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 3D turbulent velocity dispersion (σv,3D) from position–position–velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud, and compare its intrinsic σv,3D with three different measures of the velocity dispersion accessible in PPV space: (1) the spatial mean of the 2nd-moment map, σi, (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’, $\sigma _{\mathrm{(p}-\mathrm{grad)}}=(\sigma _{\mathrm{i}}^2+\sigma _{(\mathrm{c}-\mathrm{grad)}}^2)^{1/2}$. 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. We find that with a suitable correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover σv,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 full width at half-maximum f and cloud radius R, the 3D turbulent velocity dispersion can best be recovered from the gradient-corrected parent velocity dispersion via $\sigma _{v,\mathrm{3D}}= \left[(-0.29\pm 0.26)\, f/R + 1.93 \pm 0.15\right] \sigma _{\mathrm{(p}-\mathrm{grad)}}$ for f/R < 1, independent of the level of cloud rotation or LOS orientation.

Widespread subsonic turbulence in Ophiuchus North 1

“…On the other hand, simulations have shown that turbulence can also cause small-scale fluctuations on the measured velocity centroids (Stewart & Federrath 2022), which should affect the patterns in our ∇ maps (Fig. 6).…”

“…The observed σ nt can also be higher than the intrinsic turbulence velocity dispersion, because the variation of LSR velocity centroids within the beam can partially arise from the ordered motions (e.g., rotation, shear motions) rather than pure turbulence (see also Stewart & Federrath 2022). Making use of the derived local velocity gradients, we could roughly estimate the contributions to the observed σ nt .…”

“…The representation of ∇ in the red and blue dashed boxes appears to be dominated by a northeast-southwest velocity gradient which is almost perpendicular to the filament's long axis and the plane-of-the-sky magnetic field. Such transverse velocity A82, page 7 of 15 A&A 663, A82 (2022) gradients can be caused by filament rotation (e.g., Zhang et al 2020;Stewart & Federrath 2022). However, ∇ in the red and blue dashed boxes show opposite directions, ruling out the filament's rigid rotation.…”

Widespread subsonic turbulence in Ophiuchus North 1

“…∇ in the red and blue dashed boxes appear to be dominated by a northeast-southwest velocity gradient which is almost perpendicular to the filament's long axis and the plane-of-the-sky magnetic field. Such transverse velocity gradients can be caused by filament rotation (e.g., Zhang et al 2020;Stewart & Federrath 2022). However, ∇ in the red and blue dashed boxes show opposite directions, ruling out the filament's rigid rotation.…”

Ion alfvén velocity fluctuations and implications for the diffusion of streaming cosmic rays

“…Hence, the dissipation in our turbulence is purely numerical. Because the ion Alfvén velocity fluctuations are dominated by the low-k modes (see Supplementary Figure S2, which shows that the rms statistics converge quickly as the number of grid elements in the simulations increase) the macroscopic diffusion of SCRs ought to be also controlled by the low-k modes (low in the case of observations may either correspond to modes comparable to the scale of the driving source, or the largest modes in the observational region that is being examined, see e.g., Federrath et al, 2016;Stewart and Federrath 2022). This means the exact prescription for dissipation ought not to matter for the ion Alfvén velocity statistics that we describe in this study.…”