A New Method for Constraining Molecular Cloud Thickness: A study of
  Taurus, Perseus and Ophiuchus
  The core velocity dispersion (CVD) is a potentially useful tool for studying
the turbulent velocity field of molecular clouds. CVD is based on centroid
velocities of dense gas clumps, thus is less prone to density fluctuation and
reflects more directly the cloud velocity field. Prior work demonstrated that
the Taurus molecular cloud CVD resembles the well-known Larson's linewidth-size
relation of molecular clouds. In this work, we studied the dependence of the
CVD on the line-of-sight thickness of molecular clouds, a quantity which cannot
be measured by direct means. We produced a simple statistical model of cores
within clouds and analyzed the CVD of a variety of hydrodynamical simulations.
We show that the relation between the CVD and the 2D projected separation of
cores ($L_{2D}$) is sensitive to the cloud thickness. When the cloud is thin,
the index of CVD-$L_{2D}$ relation ($\gamma$ in the relation CVD$\sim
L_{2D}^{\gamma}$) reflects the underlying energy spectrum ($E(k)\sim
k^{-\beta}$) in that $\gamma\sim(\beta-1)/2$. The CVD-$L_{2D}$ relation becomes
flatter ($\gamma\to 0$) for thicker clouds. We used this result to constrain
the thicknesses of Taurus, Perseus, and Ophiuchus. We conclude that Taurus has
a ratio of cloud depth to cloud length smaller than about 1/10-1/8, i.e. it is
a sheet. A simple geometric model fit to the linewidth-size relation indicates
that the Taurus cloud has a $\sim 0.7$ pc line-of-sight dimension. In contrast,
Perseus and Ophiuchus are thicker and have ratios of cloud depth to cloud
length larger than about 1/10-1/8.
