A new method for spatially resolving the turbulence driving mixture in the ISM with application to the Small Magellanic Cloud

Turbulence plays a crucial role in shaping the structure of the interstellar medium. The ratio of the three-dimensional density contrast (\(\sigma_{\rho/\rho_0}\)) to the turbulent sonic Mach number (\(\mathcal{M}\)) of an isothermal, compressible gas describes the ratio of solenoidal to compressive modes in the turbulent acceleration field of the gas, and is parameterised by the turbulence driving parameter: \(b=\sigma_{\rho/\rho_0}/\mathcal{M}\). The turbulence driving parameter ranges from \(b=1/3\) (purely solenoidal) to \(b=1\) (purely compressive), with \(b=0.38\) characterising the natural mixture (1/3~compressive, 2/3~solenoidal) of the two driving modes. Here we present a new method for recovering \(\sigma_{\rho/\rho_0}\), \(\mathcal{M}\), and \(b\), from observations on galactic scales, using a roving kernel to produce maps of these quantities from column density and centroid velocity maps. We apply our method to high-resolution HI emission observations of the Small Magellanic Cloud (SMC) from the GASKAP-HI survey. We find that the turbulence driving parameter varies between \(b\sim 0.3\) and \(b\sim 1.0\) within the main body of the SMC, but the median value converges to \(b\sim0.51\), suggesting that the turbulence is overall driven more compressively (\(b>0.38\)). We observe no correlation between the \(b\) parameter and HI or H\(\alpha\) intensity, indicating that compressive driving of HI turbulence cannot be determined solely by observing HI or H\(\alpha\) emission density, and that velocity information must also be considered. Further investigation is required to link our findings to potential driving mechanisms such as star-formation feedback, gravitational collapse, or cloud-cloud collisions.