On the Three-Dimensional Structure of Local Molecular Clouds
  We leverage the 1 pc spatial resolution of the Leike et al. 2020 3D dust map
to characterize the three-dimensional structure of nearby molecular clouds ($d
\lesssim 400$ pc). We start by "skeletonizing" the clouds in 3D volume density
space to determine their "spines," which we project on the sky to constrain
cloud distances with $\approx 1\%$ uncertainty. For each cloud, we determine an
average radial volume density profile around its 3D spine and fit the profiles
using Gaussian and Plummer functions. The radial volume density profiles are
well-described by a two-component Gaussian function, consistent with clouds
having broad, lower-density outer envelopes and narrow, higher-density inner
layers. The ratio of the outer to inner envelope widths is $\approx 3:1$. We
hypothesize that these two components may be tracing a transition between
atomic and diffuse molecular gas or between the unstable and cold neutral
medium. Plummer-like models can also provide a good fit, with molecular clouds
exhibiting shallow power-law wings with density, $n$, falling off like $n^{-2}$
at large radii. Using Bayesian model selection, we find that parameterizing the
clouds' profiles using a single Gaussian is disfavored. We compare our results
with 2D dust extinction maps, finding that the 3D dust recovers the total cloud
mass from integrated approaches with fidelity, deviating only at higher levels
of extinction ($A_V \gtrsim 2 - 3$ mag). The 3D cloud structure described here
will enable comparisons with synthetic clouds generated in simulations,
offering unprecedented insight into the origins and fates of molecular clouds
in the interstellar medium.
