The Power Spectrum and Structure Function of the Gamma-Ray Emission from the Large Magellanic Cloud

Abstract

The Fermi-LAT observational data of the diffuse γ ray emission from the Large Magellanic Cloud (LMC) were examined to test for the existence of underlying long-range correlations. A statistical test applied to the data indicated that the probability that data are random is extremely small. Thus we proceeded and have used the counts-number data to compute 2D spatial autocorrelation, power spectrum, and structure function. The most important result of the present study is a clear indication for large-scale spatial underlying correlations. This is evident in all the functions mentioned above. The 2D power spectrum has a logarithmic slope of −3 on large spatial scales and a logarithmic slope of −4 on small spatial scales. The structure function has logarithmic slopes equaling 1 and 2 for the large and small scales, respectively. The logarithmic slopes of the structure function and the power spectrum are consistent. A plausible interpretation of these results is the existence of a large-scale supersonic compressible turbulence with a 3D logarithmic slope of −4 extending over scales comparable to the size of the LMC. Both the power spectrum and structure function exhibit steeper logarithmic slopes for smaller spatial scales. This is interpreted as an indication that the turbulent region has an effective depth of about 1.5 kpc.