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 corr
elation between the infrared (IR) and free-free/synchrotron radio continuum emission at 20 cm from the two local group galaxies M31 and M33 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 M33 than in M31 on small scales (<1 kpc), but it is weaker than in M31 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 M33 than in M31. On large scales, the difference is due to the thick disk/halo in M33, which is absent in M31. A comparison of our data with data on NGC6946, the LMC and M51 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.
In a search for the signature of turbulence in the diffuse interstellar medium in gas density distributions, we determined the probability distribution functions (PDFs) of the average volume densities of the diffuse gas. The densities were derived fr
om dispersion measures and HI column densities towards pulsars and stars at known distances. The PDFs of the average densities of the diffuse ionized gas (DIG) and the diffuse atomic gas are close to lognormal, especially when lines of sight at |b|<5 degrees and |b|>=5 degrees are considered separately. The PDF of <n_HI> at high |b| is twice as wide as that at low |b|. The width of the PDF of the DIG is about 30 per cent smaller than that of the warm HI at the same latitudes. The results reported here provide strong support for the existence of a lognormal density PDF in the diffuse ISM, consistent with a turbulent origin of density structure in the diffuse gas.
