Analytical models of X-shape magnetic fields in galactic halos
  External spiral galaxies seen edge-on exhibit X-shape magnetic fields in
their halos. Whether the halo of our own Galaxy also hosts an X-shape magnetic
field is still an open question. We would like to provide the necessary
analytical tools to test the hypothesis of an X-shape magnetic field in the
Galactic halo. We propose a general method to derive analytical models of
divergence-free magnetic fields whose field lines are assigned a specific
shape. We then utilize our method to obtain four particular models of X-shape
magnetic fields in galactic halos. In passing, we also derive two particular
models of predominantly horizontal magnetic fields in galactic disks. All our
field models have spiraling field lines with spatially varying pitch angle. Our
four halo field models do indeed lead to X patterns in synthetic synchrotron
polarization maps. Their precise topologies can all be explained by the action
of a wind blowing outward from the galactic disk or from the galactic center.
In practice, our field models may be used for fitting purposes or as inputs to
various theoretical problems.
