MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

To study the structure of interstellar matter we have applied the conc ept of fractal curves to the brightness contours of maps of interstell ar clouds and from these estimated the fractal dimension for some of t hem. We used the so-called perimeter-area relation as the basis for th ese estimates. We concentrate on the influence of measurement limitati ons on the accuracy of the determination of the fractal dimension from observations. Problems and pitfalls are discussed in detail. We show that to obtain reliable results the signal-to-noise ratio (if defined properly for extended objects) must be higher than about 20. This is n ot a strict rule, however. Further, not only is a large-enough dynamic range of enclosed contour areas needed (a criterion which is related to the signal-to-noise ratio), but it is necessary (but not necessaril y sufficient) that the smallest area is at least 25 pixels. Even when all these criteria are fulfilled, the accuracy one can expect for the fractal dimension is only of the order of 0.05. Estimates of the fract al dimension are presented for two different cloud types, high-velocit y HI clouds (HVCs) and infrared cirrus. These estimates generally rang e between 1.35 and 1.5, somewhat higher than found in previous, simila r studies. However, for the one object that this and other studies hav e in common, we find the same value of 1.23.