pm 0.8$ km s^-1 by Gaussian-fit. The emission line is optically thin in the VP as mentioned previously. The sound velocity of C³⁴S molecules is estimated to be $c_{\mathrm{s,C34S}}=\sqrt{\frac{k_{\mathrm{B}}T_{\mathrm{K}}}{\mu_{\mathrm{C34S}}m_{\mathrm{H}}}}\simeq 0.1$ km s^-1 at $T_{\mathrm{K}}=80$ K where $\mu_{\mathrm{C34S}}$ is the molecular weight of a C³⁴S molecule, $\mu_{\mathrm{C34S}}=46$, and $m_{\mathrm{H}}$ 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 C³⁴S emission line is assumed to be $n\mathrm{(H_{2})}\sim 5\times 10^{4}$cm^-3 at $T_{\mathrm{K}}=80$ K. Consequently, the magnetic field strength in the VP is estimated to be $B_{\bot}\sim 3$mGauss.

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.

The critical mass per unit length of molecular filaments is given by

where $\sigma_{\mathrm{tot}}$ is the total velocity dispersion which is given by $\sigma_{\mathrm{tot}}=\sqrt{\sigma_{\mathrm{nonth}}^{2}+c_{\mathrm{s}}^{2}+\frac{1}{2}V_{\mathrm{A}}^{2}}$ 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 $\sigma_{\mathrm{nonth}}=\sqrt{\frac{\Delta v_{\mathrm{int}}^{2}-c_{\mathrm{s,C34S}}^{2}}{8ln2}}=5.9\pm 0.3$ km s^-1. The sound velocity in the VP is estimated to be $c_{\mathrm{s}}=\sqrt{\frac{k_{\mathrm{B}}T_{\mathrm{K}}}{\mu m_{\mathrm{H}}}}\simeq 0.5$ km s^-1 at $T_{\mathrm{K}}=80$ K where $\mu$ is the mean molecular weight, $\mu=2.8$. While the Alfvèn velocity is estimated to be $V_{\mathrm{A}}=\frac{1300B}{\sqrt{n({\mathrm{H_{2}}}})}\simeq 17$ km s^-1 at the magnetic field strength of $B\sim 3$ mGauss and the molecular gas density of $n(\mathrm{H_{2}})\sim 5\times 10^{4}$ 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 $M_{\mathrm{line,crit}}=\frac{2\sigma_{\mathrm{tot}}^{2}}{G}\sim 8\times 10^{4}$ $M_{\odot}$ 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 $\sigma_{\mathrm{nonth}}=5.1\pm 0.3$ km s^-1. The critical mass per unit length of the MFB is $M_{\mathrm{line,crit}}\gtrsim 1\times 10^{4}$ $M_{\odot}$ pc^-1.

On the other hands, the LTE mass per unit length of the VP is given by

where $M_{\mathrm{LTE}}$ is the LTE molecular cloud mass estimated in Subsection 4.4, $M_{\mathrm{LTE}}\sim 4\times 10^{4}(\frac{T_{\mathrm{ex}}}{80})M_{\odot}$, $L$ is the the length of the VP, $L\sim 8$ pc, and $n$ is the number of the observed filaments, $n\sim 3$ (see Figures 3a and 4a). Therefore, the LTE mass per unit length of the VP is estimated to be $M_{\mathrm{line,LTE}}\sim 2\times 10^{3}(\frac{T_{\mathrm{ex}}}{80})$ $M_{\odot}$ pc^-1. Using the same procedure, the LTE mass per unit length of the MFB is estimated to be $M_{\mathrm{line,LTE}}\sim 3\times 10^{3}(\frac{T_{\mathrm{ex}}}{80})$ $M_{\odot}$ pc^-1. Because the inclination angles of the VP and MFB 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.