arXiv subjects

Nadine Nettelmann

Publications and source records attributed to Nadine Nettelmann.

At least 19 recordsLinked to original sources

arXiv2025

Roadmap for warm dense matter physics

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations \& experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

physics.plasm-ph↗

arXiv2025

Jupiter's Interior with an Inverted Helium Gradient

Jupiter's gravity field observed by NASA's Juno spacecraft indicates that the density in the 10--100 GPa region is lower than one would expect from a H/He adiabat with 0.5-5x solar water abundance as has been observationally inferred in Jupiter's atmosphere, supported by the 2--4$\times$ solar enrichment in the heavy noble gases and other volatiles observed by the Galileo entry probe. Here, we assume that Jupiter's envelope harbors a radiative window at ~0.975-0.99 RJ. This outer stable layer (OSL) delays particle exchange and accelerates the cooling of the deep interior. Consequently, the He-depletion at the Mbar-level where H/He phase separation occurs would be stronger than seen in the atmosphere. We find that the inverted He-gradient across the OSL leads to atmospheric heavy element abundances that are up to dZatm=0.03 (+2x solar) higher than for adiabatic models. With an additional inverted Z-gradient, Zatm up to 3x solar is possible. Models with 1x solar Zatm have a dilute core confined to the inner 0.2-0.3 MJ (0.4-0.5 RJ), smaller than in adiabatic models. Models with 3x solar Zatm have a largely homogeneous-Z interior at 1x solar. The low observed atmospheric Ne/He ratio suggests that Ne is transported through the OSL as efficiently as He is and at an enhanced diffusivity as is characteristic of double diffusive convection. Better knowledge of the H/He-EOS in the 10--100 GPa region and of the H/He phase diagram is needed to understand Jupiter's interior structure.

astro-ph.EP↗

arXiv2024

Evolution of steam worlds: energetic aspects

Sub-Neptunes occupy an intriguing region of planetary mass-radius space, where theoretical models of interior structure predict that they could be water-rich, where water is in steam and supercritical state. Such planets are expected to evolve according to the same principles as canonical H$_2$-He rich planets, but models that assume a water-dominated atmosphere consistent with the interior have not been developed yet. Here, we present a state of the art structure and evolution model for water-rich sub-Neptunes. Our set-up combines an existing atmosphere model that controls the heat loss from the planet, and an interior model that acts as the reservoir of energy. We compute evolutionary tracks of planetary radius over time. We find that planets with pure water envelopes have smaller radii than predicted by previous models, and the change in radius is much slower (within $\sim$10\%). We also find that water in the deep interior is colder than previously suggested, and can transition from plasma state to superionic ice, which can have additional implications for their evolution. We provide a grid of evolutionary tracks that can be used to infer the bulk water content of sub-Neptunes. We compare the bulk water content inferred by this model and other models available in the literature, and find statistically significant differences between models when the uncertainty on measured mass and radius are both smaller than 10\%. This study shows the importance of pursuing efforts in the modeling of volatile-rich planets, and how to connect them to observations.

astro-ph.EP↗

arXiv2024

Uranus Study Report: KISS

Determining the internal structure of Uranus is a key objective for planetary science. Knowledge of Uranus's bulk composition and the distribution of elements is crucial to understanding its origin and evolutionary path. In addition, Uranus represents a poorly understood class of intermediate-mass planets (intermediate in size between the relatively well studied terrestrial and gas giant planets), which appear to be very common in the Galaxy. As a result, a better characterization of Uranus will also help us to better understand exoplanets in this mass and size regime. Recognizing the importance of Uranus, a Keck Institute for Space Studies (KISS) workshop was held in September 2023 to investigate how we can improve our knowledge of Uranus's internal structure in the context of a future Uranus mission that includes an orbiter and a probe. The scientific goals and objectives of the recently released Planetary Science and Astrobiology Decadal Survey were taken as our starting point. We reviewed our current knowledge of Uranus's interior and identified measurement and other mission requirements for a future Uranus spacecraft, providing more detail than was possible in the Decadal Survey's mission study and including new insights into the measurements to be made. We also identified important knowledge gaps to be closed with Earth-based efforts in the near term that will help guide the design of the mission and interpret the data returned.

astro-ph.IM↗

arXiv2024

H$_{2}$-H$_{2}$O demixing in Uranus and Neptune: Adiabatic structure models

Demixing properties of planetary major constituents influence the interior structure and evolution of planets. Comparing experimental and computational data on the miscibility of hydrogen and water to adiabatic profiles suggests phase separation between these components occurs in the ice giants Uranus and Neptune. We aim to predict the atmospheric water abundance and transition pressure between the water-poor outer envelope and the water-rich deep interior in Uranus and Neptune. We construct seven H2-H2O phase diagrams from the available experimental and computational data. We compute interior adiabatic structure models and compare these to the phase diagrams to infer whether demixing is occurring. We obtain a strong water depletion in the top layer due to rain-out of water and find upper limits on the atmospheric water mass fraction Z_atm of 0.21 for Uranus and 0.16 for Neptune. The transition from the water-poor to the water-rich layer is sharp and occurs at pressures P_Z between 4 and 11 GPa. Using these constraints on Z_atm and P_Z, we find that the observed gravitational harmonics J2 and J4 can be reproduced if P_Z > 10 GPa in Uranus and > 5 GPa in Neptune, and if the deep interior has a high primordial water mass fraction of 0.8, unless rocks are also present. The agreement with J4 is improved if rocks are confined deeper than P_Z, for instance below a rock cloud level at 2000 K (20-30 GPa). These findings confirm classical few-layer models and suggest that a layered structure may result from a combination of primordial mass accretion and subsequent phase separation. Reduced observational uncertainty in J4 and its dynamic contribution, atmospheric water abundance measurements from an Orbiter with a Probe mission to Uranus (UOP) or Neptune, and better understanding of the mixing behaviour of constituents are needed to constrain the interiors of ice giants.

astro-ph.EP↗

arXiv2023

On the hypothesis of an inverted Z-gradient inside Jupiter

Models of Jupiter s interior struggle to agree with measurements of the atmospheric composition. Interior models favour a subsolar or solar abundance of heavy elements Z while atmospheric measurements suggest a supersolar abundance. One potential solution may be the presence of an inverted Z-gradient, namely an inward decrease of Z, which implies a larger heavy element abundance in the atmosphere than in the outer envelope. We investigate two scenarios in which the inverted Z gradient is located either where helium rain occurs (Mbar level) or at upper levels (kbar level) where a radiative region could exist. We aim to assess how plausible these scenarios are. We calculate interior and evolution models of Jupiter with such inverted Z-gradient and use constraints on the stability and the formation of an inverted Z-gradient. We find that an inverted Z-gradient at the location of helium rain cannot work as it requires a late accretion and of too much material. We find interior models with an inverted Z-gradient at upper levels, due to a radiative zone preventing downward mixing, that could satisfy the present gravity field of the planet. However, our evolution models suggest that this second scenario might not be in place. An inverted Z-gradient in Jupiter could be stable. Yet, its presence either at the Mbar level or kbar level is rather unlikely.

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↗

arXiv2022

The nature of gas giant planets

Revealing the true nature of the gas giant planets in our Solar System is challenging. The masses of Jupiter and Saturn are about 318 and 95 Earth masses, respectively. While they mostly consist of hydrogen and helium, the total mass and distribution of the heavier elements, which reveal information on their origin, are still unknown. Recent accurate measurements of the gravitational fields of Jupiter and Saturn together with knowledge of the behavior of planetary materials at high pressures allow us to better constrain their interiors. Updated structure models of Jupiter and Saturn suggest that both planets have complex interiors that include composition inhomogeneities, non-convective regions, and fuzzy cores. In addition, it is clear that there are significant differences between Jupiter and Saturn and that each giant planet is unique. This has direct implications for giant exoplanet characterization and for our understanding of gaseous planets as a class of astronomical objects. In this review we summarize the methods used to model giant planet interiors and recent developments in giant planet structure models.

astro-ph.EP↗

arXiv2022

Revelations on Jupiter's Formation, Evolution and Interior: Challenges from Juno Results

The Juno mission has revolutionized and challenged our understanding of Jupiter. As Juno transitioned to its extended mission, we review the major findings of Jupiter's internal structure relevant to understanding Jupiter's formation and evolution. Results from Juno's investigation of Jupiter's interior structure imply that the planet has compositional gradients and is accordingly non-adiabatic, with a complex internal structure. These new results imply that current models of Jupiter's formation and evolution require a revision. In this paper, we discuss potential formation and evolution paths that can lead to an internal structure model consistent with Juno data, and the constraints they provide. We note that standard core accretion formation models, including the heavy-element enrichment during planetary growth is consistent with an interior that is inhomogeneous with composition gradients in its deep interior. However, such formation models typically predict that this region, which could be interpreted as a primordial dilute core, is confined to about 10% of Jupiter's total mass. In contrast, structure models that fit Juno data imply that this region contains 30% of the mass or more. One way to explain the origin of this extended region is by invoking a relatively long (about 2 Myrs) formation phase where the growing planet accretes gas and planetesimals delaying the runaway gas accretion. Alternatively, Jupiter's fuzzy core could be a result of a giant impact or convection post-formation. These novel scenarios require somewhat special and specific conditions. Clarity on the plausibility of such conditions could come from future high-resolution observations of planet-forming regions around other stars, from the observed and modeled architectures of extrasolar systems with giant planets, and future Juno data obtained during its extended mission.

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arXiv2021

Exoplanetary Interiors

The first mass-estimate of an exoplanet around a Sun-like star, 51 Peg b and the first radius measurement of an exoplanet, HD209458b pointed to the challenges of understanding the atmosphere, interior, and evolution of exoplanets including the possibility of mass loss of planets on close-orbits that are exposed to strong irradiation. These discoveries raised the question of heating and inflation mechanisms, and of the nature of these objects in terms of composition compared to the known planets in the Solar system. The field of exoplanet interior modeling was born. Here, we outline and discuss current big science questions: (i) What is the amount of heavy elements in a planet and do all planets possess an iron-rock core? We suggest that a promising and novel approach for exoplanets can be measuring their tidal response in form of the Love numbers h2 and k2. (ii) How much and through what mechanisms are the interiors of planets heated or delayed from cooling? Many strongly irradiated gaseous planets require an additional heat source to explain their large radii. (iii) What is the origin of the observed populations in the radius-period diagram? Objects in and along the radius valley are excellent targets to study planetary formation and evaporation. (iv) What does the composition of rocky planets tell us about their formation? Planets more iron-rich than Mercury are found, as well as planets that if rocky, are depleted in iron with respect to Earth. We do not have yet a reliable formation theory that would explain their existence.

astro-ph.EP↗

arXiv2021

Thermal evolution of Uranus and Neptune II -- Deep thermal boundary layer

Thermal evolution models suggest that the luminosities of both Uranus and Neptune are inconsistent with the classical assumption of an adiabatic interior. Such models commonly predict Uranus to be brighter and, recently, Neptune to be fainter than observed. In this work, we investigate the influence of a thermally conductive boundary layer on the evolution of Uranus- and Neptune-like planets. This thermal boundary layer (TBL) is assumed to be located deep in the planet, and be caused by a steep compositional gradient between a H-He-dominated outer envelope and an ice-rich inner envelope. We investigate the effect of TBL thickness, thermal conductivity, and the time of TBL formation on the planet's cooling behaviour. The calculations were performed with our recently developed tool based on the Henyey method for stellar evolution. We make use of state-of-the-art equations of state for hydrogen, helium, and water, as well as of thermal conductivity data for water calculated via ab initio methods. We find that even a thin conductive layer of a few kilometres has a significant influence on the planetary cooling. In our models, Uranus' measured luminosity can only be reproduced if the planet has been near equilibrium with the solar incident flux for an extended time. For Neptune, we find a range of solutions with a near constant effective temperature at layer thicknesses of 15 km or larger, similar to Uranus. In addition, we find solutions for thin TBLs of few km and strongly enhanced thermal conductivity. A $\sim$ 1$~$Gyr later onset of the TBL reduces the present $ΔT$ by an order of magnitude to only several 100 K. Our models suggest that a TBL can significantly influence the present planetary luminosity in both directions, making it appear either brighter or fainter than the adiabatic case.

astro-ph.EP↗

arXiv2020

Keys of a Mission to Uranus or Neptune, the Closest Ice Giants

Uranus and Neptune are the archetypes of "ice giants", a class of planets that may be among the most common in the Galaxy. They hold the keys to understand the atmospheric dynamics and structure of planets with hydrogen atmospheres inside and outside the solar system; however, they are also the last unexplored planets of the Solar System. Their atmospheres are active and storms are believed to be fueled by methane condensation which is both extremely abundant and occurs at low optical depth. This means that mapping temperature and methane abundance as a function of position and depth will inform us on how convection organizes in an atmosphere with no surface and condensates that are heavier than the surrounding air, a general feature of giant planets. Owing to the spatial and temporal variability of these atmospheres, an orbiter is required. A probe would provide a reference atmospheric profile to lift ambiguities inherent to remote observations. It would also measure the abundances of noble gases which can be used to reconstruct the history of planet formation in the Solar System. Finally, mapping the planets' gravity and magnetic fields will be essential to constrain their global composition, atmospheric dynamics, structure and evolution. An exploration of Uranus or Neptune will be essential to understand these planets and will also be key to constrain and analyze data obtained at Jupiter, Saturn, and for numerous exoplanets with hydrogen atmospheres.

astro-ph.IM↗

arXiv2020

Uranus and Neptune: Origin, Evolution and Internal Structure

There are still many open questions regarding the nature of Uranus and Neptune, the outermost planets in the Solar System. In this review we summarize the current-knowledge about Uranus and Neptune with a focus on their composition and internal structure, formation including potential subsequent giant impacts, and thermal evolution. We present key open questions and discuss the uncertainty in the internal structures of the planets due to the possibility of non-adiabatic and inhomogeneous interiors. We also provide the reasoning for improved observational constraints on their fundamental physical parameters such as their gravitational and magnetic fields, rotation rates, and deep atmospheric composition and temperature. Only this way will we be able to improve our understating of these planetary objects, and the many similar-sized objects orbiting other stars.

astro-ph.EP↗

arXiv2019

Machine learning inference of the interior structure of low-mass exoplanets

We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number $k_2$ bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding $k_2$as an input to the MDN significantly decreases the degeneracy of the possible interior structures.

astro-ph.EP↗

arXiv2019

The Effect of Clouds as an Additional Opacity Source on the Inferred Metallicity of Giant Exoplanets

Atmospheres regulate the planetary heat loss and therefore influence planetary thermal evolution. Uncertainty in a giant planet's thermal state contributes to the uncertainty in the inferred abundance of heavy elements it contains. Within an analytic atmosphere model, we here investigate the influence that different cloud opacities and cloud depths can have on the metallicity of irradiated extrasolar gas giants, which is inferred from interior models. In this work, the link between inferred metallicity and assumed cloud properties is the thermal profile of atmosphere and interior. Therefore, we perform coupled atmosphere, interior, and evolution calculations. The atmosphere model includes clouds in a much simplified manner; it includes long-wave absorption but neglects shortwave scattering. Within that model, we show that optically thick, high clouds have negligible influence, whereas deep-seated, optically very thick clouds can lead to warmer deep tropospheres and therefore higher bulk heavy element mass estimates. For the young hot Jupiter WASP-10b, we find a possible enhancement in inferred metallicity of up to 10% due to possible silicate clouds at $\sim$0.3 bar. For WASP-39b, whose observationally derived metallicity is higher than predicted by cloudless models, we find an enhancement by at most 50%. However, further work on cloud properties and their self-consistent coupling to the atmospheric structure is needed in order to reduce uncertainties in the choice of model parameter values, in particular of cloud opacities.

astro-ph.EP↗

arXiv2019

Thermal evolution of Uranus and Neptune I: adiabatic models

The brightness of Neptune is often found to be in accordance with an adiabatic interior, while the low luminosity of Uranus challenges this assumption. Here we apply revised equation of state data of hydrogen, helium, and water and compute the thermal evolution of Uranus and Neptune assuming an adiabatic interior. For this purpose, we have developed a new planetary model and evolution code. We investigate the influence of albedo, solar energy influx, and equations of state of H and He, and water on the cooling time. Our cooling times of about $τ_\text{U}=5.1\times 10^9\text{ years}$ for Uranus and $τ_\text{N}=3.7\times 10^9\text{ years}$ for Neptune bracket the known age of the planets of $4.56\times 10^9\text{ years}$ implying that neither planet's present-day luminosity can be explained by adiabatic cooling. We also find that uncertainties on input parameters such as the level of irradiation matter generally more for Uranus than for Neptune. Our results suggest that in contrast to common assumptions, neither planet is fully adiabatic in the deeper interior.

astro-ph.EP↗

arXiv2019

Tesseral harmonics of Jupiter from static tidal response

The Juno Orbiter is measuring the three-dimensional gravity field perturbation of Jupiter induced by its rapid rotation, zonal flows, and tidal response to its major natural satellites. This paper aims to provide the contributions to the tesseral harmonics coefficients Cnm, Snm, and the Love numbers knm to be expected from static tidal response in the gravity field of rotating Jupiter. For that purpose, we apply the method of Concentric Maclaurin Ellipsoids (CMS). As we are interested in the variation of the tidal potential with the longitudes of the moons, we take into account the simultaneous presence of the satellites Io, Europa, and Ganymede. We assume co-planar, circular orbits with normals parallel to Jupiter's spin axis. The planet-centered longitude of Io in the three-moon case is arbitrarily assumed varphi = 0. Under these assumptions we find maximum amplitudes and fluctuations of 3.5 times 10^-8 +- 15% for C22. For the Love numbers, largest variation of 10% to 20% is seen in k42 and k62, whereas the values k2, k33, and k44 fall into narrow ranges of 0.1% uncertainty or less. In particular, we find k2=k2,Io(1 +- 0.02%) where k2,Io=0.5897 is the static tidal response to lone Io. Our obtained gravity field perturbation leads to a maximum equatorial shape deformation of up to 28m. We suggest that should Juno measurements of the knm deviate from those values, it may be due to dynamic or dissipative effects on Jupiter's tidal response. Finally, an analytic expression is provided to calculate the tesseral harmonics contribution from static tidal response for any configuration of the satellites.

astro-ph.EP↗

arXiv2017

Planetary Ices and the Linear Mixing Approximation

The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ($\mathrm{T_{core}} \mathtt{\sim}$ 4000 K).

astro-ph.EP↗