We present a detailed analysis of narrow of NaI and KI absorption resonance lines toward nearly 40 T Tauri stars in Taurus with the goal of clarifying their origin. The NaI 5889.95 angstrom line is detected toward all but one source, while the weaker KI 7698.96 angstrom line in about two thirds of the sample. The similarity in their peak centroids and the significant positive correlation between their equivalent widths demonstrate that these transitions trace the same atomic gas. The absorption lines are present towards both disk and diskless young stellar objects, which excludes cold gas within the circumstellar disk as the absorbing material. A comparison of NaI and CO detections and peak centroids demonstrates that the atomic and molecular gas are not co-located, the atomic gas is more extended than the molecular gas. The width of the atomic lines corroborates this finding and points to atomic gas about an order of magnitude warmer than the molecular gas. The distribution of NaI radial velocities shows a clear spatial gradient along the length of the Taurus molecular cloud filaments. This suggests that absorption is associated with the Taurus molecular cloud. Assuming the gradient is due to cloud rotation, the rotation of the atomic gas is consistent with differential galactic rotation while the rotation of the molecular gas, although with the same rotation axis, is retrograde. Our analysis shows that narrow NaI and KI absorption resonance lines are useful tracers of the atomic envelope of molecular clouds. In line with recent findings from giant molecular clouds, our results demonstrate that the velocity fields of the atomic and molecular gas are misaligned. The angular momentum of a molecular cloud is not simply inherited from the rotating Galactic disk from which it formed but may be redistributed by cloud-cloud interactions.
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