Magnetohydrodynamic simulations of a Uranus-at-equinox type rotating magnetosphere

Within the Solar System all the planets, with the exception of Venus and Mars, have an intrinsic magnetic field strong enough to interact with the solar wind and form a complex magnetosphere. The structure of the magnetosphere depends greatly on the speed of rotation of the planet and the orientation of its two remarkable axes: the magnetic axis and the rotational axis.

Uranus is the only planet in the solar system that combines the following three characteristics: it is a fast rotator, its axis of rotation is almost parallel to the plane of the ecliptic (the plane in which the solar wind flows) and its magnetic axis is almost perpendicular to the axis of rotation. The large angle between the magnetic axis and the axis of rotation results in a particularly dynamic magnetosphere, which varies considerably over the course of a planetary day but also from season to season. At the solstice the axis of rotation of the planet is directed towards the Sun, and thus faces the wind, whereas at the equinox the axis of rotation is oriented perpendicular to the wind.

Figure 1: Orientation of the magnetic axis and the rotation axis used to simulate a Uranus-like planet in equinox configuration. The solar wind comes from the left and blows perpendicular to the axis of rotation of the planet. Over the course of a day the angle between the magnetic axis (in red) and the direction of the solar wind changes from 0° to 360° (from G&P 2020).

In the G&P 2020 paper, the equinox configuration is explored using magnetohydrodynamic (MHD) simulations. To facilitate interpretation, the axis of rotation was placed in the plane of the ecliptic and its angle to the magnetic axis was increased to 90o as shown in Figure 1.

A qualitative illustration of the structure formed by the magnetic field lines of Uranus during the equinox period is shown in Figure 2 for the case of a wind carrying no magnetic field. Only one hemisphere is shown because, due to the symmetry of the chosen configuration (see Figure 1), each hemisphere is the mirror image of the other. The simulation shows that the planetary magnetic field lines wind and stretch as a result of rotation and bend as a result of the pressure exerted by the solar wind.

One of the main conclusions of the G&P 2020 paper is that the planet’s magnetic field lines that form the complex magnetic structure in Figure 2 are asymptotically accelerated to wind speed. The thesis that is defended in the paper is that the acceleration in the case of a fast rotator like Uranus occurs mainly in the immediate vicinity of the planet over a distance of the order of the distance travelled by the Alfvén magnetohydrodynamic wave during a planetary rotation. In this case the acceleration is the result of the combined effect of the centrifugal force, linked to the planetary rotation, and the electromagnetic force linked to the compression and deformation of the magnetic field resulting from the rotation. The wind thus contributes to bending the magnetic field lines in the opposite direction to the Sun, but only marginally contributes to their acceleration.

Figure 2: Winding of magnetic field lines in the magnetosphere of a rapidly rotating planet of the Uranus type during the equinox period. The blue and red lines are connected to the opposite magnetic poles of the planet. They are wound by the planetary rotation. In black are the plasma flow lines of the solar wind. The effect of the wind is to bend the magnetic field lines away from the Sun (from G&P 2020).

According to the editors of the journal Astronomy & Astrophysics, this paper demonstrates the enormous potential for numerical simulations to study some of the physical phenomena that govern the magnetospheres of the ice giants Uranus and Neptune or those of the exoplanets (e.g., auroral activity, non-thermal emission and the limits of atmospheric escape).

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