Introduction
In early 1980s, NH3 was identified as an excellent tracer of the cold, dense gas associated with highly extinguished compact regions visible on photographic plates for the preceding 75 years (e.g. \citealp{1927cdos.book.....B}). These regions were named "dense cores" by \citet{1983ApJ...264..517M}, and their properties were studied and documented in a series of papers throughout the 1980s and 1990s whose titles began with "Dense Cores in Dark Clouds:" \citep{1983ApJ...264..517M,1983ApJ...266..309M,1983ApJ...270..105M,1983ApJ...270..589B,1988ApJ...324..907M,1991ApJ...376..561M,1992ApJ...384..523F,1993ApJ...406..528G,1994ApJ...433...96V,1994ApJ...433..117L,1998ApJ...506..743B,2000ApJ...532.1038V,2002ApJ...572..238C}. Essentially since the start of that series, astronomers have used the "dense core" paradigm as a way to think about the small (~0.1 pc; \citealp{1983ApJ...266..309M}), prolate but roundish (aspect ratio near 2; \citealp{1991ApJ...376..561M}), quiescent (velocity dispersion near-thermal; \citealp{1992ApJ...384..523F}), blobs of gas that have the ability to form stars like the Sun. Whether these individual cores exist inside of the clusters where more massive stars form (ref xx), how long-lived and/or transient these cores might be (ref xx); and how they relate to the ubiquitous filamentary structure inside star forming regions (ref xx) are all still open questions. Nonetheless, a blob of gas collapsing under its own weight to form a star remains as the central theme in the minds of most astronomers thinking about "dense cores." An important detail of this simple picture is that that angular momentum associated with the gas that collapses causes a disk to form around the star as it accretes matter from its surroundings. The properties of the disk will be in large part set by the rotational properties of the collapsing gas, which in turn set limits on the planet formation process that takes place in that disk. Thus, there has historically been great interest in measuring the angular momentum of dense cores.
The first comprehensive work on measuring velocity gradients as a means to estimate angular momentum in dense cores, was presented in \citet{Goodman1993}, using measurements of 43 NH3 cores. Since then, that work, now nearly a quarter-century old, has become the standard reference for angular momentum values input to models of star and planet formation. But, in that quarter-century, our view of dense cores and star forming regions has changed significantly, both observationally and theoretically. High-resolution, extended, observations at a variety of wavelengths have shown that cores are the densest parts of a network of filamentary structures, often seen at an intersection of filaments. (ref xx). Detailed spectral-line mapping has shown that at least some cores exhibit a rapid "transition" from a "turbulent" regime well-described by Larson's relations \citep{1981MNRAS.194..809L} to a "coherent" regime \citep{1998ApJ...504..223G} where observed line widths stop decreasing with size, and instead plateau at a value that is nearly purely thermal \citep{2010ApJ...712L.116P}. And, many simulations (e.g. Smith 20xx, xx) show that "the mass" of a dense core is not a well-established, long-lived, number, since the material that defines the "core" seems to come and go due to the nature of turbulence (xx), and potentially also due to competitive accretion (xx).
This paper is designed to re-evaluate the role of rotation in star and planet formation, by taking a new, contextualized, look at the velocity gradients observed on scales from those probed in \citet{Goodman1993} down to recent VLA observations (Pineda et al., 2017). Critically, we measure and interpret gradients in high-resolution single-dish (GBT) observations of 18 dense cores observed as part of the GAS Survey (Paper I; \citealp{2017ApJ...843...63F}). The GAS data fills in the gap in spatial scales (resolution approaching ~ 0.02 pc at the distance of the molecular cloud in Ophiuchus and Taurus) between the \citet{1993ApJ...406..528G} measurements and interferometric observations. At the low-mass end of that GAS population, we can find objects that exhibit a transition to velocity coherence, but whose mass is very small, which raises questions about the nature of "dense cores" and about the meaning of the velocity gradients found to be associated with gas at various scales.
It is possible, as \citet{Burkert:2000cm} speculated, that velocity gradients observed are just small field-of-view samples of the velocity field in a turbulent cascade. So, we should consider how such a "turbulence" oriented view would change the use of gradient-derived estimates of "rotation" as inputs to star and planet formation models. If a core is observed already in the process of forming a star (hosting a protostellar source, and/or shown to be infalling), then perhaps a gradient-based estimate of the rotation (really, angular momentum) in that core is still a relevant input to models of the core's collapse. But, what if a core is still accreting a good deal of material from its surroundings? How might that accretion change the ratio of rotational to gravitational energy in the entity that eventually collapses to form a star/disk system? And, even more curiously, how should we think about gradients measured for tiny bits of NH3 gas whose mass are likely much less than the stars in whose formation they may eventually be involved? We see several such tiny bits in the GAS data exhibiting the same kind of transition to velocity coherence as do larger star-forming cores, and we speculate toward the end of this paper about the nature of these "droplets" in the process of star formation.
We present information in this paper in the following order. First, in §\ref{797350}, we explain the nature of the GAS Survey, and of the Herschel data used to estimate the mass of gas associated with the NH3 structures probed by GAS. Then, we explain the selection criteria, based on density morphology and velocity coherence, used to select which GAS objects we continue to study (§\ref{988456}). Next, we summarize the methods used here to measure velocity gradients (§\ref{649016}). We then present the measured gradients in the context of the (larger-scale) \citet{Goodman1993} values, and connect them also to estimates of angular momentum made using NH3 observations at the VLA (Pineda et al., 2017), in §\ref{501029}. We show that the properties of the smaller objects we find in the GAS data form natural continuations, along relatively well-defined power-laws, of those studied at lower resolution and sensitivity earlier. Given, though, that observed relations seem so continuous even down to the scales of very small "droplets" unlikely to form stars on their own (§\ref{577174}), we consider in extra detail the role that pressure confinement (see \citealp{2017ApJ...846..144K} and the comparison we presented in Paper I) may play in creating or maintaining small concentrations of dense gas in the discussion in §\ref{870494}.
This is the second part of a two-part analysis of basic properties of the droplets. Below we refer to the first paper as Paper I.
Data
Green Bank Ammonia Survey (GAS)
The GBT Ammonia Survey (GAS; \citealp{Friesen2017}) is a Large Program at the Green Bank Telescope (GBT) to map all Gould-Belt star forming regions with AV ≥ 7 mag visible from the northern hemisphere in emission from NH3 and other key molecules. The data used in this work are from the first data release (DR1) of the GAS that includes four nearby star forming regions: L1688 in Ophiuchus, B18 in Taurus, NGC1333 in Perseus, and Orion A.