Multi-scale radio-infrared correlations in M 31 and M 33: The role of magnetic fields and star formation

Interstellar magnetic fields and the propagation of cosmic ray electrons have an important impact on the radio-infrared (IR) correlation in galaxies. This becomes evident when studying different spatial scales within galaxies. We investigate the correlation between the IR and free-free/synchrotron radio continuum emission at 20 cm from the two local group galaxies M 31 and M 33 on spatial scales between 0.4 and 10 kpc. The multi-scale radio-IR correlations have been carried out using a wavelet analysis. The free-free and IR emission are correlated on all scales, but on some scales the synchrotron emission is only marginally correlated with the IR emission. The synchrotron-IR correlation is stronger in M 33 than in M 31 on small scales (<1 kpc), but it is weaker than in M 31 on larger scales. Taking the smallest scale on which the synchrotron-IR correlation exists as the propagation length of cosmic ray electrons, we show that the difference on small scales can be explained by the smaller propagation length in M 33 than in M 31. On large scales, the difference is due to the thick disk/halo in M 33, which is absent in M 31. A comparison of our data with data on NGC 6946, the LMC and M 51 suggests that the propagation length is determined by the ratio of ordered-to-turbulent magnetic field strength, which is consistent with diffusion of CR electrons in the ISM. As the diffusion length of CR electrons influences the radio-IR correlation, this dependence is a direct observational evidence of the importance of magnetic fields for the radio-IR correlation within galaxies. The star-formation rate per surface area only indirectly influences the diffusion length as it increases the strength of the turbulent magnetic field.