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Droplets II: Internal Velocity Structures and Potential Rotational Motions in Pressure-dominated Coherent Structures

We present an analysis of the internal velocity structures of the newly identified sub-0.1 pc coherent structures, droplets, in L1688 and B18. By fitting 2D linear velocity fields to the observed maps of velocity centroids, we determine the magnitudes of linear velocity gradients and examine the potential rotational motions that could lead to the observed velocity gradients. The results show that the droplets follow the same power-law relation between the velocity gradient and size found for larger-scale dense cores. Assuming that rotational motion giving rise to the observed velocity gradient in each core is a solid-body rotation of a rotating body with a uniform density, we derive the "net rotational motions" of the droplets. We find a ratio between rotational and gravitational energies, $β$, of $\sim 0.046$ for the droplets, and when including both droplets and larger-scale dense cores, we find $β\sim 0.039$. We then examine the alignment between the velocity gradient and the major axis of each droplet, using methods adapted from the histogram of relative orientations (HRO) introduced by Soler et al. (2013). We find no definitive correlation between the directions of velocity gradients and the elongations of the cores. Lastly, we discuss physical processes other than rotation that may give rise to the observed velocity field.