DENSE CORES IN DARK CLOUDS .6. SHAPES

Forty-eight line intensity maps of 16 dense cores in dark clouds are compared, based on observations in the 13 mm line of NH3 and in the 3 mm lines of CS and (CO)-O-18. The core maps have mean FWHM size 0.15 pc (NH3), 0.27 pc (CS), and 0.36 pc ((CO)-O-18). From line to line, the maps are similar in their position on the sky, in their axial ratio 0.5-0.6, and in the alignment of their long axes, usually within 20-degrees. Elongation is thus a common characteristic of dense cores. Therefore, cores are not generally in isolated equilibrium between self-gravity and isotropic random motions. Elongation is evident in cores with and without stars, so it precedes, rather than follows, star formation. The typical observed axial ratio can arise from identical oblate spheroids, if they are highly flattened, with axial ratio less than 0.1-0.3, or from prolate spheroids, if they are modestly elongated, with axial ratio 0.4-0.5. Six of the 16 cores are likely to be prolate because they align with, and are integral parts of, more extended structures seen in obscuration and/or CO line emission. The 10 other cores have less certain three-dimensional shape. Their elongation cannot generally arise from rotational flattening, because they lack the necessary velocity shift in magnitude, direction, or both. Their line widths, column densities, and sizes are equally consistent with virial equilibrium models of spheres, magnetized or rotating oblate spheroids, and finite segments of infinitely long prolate cylinders. The prevalence of prolate cores suggests that initial conditions for low-mass star formation should in some cases include prolate geometry. Prolate cores cannot be described by isolated equilibrium models, so models of prolate environments, and the development of prolate fragments, may be an important part of their description.