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Fractal Dimension of Interstellar Clouds: Opacity and Noise Effects

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 (Df) 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 Df. We focus on two different fractal dimension estimators, namely, the perimeter-area-based dimension (Dper) and the mass-size dimension (Dm). We first use simulated fractal clouds to show that opacity does not affect the estimation of Dper. However, Dm 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 Dper and Dm, decreasing the final estimation of Df. We apply these methods to emission maps of the Ophiuchus, Perseus, and Orion molecular clouds in different molecular lines, and we obtain that the fractal dimension is always in the range 2.6 ≲ Df ≲ 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.