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Characterizing Cosmic-Ray Propagation in Massive Star-Forming Regions: The Case of 30 Doradus and the Large Magellanic Cloud

Using infrared, radio, and gamma-ray data,we investigate the propagation characteristics of cosmic-ray (CR) electrons and nuclei in the 30 Doradus (30\,Dor) star-forming region in the Large Magellanic Cloud (LMC) using a phenomenological model based on the radio-far-infrared correlation within galaxies. Employing a correlation analysis, we derive an average propagation length of \sim 100-140 pc for \sim 3 GeV CR electrons resident in 30 Dor from consideration of the radio and infrared data. Assuming that the observed gamma-ray emission towards 30 Dor is associated with the star-forming region, and applying the same methodology to the infrared and gamma-ray data, we estimate a \sim 20 GeV propagation length of 200-320 pc for the CR nuclei. This is approximately twice as large as for\sim 3 GeV CR electrons, corresponding to a spatial diffusion coefficient that is \sim 4 times higher, scaling as (R/GV)^δ with δ\approx 0.7-0.8 depending on the smearing kernel used in the correlation analysis. This value is in agreement with the results found by extending the correlation analysis to include \sim 70 GeV CR nuclei traced by the 3-10 GeV gamma-ray data (δ\approx 0.66+/-0.23). Using the mean age of the stellar populations in 30 Dor and the results from our correlation analysis, we estimate a diffusion coefficient D_{R} \approx 0.9-1.0 \times10^27 (R/GV)^{0.7} cm^2 s^-1. We compare the values of the CR electron propagation length and surface brightness for 30 Dor and the LMC as a whole with those of entire disk galaxies. We find that the trend of decreasing average CR propagation distance with increasing disk-averaged star formation activity holds for the LMC, and extends down to single star-forming regions, at least for the case of 30 Dor.