Why is the magnetic axis of Uranus and Neptune off center?

Question

It(Uranus) rotates on its side, tilted almost 98 degrees from the plane of its orbit around the sun. The axis of its magnetic field is tilted too, at a 59-degree angle from the rotational axis. The magnetic field is also off-center, with the field lines emerging about a third of the way toward the south pole. (source)

Neptune's magnetic field is tilted 47 from the planet's rotation axis and is offset at least 0.55 radii, about 8,500 mi (13,500 km) from the physical center. The dynamo electric currents produced within the planet, therefore, must be relatively closer to the surface than for Earth, Jupiter, or Saturn. Because of its unusual orientation, and the tilt of the planet's rotation axis, Neptune's magnetic field goes through dramatic changes as the planet rotates in the solar wind. (source)

So, it is well established that the magnetic axis of Uranus and Neptune is off-center and due to this, the planets faces the following consequences:

1. the magnetosphere is irregular
2. the strength of magnetic field varies, almost opening and closing periodically as the magnetic field lines disconnect and reconnect
3. the orientation of magnetic field changes constantly.

But, why is the magnetic axis off-center in the first place? I found no source answering that. Is it due to alignment/orbit/internal heating mechanism of the planets?

Answer 1

_{Disclaimer: This answer is inspired by Magnetic fields of Uranus and Neptune: Metallic fluid hydrogen by Nellis [2017], who explains the center offset of the ice-giants' magnetic fields by contrasting them with Earth's magnetic field.}

Earth's axisymmetric magnetic field

The most researched magnetic field in our Solar System is, of course, Earth. Nellis 2017 explains how coupling between the rotational motion and convective dynamo motions in the Earth's outer core cause the magnetic axis to drive towards alignment to the spin axis:

Because rotational motion (RM) of Earth is strongly coupled into convective dynamo (CD) motions of its fluid-Fe outer core, planetary RM stabilizes convective motions that generate a dipolar magnetic field. If a convective fluctuation occurs which tends to destabilize a given dipolar axis, then strong RM-CD coupling either drives convective motions that essentially restore the initial orientation or CD fluctuations that drive the initial magnetic axes out of orientational equilibrium are so strong that RM-CD coupling eventually drives the dipolar axis into an alignment anti-parallel to its initial one.

Uranus/Neptune non-axisymmetric magnetic fields

Voyager 2 measured both gravitational moments as well as the magnetic fields of both Uranus and Neptune. These measurements helped develop models of planetary composition as well as models of magnetic field generators. For Uranus/Neptune, the fields are generated near the surface at radii as large as $\approx0.9R_U/R_N$, while the Earth's magnetic field is generated much deeper at $\approx0.5R_E$.

The magnetic generation near the surface, as well as the H-HE envelope (again according to Nellis) means that:

local convective dynamo motions of fluids that produce the magnetic fields are essentially decoupled from global rotational motions [...]. The dynamos of U/N would then be relatively free to wander as local convective fluctuations dictate. Thus, tilt angles and center-offsets of their fields would vary slowly over the age of the Solar System.

Summary

The Earth's composition and convective liquid outer-core currents cause a coupling between the rotational motion of the Earth and the convective dynamo motion. This drives the magnetic axis to align with the spin axis, which passes through the center-of-mass. No similar strong coupling exists for Neptune and Uranus, which means the magnetic axis on each of these planets is free to wander both in orientation and offset from the spin axis and center of mass due to local surface convection currents.