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$α$ emission. The H$α$ radiation was corrected for extinction using a linear combination of the observed H$α$ and 24 $μ$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 $\rm{\langle B_{eq}\rangle} \simeq 9 \rm{μG}$ in the disk, and a mean strength of $\rm{\langle B_{eq}\rangle}~\simeq 7~\rm{μG}$ 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.