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 } ) ^ { \delta } with \delta \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 ( \delta \approx 0.66 \pm 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 \times 10 ^ { 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 .