The Effect of Projection on Derived Mass-Size and Linewidth-Size Relationships

TL;DR

This study investigates how geometric projection influences the derived mass-size and linewidth-size relationships in molecular clouds, revealing that projection effects can significantly distort these correlations and impact virial analysis interpretations.

Contribution

It demonstrates the impact of projection effects on Larson's laws using hydrodynamic simulations, highlighting potential misinterpretations in observational analyses.

Findings

Projection causes smaller scale clumps to appear more massive in 2D maps.

Linewidth-size relationships differ between 3D simulation and synthetic observations.

Virial parameters are similar in 3D and projected data, but linewidth and mass-size discrepancies caution against simple virial analysis.

Abstract

Power law mass-size and linewidth-size correlations, two of "Larson's laws," are often studied to assess the dynamical state of clumps within molecular clouds. Using the result of a hydrodynamic simulation of a molecular cloud, we investigate how geometric projection may affect the derived Larson relationships. We find that large scale structures in the column density map have similar masses and sizes to those in the 3D simulation (PPP). Smaller scale clumps in the column density map are measured to be more massive than the PPP clumps, due to the projection of all emitting gas along lines of sight. Further, due to projection effects, structures in a synthetic spectral observation (PPV) may not necessarily correlate with physical structures in the simulation. In considering the turbulent velocities only, the linewidth-size relationship in the PPV cube is appreciably different from that measured from the simulation. Including thermal pressure in the simulated linewidths imposes a minimum linewidth, which results in a better agreement in the slopes of the linewidth-size relationships, though there are still discrepancies in the offsets, as well as considerable scatter. Employing commonly used assumptions in a virial analysis, we find similarities in the computed virial parameters of the structures in the PPV and PPP cubes. However, due to the discrepancies in the linewidth- and mass- size relationships in the PPP and PPV cubes, we caution that applying a virial analysis to observed clouds may be misleading due to geometric projection effects. We speculate that consideration of physical processes beyond kinetic and gravitational pressure would be required for accurately assessing whether complex clouds, such as those with highly filamentary structure, are bound.