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

## TL;DR

This study investigates the internal velocity structures of small, pressure-dominated coherent structures called droplets in molecular clouds, analyzing their potential rotational motions and comparing their properties to larger dense cores.

## Contribution

It introduces a detailed analysis of sub-0.1 pc droplets, including velocity gradient measurements, rotational energy estimates, and orientation studies, expanding understanding of small-scale structures in star-forming regions.

## Key findings

- Droplets follow the same velocity gradient-size relation as larger cores.
- The ratio of rotational to gravitational energy in droplets is approximately 0.046.
- No clear correlation between velocity gradient directions and droplet elongations.

## Abstract

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, $\beta$, of $\sim 0.046$ for the droplets, and when including both droplets and larger-scale dense cores, we find $\beta \sim 0.039$. 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.