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.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor change
The Interstellar Medium has a fractal structure, in the sense that gas and dust distribute in a hierarchical and selfsimilar manner. Stars in new-born cluster probably follow the same fractal patterns of their parent molecular clouds. Moreover, it seems that older clusters tend to distribute their stars with radial density profiles. Thus, it is expected that clusters form with an initial fractal distribution of stars that eventually evolves toward centrally concentrated distributions. Is this really the case? This simple picture on to the origin and early evolution of star clusters and associations is very far from being clearly understood. There can be both young clusters exhibiting radial patterns and evolved clusters showing fractal structure. Additionally, the fractal structure of some open clusters is very different from that of the Interstellar Medium in the Milky Way. Here we summarize and discuss observational and numerical evidences concerning this subject.
There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. The measurement of the fractal dimension (D f ) of interstellar clouds is a simple way to characterize this fractal structure, but several factors, both intrinsic to the clouds and to the observations, may contribute to affect the values obtained. In this work we study the effects that opacity and noise have on the determination of D f . We focus on two different fractal dimension estimators: the perimeter-area based dimension (D per ) and the mass-size dimension (D m ). We first use simulated fractal clouds to show that opacity does not affect the estimation of D per . However, D m tends to increase as opacity increases and this estimator fails when applied to optically thick regions. In addition, very noisy maps can seriously affect the estimation of both D per and D m , decreasing the final estimation of D f . We apply these methods to emission maps of Ophiuchus, Perseus and Orion molecular clouds in different molecular lines and we obtain that the fractal dimension is always in the range 2.6 D f 2.8 for these regions. These results support the idea of a relatively high (> 2.3) average fractal dimension for the interstellar medium, as traced by different chemical species.
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