2 Cloud rotational observations

The data summarised in Table 1 has been compiled from published sources dating between 1972 and the present. It includes a broad range of information for clouds where velocity gradients have been attributed to rotation. In a few cases, explanations for these gradients have additionally been sought in terms of other mechanisms, and certain of these suggestions are indicated in the footnotes. In particular (and as noted in Sect. 1), the superposition of kinematically separate components (see discussion in Sect. 4), or tilted aspherical outflows may lead to very similar projected kinematic structures; it is often extremely difficult to distinguish between these various mechanisms.

For the large majority of sources in the present sample, however, rotation has been regarded as the most likely and sole explanation for observed large scale velocity gradients.

Certain of the clouds have been observed several times, although for these cases we have included only a representative sample of observations in Table 1. As a consequence, the table includes data referring to 111 individual sets of observations, and 156 differing sources and/or spatially distinct regions within the same source.

The various data headings may be summarised as follows. Columns 1-7 refer to the cloud designation, co-ordinates, distance, LSR velocity, and line width as detailed in the various references cited in Col. 15; in a very few cases, we have altered quoted distances where previous estimates conflict with more recent values. Similarly, we have (where possible) used line widths corresponding to low optical depth transitions. The dimension L (Col. 7) refers to the projected region of cloud over which gradients were measured. Column 8 indicates the molecular transitions used in acquiring the results, whilst $\Omega$ corresponds to the angular rotational velocity deduced from projected velocity gradients. $\Gamma$ is an estimate of cloud axial ratio (major axis/minor axis) based on the spatial variation in emission contours over the projected region of rotation, whilst M is the non-virial mass of the zone based (usually) on estimates of column density (values $M_{\rm ast}$ (in parentheses) correspond to the embedded stellar mass). $\Theta$ (Col. 12) represents the projected orientation of the angular velocity vector $\Omega$ with respect to the galactic plane, whereby a vector $\Omega$ oriented towards the north galactic pole is taken to have an inclination $\Theta=90^\circ$, whilst one pointing towards the south galactic pole has $\Theta=270^\circ$. The orientation of this vector relative to the cloud major axis is also represented (Col. 13), whereby we indicate those clouds for which $\Omega$ resides within $30^\circ$ of the minor axis (designated Y; that is, the maximum velocity gradient lies along the cloud major axis), and those cases where this is not the case (designated N).

Finally, we have attempted to broadly categorise the regions based largely on descriptions provided in the references. Thus, MS, MI, and ML are, respectively, isolated small, intermediate, and large clouds (this latter category also including, and largely consisting of complexes). Condensations within such regions are adjectivaly indicated through the appended letter C (thus MIC is a condensation within an intermediate sized cloud), whilst filamentary cloud structures are represented by F. Finally, clumps are designated by CL, whilst rings and disks are indicated by D/R.

Note that in order to represent this data on a uniform basis, it has often been necessary to evaluate parameters using published maps and spectra, rather than employing values quoted in the respective references.

  

Table 2: Parametric trends in molecular clouds

Finally, the results of a least squares analysis for selective logarithmic rotational parameters is summarised in Table 2, where F(y) = a + bF(x), and we include determinations for angular momentum J, specific angular momentum J/M, non-virial mass M, and angular velocity $\Omega$. N is the total sample number, and r is the correlation coefficient. The nature of these trends will be discussed more fully in the proceeding sections.