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We developed methods for mapping spatial variations of the spatial power spectrum (SPS) and structure function slopes, with the goal of connecting the statistical properties of neutral hydrogen (H i) with the turbulent drivers. The new methods were applied to the H i observations of the Small and Large Magellanic Clouds (SMC and LMC). In the case of the SMC, we find highly uniform turbulent properties of H i, with no evidence for local enhancements of turbulence due to stellar feedback. These properties could be caused by a significant turbulent driving on large scales. Alternatively, the significant line-of-sight depth of the SMC could be masking out localized regions with a steeper SPS slope caused by stellar feedback. In contrast to the SMC, the LMC H i shows a large diversity in terms of its turbulent properties. Across most of the LMC, the small-scale SPS slope is steeper than the large-scale slope due to the presence of the H i disk. On small spatial scales, we find several areas of localized steepening of the SPS slope around major H ii regions, with the 30 Doradus region being the most prominent. This is in agreement with predictions from numerical simulations, which suggest a steepening of the SPS slope due to stellar feedback that erodes and destroys interstellar clouds. We also find a localized steepening of the large-scale SPS slope in the outskirts of the LMC. This is likely caused by the flaring of the H i disk, or alternatively, by ram-pressure stripping of the LMC disk due to the interactions with the surrounding halo gas.