A physical model for the magnetosphere of Uranus at solstice time

Abstract

Context. Uranus is the only planet in the Solar System whose rotation axis and orbital plane are nearly parallel to each other. Uranus is also the planet with the largest angle between the rotation axis and the direction of its magnetic dipole (roughly 59°). Consequently, the shape and structure of its magnetospheric tail is very different to those of all other planets in whichever season one may consider. The only in situ measurements were obtained in January 1986 during a flyby of the Voyager II spacecraft. At that date, Uranus was near solstice time, but unfortunately the data collected by the spacecraft were much too sparse to allow for a clear view of the structure and dynamics of its extended magnetospheric tail. Later numerical simulations revealed that the magnetic tail of Uranus at solstice time is helically shaped with a characteristic pitch of the order of 1000 planetary radii. Aims. We aim to propose a magnetohydrodynamic model for the magnetic tail of Uranus at solstice time. Methods. We constructed our model based on a symmetrised version of the Uranian system by assuming an exact alignment of the solar wind and the planetary rotation axis and an angle of 90° between the planetary magnetic dipole and the rotation axis. We do also postulate that the impinging solar wind is steady and unmagnetised, which implies that the magnetosphere is quasi-steady in the rotating planetary frame and that there is no magnetic reconnection at the magnetopause. Results. One of the main conclusions is that all magnetic field lines forming the extended magnetic tail follow the same qualitative evolution from the time of their emergence through the planet's surface and the time of their late evolution after having been stretched and twisted several times downstream of the planet. In the planetary frame, these field lines move on magnetic surfaces that wind up to form a tornado-shaped vortex with two foot points on the planet (one in each magnetic hemisphere). The centre of the vortex (the eye of the tornado) is a simple double helix with a helical pitch (along the symmetry axis z) λ = τ[vz+Bz/(μ0ρ)1/2], where τ is the rotation period of the planet, μ0 the permeability of vacuum, ρ the mass density, vz the fluid velocity, and Bz the magnetic field where all quantities have to be evaluated locally at the centre of the vortex. In summary, in the planetary frame, the motion of a typical magnetic field of the extended Uranian magnetic tail is a vortical motion, which asymptotically converges towards the single double helix, regardless of the line's emergence point on the planetary surface.