Study of HI Turbulence in the SMC Using Multi-point Structure Functions

TL;DR

This study uses high-resolution GASKAP-HI data and multi-point structure functions to dissect HI turbulence in the Small Magellanic Cloud. By comparing two-point and seven-point SFs of the velocity-integrated HI intensity $W_{\rm HI}$, the authors identify a break in the seven-point SF at $l_{\rm SF}\sim34$–$84$ pc (median $\sim50$ pc) and measure a small-scale slope of $SF_{7pt}(8\text{ pc}-50\text{ pc})\approx1.55\pm0.14$, indicating genuine small-scale turbulence at ~50 pc scales. They find significant correlations between the seven-point SF slopes and stellar feedback indicators, such as H$\alpha$ emission, YSO counts, and HI shell counts, suggesting feedback drives or modulates small-scale HI turbulence. The sonic Mach numbers are subsonic ($M_s<1$), compatible with a warm neutral medium-dominated HI, and subregional analyses reveal spatial variation tied to local feedback environments. Overall, the work demonstrates the utility of multi-point SFs in isolating small-scale turbulence and links local feedback to turbulence characteristics in a low-metallicity, nearby galaxy.

Abstract

Turbulence in the interstellar medium (ISM) plays an important role in many physical processes, including forming stars and shaping complex ISM structures. In this work, we investigate the HI turbulent properties of the Small Magellanic Cloud (SMC) to reveal what physical mechanisms drive the turbulence and at what scales. Using the high-resolution HI data of the Galactic ASKAP (GASKAP) survey and multi-point structure functions (SF), we perform a statistical analysis of HI turbulence in 34 subregions of the SMC. Two-point SFs tend to show a linear trend, and their slope values are relatively uniform across the SMC, suggesting that large-scale structures exist and are dominant in the two-point SFs. On the other hand, seven-point SF enables us to probe small-scale turbulence by removing large-scale fluctuations, which is difficult to achieve with the two-point SFs. In the seven-point SFs, we find break features at scales of 34-84 pc, with a median scale of $\sim$50 pc. This result indicates the presence of small-scale turbulent fluctuations in the SMC and quantifies its scale. In addition, we find strong correlations between slope values of the seven-point SFs and the stellar feedback-related quantities (e.g., H$α$ intensities, the number of young stellar objects, and the number of HI shells), suggesting that stellar feedback may affect the small-scale turbulent properties of the HI gas in the SMC. Lastly, estimated sonic Mach numbers across the SMC are subsonic, which is consistent with the fact that the HI gas of the SMC primarily consists of the warm neutral medium.

Figures (6)

• Figure 1: GASKAP + Parkes H i integrated intensity map of the SMC with a pixel size of 28$\hbox{$^{\prime\prime}$}$. Pixels (white) with S/N $<$ 5 are masked. The 35 subregions where we calculate structure functions are overlaid on the $W_{\rm HI}$ map. Each subregion (840 pc $\times$ 840 pc) is indicated by its corresponding number. Subregion 35 (marked with a large cross) was discarded in our analysis since more than 50% of the pixels in this region have a low S/N ($<$5). The left and middle dashed rectangles show the Wing and the Bar locations, respectively. The directions to the Magellanic Stream and the Large Magellanic Cloud are indicated by two arrows mcclure2018gerrard2023. The small crosses are the representative star-forming regions in the SMC takekoshi2017saldano2023.
• Figure 2: YSOs (blue X mark) and H i shell (black cross) distributions on the convolved H$\alpha$ image (color scale). The H i column density distribution is shown in its H i contour (gray) levels of 2 and 4 $\times$ 10$^{21}$ cm$^{-2}$.
• Figure 3: Cartoon showing various results of multi-point SF calculations for a complex structure, including small- and large-scale fluctuations. This image is reproduced based on Figure 1 of cho2019. (a) In the case of complete removal of large-scale fluctuation (Case A), the multi-point SF becomes flat beyond the scale length of the small-scale fluctuation ($l_{\rm SF}$). (b) In the case of partial removal of large-scale fluctuation (Case B), the multi-point SF shows a break feature and keeps increasing afterwards.
• Figure 4: Two- and seven-point SFs for the entire $W_{\rm HI}$ map of the SMC. Two- and seven-point SFs are shown in black and green, respectively. In the log-log plane, while the two-point SF is linear, the seven-point SF show a break (red cross) at a spatial scale of $\sim$50 pc. The slope of the two-point SF was estimated in the range of 8 pc to 1890 pc, just before the appearance of the turnover (green dashed line). Its slope value is 1.39 $\pm$ 0.01. The slope of the seven-point SF estimated over small scales (8$-$50 pc) is 1.55 $\pm$ 0.14.
• Figure 5: Results of the two-point SFs (black line) for the 34 subregions, overlaid on the $W_{\rm HI}$ map of the SMC. Their error bars are shown in black, but most of the error bars are quite small. The linear fit (red dashed lines) was performed in each subregion. The slope values (black) estimated from the two-point SFs range from $\sim$0.69 to $\sim$1.62.