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 ($σ_{v,3D}$) from position-position-velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud and compare its intrinsic $σ_{v,3D}$ with three different measures of the velocity dispersion accessible in PPV space: 1) the spatial mean of the 2nd-moment map, $σ_i$, 2) the standard deviation of the gradient/rotation-corrected 1st-moment map, $σ_{(c-grad)}$, and 3) a combination of 1) and 2), called the 'gradient-corrected parent velocity dispersion', $σ_{(p-grad)}=(σ^2_i+σ^2_{(c-grad)})^{1/2}$. 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 $σ_{v,3D}$, 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 $σ_{v,3D}=[(-0.29\pm0.26)f/R+1.93\pm0.15]σ_{(p-grad)}$ for $f/R<1$, independent of the level of cloud rotation or LOS orientation.