Analytical models of X-shape magnetic fields in galactic halos

Abstract

Context. 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. Aims. We would like to provide the necessary analytical tools to test the hypothesis of an X-shape magnetic field in the Galactic halo. Methods. 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. Results. 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.

X-shape magnetic fields in galactic halos

“…In this section, I present the four analytical models that [4] constructed to describe X-shape magnetic fields in galactic halos. Each of these models is initially defined by the shape of its field lines together with the distribution of the magnetic flux density on a given reference surface.…”

“…Each of these models is initially defined by the shape of its field lines together with the distribution of the magnetic flux density on a given reference surface. Using the Euler formalism [8,11], [4] derived the corresponding analytical expression of the magnetic field vector, (B r , B ϕ , B z ), as a function of galactocentric cylindrical coordinates, (r, ϕ, z).…”

“…It then follows (see [4] for the detailed derivation) that the radial and vertical field components can be written as…”

“…Several physical scenarios have been put forward to explain the origin of X-shape magnetic fields in galactic halos (see [4]). The first class of scenarios rests on the hypothesis that the X shape pertains to the large-scale regular magnetic field.…”

“…However, conventional dynamo fields do not naturally come with an X shape. To overcome this difficulty, a large-scale galactic wind has been invoked [12,1,6, 10] -either a wind originating near the galactic plane and advecting the disk dynamo field into the halo, or a wind blowing from the base of the halo and stretching out the halo dynamo field into an X shape [4]. In the second class of scenarios, the X shape pertains to a small-scale anisotropic random field.…”