The Fractal Dimension of Projected Clouds

The interstellar medium seems to have an underlying fractal structure whichcan be characterized through its fractal dimension. However, interstellarclouds are observed as projected two-dimensional images, and the projection ofa tri-dimensional fractal distorts its measured properties. Here we usesimulated fractal clouds to study the relationship between the tri-dimensionalfractal dimension (D_f) of modeled clouds and the dimension resulting fromtheir projected images. We analyze different fractal dimension estimators: thecorrelation and mass dimensions of the clouds, and the perimeter-baseddimension of their boundaries (D_per). We find the functional forms relatingD_f with the projected fractal dimensions, as well as the dependence on theimage resolution, which allow to estimatethe "real" D_f value of a cloud fromits projection. The application of these results to Orion A indicates in aself-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a valuehigher than the result D_per+1 = 2.3 some times assumed in literature forinterstellar clouds.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor change