A new method for measuring the 3D turbulent velocity dispersion of molecular clouds

Abstract

The structure and star formation activity of a molecular cloud are fundamentally linked to its internal turbulence. However, accurately measuring the turbulent velocity dispersion is challenging due to projection effects and observational limitations, such as telescope resolution, particularly for clouds that include non-turbulent motions, such as large-scale rotation. Here we develop a new method to recover the three-dimensional (3D) turbulent velocity dispersion (${\sigma }_{v,3D}$) from position-position-velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud and compare its intrinsic ${\sigma }_{v,3D}$ with three different measures of the velocity dispersion accessible in PPV space: 1) the spatial mean of the 2nd-moment map, ${\sigma }_i$, 2) the standard deviation of the gradient/rotation-corrected 1st-moment map, ${\sigma }_{(c-grad)}$, and 3) a combination of 1) and 2), called the 'gradient-corrected parent velocity dispersion', ${\sigma }_{(p-grad)}=({\sigma }_i^2+{\sigma }_{(c-grad)}^2{)}^{1/2}$. We show that the gradient correction is crucial in order to recover purely turbulent motions of the cloud, independent of the orientation of the cloud with respect to the line of sight (LOS). We find that with a suitable correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover ${\sigma }_{v,3D}$, with method 3 being the most robust and reliable. We determine the correction factor as a function of the telescope beam size for different levels of cloud rotation, and find that for a beam FWHM $f$ and cloud radius $R$, the 3D turbulent velocity dispersion can best be recovered from the gradient-corrected parent velocity dispersion via ${\sigma }_{v,3D}=[(-0.29\pm 0.26)f/R+1.93\pm 0.15]{\sigma }_{(p-grad)}$ for $f/R<1$, independent of the level of cloud rotation or LOS orientation.

15 pages, 10 figures. MNRAS, accepted

References in corpus (17)

• Theory of Star Formation
• The Statistics of Supersonic Isothermal Turbulence
• Analytical theory for the initial mass function: CO clumps and prestellar cores
• Modeling Collapse and Accretion in Turbulent Gas Clouds: Implementation and Comparison of Sink Particles in AMR and SPH
• A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence
• What determines the density structure of molecular clouds ? A case study of Orion B with Herschel
• The link between turbulence, magnetic fields, filaments, and star formation in the Central Molecular Zone cloud G0.253+0.016
• Modeling jet and outflow feedback during star cluster formation
• The sonic scale revealed by the world's largest supersonic turbulence simulation
• Unfolding the Laws of Star Formation: The Density Distribution of Molecular Clouds
• A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes
• Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths
• The SAMI Galaxy Survey: energy sources of the turbulent velocity dispersion in spatially-resolved local star-forming galaxies
• Testing Star Formation Laws on Spatially Resolved Regions in a $z\approx 4.3$ Starburst Galaxy
• An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds
• The role of initial magnetic field structure in the launching of protostellar jets
• Testing the Turbulent Origin of the Stellar Initial Mass Function

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