The power spectrum and structure function of the Gamma Ray emission from the Large Magellanic Cloud

TL;DR

This study analyzes Fermi-LAT gamma-ray data from the Large Magellanic Cloud, revealing large-scale correlations and turbulence characteristics in star-forming regions through power spectrum and structure function analysis.

Contribution

It provides the first detailed analysis of gamma-ray spatial correlations in the LMC, indicating large-scale turbulence and underlying physical processes.

Findings

Detection of large-scale spatial correlations in gamma-ray emission

Power spectrum slopes suggestive of compressible turbulence

Turbulent region depth estimated at about 1.5 kpc

Abstract

The Fermi-LAT observational data of the diffuse $\gamma$ 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 $\sim 10^{-99}$. 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 {\bf 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 {\it compressible turbulence} with a 3D logarithmic slope of -4 extending over the entire extent of the LMC. This may reflect the fact that the $\gamma$ Ray emission is in star forming regions, where jets and shocks are abundant. 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.