The structure and star-forming activity of a molecular cloud is fundamentally related to its internal turbulence. However, accurately measuring the dispersion of turbulent speed is difficult due to projection effects and observation limitations, such as telescope resolution, especially for clouds that include non-turbulent movements, such as than large-scale rotation. Here, we develop a new method to recover the 3D turbulent velocity dispersion (σv, 3d) from the position-position-speed (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud, and compare its intrinsicv, 3d with three different measurements of the dispersion of accessible speeds in the PPV space: (1) the spatial average of the map of the 2nd moment,I, (2) the standard deviation of the 1st moment map corrected for gradient / rotation,(c – grad), and (3) a combination of (1) and (2), called “gradient corrected parent velocity dispersion”, | $ sigma _ { mathrm {(p} – mathrm {grad)}} = ( sigma _ { mathrm {i}} ^ 2+ sigma _ {( mathrm {c} – mathrm {grad )}} ^ 2) ^ {1/2} $ | ⁠. We show that the correction of the gradient is crucial to recover purely turbulent movements of the cloud, independent of the orientation of the cloud with respect to the line of sight. We find that with an appropriate correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover σv, 3d, method 3 being the most robust and reliable. We determine the correction factor based on the size of the telescope beam for different levels of cloud rotation, and find that for a full width beam at half height F and ray of clouds R, the 3D turbulent speed dispersion can best be recovered from the gradient corrected parent speed dispersion via | $ sigma _ {v, mathrm {3D}} = left[(-0.29pm 0.26), f/R + 1.93 pm 0.15right] sigma _ { mathrm {(p} – mathrm {grad)}} $ | for F/R

© 2021 The Author (s) Posted by Oxford University Press on behalf of the Royal Astronomical Society

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