Top-left: Histrograms of the $T_{\mathrm{e}\mathrm{x}}^n/T_{\mathrm{e}\mathrm{x}}^i$ ratio values, where the ion is N₂D⁺(2 – 1) in black and N₂D⁺(1-0) in blue. The velocity data cubes are all smoothed to the spatial resolution of N₂D⁺(1 – 0) with HPBW of 34″. The mean and standard deviation of the distributions are given in Table C.1. The inset shows the scatter plot of the T_ex values and their uncertainties. The oblique line indicates the 1:1 relation. Top-right: Similar as the top-left panel for the τ values. Bottom-left: Scatter plot of the velocity dispersion. The oblique solid and dashed blue lines indicate the 1:1 and the 0.012 km/s relations, respectively. Bottom-right: Scatter plot of the centroid velocity of N₂D⁺(2 – 1) in red, pNH₂D in blue, and N₂D⁺(1 – 0) in purple versus the $N_{{\mathrm{H}}_2}$ column density derived from Herschel for data points with N_H2 > 1.7 × 10²² cm⁻². The vertical gray lines show the fitting uncertainties of V_lsr.