arXiv subjects

Johannes Wicht

Publications and source records attributed to Johannes Wicht.

At least 19 recordsLinked to original sources

arXiv2025

Reconstructing wind fields from gravitational data on gas giants: An investigation of mathematical methods

The atmospheric structure of gas giants, especially those of Jupiter and Saturn, has been an object of scientific studies for a long time. The measurement of the gravitational fields by the Juno mission for Jupiter and the Cassini mission for Saturn offered new possibilities to study the interior structure of these planets. Accordingly, the reconstruction of the wind velocities from gravitational data on gas giants has been the subject of many research papers over the years, yet the mathematical foundations of this inverse problem and its numerical resolution have not been studied in detail. This article suggests a rigorous mathematical theory for inferring the wind fields of gas giants. In particular, an orthonormal basis is derived which can be associated to models of the gravitational potential and the interior wind velocity field. Moreover, this approach provides the foundations for existing resolution concepts of the inverse problem.

math-ph↗

arXiv2024

A common law for the differential rotation of planets and stars

All planets and stars rotate. All gas planets in our solar system, the Sun, and many stars show a pattern of east- or westward mean flows. This phenomenon is known as differential rotation in the stellar and as zonal jets in the planetary context. Observations, laboratory experiments and simulations show that the zonal flow kinetic energy scales like $\ell^{-5}$, where $\ell$ is the spherical harmonic degree (which is effectively a latitudinal wave number). Here, we analyze observation of the Sun, as well as simulations of the dynamics in Saturn and in the outer atmosphere of an ultra-hot Jupiter. While these systems are very different, they all develop strong zonal winds that obey the $\ell^{-5}$ scaling. Our results strongly suggest that there is a simple common mechanism that shapes zonal mean flows in planets and stars independent of the flow driving.

astro-ph.SR↗

arXiv2024

Transition to turbulence in the wide-gap spherical Couette system

The spherical Couette system consists of two differentially rotating concentric spheres with a fluid filled in between. We study a regime where the outer sphere is rotating rapidly enough so that the Coriolis force is important and the inner sphere is rotating either slower or in the opposite direction with respect to the outer sphere. We numerically study the sudden transition to turbulence at a critical differential rotation seen in experiments at BTU Cottbus - Senftenberg, Germany and investigate its cause. We find that the source of turbulence is the boundary layer on the inner sphere, which becomes centrifugally unstable. We show that this instability leads to generation of small scale structures which lead to turbulence in the bulk, dominated by inertial waves, a change in the force balance near the inner boundary, the formation of a mean flow through Reynolds stresses, and consequently, to an efficient angular momentum transport. We compare our findings with axisymmetric simulations and show that there are significant similarities in the nature of the flow in the turbulent regimes of full 3D and axisymmetric simulations but differences in the evolution of the instability that leads to this transition. We find that a heuristic argument based on a Reynolds number defined using the thickness of the boundary layer as a length scale helps explain the scaling law of the variation of critical differential rotation for transition to turbulence with rotation rate observed in the experiments.

physics.flu-dyn↗

arXiv2024

Westward hotspot offset explained by subcritical dynamo action in an ultra-hot Jupiter atmosphere

Hot Jupiters are tidally-locked Jupiter-sized planets close to their host star. They have equilibrium temperatures above about 1000 K. Photometric observations find that the hotspot, the hottest location in the atmosphere, is shifted with respect to the substellar point. Some observations show eastward and some show westward hotspot offsets, while hydrodynamic simulations show an eastward offset due to advection by the characteristic eastward mean flow. In particular for ultra-hot Jupiters with equilibrium temperatures above 2000 Kelvin, electromagnetic effects must be considered since the ionization-driven significant electrical conductivity and the subsequent induction of magnetic fields likely result in substantial Lorentz forces. We here provide the first magnetohydrodynamic numerical simulation of an ultra-hot Jupiter atmosphere at an equilibrium temperature of about 2400 K that fully captures non-linear electromagnetic induction effects. We find a new turbulent flow regime, hitherto unknown for hot Jupiters. Its main characteristic is a break-down of the well-known laminar mean flows. This break-down is triggered by strong local magnetic fields. These fields are maintained by a subcritical dynamo process. It is initiated by a sufficiently strong background field from an assumed deep dynamo region at a realistic amplitude around 2.5 G. Our results show a zero or westward hotspot offset for the dynamo case, depending on atmospheric properties, while the hydrodynamic case has the usual eastward offset. Since our simulation has an eastward mean flow at the equator, radial flows must be important for producing the zero or westward hotspot offset. A subcritical dynamo offers a new scenario for explaining the diversity of observed hotspot offsets. In this scenario, the dynamo has been initiated by sufficiently strong fields at some time in the past only for a part of the population.

astro-ph.EP↗

arXiv2024

The Effects of a Stably Stratified Region with radially varying Electrical Conductivity on the Formation of Zonal Winds on Gas Planets

The outer areas of Jupiter and Saturn have multiple zonal winds, reaching the high latitudes, that penetrate deep into the planets' interiors, as suggested by gravity measurements. These characteristics are replicable in numerical simulations by including both a shallow stably stratified layer, below a convecting envelope, and increasing electrical conductivity. A dipolar magnetic field, assumed to be generated by a dynamo below our model, is imposed. We find that the winds' depth into the stratified layer depends on the local product of the squared magnetic field strength and electrical conductivity. The key for the drop-off of the zonal winds is a meridional circulation which perturbs the density structure in the stable layer. In the stable region its dynamics is governed by a balance between Coriolis and electromagnetic forces. Our models suggest that a stable layer extending into weakly conducting regions could account for the observed deep zonal wind structures.

astro-ph.EP↗

arXiv2022

Direct driving of simulated planetary jets by upscale energy transfer

The precise mechanism that forms jets and large-scale vortices on the giant planets is unknown. An inverse cascade has been suggested. Alternatively, energy may be directly injected by small-scale convection. Our aim is to clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a system of rapidly rotating, deep, geostrophic spherical-shell convection. We analyze the nonlinear scale-to-scale transfer of kinetic energy in such simulations as a function of the azimuthal wave number, m. We find that the main driving of the jets is associated with upscale transfer directly from the small convective scales to the jets. This transfer is very nonlocal in spectral space, bypassing large-scale structures. The jet formation is thus not driven by an inverse cascade. Instead, it is due to a direct driving by Reynolds stresses from small-scale convective flows. Initial correlations are caused by the effect of uniform background rotation and shell geometry on the flows. While the jet growth suppresses convection, it increases the correlation of the convective flows, which further amplifies the jet growth until it is balanced by viscous dissipation. To a much smaller extent, energy is transferred upscale to large-scale vortices directly from the convective scales, mostly outside the tangent cylinder. There, large-scale vortices are not driven by an inverse cascade either. Inside the tangent cylinder, the transfer to large-scale vortices is weaker, but more local in spectral space, leaving open the possibility of an inverse cascade as a driver of large-scale vortices. In addition, large-scale vortices receive kinetic energy from the jets via forward transfer. We therefore suggest a jet instability as an alternative formation mechanism of largescale vortices. Finally, we find that the jet kinetic energy scales as $\ell^{-5}$, the same as for the zonostrophic regime.

astro-ph.EP↗

arXiv2022

Magnetic induction processes in Hot Jupiters, application to KELT-9b

The small semi-major axes of Hot Jupiters lead to high atmospheric temperatures of up to several thousand Kelvin. Under these conditions, thermally ionised metals provide a rich source of charged particles and thus build up a sizeable electrical conductivity. Subsequent electromagnetic effects, such as the induction of electric currents, Ohmic heating, magnetic drag, or the weakening of zonal winds have thus far been considered mainly in the framework of a linear, steady-state model of induction. For Hot Jupiters with an equilibrium temperature $T_{eq} > 1500$ K, the induction of atmospheric magnetic fields is a runaway process that can only be stopped by non-linear feedback. For example, the back-reaction of the magnetic field onto the flow via the Lorentz force or the occurrence of magnetic instabilities. Moreover, we discuss the possibility of self-excited atmospheric dynamos. Our results suggest that the induced atmospheric magnetic fields and electric currents become independent of the electrical conductivity and the internal field, but instead are limited by the planetary rotation rate and wind speed. As an explicit example, we characterise the induction process for the hottest exoplanet, KELT-9b by calculating the electrical conductivity along atmospheric $P-T$-profiles for the day- and nightside. Despite the temperature varying between 3000 K and 4500 K, the resulting electrical conductivity attains an elevated value of roughly 1 S/m throughout the atmosphere. The induced magnetic fields are predominately horizontal and might reach up to a saturation field strength of 400 mT, exceeding the internal field by two orders of magnitude.

astro-ph.EP↗

arXiv2021

Ionization and transport in partially ionized multicomponent plasmas: Application to atmospheres of hot Jupiters

We study ionization and transport processes in partially ionized multicomponent plasmas. The plasma composition is calculated via a system of coupled mass action laws. The electronic transport properties are determined by the electron-ion and electron-neutral transport cross sections. The influence of electron-electron scattering is considered via a correction factor to the electron-ion contribution. Based on this data, the electrical and thermal conductivity as well as the Lorenz number are calculated. For the thermal conductivity, we consider also the contributions of the translational motion of neutral particles and of the dissociation, ionization, and recombination reactions. We apply our approach to a partially ionized plasma composed of hydrogen, helium, and a small fraction of metals (Li, Na, Ca, Fe, K, Rb, Cs) as typical for hot Jupiter atmospheres. We present results for the plasma composition and the transport properties as function of density and temperature and then along typical P-T profiles for the outer part of the hot Jupiter HD 209458b. The electrical conductivity profile allows revising the Ohmic heating power related to the fierce winds in the planet's atmosphere. We show that the higher temperatures suggested by recent interior models could boost the conductivity and thus the Ohmic heating power to values large enough to explain the observed inflation of HD 209458b.

physics.plasm-ph↗

arXiv2021

Linking Zonal Winds and Gravity II: explaining the equatorially antisymmetric gravity moments of Jupiter

The recent gravity field measurements of Jupiter (Juno) and Saturn (Cassini) confirm the existence of deep zonal flows reaching to a depth of 5\% and 15\% of the respective radius. Relating the zonal wind induced density perturbations to the gravity moments has become a major tool to characterise the interior dynamics of gas giants. Previous studies differ with respect to the assumptions made on how the wind velocity relates to density anomalies, on the functional form of its decay with depth, and on the continuity of antisymmetric winds across the equatorial plane. Most of the suggested vertical structures exhibit a rather smooth radial decay of the zonal wind, which seems at odds with the observed secular variation of the magnetic field and the prevailing geostrophy of the zonal winds. Moreover, the results relied on an artificial equatorial regularisation or ignored the equatorial discontinuity altogether. We favour an alternative structure, where the equatorially antisymmetric zonal wind in an equatorial latitude belt between $\pm 21^\circ$ remains so shallow that it does not contribute to the gravity signal. The winds at higher latitudes suffice to convincingly explain the measured gravity moments. Our results indicate that the winds are geostrophic, i.e. constant along cylinders, in the outer $3000\,$ km and decay rapidly below. The preferred wind structure is 50\% deeper than previously thought, agrees with the measured gravity moment, is compliant with the magnetic constraints and the requirement of an adiabatic atmosphere and unbiased by the treatment of the equatorial discontinuity.

astro-ph.EP↗

arXiv2019

Linking Zonal Winds and Gravity: The Relative Importance of Dynamic Self Gravity

Recent precise measurements at Jupiter's and Saturn's gravity fields constrain the properties of the zonal flows in the outer envelopes of these planets. A simplified dynamic equation, sometimes called the thermal wind or thermo-gravitational wind equation, establishes a link between zonal flows and the related buoyancy perturbation, which in turn can be exploited to yield the dynamic gravity perturbation. Whether or not the action of the dynamic gravity perturbation needs to be explicitly included in this equation, an effect we call the Dynamic Self Gravity (DSG), has been a matter of intense debate. We show that, under reasonable assumptions, the equation can be solved (semi) analytically. This allows us to quantify the impact of the DSG on each gravity harmonic, practically independent of the zonal flow or the details of the planetary interior model. The impact decreases with growing spherical harmonic degree l. For degrees l=2 to about l=4, the DSG is a first order effect and should be taken into account in any attempt of inverting gravity measurements for zonal flow properties. For degrees of about l=5 to roughly l=10, the relative impact of DSG is about 10% and thus seems worthwhile to include, in particular since this comes at little extra costs with the method presented here. For yet higher degrees, is seems questionable whether gravity measurements or interior models will ever reach the required precision equivalent of the DSG impact of only a few percent of less.

astro-ph.EP↗

arXiv2019

Dynamo Action of Jupiter's Zonal Winds

The new data delivered by NASA's Juno spacecraft significantly increase our understanding of Jupiter's internal dynamics. The gravity data constrain the depth of the zonal flows observed at cloud level and suggest that they slow down considerably at a depth of about $0.96\,r_J$, where $r_J$ is the mean radius at the one bar level. Juno's magnetometer reveals the planet's internal magnetic field. We combine the new zonal flow and magnetic field models with an updated electrical conductivity profile to assess the zonal wind induced dynamo action, concentrating on the outer part of Jupiter's molecular hydrogen region where the conductivity increases very rapidly with depth. Dynamo action remains quasi-stationary and can thus reasonably be estimated where the magnetic Reynolds number remains smaller than one, which is roughly the region above $0.96\,r_J$. We calculate that the locally induced radial magnetic field reaches rms values of about $10^{-6}\,$T in this region and may just be detectable by the Juno mission. Very localized dynamo action and a distinct pattern that reflects the zonal wind system increases the chance to disentangle this locally induced field from the background field. The estimates of the locally induced currents also allow calculating the zonal flow related Ohmic heating and associated entropy production. The respective quantities remain below new revised predictions for the total dissipative heating and total entropy production in Jupiter for any of the explored model combinations. Thus neither Ohmic heating nor entropy production offer additional constraints on the depth of the zonal winds.

astro-ph.EP↗

arXiv2018

Penetrative Convection in Partly Stratified Rapidly Rotating Spherical Shells

Celestial objects host interfaces between convective and stable stratified interior regions. The interaction between both, e.g., the transfer of heat, mass, or angular momentum depends on whether and how flows penetrate into the stable layer. Powered from the unstable, convective regions, radial flows can pierce into the stable region depending on their inertia (overshooting). In rapidly rotating systems, the dynamics are strongly influenced by the Coriolis force and radial flows penetrate in stratified regions due to the geostrophic invariance of columnar convection even in the limit of vanishing inertia. Within this study, we numerically investigate both mechanisms and hence explore the nature of penetrative convection in rapidly rotating spherical shells. The study covers a broad range of system parameters, such as the strength of the stratification relative to the Coriolis force or the inertia. Guided by the application to Saturn, we model a sandwiched stable stratified layer (SSL) surrounded by two convective zones. A comprehensive analysis of the damping behavior of convective flows at the edges of the SSL showed that the mean penetration depth is controlled by the ratio of stratified and unstratified buoyancy gradients and is hence independent of rotation. A scaling law is derived and suggests that the penetration depth decreases with the square root of the ratio of unstabilizing and stabilizing entropy gradients. The influence of the Coriolis force, however, is evident by a modulation of the penetration depth along latitude, since convective columns are elongated vertically and hence pierce predominantly into the SSL around mid-latitudes and outside the tangent cylinder. Our result also show that the penetration depth decreases linearly with the flow length scale (low pass filter), confirming predictions from the linear theory of rotating partially stratified convection.

astro-ph.EP↗

arXiv2018

Dynamo Action in the Steeply Decaying Conductivity Region of Jupiter-like Dynamo Models

The Juno mission is delivering spectacular data of Jupiter's magnetic field, while the gravity measurements finally allow constraining the depth of the winds observed at cloud level. However, to which degree the zonal winds contribute to the planet's dynamo action remains an open question. Here we explore numerical dynamo simulations that include an Jupiter-like electrical conductivity profile and successfully model the planet's large scale field. We concentrate on analyzing the dynamo action in the Steeply Decaying Conductivity Region (SDCR) where the high conductivity in the metallic Hydrogen region drops to the much lower values caused by ionization effects in the very outer envelope of the planet. Our simulations show that the dynamo action in the SDCR is strongly ruled by diffusive effects and therefore quasi stationary. The locally induced magnetic field is dominated by the horizontal toroidal field, while the locally induced currents flow mainly in the latitudinal direction. The simple dynamics can be exploited to yield estimates of surprisingly high quality for both the induced field and the electric currents in the SDCR. These could be potentially be exploited to predict the dynamo action of the zonal winds in Jupiter's SDCR but also in other planets.

astro-ph.EP↗

arXiv2018

Material Properties for the Interiors of Massive Giant Planets and Brown Dwarfs

We present thermodynamic material and transport properties for the extreme conditions prevalent in the interiors of massive giant planets and brown dwarfs. They are obtained from extensive \textit{ab initio} simulations of hydrogen-helium mixtures along the isentropes of three representative objects. In particular, we determine the heat capacities, the thermal expansion coefficient, the isothermal compressibility, and the sound velocity. Important transport properties such as the electrical and thermal conductivity, opacity, and shear viscosity are also calculated. Further results for associated quantities including magnetic and thermal diffusivity, kinematic shear viscosity, as well as the static Love number $k_2$ and the equidistance are presented. In comparison to Jupiter-mass planets, the behavior inside massive giant planets and brown dwarfs is stronger dominated by degenerate matter. We discuss the implications on possible dynamics and magnetic fields of those massive objects. The consistent data set compiled here may serve as starting point to obtain material and transport properties for other substellar H-He objects with masses above one Jovian mass and finally may be used as input for dynamo simulations.

astro-ph.EP↗

arXiv2017

Modeling and predicting the short term evolution of the Geomagnetic field

The coupled evolution of the magnetic field and the flow at the Earth's core mantle boundary is modeled within the 1900.0-2014.0 time period. To constraint the dynamical behavior of the system with a core field model deriving from direct measurements of the Earth's magnetic field we used an Ensemble Kalman filter algorithm. By simulating an ensemble of possible states, access to the complete statistical properties of the considered fields is available. Furthermore, the method enables to provide predictions and to assess their reliability. In this study, we could highlight the cohabitation of two distinct flow regimes. One associated with the large scale part of the eccentric gyre, which evolves slowly in time and posses a very long memory of its past, and a faster one associated with the small scale velocity field. We show that the latter can exhibit rapid variations in localized areas. The combination of the two regimes can predict quite well the decadal variations in length of day, but it can also explain the discrepancies between the physically predicted and the observed trend in these variations. Hindcast tests demonstrate that the model is well balanced and that it can provide accurate short term predictions of a mean state and its associated uncertainties. However, magnetic field predictions are limited by the high randomization rate of the different velocity field scales, and after approximately 2000 years of forecast, no reliable information on the core field can be recovered.

physics.geo-ph↗

arXiv2017

Physical conditions for Jupiter-like dynamo models

The Juno mission will measure Jupiter's magnetic field with unprecedented precision and provide a wealth of additional data that will allow to constrain the planet's interior structure and dynamics. Here we analyse 66 numerical simulations in order to explore the sensitivity of the dynamo-generated magnetic field to the planets interior properties. The degree l=4 field model VIP4 and up-to-date interior models based on ab initio simulations serve as benchmarks. Our results suggest that VIP4-like magnetic fields can be found for a number of different models. We find that whether we assume an ideal gas or use the more realistic interior model based on ab initio simulations makes no difference. However, two other factors are important. Low Rayleigh number leads to strong axial dipole contribution while the axial dipole dominance is lost when the convective driving is too strong. The required intermediate range that yields Jupiter-like magnetic fields depends on the other system properties. The second factor is the convective magnetic Reynolds number profile Rmc(r), a product of the non-axisymmetric flow velocity and electrical conductivity. We find that the depth where Rmc exceeds about 50 is a good proxy for the top of the dynamo region. When the dynamo region sits too deep, the axial dipole is once more too dominant due to geometric reasons. We extrapolated our results to Jupiter and the result suggests that the Jovian dynamo extends to 95% of the planetary radius. The zonal flows in our simulations are dominated by an equatorial jet largely confined to the molecular layer. Where the jet reaches down to higher electrical conductivities, it is gives rise to a secondary alpha-Omega dynamo that modifies the dipole-dominated field produced deeper in the planet. This secondary dynamo can lead to strong magnetic field patches at low latitudes that seem compatible with the VIP4 model.

astro-ph.EP↗

arXiv2017

Mercury's magnetic field in the MESSENGER era

MESSENGER magnetometer data show that Mercury's magnetic field is not only exceptionally weak but also has a unique geometry. The internal field resembles an axial dipole that is offset to the North by 20% of the planetary radius. This implies that the axial quadrupol is particularly strong while the dipole tilt is likely below 0.8 degree. The close proximity to the sun in combination with the weak internal field results in a very small and highly dynamic Hermean magnetosphere. We review the current understanding of Mercury's internal and external magnetic field and discuss possible explanations. Classical convection driven core dynamos have a hard time to reproduce the observations. Strong quadrupol contributions can be promoted by different measures, but they always go along with a large dipole tilt and generally rather small scale fields. A stably stratified outer core region seems required to explain not only the particular geometry but also the weakness of the Hermean magnetic field. New interior models suggest that Mercury's core likely hosts an iron snow zone underneath the core-mantle boundary. The positive radial sulfur gradient likely to develop in such a zone would indeed promote stable stratification. However, even dynamo models that include the stable layer show Mercury-like magnetic fields only for a fraction of the total simulation time. Large scale variations in the core-mantle boundary heat flux promise to yield more persistent results but are not compatible with the current understanding of Mercury's lower mantle.

astro-ph.EP↗

arXiv2016

Reversal and amplification of zonal flows by boundary enforced thermal wind

Zonal flows in rapidly-rotating celestial objects such as the Sun, gas or ice giants form in a variety of surface patterns and amplitudes. Whereas the differential rotation on the Sun, Jupiter and Saturn features a super-rotating equatorial region, the ice giants, Neptune and Uranus harbour an equatorial jet slower than the planetary rotation. Global numerical models covering the optically thick, deep-reaching and rapidly rotating convective envelopes of gas giants reproduce successfully the prograde jet at the equator. In such models, convective columns shaped by the dominant Coriolis force typically exhibit a consistent prograde tilt. Hence angular momentum is pumped away from the rotation axis via Reynolds stresses. Those models are found to be strongly geostrophic, hence a modulation of the zonal flow structure along the axis of rotation, e.g. introduced by persistent latitudinal temperature gradients, seems of minor importance. Within our study we stimulate these thermal gradients and the resulting ageostrophic flows by applying an axisymmetric and equatorially symmetric outer boundary heat flux anomaly ($Y_{20}$) with variable amplitude and sign. Such a forcing pattern mimics the thermal effect of intense solar or stellar irradiation. Our results suggest that the ageostrophic flows are linearly amplified with the forcing amplitude $q^\star$ leading to a more pronounced dimple of the equatorial jet (alike Jupiter). The geostrophic flow contributions, however, are suppressed for weak $q^\star$, but inverted and re-amplified once $q^\star$ exceeds a critical value. The inverse geostrophic differential rotation is consistently maintained by now also inversely tilted columns and reminiscent of zonal flow profiles observed for the ice giants. Analysis of the main force balance and parameter studies further foster these results.

physics.geo-ph↗