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.
We investigate whether the method of wavelet-based Faraday rotation measure (RM) Synthesis can help us to identify structures of regular and turbulent magnetic fields in extended magnetized objects, such as galaxies and galaxy clusters. Wavelets allo
w us to reformulate the RM synthesis method in a scale-dependent way and to visualize the data as a function of Faraday depth and scale. We present observational tests to recognize magnetic field structures. A region with a regular magnetic field generates a broad disk in Faraday space (Faraday spectrum), with two horns when the distribution of cosmic-ray electrons is broader than that of the thermal electrons. Each magnetic field reversal generates one asymmetric horn on top of the disk. A region with a turbulent field can be recognized as a Faraday forest of many components. These tests are applied to the spectral ranges of various synthesis radio telescopes. We argue that the ratio of maximum to minimum wavelengths determines the range of scales that can be identified in Faraday space. A reliable recognition of magnetic field structures requires the analysis of data cubes in position-position-Faraday depth space (PPF cubes), observed over a wide and continuous wavelength range, allowing the recognition of a wide range of scales as well as high resolution in Faraday space. The planned Square Kilometre Array (SKA) will fulfill this condition and will be close to representing a perfect Faraday telescope. The combination of data from the Low Frequency Array (LOFAR) and the Expanded Very Large Array (EVLA) appears to be a promising approach for the recognition of magnetic structures on all scales. The addition of data at intermediate frequencies from the Westerbork Synthesis Radio Telescope (WSRT) or the Giant Meterwave Radio Telescope (GMRT) would fill the gap between the LOFAR and EVLA frequency ranges.
RM Synthesis was recently developed as a new tool for the interpretation of polarized emission data in order to separate the contributions of different sources lying on the same line of sight. Until now the method was mainly applied to discrete sourc
es in Faraday space (Faraday screens). Here we consider how to apply RM Synthesis to reconstruct the Faraday dispersion function, aiming at the further extraction of information concerning the magnetic fields of extended sources, e.g. galaxies. The main attention is given to two related novelties in the method, i.e. the symmetry argument in Faraday space and the wavelet technique. We give a relation between our method and the previous applications of RM Synthesis to point-like sources. We demonstrate that the traditional RM Synthesis for a point-like source indirectly implies a symmetry argument and, in this sense, can be considered as a particular case of the method presented here. Investigating the applications of RM Synthesis to polarization details associated with small-scale magnetic fields, we isolate an option which was not covered by the ideas of the Burn theory, i.e. using quantities averaged over small-scale fluctuations of magnetic field and electron density. We describe the contribution of small-scale fields in terms of Faraday dispersion and beam depolarization. We consider the complex polarization for RM Synthesis without any averaging over small-scale fluctuations of magnetic field and electron density and demonstrate that it allows us to isolate the contribution from small-scale field.
Faraday Rotation Measure (RM) Synthesis, as a method for analyzing multi-channel observations of polarized radio emission to investigate galactic magnetic fields structures, requires the definition of complex polarized intensity in the range of the n
egative lambda square. We introduce a simple method for continuation of the observed complex polarized intensity into this domain using symmetry arguments. The method is suggested in context of magnetic field recognition in galactic disks where the magnetic field is supposed to have a maximum in the equatorial plane. The method is quite simple when applied to a single Faraday-rotating structure on the line of sight. Recognition of several structures on the same line of sight requires a more sophisticated technique. We also introduce a wavelet-based algorithm which allows us to consider a set of isolated structures. The method essentially improves the possibilities for reconstruction of complicated Faraday structures using the capabilities of modern radio telescopes.
