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 $\lambda\lambda$ 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.
