To identify the fibers seen in the PPV space, we apply the agglomerative clustering implementation in the scikit-learn package
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https://scikit-learn.org/stable/
 (Pedregosa et al. 2011) to the PPV points for each transition. The agglomerative clustering algorithm groups points in N-dimensional space via recursively merging points or clusters (i.e., groups of points) into higher-order clusters such that the pair of points or clusters to be merged minimally increases the linkage distance (Ward 1963). To make the clustering procedure adjustable, we introduce two parameters t

x
 and t

v
 in defining the linkage distance of two PPV points:
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slink,ij=[tx(xi−xj)]2+yi−yj2+vi−vjtv2,

where x and y are the spatial coordinates in physical units, and v is the LoS velocity. For each transition, we adjust the parameters (t

x
, t

v
) and run the algorithm with the modified coordinates of the PPV points as input. By practice we found that the best values of (t

x
, t

v
) for identifying the fiber structures in the H13CO+, N2H+, and NH2D data are (2.8 pc, 1.0 km s−1pc−1), (0.5 pc, 0.8 km s−1pc−1), and (1.0 pc, 2.0 km s−1pc−1), respectively, with which the DR21(OH) ridge is decomposed into 3, 3, and 2 fibers in the PPV space. Figure 4 shows the identified fibers projected on the PoS and their PV plots, with the color coding representing different velocities. In the H13CO+ data, three fibers with roughly north–south orientations are clearly seen; these fibers have distinct velocities, forming a trident with the junction approximately coincident with the DR21(OH) core. We name the three fibers as f1, f2, and f3 from east to west. Among the fibers, f1 is clearly tracing the central-densest part of the dust ridge well known from previous dust-continuum observations (Motte et al. 2007; Hennemann et al. 2012); f2 and f3 are relatively new, not seen in the dust emission, but previous single-dish H13CO+ (1 − 0) observations showed that the ridge slight moves from east to west with the velocity increasing from −5 km s−1 to 0 km s−1 (Schneider et al. 2010), in a manner consistent with the positions and velocities of the three fibers identified here. In particular, f3 is also discernible in the H13CO+(1 − 0) map in Schneider et al. (2010; see their Figure A3), though at a much lower resolution. Given the LoS velocities of the fibers and the existing observations suggesting that the DR21(OH) ridge is in a global collapse (Schneider et al. 2010), one may expect that f1 and f3 are on the far side and the near side along LoS, respectively, and that f2 is probably in the middle. The three fibers in the N2H+ line are less prominent yet are still clearly seen with positions and velocities consistent with those in the H13CO+ line, indicating that they are tracing the same physical entities. While the whole f1 and the southern part of f3 are detected, f2 is fragmented into several parts, probably due to the regional variations of the abundances of the two molecular tracers. On the other hand, in the NH2D line, the whole f1 (though fragmented into parts) and the northern part of f2 are detected, and f3 is completely absent. The appearance of the fibers are also different from that in the H13CO+ and N2H+ lines by their more compact morphologies and smaller widths. In addition, in contrast to what is seen in the H13CO+ and N2H+ lines, the southern end of f1 in the NH2D line is shifted to the west and does not coincide with the DR21(OH) core, indicating that active high-mass star formation has destroyed most of NH2D. The detection information of the fibers in the three transitions is summarized in Table 1.
Citation: Motte et al. 2007
Citation function: Uses