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Advective and diffusive cosmic ray transport in galactic haloes

We present 1D cosmic ray transport models, numerically solving equations of pure advection and diffusion for the electrons and calculating synchrotron emission spectra. We find that for exponential halo magnetic field distributions advection leads to approximately exponential radio continuum intensity profiles, whereas diffusion leads to profiles that can be better approximated by a Gaussian function. Accordingly, the vertical radio spectral profiles for advection are approximately linear, whereas for diffusion they are of `parabolic' shape. We compare our models with deep ATCA observations of two edge-on galaxies, NGC 7090 and 7462, at $λλ$ 22 and 6 cm. Our result is that the cosmic ray transport in NGC 7090 is advection dominated with $V=150^{+80}_{-30}~\rm km\,s^{-1}$, and that the one in NGC 7462 is diffusion dominated with $D=3.0\pm 1.0 \times 10^{28}E_{\rm GeV}^{0.5}~\rm cm^2\,s^{-1}$. NGC 7090 has both a thin and thick radio disc with respective magnetic field scale heights of $h_{\rm B1}=0.8\pm 0.1$ kpc and $h_{\rm B2}=4.7\pm 1.0$ kpc. NGC 7462 has only a thick radio disc with $h_{\rm B2}=3.8\pm 1.0$ kpc. In both galaxies, the magnetic field scale heights are significantly smaller than what estimates from energy equipartition would suggest. A non-negligible fraction of cosmic ray electrons can escape from NGC 7090, so that this galaxy is not an electron calorimeter.