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

Using infrared, radio, and γ-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 ~100-140 pc for ~3 GeV CR electrons resident in 30 Dor from consideration of the radio and infrared data. Assuming that the observed γ-ray emission toward 30 Dor is associated with the star-forming region, and applying the same methodology to the infrared and γ-ray data, we estimate a ~20 GeV propagation length of 200-320 pc for the CR nuclei. This is approximately twice as large as for ~3 GeV CR electrons, corresponding to a spatial diffusion coefficient that is ~4 times higher, scaling as (R/GV)^δ with δ ≈ 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 ~70 GeV CR nuclei traced by the 3-10 GeV γ-ray data (δ ≈ 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 ≈ (0.9-1.0) × 10²⁷(R/GV)^0.7 cm² 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.