Multi-scale Radio-IR Correlations in M31 and M33: 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 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.
