Hierarchical structure analysis of interstellar clouds using nonorthogonal wavelets

We introduce the use of Laplacian pyramid transforms, a form of nonorthogonal wavelets, to analyze the structure of interstellar clouds. These transforms are generally better suited for analyzing structure than orthogonal wavelets because they provide more flexibility in the structure of the encoding functions - here circularly symmetric bandpass filters. This technique is applied to CO maps of Barnard 5. In the (C-13)O maps, for example, we identify 60 different fragments and clumps, as well as several cavities, or bubbles. Many features show evidence of hierarchical structure, with most of the power in the largest wavelengths. The clumps have a more chaotic structure at small wavelengths than expected for Kolmogorov turbulence, and a mass distribution proportional to M exp -5/3. The structure analysis is consistent with a picture where gravity, energy injection, compressible turbulence, and coalescence play an important role in the dynamics of B5.