Examining Turbulence in Galactic Molecular Clouds - II: Continuity of Turbulence Cascading in a Portion of the Local Arm

TL;DR

Ma, Chen, and Wang analyze turbulence in a Local Arm segment using MWISP $^{12}$CO (J=1-0) data, treating the region as a continuous turbulent medium by slicing the PPV cube into equal-kinematic-distance layers. They compute velocity structure functions and spatial power spectra across slices, finding a cascade from $\sim 400$ pc down to sub-parsec scales and SPS slopes that approach theoretical expectations, with scale-dependent variation. Extended self-similarity shows cloud-to-cloud velocity differences follow the same scaling as intra-cloud turbulence, implying a large-scale driving process. Velocity increments exhibit strong intermittency well described by a Normal Inverse Gaussian distribution, while density increments show weaker non-Gaussian tails; a simple energetic argument suggests Galactic differential rotation can supply the large-scale shear needed to maintain the cascade, though real ISM complexities warrant further study.

Abstract

We use $^{12}$CO (J=1-0) MWISP data to study turbulence in a segment of the Local Arm. Velocity slices at different kinematic distances show similar spatial power spectra (SPSs) and structure functions (SFs), demonstrating that the entire region forms a single turbulent field with a cascade extending from $\sim 400$ pc to sub-parsec scales. The SPS slopes of both the intensity and velocity fields exhibit a systematic scale dependence that approaches the values expected from turbulence models. Cloud-to-cloud VSFs follow similar trends to the pixel-by-pixel VSFs in the extended self-similarity (ESS) scaling, indicating that velocity differences among clouds arise from large-scale turbulent motions. Velocity- and intensity-increment maps reveal filamentary, intermittent structures. The PDFs of the velocity increments display strong non-Gaussianity and are well fitted by the normal inverse gaussian (NIG) distribution, whereas the intensity increments show much weaker tails. A simple energetic estimate suggests that Galactic differential rotation is able to supply the large-scale shear required to maintain the observed turbulence.

Figures (7)

• Figure 1: (a) Integrated intensity map of $^{12}$CO ($J$=1-0) emission in the selected region of the second Galactic quadrant, integrated over the velocity range from -27 to 10 km s$^{-1}$. (b) Longitude-velocity ($lon$-$v$) diagram of the $^{12}$CO emission, integrated over the latitude range from -5$^{\circ}$ to 5$^{\circ}$. The dashed lines indicate the velocity boundaries used to define different kinematic distance slices based on the Galactic rotation curve from Reid2019.
• Figure 2: Second-order (p=2) SFs of (a) the gradient-corrected intensity-weighted velocity (moment 1) and (b) the integrated intensity (moment 0) for different slices. The color of each curve indicates the kinematic distance of the corresponding slice. The theoretical slopes from the Kolmogorov1941a and Boldyrev2002a models, as well as the average slope for individual molecular clouds from Ma2025 are shown as arrows for reference.
• Figure 3: SPSs of (a) the intensity-weighted velocity and (b) the integrated intensity for different velocity slices. The color of each curve indicates the kinematic distance of the corresponding slice. The theoretical slopes from the Kolmogorov1941a and Burgers bec2007burgers models are shown as dashed lines.
• Figure 4: Extended self-similarity (ESS) scaling analysis, showing the relationship between S$_i$ (for $i = 1, 2$) and S$_3$ for the molecular gas. The dots represent the VSFs calculated pixel by pixel from the $^{12}$CO centroid velocity map, while the cyan triangles and orange circles denote the VSFs derived from the $^{12}$CO and $^{13}$CO molecular-cloud catalogs identified by the DBSCAN algorithm, respectively. The dashed lines indicate the best-fit power-law relations for the VSFs of the velocity map derived within $[-27, 10]$ km s$^{-1}$. The corresponding power-law exponents are labeled above each dashed line.
• Figure 5: Tests of sampling effects on the VSFs and SPSs using MHD simulation data. (a) and (b): Examples of masks generated using threshold values of $10^{5}$ and $10^{5.5}$, respectively (physical meaning of the values is not important). (c) and (d): The resulting 2nd-order VSFs and SPSs computed from the masked velocity fields. Different colors correspond to different masking thresholds.