High-resolution radio continuum survey of M33 II. Thermal and nonthermal emission

Context. Constraints on the origin and propagation of cosmic rays can be achieved by studying the variation in the spectral index of the synchrotron emission across external galaxies. Aims. To determine the variation in the nonthermal radio spectral index in the nearby spiral galaxy M33 at a linear resolution of 360 pc. Methods. 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 160μm and a standard dust model, we deredden the Hα emission. The extinction corrected Hα emission serves as a template for the thermal free-free radio emission. Subtracting from the observed 3.6 cm and 20 cm emission (Effelsberg and the VLA) this free-free emission, we obtain the nonthermal maps. A constant electron temperature used to obtain the thermal radio intensity seems appropriate for M 33 which, unlike the Milky Way, has a shallow metallicity gradient. Results. For the first time, we derive the distribution of the nonthermal spectral index across a galaxy, M33. We detect strong nonthermal emission from the spiral arms and star-forming regions. Wavelet analysis shows that at 3.6 cm the nonthermal emission is dominated by contributions from star-forming regions, while it is smoothly distributed at 20 cm. For the whole galaxy, we obtain thermal fractions of 51% and 18% at 3.6 cm and 20 cm, respectively. The thermal emission is slightly stronger in the southern than in the northern half of the galaxy. We find a clear radial gradient of mean extinction in the galactic plane. Conclusions. The nonthermal spectral index map indicates that the relativistic electrons suffer energy-loss when diffusing from their origin in star-forming regions towards interarm regions and the outer parts of the galaxy. We also conclude that the radio emission is mostly nonthermal at R> 5 kpc in M33.