A multi-scale study of infrared and radio emission from Scd galaxy M 33

Aims. We investigate the energy sources of the infrared (IR) emission and their relation to the radio continuum emission at various spatial scales within the Scd galaxy M 33. Methods. We use the data at the Spitzer wavelengths of 24, 70, and 160 mu m, as well as recent radio continuum maps at 3.6 cm and 20 cm observed with the 100-m Effelsberg telescope and VLA, respectively. We use the wavelet transform of these maps to a) separate the diffuse emission components from compact sources, b) compare the emission at different wavelengths, and c) study the radio-IR correlation at various spatial scales. An Ha map serves as a tracer of the star forming regions and as an indicator of the thermal radio emission. Results. The bright HII regions affect the wavelet spectra causing dominant small scales or decreasing trends towards the larger scales. The dominant scale of the 70 mu m emission is larger than that of the 24 mu m emission, while the 160 mu m emission shows a smooth wavelet spectrum. The radio and Ha maps are well correlated with all 3 MIPS maps, although their correlations with the 160 mu m map are weaker. After subtracting the bright HII regions, the 24 and 70 mu m maps show weaker correlations with the 20 cm map than with the 3.6 cm map at most scales. We also find a strong correlation between the 3.6 cm and Ha emission at all scales. Conclusions. Comparing the results with and without the bright HII regions, we conclude that the IR emission is influenced by young, massive stars increasingly with decreasing wavelength from 160 to 24 mu m. The radio-IR correlations indicate that the warm dust-thermal radio correlation is stronger than the cold dust-non-thermal radio correlation at scales smaller than 4 kpc. A perfect 3.6 cm-H alpha correlation implies that extinction has no significant effect on Ha emitting structures.