arXiv subjects

Simon Müller

Publications and source records attributed to Simon Müller.

At least 37 records · Page 2Linked to original sources

arXiv2024

Giant exoplanet composition: Why do the hydrogen-helium equation of state and interior structure matter?

Revealing the internal composition and structure of giant planets is fundamental for understanding planetary formation. However, the bulk composition can only be inferred through interior models. As a result, advancements in modelling aspects are essential to better characterise the interiors of giant planets. We investigate the effects of model assumptions such as the interior structure and the hydrogen-helium (H-He) equation of state (EOS) on the inferred interiors of giant exoplanets. We first assess these effects on a few test cases and compare H-He EOSs. We then calculate evolution models and infer the planetary bulk metallicity of 45 warm exoplanets, ranging from 0.1 to 10~$M_{\rm J}$. Planets with masses between about 0.2 and 0.6~$M_{\rm J}$ are most sensitive to the H-He EOS. Updating the H-He EOS reduces the inferred heavy-element mass, with an absolute difference in bulk metallicity of up to 13\%. Concentrating heavy elements in a core, rather than distributing them uniformly (and scaling opacities with metallicity), reduces the inferred metallicity (up to 17\%). The assumed internal structure, along with its effect on the envelope opacity, has the greatest effect on the inferred composition of massive planets ($M_{\rm p}>4~M_{\rm J}$). For $M_{\rm p}>0.6~M_{\rm J}$, the observational uncertainties on radii and ages lead to uncertainties in the inferred metallicity (up to 31\%) which are larger than the ones associated with the used H-He EOS and the assumed interior structure. However, for planets with $0.2<M_{\rm p}<0.6~M_{\rm J}$, the theoretical uncertainties are larger. Advancements in equations of state and our understanding of giant planet interior structures combined with accurate measurements of the planetary radius and age are crucial for characterising giant exoplanets.

astro-ph.EP↗

arXiv2024

The interior of Uranus: Thermal profile, bulk composition and the distribution of rock, water and hydrogen and helium

We present improved empirical density profiles of Uranus and interpret them in terms of their temperature and composition using a new random algorithm. The algorithm to determine the temperature and composition is agnostic with respect to the temperature gradient in non-isentropic regions and chooses randomly amongst all possible gradients that are stable against convection and correspond to an Equation of State compatible composition. Our empirical models are based on an efficient implementation of the Theory of Figures up to 10th order including a proper treatment of the atmosphere. The accuracy of 10th order ToF enables us to present accurate calculations of the gravitational moments of Uranus up to $J_{14}$: $J_{6} = ( 5.3078 \pm 0.3312)\cdot10^{-7}$, $J_{8} = (-1.1114 \pm 0.1391)\cdot10^{-8}$, $J_{10} = ( 2.8616 \pm 0.5466)\cdot10^{-10}$, $J_{12} = (-8.4684 \pm 2.0889)\cdot10^{-12}$ and $J_{14} = ( 2.7508 \pm 0.7944)\cdot10^{-13}$. We consider two interior models of Uranus that differ with respect to the maximal number of materials allowed per layer of Uranus (three vs. four composition components). The case with three materials does not allow Hydrogen and Helium in deeper parts of Uranus and results in a higher water abundance which leads to lower central temperatures. On the other hand, the models with four materials allow H-He to be mixed into the deeper interior and lead to rock-dominated solutions. We find that these four composition components models are less reliable due to the underlying empirical models incompatibility with realistic Brunt frequencies. Most of our models are found to be either purely convective with the exception of boundary layers, or only convective in the outermost region. Almost all of our models possess a region that is convective and consists of ionic H$_{2}$O which could explain the generation of Uranus' magnetic field.

astro-ph.EP↗

arXiv2024

Exploring pNIPAM Lyogels: Experimental Study on Swelling Equilibria in Various Organic Solvents and Mixtures, Supported by COSMO-RS Analysis

Stimuli-responsive lyogels are considered to be smart materials due to their capability of undergoing significant macroscopic changes in response to external triggers. Due to their versatile and unique properties, smart lyogels exhibit great potential in various applications such as drug delivery or actuation processes. While Poly-N-isopropylacrylamide (pNIPAM) is widely known as a thermo-responsive material, it also shows significant solvent-responsive swelling behavior. As polar solvents induce strong swelling due to hydrogen bonding with the amide group, nonpolar solvents lead to significant shrinkage of the lyogels. The aim of this study is to investigate and to model this behavior for future application in chemical or biochemical reactors. As a current area of research, incorporating smart hydrogel technology into (bio-)chemical reactors facilitates the development of smart reactor systems. Applying thermodynamic modelling with the gE model COSMO-RS on the monomer or oligomers of pNIPAM, the correlation between solvent-polymer interactions and the degree of swelling can be observed. pNIPAM derivatives exhibit low infinitive dilution activity coefficients (IDACs) in polar solvents with large degrees of swelling, while displaying an increase of IDACs in nonpolar solvents. Hydrogen bonds dominate the swelling behavior of lyogels not only in pure solvents but also in mixtures of solvents with varying polarity. Even in mixtures containing high amounts of nonpolar solvents, large degrees of swelling were observed due to the uptake of the polar solvent in the lyogel matrix. This effect can be observed in binary solvent mixtures but also in representative mixtures along an esterification reaction with varying carboxylic chain length of alcohol and carboxylic acids.

cond-mat.soft↗

arXiv2024

Evolution of Jupiter and Saturn with helium rain

Phase separation between hydrogen and helium at high pressures and temperatures leads to the rainout of helium in the deep interiors of Jupiter and Saturn. This process, also known as "helium rain", affects their long-term evolution. Therefore, modelling the evolution and internal structure of Jupiter and Saturn (and giant exoplanets) relies on the phase diagram of hydrogen and helium. In this work, we simulate the evolution of Jupiter and Saturn with helium rain by applying different phase diagrams of hydrogen and helium. We find that consistency between Jupiter s evolution and the Galileo measurement of its atmospheric helium abundance is achieved only if a shift in temperature in the existing phase diagrams is applied (-1250 K, +350 K or -3850 K depending on the used phase diagram). We next use the shifted phase diagrams to model Saturn s evolution and find consistent solutions for both planets. We confirm that demixing in Jupiter is modest while in Saturn, the process of helium rain is significant. We find that Saturn has a large helium gradient and a helium ocean. Saturn s atmospheric helium mass fraction is estimated to be between 0.13 and 0.16. We also investigate how the used hydrogen-helium equation of state and atmospheric model affect the planetary evolution and find that the predicted cooling times can change by several hundred million years. Constraining the level of super-adiabaticity in the helium gradient formed in Jupiter and Saturn remains challenging and should be investigated in detail in future research. We conclude that further explorations of the immiscibility between hydrogen and helium are valuable as this knowledge directly affects the evolution and current-state structure of Jupiter and Saturn. Finally, we argue that measuring Saturn s atmospheric helium content is crucial for constraining Saturn s evolution as well as the hydrogen-helium phase diagram.

astro-ph.EP↗

arXiv2024

An extended low-density atmosphere around the Jupiter-sized planet WASP-193 b

Gas giants transiting bright nearby stars provide crucial insights into planetary system formation and evolution mechanisms. Most of these planets exhibit certain average characteristics, serving as benchmarks for our understanding of planetary systems. However, outliers like the planet we present in this study, WASP-193b, offer unique opportunities to explore unconventional formation and evolution processes. This planet completes an orbit around its Vmag=12.2 F9 main-sequence host star every 6.25 d. Our analyses found that WASP-193b has a mass of Mp=0.139+/-0.029 MJup and a radius of Rp=1.464+/-0.058 RJup, translating into an extremely low density of rho_p = 0.059+/-0.014 g/cm^3, at least one order of magnitude less than standard gas giants like Jupiter. Typical gas giants such as Jupiter have densities that range between 0.2 and 2 g/cm^3. The combination of its large transit depth (dF~1.4%), its extremely-low density, its high-equilibrium temperature (Teq = 1254+/-31 K), and the infrared brightness of its host star (magnitude Kmag=10.7) makes WASP-193b an exquisite target for characterization by transmission spectroscopy (transmission spectroscopy metric: TSM~600). One single JWST transit observation would yield detailed insights into its atmospheric properties and planetary mass, providing a unique window to explore the mechanisms behind its exceptionally low density and shed light on giant planets' diverse nature.

astro-ph.EP↗

arXiv2024

Predicting solvation free energies for neutral molecules in any solvent with openCOSMO-RS

The accurate prediction of solvation free energies is critical for understanding various phenomena in the liquid phase, including reaction rates, equilibrium constants, activity coefficients, and partition coefficients. Despite extensive research, precise prediction of solvation free energies remains challenging. In this study, we introduce openCOSMO-RS 24a, an improved version of the open-source COSMO-RS model, capable of predicting solvation free energies alongside other liquid-phase properties. We parameterize openCOSMO-RS 24a using quantum chemical calculations from ORCA 6.0, leveraging a comprehensive dataset that includes solvation free energies, partition coefficients, and infinite dilution activity coefficients for various solutes and solvents at 25 °C. Additionally, we develop a Quantitative Structure-Property Relationships model to predict molar volumes of the solvents, an essential requirement for predicting solvation free energies from structure alone. Our results show that openCOSMO-RS 24a achieves an average absolute deviation of 0.45 kcal/mol for solvation free energies, 0.76 for partition coefficients, and 0.51 for infinite dilution activity coefficients, demonstrating improvements over the previous openCOSMO-RS 22 parameterization and comparable results to COSMOtherm 24 TZVP. A new command line interface for openCOSMO-RS 24a was developed which allows easy acces to the solvation energy model directly from within ORCA 6.0. This represents a significant advancement in the predictive modeling of solvation free energies and other solution-phase properties, providing researchers with a robust tool for applications in chemical and materials science.

physics.chem-ph↗

arXiv2024

TOI-2374 b and TOI-3071 b: two metal-rich sub-Saturns well within the Neptunian desert

We report the discovery of two transiting planets detected by the Transiting Exoplanet Survey Satellite (TESS), TOI-2374 b and TOI-3071 b, orbiting a K5V and an F8V star, respectively, with periods of 4.31 and 1.27 days, respectively. We confirm and characterize these two planets with a variety of ground-based and follow-up observations, including photometry, precise radial velocity monitoring and high-resolution imaging. The planetary and orbital parameters were derived from a joint analysis of the radial velocities and photometric data. We found that the two planets have masses of $(57 \pm 4)$ $M_\oplus$ or $(0.18 \pm 0.01)$ $M_J$, and $(68 \pm 4)$ $M_\oplus$ or $(0.21 \pm 0.01)$ $M_J$, respectively, and they have radii of $(6.8 \pm 0.3)$ $R_\oplus$ or $(0.61 \pm 0.03)$ $R_J$ and $(7.2 \pm 0.5)$ $R_\oplus$ or $(0.64 \pm 0.05)$ $R_J$, respectively. These parameters correspond to sub-Saturns within the Neptunian desert, both planets being hot and highly irradiated, with $T_{\rm eq} \approx 745$ $K$ and $T_{\rm eq} \approx 1812$ $K$, respectively, assuming a Bond albedo of 0.5. TOI-3071 b has the hottest equilibrium temperature of all known planets with masses between $10$ and $300$ $M_\oplus$ and radii less than $1.5$ $R_J$. By applying gas giant evolution models we found that both planets, especially TOI-3071 b, are very metal-rich. This challenges standard formation models which generally predict lower heavy-element masses for planets with similar characteristics. We studied the evolution of the planets' atmospheres under photoevaporation and concluded that both are stable against evaporation due to their large masses and likely high metallicities in their gaseous envelopes.

astro-ph.EP↗

arXiv2024

A comprehensive approach to incorporating intermolecular dispersion into the openCOSMO-RS model. Part 1: Halocarbons

The COSMO-RS (Conductor-like Screening Model for Real Solvents) is a predictive thermodynamic model that has found diverse applications in various domains like chemical engineering, environmental chemistry, nanotechnology, material science, and biotechnology. Its core concept involves calculating the screening charge density on the surface of each molecule and letting these surface patches interact with each other to calculate thermodynamic properties. In this study, we aim to enhance the performance of the open-source implementation openCOSMO-RS by incorporating dispersive interactions between the paired segments. Several parametrizations were systematically evaluated through the extensive regression analysis using a comprehensive database of Vapor-Liquid Equilibrium (VLE), Liquid-Liquid Equilibrium (LLE) and Infinite Dilution Activity Coefficients (IDACs). Furthermore, the influence of different combinatorial terms on the model performance was investigated. Our findings indicate that incorporating dispersive interactions significantly improves the accuracy of phase equilibrium predictions for halocarbons and refrigerant mixtures.

cond-mat.soft↗

arXiv2024

Can Jupiter's atmospheric metallicity be different from the deep interior?

Updated formation and structure models of Jupiter predict a metal-poor envelope. This is at odds with the two to three times solar metallicity measured by the Galileo probe. Additionally, Juno data imply that water and ammonia are enriched. Here we explore whether Jupiter can have a deep radiative layer separating the atmosphere from the deeper interior. The radiative layer could be caused by a hydrogen-transparency window or depletion of alkali metals. We show that heavy-element accretion during Jupiter's evolution can lead to the desired atmospheric enrichment and that this configuration is stable over billions of years. The origin of the heavy elements could be cumulative small impacts or one large impact. The preferred scenario requires a deep radiative zone due to a local reduction of the opacity at $\sim$ 2000 K by $\sim$ 90%, which is supported by Juno data, and vertical mixing through the boundary with a similar efficiency to molecular diffusion ($D \lesssim 10^{-2}$ cm$^2$/s). Therefore, most of Jupiter's molecular envelope could have solar composition while its uppermost atmosphere is enriched with heavier elements. The enrichment likely originates from the accretion of solid objects. This possibility resolves the long-standing mismatch between Jupiter's interior models and atmospheric composition measurements. Furthermore, our results imply that the measured atmospheric composition of exoplanets does not necessarily reflect their bulk compositions. We also investigate whether the enrichment could be due to the erosion of a dilute core and show that this is highly unlikely. The core-erosion scenario is inconsistent with evolution calculations, the deep radiative layer, and published interior models.

astro-ph.EP↗

arXiv2024

The mass-radius relation of exoplanets, revisited

Determining the mass-radius ($M$-$R$) relation of exoplanets is important for exoplanet characterization. Here we present a re-analysis of the $M$-$R$ relations and their transitions using exoplanetary data from the PlanetS catalog which only includes planets with reliable mass and radius determinations. We find that "small planets" correspond to planets with masses of up to $\sim4.4 M_\oplus$ (within 17%) where $R \propto M^{0.27}$. Planets with masses between $\sim4.4$ and $127 M_\oplus$ (within 5%) can be viewed as "intermediate-mass" planets, where $R \propto M^{0.67}$. Massive planets, or gas giant planets, are found to have masses beyond $127 M_\oplus$ with an $M$-$R$ relation of $R \propto M^{-0.06}$. By analyzing the radius-density relation we also find that the transition between "small" to "intermediate-size" planets occurs at a planetary radius of $\sim1.6 R_\oplus$ (within 3%). Our results are consistent with previous studies and provide an ideal fit for the currently-measured planetary population.

astro-ph.EP↗

arXiv2024

Searching for Giant Exoplanets around M-dwarf Stars (GEMS) I: Survey Motivation

Recent discoveries of transiting giant exoplanets around M-dwarf stars (GEMS), aided by the all-sky coverage of TESS, are starting to stretch theories of planet formation through the core-accretion scenario. Recent upper limits on their occurrence suggest that they decrease with lower stellar masses, with fewer GEMS around lower-mass stars compared to solar-type. In this paper, we discuss existing GEMS both through confirmed planets, as well as protoplanetary disk observations, and a combination of tests to reconcile these with theoretical predictions. We then introduce the \textit{Searching for GEMS} survey, where we utilize multi-dimensional nonparameteric statistics to simulate hypothetical survey scenarios to predict the required sample size of transiting GEMS with mass measurements to robustly compare their bulk-density with canonical hot-Jupiters orbiting FGK stars. Our Monte-Carlo simulations predict that a robust comparison requires about 40 transiting GEMS (compared to the existing sample of $\sim$ 15) with 5-$σ$ mass measurements. Furthermore, we discuss the limitations of existing occurrence estimates for GEMS, and provide a brief description of our planned systematic search to improve the occurrence rate estimates for GEMS.

astro-ph.EP↗

arXiv2024

Uranus' Complex Internal Structure

Uranus' bulk composition remains unknown. Although there are clear indications that Uranus' interior is not fully convective, and therefore has a non-adiabatic temperature profile, many interior models continue to assume an adiabatic interior. In this paper we present a new method to interpret empirical structure models in terms of composition and for identifying non-convective regions. We also explore how the uncertainty in Uranus' rotation period and winds affect the inferred composition and temperature profile. We use Uranus' density profiles from previous work where the density is represented by up to three polytropes. Using our new method, we find that these empirical models imply that Uranus' interior includes non-adiabatic regions. This leads to significantly hotter internal temperatures that can reach a few 10$^3$ K and higher bulk heavy-element abundances (up to 1 M$_\oplus$) compared to standard adiabatic models. We find that the assumed rotation period strongly affects the inferred composition while the winds have a negligible effect. Although solutions with only H-He and rock are possible, we find that the maximum water-to-rock ratio in Uranus for our models ranges between 2.6 and 21. This is significantly lower compared to standard adiabatic models. We conclude that it is important to include non-adiabatic regions in Uranus structure models as they significantly affect the inferred temperature profile, and therefore the inferred bulk heavy-element abundance. In addition, we suggest that it is of great value to measure Uranus' gravitational field and determine its rotation period in order to decrease the uncertainty in Uranus' bulk composition.

astro-ph.EP↗

arXiv2024

Thermodynamic modeling using Extended UNIQUAC and COSMO-RS-ES models: Case study of the cesium nitrate - water system over a large range of temperatures

A comparison of two thermodynamic models is presented using the water-cesium nitrate system as case study. Both models were able to model the thermodynamic properties such as the osmotic coefficient, vapor pressure, mean activity coefficient and solubility with good accuracy. We show that it is possible to reproduce the temperature dependency of the properties using a simple set of parameters in the case of Extended UNIQUAC. Furthermore, COSMO-RS-ES is a completely predictive model adjusted to data at 298.15 K, which is applied for the first time to other temperatures.

cond-mat.soft↗

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↗

arXiv2023

TOI-4201: An Early M-dwarf Hosting a Massive Transiting Jupiter Stretching Theories of Core-Accretion

We confirm TOI-4201 b as a transiting Jovian mass planet orbiting an early M dwarf discovered by the Transiting Exoplanet Survey Satellite. Using ground based photometry and precise radial velocities from NEID and the Planet Finder Spectrograph, we measure a planet mass of 2.59$^{+0.07}_{-0.06}$ M$_{J}$, making this one of the most massive planets transiting an M-dwarf. The planet is $\sim$0.4\% the mass of its 0.63 M$_{\odot}$ host and may have a heavy element mass comparable to the total dust mass contained in a typical Class II disk. TOI-4201 b stretches our understanding of core-accretion during the protoplanetary phase, and the disk mass budget, necessitating giant planet formation to either take place much earlier in the disk lifetime, or perhaps through alternative mechanisms like gravitational instability.

astro-ph.EP↗

arXiv2023

Towards a new era in giant exoplanet characterisation

Determining the composition of giant exoplanets is crucial for understanding their origin and evolution. However, the planetary bulk composition is not measured directly but must be deduced from a combination of mass-radius measurements, knowledge of the planetary age and evolution simulations. Accurate determinations of stellar ages, mass-radius, and atmospheric compositions from upcoming missions can significantly improve the determination of the heavy-element mass in giant planets. In this paper, we first demonstrate the importance of an accurate age measurement, as expected from Plato, in constraining the planetary properties. Well-determined stellar ages can reduce the bulk-metallicity uncertainty up to about a factor of two. We next infer the bulk metallicity of warm giants from the Ariel mission reference sample and identify the Ariel high-priority targets for which a measured atmospheric metallicity can clearly break the degeneracy in the inferred composition. We show that knowledge of the atmospheric metallicity can broadly reduce the bulk-metallicity uncertainty by a factor of four to eight. We conclude that the accurate age determination from Plato and atmospheric measurements by Ariel and the James Webb Space Telescope will play a key role in revealing the composition of giant exoplanets.

astro-ph.EP↗

arXiv2023

Warm giant exoplanet characterisation: current state, challenges and outlook

The characterisation of giant exoplanets is crucial to constrain giant planet formation and evolution theory and for putting the solar-system's giant planets in perspective. Typically, mass-radius (M-R) measurements of moderately irradiated warm Jupiters are used to estimate the planetary bulk composition, which is an essential quantity for constraining giant planet formation, evolution and structure models. The successful launch of the James Webb Space Telescope (JWST) and the upcoming ARIEL mission open a new era in giant exoplanet characterisation as atmospheric measurements provide key information on the composition and internal structure of giant exoplanets. In this review, we discuss how giant planet evolution models are used to infer the planetary bulk composition, and the connection between the compositions of the interior and atmosphere. We identify the important theoretical uncertainties in evolution models including the equations of state, atmospheric models, chemical composition, interior structure and main energy transport processes. Nevertheless, we show that that atmospheric measurements by JWST and ARIEL and the accurate determination of stellar ages by PLATO can significantly reduce the degeneracy in the inferred bulk composition. Furthermore, we discuss the importance of evolution models for the characterisation of direct-imaged planets. We conclude that giant planet theory has a critical role in the interpretation of observation and emphasise the importance of advancing giant planet theory.

astro-ph.EP↗

arXiv2023

Evaluation and Refinement of the novel predictive electrolyte model COSMO-RS-ES based on solid-liquid equilibria of salts and Gibbs free Energies of Transfer of Ions

The new predictive electrolyte model COSMO-RS-ES is evaluated and refined for the calculation of solubilities of salts in mixed solvent systems. It is demonstrated that the model is capable of predicting solid-liquid equilibria at 25 °C for ammonium and alkali metal salts quite accurately in a wide variety of solvent mixtures. Furthermore, through the introduction of Gibbs free energies of transfer of single ions it is shown that the model performance can be improved even further. This new data type also allows for an ion-specific way of evaluating the model for the first time. For some systems when calculating the solubility, larger deviations are observed, but for the vast majority of systems the model delivers good predictions. This shows that COSMO-RS-ES is a valuable tool for calculation of phase equilibria in electrolyte systems especially when the scarcity of data impede the application of models that require a higher number of parameters.

cond-mat.stat-mech↗