Magnetic Fields and Accreting Giant Planets around PDS 70

Recent high-spatial/spectral-resolution observations have enabled the formation mechanisms of giant planets to be constrained, especially at the final stages. The current interpretation of such observations is that these planets undergo magnetospheric accretion, suggesting the importance of planetary magnetic fields. We explore the properties of accreting, magnetized giant planets surrounded by their circumplanetary disks, using the physical parameters inferred for PDS 70 b/c. We compute the magnetic field strength and the resulting spin rate of giant planets and find that these planets may possess dipole magnetic fields of either a few 10 G or a few 100 G; the former is the natural outcome of planetary growth and radius evolution, while the resulting spin rate cannot reproduce the observations. For the latter, a consistent picture can be drawn, where strong magnetic fields induced by hot planetary interiors lead both to magnetospheric accretion and to spin-down due to disk locking. We also compute the properties of circumplanetary disks in the vicinity of these planets, taking into account planetary magnetic fields. The resulting surface density becomes very low, compared with the canonical models, implying the importance of radial movement of satellite-forming materials. Our model predicts a positive gradient of the surface density, which invokes traps for both satellite migration and radially drifting dust particles. This work thus concludes that the final formation stages of giant planets are similar to those of low-mass stars such as brown dwarfs, as suggested by recent studies.

Possible Role of Non-Stationarity of Magnetohydrodynamic Turbulence in Understanding of Geomagnetic Excursions

The natural simplifying assumptions often put forward in the theoretical investigations of the magnetohydrodynamic turbulence are that the turbulent flow is statistically isotropic, homogeneous and stationary. Of course, the natural turbulence in the planetary interiors, such as the liquid core of the Earth is neither, which has important consequences for the dynamics of the planetary magnetic fields generated via the hydromagnetic dynamo mechanism operating in the interiors of the planets. Here we concentrate on the relaxation of the assumption of statistical stationarity of the turbulent flow and study the effect of turbulent wave fields in the Earth’s core, which induces non-stationarity, on the turbulent resistivity in the non-reflectionally symmetric flow and the geodynamo effect. It is shown that the electromotive force, including the so-called α-effect and the turbulent magnetic diffusivity η¯, induced by non-stationary turbulence, evolves slowly in time. However, the turbulent α¯ coefficient, responsible for the dynamo action and η¯ evolve differently in time, thus creating periods of enhanced and suppressed turbulent diffusion and dynamo action somewhat independently. In particular, periods of enhanced α¯ may coincide with periods of suppressed diffusion, leading to a stable and strong field period. On the other hand, it is shown that when enhanced diffusion occurs simultaneously with suppression of the α-effect, this leads to a sharp drop in the intensity of the large-scale field, corresponding to a geomagnetic excursion.

Kinematic dynamos in triaxial ellipsoids

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

Capon’s method for planetary magnetic field analysis

<p>Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of seismics and space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury’s magnetic field analysis. The mathematical foundations and the practical application of the Capon method are discussed in a rigorous fashion by extending its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon’s method by making use of diagonal loading is considered.</p>

Mathematical foundation of Capon's method for planetary magnetic field analysis

Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury's magnetic field analysis. The practical application and limits of the Capon method are discussed in a rigorous fashion by formulating its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon's method by making use of diagonal loading is considered.

The underexplored frontier of ice giant dynamos

The Voyager 2 flybys of Uranus and Neptune revealed the first multipolar planetary magnetic fields and highlighted how much we have yet to learn about ice giant planets. In this review, we summarize observations of Uranus’ and Neptune’s magnetic fields and place them in the context of other planetary dynamos. The ingredients for dynamo action in general, and for the ice giants in particular, are discussed, as are the factors thought to control magnetic field strength and morphology. These ideas are then applied to Uranus and Neptune, where we show that no models are yet able to fully explain their observed magnetic fields. We then propose future directions for missions, modelling, experiments and theory necessary to answer outstanding questions about the dynamos of ice giant planets, both within our solar system and beyond. This article is part of a discussion meeting issue ‘Future exploration of ice giant systems’.

Particle Motions in Planetary Magnetic Fields: Europlanet Service

<p>The trapping of charged particles in planetary magnetic fields is a process which underpins many important aspects of planetary magnetospheres, such as ring current evolution, particle acceleration, and the flow of current through the system, both free and bound. As part of our effort for the Europlanet project, the UCL group have developed codes which accurately model the trajectories of charged particles in magnetic field models appropriate for the magnetospheres of Jupiter and Saturn. These will form the basis of a service for the SPIDER task. In this presentation, we show examples of ion trajectories at both planets for representative 'start values' of equatorial distance, pitch angle, and values of particle energy. The simulations provide an indication of how particle orbits become less adiabatic as one approaches energies where gyroradii become comparable to magnetic field curvature radius. The disk-like fields of the gas giants are particularly effective at 'scattering' adequately high-energy particle trajectories as they cross the equator, where the field lines are most 'pinched' and have the smallest length scales.</p>

Constraining the depth of the winds on Uranus and Neptune via Ohmic dissipation

ABSTRACT Determining the depth of atmospheric winds in the outer planets of the Solar system is a key topic in planetary science. We provide constraints on these depths in Uranus and Neptune via the total induced Ohmic dissipation, due to the interaction of the zonal flows and the planetary magnetic fields. An upper bound can be placed on the induced dissipation via energy and entropy flux throughout the interior. The induced Ohmic dissipation is directly linked to the electrical conductivity profile of the materials involved in the flow. We present a method for calculating electrical conductivity profiles of ionically conducting hydrogen–helium–water mixtures under planetary conditions, using results from ab initio simulations. We apply this prescription on several ice giant interior structure models available in the literature, where all the heavy elements are represented by water. According to the energy (entropy) flux budget, the maximum penetration depth for Uranus lies above 0.93 RU (0.90 RU) and for Neptune above 0.95 RN (0.92 RN). These results for the penetration depths are upper bounds and are consistent with previous estimates based on the contribution of the zonal winds to the gravity field. As expected, interior structure models with higher water abundance in the outer regions also have a higher electrical conductivity and therefore reach the Ohmic limit at shallower regions. Thus, our study shows that the likelihood of deep-seated winds on Uranus and Neptune drops significantly with the presence of water in the outer layers.