CHANG-ES XIX: Galaxy NGC 4013 -- a diffusion-dominated radio halo with plane-parallel disk and vertical halo magnetic fields.

Using the Continuum HAloes in Nearby Galaxies - an EVLA Survey (CHANG-ES) radio continuum data from the Karl G. Jansky Very Large Array (VLA) in two frequency bands (C-band, L-band), we analyzed the radio properties, including polarization and the transport processes of the CR electrons (CREs), in the edge-on spiral galaxy NGC 4013. Supplementary LOw-Frequency ARray (LOFAR) data at 150MHz are used to study the low-frequency properties of this galaxy and X-ray (Chandra, XMM-Newton) data are used to investigate the central region. The central point source dominates the radio continuum in both CHANG-ES bands, but no clear AGN classification is possible at this time. The scale height analysis shows that Gaussian fits, with halo scale heights of 1.2 kpc in C-band, 2.0 kpc in L-band, and 3.1 kpc at 150 MHz, better represent the intensity profiles than do exponential fits. The radio continuum halo of NGC 4013 in C-band is rather small, while the low-frequency LOFAR data reveal a large halo. The polarization data reveal plane-parallel, regular magnetic fields within the entire disk and vertical halo components out to heights of about 6 kpc indicating the presence of an axisymmetric field having a radial component pointing outwards. The mean magnetic field strength of the disk of NGC 4013 of 6.6 $\mu$G (using the revised equipartition formula) is rather small. The interaction and the low star formation rate (SFR) across the disk of NGC 4013 probably influence the appearance of its radio continuum. Several observable quantities give consistent evidence that the CR transport in the halo of NGC 4013 is diffusive: the frequency dependence of the synchrotron scale height, the disk/halo flux density ratio, the vertical profile of the synchrotron spectral index, the small propagation speed measured modeled with spinnaker, and the low temperature of the X-ray emitting hot gas.