Quantifying Observational Projection Effects Using Molecular Cloud
  Simulations
  The physical properties of molecular clouds are often measured using
spectral-line observations, which provide the only probes of the clouds'
velocity structure. It is hard, though, to assess whether and to what extent
intensity features in position-position-velocity (PPV) space correspond to
"real" density structures in position-position-position (PPP) space. In this
paper, we create synthetic molecular cloud spectral-line maps of simulated
molecular clouds, and present a new technique for measuring the reality of
individual PPV structures. Our procedure projects density structures identified
in PPP space into corresponding intensity structures in PPV space and then
measures the geometric overlap of the projected structures with structures
identified from the synthetic observation. The fractional overlap between a PPP
and PPV structure quantifies how well the synthetic observation recovers
information about the 3D structure. Applying this machinery to a set of
synthetic observations of CO isotopes, we measure how well spectral-line
measurements recover mass, size, velocity dispersion, and virial parameter for
a simulated star-forming region. By disabling various steps of our analysis, we
investigate how much opacity, chemistry, and gravity affect measurements of
physical properties extracted from PPV cubes. For the simulations used here,
our results suggest that superposition induces a ~40% uncertainty in masses,
sizes, and velocity dispersions derived from 13CO. The virial parameter is most
affected by superposition, such that estimates of the virial parameter derived
from PPV and PPP information typically disagree by a factor of ~2. This
uncertainty makes it particularly difficult to judge whether gravitational or
kinetic energy dominate a given region, since the majority of virial parameter
measurements fall within a factor of 2 of the equipartition level alpha ~ 2.
