CHANG-ES XIV: Cosmic-ray propagation and magnetic field strengths in the
  radio halo of NGC 4631
  NGC 4631 is an interacting galaxy that exhibits one of the largest, gaseous
halos observed among edge-on galaxies. We aim to examine the synchrotron and
cosmic-ray propagation properties of its disk and halo emission with new radio
continuum data. Radio continuum observations of NGC 4631 were performed with
the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C and D array
configurations, and at L-band (1.57 GHz) in the B, C, and D array
configurations. Complementary observations of NGC 4631 with the Effelsberg
telescope were performed at 1.42 and 4.85 GHz. The interferometric total
intensity data were combined with the single-dish Effelsberg data in order to
recover the missing large-scale total power emission. The thermal and
nonthermal components of the total radio emission were separated by estimating
the thermal contribution through the extinction-corrected H$\alpha$ emission.
The H$\alpha$ radiation was corrected for extinction using a linear combination
of the observed H$\alpha$ and 24 $\mu$m data. NGC 4631 has a global thermal
fraction at 5.99 (1.57) GHz of 14$\pm$3% (5.4$\pm$1.1%). The mean scale heights
of the total emission in the radio halo (thick disk) at 5.99 (1.57) GHz are
$1.79\pm0.54$ kpc ($1.75\pm0.27$ kpc) and have about the same values for the
synchrotron emission. The total magnetic field of NGC 4631 has a mean strength
of $\rm{\langle B_{eq}\rangle} \simeq 9 \rm{\mu G}$ in the disk, and a mean
strength of $\rm{\langle B_{eq}\rangle}~\simeq 7~\rm{\mu G}$ in the halo. We
also studied a double-lobed background radio galaxy southwest of NGC 4631,
which is an FR~II radio galaxy according to the distribution of spectral index
across the lobes. From the halo scale heights we estimated that the radio halo
is escape-dominated with convective cosmic ray propagation, and conclude that
there is a galactic wind in the halo of NGC 4631.
