THE EFFECT OF PROJECTION ON DERIVED MASS-SIZE AND LINEWIDTH-SIZE RELATIONSHIPS

Rahul Shetty,Jens Kauffmann,Alyssa A. Goodman,Erik W. Rosolowsky,Michael L. Norman,David C. Collins

doi:10.1088/0004-637x/712/2/1049

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.

Highlights

Though stars form in the densest cores within much more voluminous molecular clouds, the motions and forces within the parent cloud at various scales significantly shape, if not control, the evolution of the cores as they form stars
The best fit mass-size indices from the column density map and the PPV cube are similar to those derived from many observations of molecular clouds (e.g. Kauffmann et al 2010b, in preparation, Larson 1981)
We assess the effect of geometric projection in deriving cloud properties, using a simulation of a molecular cloud

Summary

Introduction

Though stars form in the densest cores within much more voluminous molecular clouds, the motions and forces within the parent cloud at various scales significantly shape, if not control, the evolution of the cores as they form stars. Observations, in particular of dust emission and extinction and of a variety of molecular lines, have provided much information about the internal structure and dynamics of molecular clouds. The scaling between the mass M and velocity dispersion σ with size scale is often studied, in both numerical models and observations of star forming regions Larson’s second law, relating σ with the ratio of M/R, is a consequence of the other two, and is often used to study the dynamic nature of the cloud, through the virial parameter α = 5σ2R/(MG). Assumptions about the virial theorem that are commonly employed to derive α, e.g. that the surface terms are negligible compared to the volume terms, may be erroneous, as discussed by Ballesteros-Paredes (2006) and Dib et al (2007)

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