6. The specific angular momentum (\(J/M\)): \(J/M \propto \mathcal{G}R^2 \propto D\).
Analysis
The goal of this paper is to examine the velocity structure in the interiors of the coherent structures found in nearby molecular clouds (Paper I), and to provide updated measurements of the velocity gradient and the potentially related rotational motions to the analysis carried out by \citet{Goodman1993}. Since most of the dense cores included in the sample by \citet{Goodman1993} are later found to be coherent cores, measuring the same quantities with similar coherent structures would guarantee that a comparison with \citet{Goodman1993} is unbiased by any intrinsic difference between the two samples. Measuring the velocity gradient and the related quantities with coherent structures also lowers the chance that the observed velocity gradient arises from coincidence in a turbulent medium \citep{Burkert2000}, since the narrow linewidths of coherent structures indicate that these structures are single entities instead of a result of projection effects. The high brightness of NH3 hyperfine line emission at the locations of these coherent structures also indicates that the measured velocity and velocity dispersion likely come from materials associated with the dense cores.
Droplets from Paper I
The identification of coherent structures are done in Paper I, using data from the DR1 of the GAS observations \citep{Friesen2017}. The identification is primarily based on the change in velocity dispersion from supersonic to subsonic values and the existence of centrally concentrated distribution of NH3 hyperfine line emission. The details of the identification are found in §3.1 of Paper I.
In Paper I, a total of 18 coherent structures are identified, with 12 coherent structures found in the L1688 region of Ophiuchus and 6 coherent structures found in the B18 region of Taurus. The identified coherent structures have a typical size (radius) of \((4\pm1)\times 10^{-2}\) pc, a typical mass of \((3^{+3}_{-2}) \times 10^{-1}\) M⊙, and nearly thermal velocity dispersions. In the virial analysis presented in Paper I, these coherent structures are found to be gravitationally unbound. Instead, the confinement of these coherent structures are likely provided by the thermal and the non-thermal motions of the ambient gas–the "ambient gas pressure." Because of their small sizes and masses and the fact that the structures may be dispersed once the pressure confinement is removed, we term these coherent structures "droplets." The larger-scale coherent cores that have been known prior to Paper I (e.g. \citealp{Goodman1998}; \citealp{Caselli2002}; \citealp{Pineda2010}) and the droplets identified in Paper I form a single population of coherent structures.
The Velocity Gradient
The fitting for the velocity gradient, based on the fitted velocity centroid of the NH3 (1, 1) hyperfine line profile, is carried out using the