A fractal analysis of the HI emission from the Large Magellanic Cloud

Fourier transform power spectra of the distribution of neutral hydrogen emi ssion in the Large Magellanic Cloud is approximately a power law over simil ar to 2 decades in length. Power spectra in the azimuthal direction look ab out the same as the rectilinear spectra. No difference is seen between powe r spectra of single-channel maps and power spectra of either the peak emiss ion map or the integrated emission map at the same location. There is a sli ght 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 interstell ar medium in the LMC is fractal, presumably the result of pervasive turbule nce, self-gravity, and self-similar stirring. The similarity between the ch annel 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 similar to 100 pc, could mark t he transition from large-scale emission that is relatively shallow on the l ine of sight to small-scale emission that is relatively thick on the line o f sight. Such a transition, if real, would provide a method to obtain the t hickness of a face-on galactic gas layer. To check this possibility, three- dimensional fractal models are made from the inverse Fourier transform of n oise with a power-law cutoff. The models are viewed in projection with a Ga ussian density distribution on the line of sight to represent a face-on gal axy disk with finite disk thickness. The density structure from turbulence is simulated in the models by using a log-normal density distribution funct ion with a scale factor dependent on the Mach number. Additional density st ructure from simulated H I phase transitions is included in some models. Af ter tuning the Mach number, galaxy thickness, and mathematical form of the phase transition, the models can be made to reproduce the observed LMC powe r spectra, the amplitude of the H I brightness fluctuations, and the probab ility 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 inte nsity variations cannot be achieved by turbulence alone; phase transitions are required. The character of the fractal H I structure in the LMC is view ed in another way by comparing positive and negative images of the integrat ed emission. For the isotropic fractal models, these two images have the sa me general appearance, but for the LMC they differ markedly. The H I is muc h more filamentary in the LMC than in an isotropic fractal, making the geom etric structure of the high-emission regions qualitatively different than t he geometric structure of the low-emission (intercloud) regions. The high-e mission regions are also more sharply peaked than the low-emission regions, suggesting that compressive events formed the high-emission regions, and e xpansion events, whether from explosions or turbulence, formed the low-emis sion regions. The character of the structure is also investigated as a func tion of scale using unsharp masks and enlargements with four different reso lutions. The circular quality of the low-emission regions and the filamenta ry quality of the high-emission regions is preserved on scales ranging from several tens to several hundreds of parsecs. The spatial scales for source s of turbulent energy input may be illustrated by rms variations in the pow er spectra with position in the galaxy. This rms decreases from similar to 0.6 at kpc scales to similar to 0.25 on similar to 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 cascade s from these large-scale energy inputs and additional energy sources with s maller sizes.