Interstellar CH absorption in the diffuse interstellar medium along the sight-lines to G10.6-0.4 (W31C), W49N, and W51

We report the detection of the ground state N, J = 1, 3/2 -> 1, 1/2 doublet of the methylidyne radical CH at similar to 532 GHz and similar to 536 GHz with the Herschel/ HIFI instrument along the sight-line to the massive star-forming regions G10.6-0.4 (W31C), W49N, and W51. While the molecular cores associated with these massive star-forming regions show emission lines, clouds in the diffuse interstellar medium are detected in absorption against the strong submillimeter background. The combination of hyperfine structure with emission and absorption results in complex profiles, with overlap of the different hyperfine components. The opacities of most of the CH absorption features are linearly correlated with those of CCH, CN, and HCO+ in the same velocity intervals. In specific narrow velocity intervals, the opacities of CN and HCO+ deviate from the mean trends, giving rise to more opaque absorption features. We propose that CCH can be used as another tracer of the molecular gas in the absence of better tracers, with [CCH]/[H-2] similar to 3.2 +/- 1.1 x 10(-8). The observed [CN]/[CH], [CCH]/[CH] abundance ratios suggest that the bulk of the diffuse matter along the lines of sight has gas densities nH = n(H) + 2n(H-2) ranging between 100 and 1000 cm(-3).