The Fractal Dimension of Projected Clouds

Abstract

The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a tri-dimensional fractal distorts its measured properties. Here we use simulated fractal clouds to study the relationship between the tri-dimensional fractal dimension (D_f) of modeled clouds and the dimension resulting from their projected images. We analyze different fractal dimension estimators: the correlation and mass dimensions of the clouds, and the perimeter-based dimension of their boundaries (D_per). We find the functional forms relating D_f with the projected fractal dimensions, as well as the dependence on the image resolution, which allow to estimatethe "real" D_f value of a cloud from its projection. The application of these results to Orion A indicates in a self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value higher than the result D_per+1 = 2.3 some times assumed in literature for interstellar clouds.

27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor changes

References in corpus (5)

• A Fractal Origin for the Mass Spectrum of Interstellar Clouds: II. Cloud Models and Power Law Slopes
• Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence
• Self-gravity as an explanation of the fractal structure of the interstellar medium
• Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium
• Scaling Relations for Turbulence in the Multiphase Interstellar Medium

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