arXiv subjects

Christoph Mordasini

Publications and source records attributed to Christoph Mordasini.

At least 73 records · Page 4Linked to original sources

arXiv2023

Planetary Population Synthesis and the Emergence of Four Classes of Planetary System Architectures

Planetary population synthesis is a tool to understand the physics of planetary system formation. It builds on a model that includes a multitude of physical processes. The outcome can be statistically compared with exoplanet observations. Here, we review the population synthesis method and then use one population to explore how different planetary system architectures emerge and which conditions lead to their formation. The systems can be classified into four main architectures: Class I of near-in situ compositionally ordered terrestrial and ice planets, Class II of migrated sub-Neptunes, Class III of mixed low-mass and giant planets, broadly similar to the Solar System, and Class IV of dynamically active giants without inner low-mass planets. These four classes exhibit distinct typical formation pathways and are characterised by certain mass scales. Class I systems form from the local accretion of planetesimals followed by a giant impact phase, and the final planet masses correspond to the `Goldreich mass'. Class II systems form when planets reach the `equality mass' (equal accretion and migration timescales) before the dispersal of the gas disc, but not large enough to allow for rapid gas accretion. Giant planets form when the `equality mass' allows for rapid gas accretion while the planet are migrating, i.e. when the critical core mass is reached. The main discriminant of the four classes is the initial mass of solids in the disc, with contributions from the lifetime and mass of the gas disc. The breakdown into classes allows to better understand which physical processes are dominant. Comparison with observations reveals certain differences to the actual population, pointing at limitation of theoretical understanding. For example, the overrepresentation of synthetic super Earths and sub-Neptunes in Class I causes these planets to be found at lower metallicities than in observations.

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arXiv2023

A framework for the architecture of exoplanetary systems. I. Four classes of planetary system architecture

We present a novel, model-independent framework for studying the architecture of an exoplanetary system at the system level. This framework allows us to characterise, quantify, and classify the architecture of an individual planetary system. Our aim in this endeavour is to generate a systematic method to study the arrangement and distribution of various planetary quantities within a single planetary system. We propose that the space of planetary system architectures be partitioned into four classes: similar, mixed, anti-ordered, and ordered. We applied our framework to observed and synthetic multi-planetary systems, thereby studying their architectures of mass, radius, density, core mass, and the core water mass fraction. We explored the relationships between a system's (mass) architecture and other properties. Our work suggests that: (a) similar architectures are the most common outcome of planet formation; (b) internal structure and composition of planets shows a strong link with their system architecture; (c) most systems inherit their mass architecture from their core mass architecture; (d) most planets that started inside the ice line and formed in-situ are found in systems with a similar architecture; and (e) most anti-ordered systems are expected to be rich in wet planets, while most observed mass ordered systems are expected to have many dry planets. We find, in good agreement with theory, that observations are generally biased towards the discovery of systems whose density architectures are similar, mixed, or anti-ordered. This study probes novel questions and new parameter spaces for understanding theory and observations. Future studies may utilise our framework to not only constrain the knowledge of individual planets, but also the multi-faceted architecture of an entire planetary system. We also speculate on the role of system architectures in hosting habitable worlds.

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arXiv2023

A framework for the architecture of exoplanetary systems. II. Nature versus nurture: Emergent formation pathways of architecture classes

In the first paper of this series, we proposed a model-independent framework for characterising the architecture of planetary systems at the system level. There are four classes of planetary system architecture: similar, mixed, anti-ordered, and ordered. In this paper, we investigate the formation pathways leading to these four architecture classes. To understand the role of nature versus nurture in sculpting the final (mass) architecture of a system, we apply our architecture framework to synthetic planetary systems -- formed via core-accretion -- using the Bern model. General patterns emerge in the formation pathways of the four architecture classes. Almost all planetary systems emerging from protoplanetary disks whose initial solid mass was less than one Jupiter mass are similar. Systems emerging from heavier disks may become mixed, anti-ordered, or ordered. Increasing dynamical interactions (planet-planet, planet-disk) tends to shift a system's architecture from mixed to anti-ordered to ordered. Our model predicts the existence of a new metallicity-architecture correlation. Similar systems have very high occurrence around low-metallicity stars. The occurrence of the anti-ordered and ordered classes increases with increasing metallicity. The occurrence of mixed architecture first increases and then decreases with increasing metallicity. In our synthetic planetary systems, the role of nature is disentangled from the role of nurture. Nature (or initial conditions) pre-determines whether the architecture of a system becomes similar; otherwise nurture influences whether a system becomes mixed, anti-ordered, or ordered. We propose the `Aryabhata formation scenario' to explain some planetary systems which host only water-rich worlds. We finish this paper with a discussion of future observational and theoretical works that may support or refute the results of this paper.

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arXiv2022

Calibrated Gas Accretion and Orbital Migration of Protoplanets in 1D Disc Models

We aim to develop a simple prescription for migration and accretion in 1D disc models, calibrated with results of 3D hydrodynamic simulations. Our focus lies on non-self-gravitating discs, but we also discuss to what degree our prescription could be applied when the discs are self-gravitating. We study migration using torque densities. Our model for the torque density is based on existing fitting formulas, which we subsequently modify to prevent premature gap-opening. At higher planetary masses, we also apply torque densities from hydrodynamic simulations directly to our 1D model. These torque densities allow modelling the orbital evolution of an initially low-mass planet that undergoes runaway-accretion to become a massive planet. The two-way exchange of angular momentum between disc and planet is included. This leads to a self-consistent treatment of gap formation that only relies on directly accessible disc parameters. We present a formula for Bondi- and Hill- gas accretion in the disc-limited regime. This formula is self-consistent in the sense that mass is removed from the disc in the location from where it is accreted. We find that the resulting evolution in mass and semi-major axis in the 1D framework is in good agreement with those from 3D hydrodynamical simulations for a range of parameters. Our prescription is valuable for simultaneously modelling migration and accretion in 1D-models. We conclude that it is appropriate and beneficial to apply torque densities from hydrodynamic simulations in 1D models, at least in the parameter space we study here. More work is needed to in order to determine whether our approach is also applicable in an even wider parameter space and in situations with more complex disc thermodynamics, or when the disc is self-gravitating.

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arXiv2022

RISTRETTO: high-resolution spectroscopy at the diffraction limit of the VLT

RISTRETTO is a visible high-resolution spectrograph fed by an extreme adaptive optics (XAO) system, to be proposed as a visitor instrument on ESO VLT. The main science goal of RISTRETTO is the detection and atmospheric characterization of exoplanets in reflected light, in particular the temperate rocky planet Proxima b. RISTRETTO will be able to measure albedos and detect atmospheric features in a number of exoplanets orbiting nearby stars for the first time. It will do so by combining a high-contrast AO system working at the diffraction limit of the telescope to a high-resolution spectrograph, via a 7-spaxel integral-field unit (IFU) feeding single-mode fibers. Further science cases for RISTRETTO include the study of accreting protoplanets such as PDS 70 b & c through spectrally-resolved H-alpha emission; and spatially-resolved studies of Solar System objects such as icy moons and the ice giants Uranus and Neptune. The project is in an advanced design phase for the spectrograph and IFU/fiber-link sub-systems, and a preliminary design phase for the AO front-end. Construction of the spectrograph and IFU/fiber-link will start at the end of 2022. RISTRETTO is a pathfinder instrument in view of similar developments at ESO ELT, in particular the SCAO-IFU mode of ELT-ANDES and the future ELT-PCS instrument.

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arXiv2022

Toward a Population Synthesis of Disks and Planets I. Evolution of Dust with Entrainment in Winds and Radiation Pressure

Millimeter astronomy provides valuable information on the birthplaces of planetary systems. In order to compare theoretical models with observations, the dust component has to be carefully calculated. Here, we aim to study the effects of dust entrainment in photoevaporative winds and the ejection and drag of dust due to effects caused by radiation from the central star. We improved and extended the existing implementation of a two-population dust and pebble description in the global Bern/Heidelberg planet formation and evolution model. Modern prescriptions for photoevaporative winds were used and we account for settling and advection of dust when calculating entrainment rates. In order to prepare for future population studies with varying conditions, we explore a wide range of disk-, photoevaporation-, and dust-parameters. We find that if dust can grow to pebble sizes, that is, if they are resistant to fragmentation or turbulence is weak, drift dominates and the entrained mass is small but larger than under the assumption of no vertical advection of grains with the gas flow. For the case of fragile dust shattering at velocities of 1 m/s - as indicated in laboratory experiments -, an order of magnitude more dust is entrained which becomes the main dust removal process. Radiation pressure effects disperse massive, dusty disks on timescales of a few 100 Myr. These results highlight the importance of dust entrainment in winds as a solid mass removal process. Furthermore, this model extension lies the basis for future statistical studies of planet formation in their birth environment.

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arXiv2022

Potential long-term habitable conditions on planets with primordial H-He atmospheres

Cold super-Earths which retain their primordial, H-He dominated atmosphere could have surfaces that are warm enough to host liquid water. This would be due to the collision induced absorption (CIA) of infra-red light by hydrogen, which increases with pressure. However, the long-term potential for habitability of such planet has not been explored yet. Here we investigate the duration of this potential exotic habitability by simulating planets of different core masses, envelope masses and semi-major axes. We find that terrestrial and super-Earth planets with masses of $\sim$1 - 10$M_{\oplus}$ can maintain temperate surface conditions up to 5 - 8 Gyr at radial distances larger than $\sim $2 AU. The required envelope masses are $\sim 10^{-4} \, M_{\oplus}$ (which is 2 orders of magnitude more massive than Earth's), but can be an order of magnitude smaller (when close-in) or larger (when far out). This result suggests that the concept of planetary habitability should be revisited and made more inclusive with respect to the classical definition.

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arXiv2022

GENGA II: GPU planetary N-body simulations with non-Newtonian forces and high number of particles

We present recent updates and improvements of the graphical processing unit (GPU) N-body code GENGA. Modern state-of-the-art simulations of planet formation require the use of a very high number of particles to accurately resolve planetary growth and to quantify the effect of dynamical friction. At present the practical upper limit is in the range of 30,000 - 60,000 fully interactive particles; possibly a little more on the latest GPU devices. While the original hybrid symplectic integration method has difficulties to scale up to these numbers, we have improved the integration method by i) introducing higher level changeover functions and ii) code improvements to better use the most recent GPU hardware efficiently for such large simulations. We added treatments of non-Newtonian forces such as general relativity, tidal interaction, rotational deformation, the Yarkovsky effect, and Poynting-Robertson drag, as well as a new model to treat virtual collisions of small bodies in the solar system. We added new tools to GENGA, such as semi-active test particles that feel more massive bodies but not each other, a more accurate collision handling and a real-time openGL visualization. We present example simulations, including a 1.5 billion year terrestrial planet formation simulation that initially started with 65,536 particles, a 3.5 billion year simulation without gas giants starting with 32,768 particles, the evolution of asteroid fragments in the solar system, and the planetesimal accretion of a growing Jupiter simulation. GENGA runs on modern NVIDIA and AMD GPUs.

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arXiv2022

RV-detected planets around M dwarfs: Challenges for core accretion models

Planet formation is sensitive to the conditions in protoplanetary disks, for which scaling laws as a function of stellar mass are known. We aim to test whether the observed population of planets around low-mass stars can be explained by these trends, or if separate formation channels are needed. We address this question by confronting a state-of-the-art planet population synthesis model with a sample of planets around M dwarfs observed by the HARPS and CARMENES radial velocity (RV) surveys. To account for detection biases, we performed injection and retrieval experiments on the actual RV data to produce synthetic observations of planets that we simulated following the core accretion paradigm. These simulations robustly yield the previously reported high occurrence of rocky planets around M dwarfs and generally agree with their planetary mass function. In contrast, our simulations cannot reproduce a population of giant planets around stars less massive than 0.5 solar masses. This potentially indicates an alternative formation channel for giant planets around the least massive stars that cannot be explained with current core accretion theories. We further find a stellar mass dependency in the detection rate of short-period planets. A lack of close-in planets around the earlier-type stars ($M_\star \gtrsim 0.4\, M_\odot$) in our sample remains unexplained by our model and indicates dissimilar planet migration barriers in disks of different spectral subtypes. Both discrepancies can be attributed to gaps in our understanding of planet migration in nascent M dwarf systems. They underline the different conditions around young stars of different spectral subtypes, and the importance of taking these differences into account when studying planet formation.

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arXiv2022

Interpreting the atmospheric composition of exoplanets: sensitivity to planet formation assumptions

Constraining planet formation based on the atmospheric composition of exoplanets is a fundamental goal of the exoplanet community. Existing studies commonly try to constrain atmospheric abundances, or to analyze what abundance patterns a given description of planet formation predicts. However, there is also a pressing need to develop methodologies that investigate how to transform atmospheric compositions into planetary formation inferences. In this study we summarize the complexities and uncertainties of state-of-the-art planet formation models and how they influence planetary atmospheric compositions. We introduce a methodology that explores the effect of different formation model assumptions when interpreting atmospheric compositions. We apply this framework to the directly imaged planet HR 8799e. Based on its atmospheric composition, this planet may have migrated significantly during its formation. We show that including the chemical evolution of the protoplanetary disk leads to a reduced need for migration. Moreover, we find that pebble accretion can reproduce the planet's composition, but some of our tested setups lead to too low atmospheric metallicities, even when considering that evaporating pebbles may enrich the disk gas. We conclude that the definitive inversion from atmospheric abundances to planet formation for a given planet may be challenging, but a qualitative understanding of the effects of different formation models is possible, opening up pathways for new investigations.

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arXiv2022

Architectures of Compact Multi-planet Systems: Diversity and Uniformity

One of the most important developments in exoplanet science in the past decade is the discovery of multi-planet systems with sub-Neptune-sized planets interior to 1~AU. This chapter explores the architectures of these planetary systems, which often display a remarkable degree of uniformity: the planets have nearly equal sizes, regular orbital spacing, low eccentricities, and small mutual inclinations. This uniformity stands in sharp contrast to the diverse nature of the exoplanet sample considered as a whole (as well as our inner solar system). We begin with a critical review of the observations -- including possible biases -- and find that these peas-in-a-pod planetary systems are apparently a common outcome of the planet formation process. Modest departures from exact uniformity suggest additional patterns, such as the planet mass slowly increasing with semi-major axis. The star formation process naturally produces circumstellar disks with the properties required to produce these planetary systems, although the solid material must move inward from its initial location. We discuss primary modes of planetary assembly, the role of orbital migration, and post-nebular atmospheric loss. Mature planetary systems are found to be near their minimum energy (tidal equilibrium) configurations; this finding provides a partial explanation for their observed properties and indicates that efficient energy dissipation must occur. Finally, we consider population synthesis models and show that peas-in-a-pod patterns emerge with reasonable choices for the input parameters. Nonetheless, interesting observational and theoretical challenges remain in order to understand how these surprisingly organized planetary systems arise from the disorder of their formation processes.

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arXiv2022

On the multiple generations of planetary embryos

Global models of planet formation tend to begin with an initial set of planetary embryos for the sake simplicity. While this approach gives valuable insights on the evolution of the initial embryos, the initial distribution itself is a bold assumption. Limiting oneself to an initial distribution may neglect essential physics that precedes, or follows said initial distribution. We wish to investigate the effect of dynamic planetary embryo formation on the formation of planetary systems. The presented framework begins with an initial disk of gas, dust and pebbles. The disk evolution, the formation of planetesimals and the formation of planetary embryos is modeled consistently. Embryos then grow by pebble, planetesimal and eventually gas accretion. Planet disk interactions and N-body dynamics with other simultaneously growing embryos is included in the framework. We show that the formation of planets can occur in multiple consecutive phases. Earlier generations grow massive by pebble accretion but are subject to fast type I migration and thus accretion to the star. The later generations of embryos that form grow to much smaller masses by planetesimal accretion, as the amount of pebbles in the disk has vanished. The formation history of planetary systems may be far more complex than an initial distribution of embryos could reflect. The dynamic formation of planetary embryos needs to be considered in global models of planet formation to allow for a complete picture of the systems evolution.

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arXiv2021

The New Generation Planetary Population Synthesis (NGPPS). IV. Planetary systems around low-mass stars

Previous work concerning planet formation around low-mass stars has often been limited to large planets and individual systems. As current surveys routinely detect planets down to terrestrial size in these systems, a more holistic approach that reflects their diverse architectures is timely. Here, we investigate planet formation around low-mass stars and identify differences in the statistical distribution of planets. We compare the synthetic planet populations to observed exoplanets. We used the Generation III Bern model of planet formation and evolution to calculate synthetic populations varying the central star from solar-like stars to ultra-late M dwarfs. This model includes planetary migration, N-body interactions between embryos, accretion of planetesimals and gas, and long-term contraction and loss of the gaseous atmospheres. We find that temperate, Earth-sized planets are most frequent around early M dwarfs and more rare for solar-type stars and late M dwarfs. The planetary mass distribution does not linearly scale with the disk mass. The reason is the emergence of giant planets for M*>0.5 Msol, which leads to the ejection of smaller planets. For M*>0.3 Msol there is sufficient mass in the majority of systems to form Earth-like planets, leading to a similar amount of Exo-Earths going from M to G dwarfs. In contrast, the number of super-Earths and larger planets increases monotonically with stellar mass. We further identify a regime of disk parameters that reproduces observed M-dwarf systems such as TRAPPIST-1. However, giant planets around late M dwarfs such as GJ 3512b only form when type I migration is substantially reduced. We quantify the stellar mass dependence of multi-planet systems using global simulations of planet formation and evolution. The results compare well to current observational data and predicts trends that can be tested with future observations.

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arXiv2021

A compositional link between rocky exoplanets and their host stars

Stars and planets both form by accreting material from a surrounding disk. Because they grow from the same material, theory predicts that there should be a relationship between their compositions. In this study, we search for a compositional link between rocky exoplanets and their host stars. We estimate the iron-mass fraction of rocky exoplanets from their masses and radii and compare it with the compositions of their host stars, which we assume reflect the compositions of the protoplanetary disks. We find a correlation (but not a 1:1 relationship) between these two quantities, with a slope of >4, which we interpret as being attributable to planet formation processes. Super-Earths and super-Mercuries appear to be distinct populations with differing compositions, implying differences in their formation processes.

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arXiv2021

The New Generation Planetary Population Synthesis (NGPPS). II. Planetary population of solar-like stars and overview of statistical results

We want to understand global observable consequences of different physical processes and initial properties on the demographics of the planetary population. We use the Generation III Bern model to perform planetary population synthesis. We synthesise five populations with each a different initial number of Moon-mass embryos per disc: 1, 10, 20, 50, and 100. The last is our nominal population around 1 Sun-mass stars. The properties of giant planets do not change much as long as there are at least 10 embryos in each system. The study of giants can thus be done with simulations requiring less computational resources. For inner terrestrial planets, only the 100-embryos population is able to attain the giant-impact stage. In that population, each planetary system contains on average 8 planets more massive than 1 $M_\oplus$. The fraction of systems with giants planets at all orbital distances is 18%, but only 1.6% are at > 10 au. Systems with giants contain on average 1.6 such planets. The frequency of terrestrial and super-Earth planets peaks at a stellar [Fe/H] of -0.2 and 0.0, respectively, being limited at lower [Fe/H] by a lack of building blocks, and by (for them) detrimental growth of more massive dynamically active planets at higher [Fe/H]. The frequency of more massive planets (Neptunian, giants) increases monotonically with [Fe/H]. The fast migration of planets in the 5-50 $M_\oplus$ range is reduced by the presence of multiple lower-mass inner planets in the multi-embryos populations. We present one of the most comprehensive simulations of (exo)planetary system formation and evolution to date. For theory, they provide the framework to observationally test the global statistical consequences of theoretical models for specific physical processes. This is a important ingredient towards the development of a standard model of planetary formation and evolution.

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arXiv2021

The New Generation Planetary Population Synthesis (NGPPS). VI. Introducing KOBE: Kepler Observes Bern Exoplanets. Theoretical perspectives on the architecture of planetary systems: Peas in a pod

(abridged) Observations of exoplanets indicate the existence of several correlations in the architecture of planetary systems. Exoplanets within a system tend to be of similar size and mass, evenly spaced, and are often ordered in size and mass. Small planets are frequently packed in tight configurations, while large planets often have wider orbital spacing. Together, these correlations are called the peas in a pod trends in the architecture of planetary systems. In this paper these trends are investigated in theoretically simulated planetary systems and compared with observations. Whether these correlations emerge from astrophysical processes or the detection biases of the transit method is examined. Synthetic planetary system were simulated using the Generation III Bern Model. KOBE, a new computer code, simulates the geometrical limitations of the transit method and applies the detection biases and completeness of the Kepler survey. This allows simulated planetary systems to be compared with observations. The architecture of synthetic planetary systems, observed via KOBE, show the peas in a pod trends in good agreement with observations. These correlations are also present in the theoretical underlying population, from the Bern Model, indicating that these trends are probably of astrophysical origin. The physical processes involved in planet formation are responsible for the emergence of evenly spaced planets with similar sizes and masses. The size--mass similarity trends are primordial and originate from the oligarchic growth of protoplanetary embryos and the uniform growth of planets at early times. Later stages in planet formation allows planets within a system to grow at different rates, thereby decreasing these correlations. The spacing and packing correlations are absent at early times and arise from dynamical interactions.

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arXiv2021

Comparison of planetary Hα-emission models: A new correlation with accretion luminosity

Accreting planets have been detected through their hydrogen-line emission, specifically H$α$. To interpret this, stellar-regime empirical correlations between the H$α$ luminosity $L_\mathrm{Hα}$ and the accretion luminosity $L_\mathrm{acc}$ or accretion rate $\dot{M}$ have been extrapolated to planetary masses, however without validation. We present a theoretical $L_\mathrm{acc}$--$L_\mathrm{Hα}$ relationship applicable to a shock at the surface of a planet. We consider wide ranges of accretion rates and masses and use detailed spectrally-resolved, non-equilibrium models of the postshock cooling. The new relationship gives a markedly higher $L_\mathrm{acc}$ for a given $L_\mathrm{Hα}$ than fits to young stellar objects, because Ly-$α$, which is not observable, carries a large fraction of $L_\mathrm{acc}$. Specifically, an $L_\mathrm{Hα}$ measurement needs ten to 100 times higher $L_\mathrm{acc}$ and $\dot{M}$ than previously predicted, which may explain the rarity of planetary H$α$ detections. We also compare the $\dot{M}$--$L_\mathrm{Hα}$ relationships coming from the planet-surface shock or implied by accretion-funnel emission. Both can contribute simultaneously to an observed H$α$ signal but at low (high) $\dot{M}$ the planetary-surface shock (heated funnel) dominates. Only the shock produces Gaussian line wings. Finally, we discuss accretion contexts in which different emission scenarios may apply, putting recent literature models in perspective, and also present $L_\mathrm{acc}$--$L_\mathrm{line}$ relationships for several other hydrogen lines.

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arXiv2021

The New Generation Planetary Population Synthesis (NGPPS). I. Bern global model of planet formation and evolution, model tests, and emerging planetary systems

Aims. Comparing theoretical models with observations allows one to make key step forward towards an understanding of planetary systems. It however requires a model able to (i) predict all the necessary observable quantities (not only masses and orbits, but also radii, luminosities, magnitudes, or evaporation rates) and (ii) address the large range in relevant planetary masses (from Mars mass to super-Jupiters) and distances (from stellar-grazing to wide orbits). Methods. We have developed a combined global end-to-end planetary formation and evolution model, the Generation III Bern model, based on the core accretion paradigm. This model solves as directly as possible the underlying differential equations for the structure and evolution of the gas disc, the dynamical state of the planetesimals, the internal structure of the planets yielding their planetesimal and gas accretion rates, disc-driven orbital migration, and the gravitational interaction of concurrently forming planets via a full N-body calculation. Importantly, the model also follows the long-term evolution of the planets on Gigayear timescales after formation including the effects of cooling and contraction, atmospheric escape, bloating, and stellar tides. Results. To test the model, we compared it with classical scenarios of Solar System formation. For the terrestrial planets, we find that we obtain a giant impact phase provided enough embryos (~100) are initially emplaced in the disc. For the giant planets, we find that Jupiter-mass planets must accrete their core shortly before the dispersal of the gas disc to prevent strong inward migration that would bring them to the inner edge of the disc. Conclusions. The model can form planetary systems with a wide range of properties. We find that systems with only terrestrial planets are often well-ordered while giant-planet bearing systems show no such similarity.

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