A Fractal Analysis of the H I Emission from the Large Magellanic Cloud

Fourier transform power spectra of the distribution of neutral hydrogen emission in the Large Magellanic Cloud is approximately a power law over ~2 decades in length. Power spectra in the azimuthal direction look about the same as the rectilinear spectra. No difference is seen between power spectra of single-channel maps and power spectra of either the peak emission map or the integrated emission map at the same location. There is a slight steepening of the average one-dimensional and two-dimensional LMC power spectra at high spatial frequencies. Delta-variance methods also show the same power-law structure. These results suggest that most of the interstellar medium in the LMC is fractal, presumably the result of pervasive turbulence, self-gravity, and self-similar stirring. The similarity between the channel and integrated maps suggests they cover about the same line-of-sight depth. The slight steepening of the power spectra at high spatial frequency, corresponding to wavelengths smaller than ~100 pc, could mark the transition from large-scale emission that is relatively shallow on the line of sight to small-scale emission that is relatively thick on the line of sight. Such a transition, if real, would provide a method to obtain the thickness of a face-on galactic gas layer. To check this possibility, three-dimensional fractal models are made from the inverse Fourier transform of noise with a power-law cutoff. The models are viewed in projection with a Gaussian density distribution on the line of sight to represent a face-on galaxy disk with finite disk thickness. The density structure from turbulence is simulated in the models by using a log-normal density distribution function with a scale factor dependent on the Mach number. Additional density structure from simulated H I phase transitions is included in some models. After tuning the Mach number, galaxy thickness, and mathematical form of the phase transition, the models can be made to reproduce the observed LMC power spectra, the amplitude of the H I brightness fluctuations, and the probability distribution function for brightness. In all cases, the H I structure arises from a relatively thin layer in the LMC; the thick part of the H I disk has little spatial structure. The large amplitude of the observed intensity variations cannot be achieved by turbulence alone; phase transitions are required. The character of the fractal H I structure in the LMC is viewed in another way by comparing positive and negative images of the integrated emission. For the isotropic fractal models, these two images have the same general appearance, but for the LMC they differ markedly. The H I is much more filamentary in the LMC than in an isotropic fractal, making the geometric structure of the high-emission regions qualitatively different than the geometric structure of the low-emission (intercloud) regions. The high-emission regions are also more sharply peaked than the low-emission regions, suggesting that compressive events formed the high-emission regions, and expansion events, whether from explosions or turbulence, formed the low-emission regions. The character of the structure is also investigated as a function of scale using unsharp masks and enlargements with four different resolutions. The circular quality of the low-emission regions and the filamentary quality of the high-emission regions is preserved on scales ranging from several tens to several hundreds of parsecs. The spatial scales for sources of turbulent energy input may be illustrated by rms variations in the power spectra with position in the galaxy. This rms decreases from ~0.6 at kpc scales to ~0.25 on ~20 pc scales. The large-scale variations are probably from known supershells. The smaller scale variations could be the result of a combination of turbulent cascades from these large-scale energy inputs and additional energy sources with smaller sizes.