Variations of the Radio Synchrotron Spectral Index in M33
  We determine the variation in the nonthermal radio spectral index in the nearby spiral galaxy M33. We separate the thermal and nonthermal components of the radio continuum emission without the assumption of a constant nonthermal spectral index. Using the Spitzer FIR data at 70 and 160 $\mu$m and a standard dust model, we de-redden the H$\alpha$ emission. The extinction-corrected H$\alpha$ emission serves as a template for the thermal free-free radio emission. Subtracting from the observed 3.6 and 20cm emission (Effelsberg and the VLA) this free-free emission, we obtain maps of the nonthermal intensity and spectral index. 
F. S. Tabatabaei, R. Beck, E. Kr\"ugel, M. Krause, E. M. Berkhuijsen,   K. D. Gordon, K. M. Menten