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.