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Bertram Bitsch

Publications and source records attributed to Bertram Bitsch.

At least 37 records · Page 2Linked to original sources

From CO$_2$- to H$_2$O-dominated atmospheres and back -- How mixed outgassing changes the volatile distribution in magma oceans around M dwarf stars

We investigate the impact of CO$_2$ on TRAPPIST-1 e, f and g during the magma ocean stage. These potentially habitable rocky planets are currently the most accessible for astronomical observations. A constraint on the volatile budget during the magma ocean stage is a link to planet formation and also needed to judge their habitability. We perform simulations with 1-100 terrestrial oceans (TO) of H$_2$O with and without CO$_2$ and for albedos 0 and 0.75. The CO$_2$ mass is scaled with initial H$_2$O by a constant factor between 0.1 and 1. The magma ocean state of rocky planets begins with a CO$_2$-dominated atmosphere but can evolve into a H$_2$O dominated state, depending on initial conditions. For less than 10 TO initial H$_2$O, the atmosphere tends to desiccate and the evolution may end with a CO$_2$ dominated atmosphere. Otherwise, the final state is a thick (>1000 bar) H$_2$O-CO$_2$ atmosphere. Complete atmosphere desiccation with less than 10 TO initial H$_2$O can be significantly delayed for TRAPPIST-1e and f, when H$_2$O has to diffuse through a CO$_2$ atmosphere to reach the upper atmosphere, where XUV photolysis occurs. As a consequence of CO$_2$ diffusion-limited water loss, the time of mantle solidification for TRAPPIST-1 e, f, and g can be significantly extended compared to a pure H$_2$O evolution by up to 40 Myrs for albedo 0.75 and by up to 200 Mrys for albedo 0. The addition of CO$_2$ further results in a higher water content in the melt during the magma ocean stage. Our compositional model adjusted for the measured metallicity of TRAPPIST-1 yields for the dry inner planets (b, c, d) an iron fraction of 27 wt-%. For TRAPPIST-1 e, this iron fraction would be compatible with a (partly) desiccated evolution scenario and a CO$_2$ atmosphere with surface pressures of a few 100 bar. A comparative study between TRAPPIST-1 e and the inner planets may yield the most insights about formation and evolution scenarios.

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Diversity of disc viscosities can explain the period ratios of resonant and non-resonant systems of hot super-Earths and mini-Neptunes

Migration is a key ingredient for the formation of close-in super-Earth and mini-Neptune systems, as it sets in which resonances planets can be trapped. Slower migration rates result in wider resonance configurations compared to higher migration rates. We investigate the influence of different migration rates, set by the disc's viscosity, on the structure of multi-planet systems growing by pebble accretion via N-body simulations. Planets in low viscosity environments migrate slower due to partial gap opening. Thus systems formed in low viscosity environments tend to have planets trapped in wider resonant configurations (typically 4:3, 3:2 and 2:1), compared to their high viscosity counterparts (mostly 7:6, 5:4 and 4:3 resonances). After gas disc dissipation, the damping forces cease and the systems can undergo instabilities, rearranging their configurations and breaking the resonance chains. The low viscosity discs naturally account for the resonant chains like Trappist-1, TOI-178 and Kepler-223, unlike high viscosity simulations which produce relatively more compact chains. About 95% of our low viscosity resonant chains became unstable, experiencing giant impacts. Dynamical instabilities in our low viscosity simulations are more violent than those of high viscosity simulations due to the effects of leftover external perturbers (P>200 days). About 50% of our final system ended with no planets within 200 days, while all our systems have remaining outer planets. We speculate that this process could be qualitatively consistent with the lack of inner planets in a large fraction of Sun-like stars. Systems produced in low viscosity simulations alone do not match the overall period ratio distribution of observations, but give a better match to the period distributions of chains, which may suggest that systems of super-Earths and mini-Neptunes form in natal discs with a diversity of viscosities.

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How external photo-evaporation changes the chemical composition of the inner disc

Stars mostly form in clusters where neighboring stars can influence proto-planetary disc evolution. Besides gravitational interactions, external photoevaporation can shape these discs. Depending on the strength of photoevaporation, discs can be destroyed within 1-2 Myrs or more gradually. We use the chemcomp code, incorporating a viscous disc evolution model with pebble drift and evaporation, to calculate the chemical composition of protoplanetary discs. This code is extended to include external photoevaporation based on the FRIED grid. Initially, the disc evolves purely viscously, with the inner disc's C/O ratio decreasing due to inward drifting and evaporating water ice pebbles. Over time, the C/O ratio increases as water vapor accretes onto the star and carbon-rich gas migrates inward. Once external photoevaporation starts, the outer disc disperses, but the inner disc's chemical evolution follows that of a purely viscous disc, as most pebbles have already drifted inward within 1 Myr. At low viscosity, the inner disc's C/O ratio remains sub-solar until dispersion by photoevaporation. At high viscosity, the C/O ratio can reach super-solar values, due to faster accretion of water vapor and inward migration of carbon-rich gas, provided the disc survives a few Myrs. In both cases, there is no significant difference in the inner disc's chemical composition compared to a purely viscous model due to the rapid inward drift of pebbles. Our model predicts that inner disc chemistry should be similar for discs subject to external photoevaporation and isolated discs, consistent with JWST observations.

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Disk and atmosphere composition of multi-planet systems

In protoplanetary disks, small mm-cm-sized pebbles drift inwards which can aid planetary growth and influence the chemical composition of their natal disks. Gaps in protoplanetary disks can hinder the effective inward transport of pebbles by trapping the material in pressure bumps. Here we explore how multiple planets change the vapour enrichment by gap opening. For this, we extend the chemcomp code to include multiple growing planets and investigate the effect of 1, 2 & 3 planets on the water content and C/O ratio in the gas disk as well as the final composition of the planetary atmosphere. We follow planet migration over evaporation fronts and find that previously trapped pebbles evaporate relatively quickly and enrich the gas. We also find that in a multi-planet system, the atmosphere composition can be reduced in carbon and oxygen compared to the case without other planets, due to the blocking of volatile-rich pebbles by an outer planet. This effect is stronger for lower viscosities because planets migrate further at higher viscosities and eventually cross inner evaporation fronts, releasing the previously trapped pebbles. Interestingly, we find that nitrogen remains super-stellar regardless of the number of planets in the system such that super-stellar values in N/H of giant planet atmospheres may be a tracer for the importance of pebble drift and evaporation.

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There is no disk mass budget problem of planet formation

The inferred dust masses from Class II protoplanetary disk observations are lower than or equal to the masses of the observed exoplanet systems. This poses the question of how planets form if their natal environments do not contain enough mass. This hypothesis has entered the literature as the "mass budget problem" of planet formation. We utilize numerical simulations of planet formation via pebble and gas accretion, including migration, in a viscously evolving protoplanetary disk, while tracing the time evolution of the dust mass. As expected, we find that the presence of a giant planet in the disk can influence the evolution of the disk itself and prevent rapid dust mass loss by trapping the dust outside its orbit. Early formation is crucial for giant planet formation, as we found in our previous work; therefore, our findings strengthen the hypothesis that planet formation has already occurred or is ongoing in Class II disks. Most importantly, we find that the optically thin dust mass significantly underestimates the total dust mass in the presence of a dust-trapping deep gap. We also show that the beam convolution would smear out the feature from a deep gap, especially if the planet forms in the inner disk. Such hidden dust mass, along with early planet formation, could be the answer to the hypothetical mass budget problem.

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A formation pathway for terrestrial planets with moderate water content involving atmospheric-volatile recycling

Of the many recently discovered terrestrial exoplanets, some are expected to harbor moderate water mass fractions of a few percent. The formation pathways that can produce planets with these water mass fractions are not fully understood. Here, we use the code chemcomp, which consists of a semi-analytical 1D protoplanetary disk model harboring a migrating and accreting planet, to model the growth and composition of planets with moderate water mass fractions by pebble accretion in a protoplanetary disk around a TRAPPIST-1 analog star. This star is accompanied by seven terrestrial planets, of which the outer four planets likely contain water mass fractions of between 1\% and 10\%. We adopt a published model that considers the evaporation of pebbles in the planetary envelope, from where recycling flows can transport the volatile vapor back into the disk. We find that with this model, the planetary water content depends on the influx rate of pebbles onto the planet. A decreasing pebble influx with time reduces the envelope temperature and consequently allows the formation of planets with moderate water mass fractions as inferred for the outer TRAPPIST-1 planets for a number of different simulation configurations. This is further evidence that the recycling of vapor is an important component of planet formation needed to explain the vast and diverse population of exoplanets.

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Mind the gap: Distinguishing disc substructures and their impact on the inner disc composition

Improved observational technologies have enabled the resolution of substructures and the measurement of chemical abundances in discs. Understanding the chemical composition of the inner disc allows us to infer the building blocks available for planet formation. Recently, the depletion of water in the inner disc has been suggested to be linked to the presence of substructures, such as gaps and rings, further out. We investigate this hypothesis further by running 1D semi-analytical models of a disc with a gap to understand the combined effects of disc viscosity, gap depth, gap location, and gap formation timescales on the inner disc composition. Our results show that for a specific value of disc viscosity, the simulation outcome can be classified into three regimes: shallow gap, "traffic jam", and deep gap. While deep gaps may already be distinguishable with moderate-resolution techniques, it is still challenging to resolve shallow gaps with the current capabilities. On the other hand, discs with traffic jams have a higher chance of being resolved when observed with a high resolution, but they may appear as an intensity enhancement or even featureless when observed with moderate to low angular resolution. In this regard, information on the inner disc composition is useful because it can help to infer the existence of traffic jams or distinguish them from deep gaps: discs with deep gaps are expected to have a low water content and thus high C/O ratio in the inner disc due to the effective blocking of pebbles, while discs with shallow gaps would demonstrate the opposite trend. Furthermore, discs with a traffic jam would have a constant inward flux of water-rich pebbles resulting in a moderate water content and sub-stellar C/O ratios. Finally, we find that the effectiveness of gaps as pebble barriers diminishes quickly when they form late, as most of the pebbles have already drifted inwards.

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A recipe for eccentricity and inclination damping for partial gap opening planets in 3D disks

In a previous paper we showed that, like the migration speed, the eccentricity damping efficiency is modulated linearly by the depth of the partial gap a planet carves in the disk surface density profile, resulting in less efficient $e$-damping compared to the prescription commonly used in population synthesis works. Here, we extend our analysis to 3D, refining our $e$-damping formula and studying how the inclination damping efficiency is also affected. We perform high resolution 3D locally isothermal hydrodynamical simulations of planets with varying masses embedded in disks with varying aspect ratios and viscosities. We extract the gap profile and orbital damping timescales for fixed eccentricities and inclinations up to the disk scale height. The limit in gap depths below which vortices appear, in the low-viscosity case, happens roughly at the transition between classical type-I and type-II migration regimes. The orbital damping timescales can be described by two linear trends with a break around gap depths $\sim80\%$ and with slopes and intercepts depending on the eccentricity and inclination. These trends are understood on physical grounds and are reproduced by simple fitting formulas whose error is within the typically uncertainty of type-I torque formulas. Thus, our recipes for the gap depth and orbital damping efficiencies yield a simple description for planet-disk interactions to use in N-body codes in the case of partial gap opening planets that is consistent with high-resolution 3D hydro-simulations. Finally, we show examples of how our novel orbital damping prescription can affect the outcome of population synthesis experiments.

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At least one in a dozen stars exhibits evidence of planetary ingestion

Stellar chemical compositions can be altered by ingestion of planetary material and/or planet formation which removes refractory material from the proto-stellar disc. These "planet signatures" appear as correlations between elemental abundance differences and the dust condensation temperature. Detecting these planet signatures, however, is challenging due to unknown occurrence rates, small amplitudes, and heterogeneous star samples with large differences in stellar ages, and therefore stars born together (i.e., co-natal) with identical compositions can facilitate such detections. While previous spectroscopic studies were limited to small number of binary stars, the Gaia satellite provides new opportunities for detecting stellar chemical signatures of planets among co-moving pairs of stars confirmed to be co-natal. Here we report high-precision chemical abundances for a homogeneous sample of 91 co-natal pairs of stars with a well-defined selection function and identify at least seven new instances of planetary ingestion, corresponding to an occurrence rate of 8%. An independent Bayesian indicator is deployed, which can effectively disentangle the planet signatures from other factors, such as random abundance variation and atomic diffusion. Our study provides new evidence of planet signatures and facilitates a deeper understanding of the star-planet-chemistry connection by providing new observational constraints on the mechanisms of planet engulfment, formation and evolution.

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Which stars can form planets: Planetesimal formation at low metallicities

The exoplanet diversity has been linked to the disc environment in which they form, where the host star metallicity and the formation pathways play a crucial role. In the context of the core accretion paradigm, the initial stages of planet formation require the growth of dust material from micrometre size to planetesimal size bodies before core accretion can kick in. Although numerous studies have been conducted on planetesimal formation, it is still poorly understood how this process takes place in low metallicity stellar environments. We explore planetesimals formation in stellar environments primarily with low metallicity. We performed global 1D viscous disc evolution simulations including grain growth, evaporation and condensation of chemical species at ice lines. We followed the formation of planetesimals during disc evolution and tested different metallicities, disc sizes and turbulent viscosity strengths. We find that at solar and sub-solar metallicities, there is a significant enhancement in the midplane dust-to-gas mass ratios at the ice lines but this leads to planetesimal formation only at the water ice line. In our simulations, [Fe/H] = -0.6 is the lowest limit of metallicity for planetesimal formation where a few Earth masses of planetesimals could form. For such extreme disc environments, large discs are more conducive than small discs for forming large amounts of planetesimals at a fixed metallicity, because the pebble flux can be maintained for a longer time resulting in a longer and more efficient planetesimal formation phase. At lower metallicities, planetesimal formation is less supported in quiescent discs compared to turbulent discs, because the pebble flux can be maintained for a longer time. The amount of planetesimals formed at sub-solar metallicities in our simulations places a limit on core sizes that could possibly only result in the formation of super-Earths.

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chemcomp: Modeling the chemical composition of planets formed in protoplanetary disks

Future observations of exoplanets will hopefully reveal detailed constraints on planetary compositions. Recently, we have developed and introduced chemcomp (Schneider & Bitsch 2021a), which simulates the formation of planets in viscously evolving protoplanetary disks by the accretion of pebbles and gas. The chemical composition of planetary building blocks (pebbles and gas) is traced by including a physical approach of the evaporation and condensation of volatiles at evaporation lines. We have now open-sourced the chemcomp code to enable comparisons between planet formation models and observational constraints by the community. The code can be found at https://github.com/AaronDavidSchneider/chemcomp, is easy to use (using configuration files) and comes with a detailed documentation and examples.

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Constraining the formation history of the HAT-P-11 system by atmospheric abundances

The chemical fingerprint of a planet reveals information about its formation history regarding when and where it formed. The water content of a planet can help to constrain its formation pathway: If the planet formed in the outer regions of the disk and migrated inward, it will be water-rich due to the accretion of water-ice-rich solids. Conversely, formation in the inner disk, where water-ice is not available, will result in a smaller atmospheric water content due to the limited accretion of water vapor. This process complicates with the presence of gap-opening giant planets. A gas giant exerts a pressure bump exterior to its orbit, preventing the further influx of pebbles into the inner system, resulting in a water-poor environment. The different formation scenarios can help to constrain the formation of the HAT-P-11 system, which contains an inner sub-Neptune with a mass of 23.4 $\mathrm{M_{\oplus}}$ and substellar water abundances ($X_\mathrm{H_2O} \approx 0.11$), as well as an outer giant planet orbiting exterior to the water-ice line. Our planet formation model encompasses planetary growth through pebble and gas accretion, along with a pebble drift and evaporation module that enables us to track the chemical composition of the disk and the planets. We find that the presence of the gas giant is necessary to block water-ice-rich material, resulting in a substellar water content for the inner sub-Neptune. If the giant planet forms too early, not enough solid material can enter the inner disk regions, preventing the efficient growth of the inner planet. This highlights the importance of the timing of giant planet formation to explain the inner system structure. Our simulations predict a roughly stellar C/O ratio with superstellar C/H and O/H for HAT-P-11b, providing constraints for future observations that are essential for gaining a more detailed understanding of its formation.

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Planetary system architectures with low-mass inner planets: Direct imaging exploration of mature systems beyond 1 au

The discovery of planets orbiting at less than 1 au from their host star and less massive than Saturn in various exoplanetary systems revolutionized our theories of planetary formation. The fundamental question is whether these close-in low-mass planets could have formed in the inner disk interior to 1 au, or whether they formed further out in the planet-forming disk and migrated inward. Exploring the role of additional giant planets in these systems may help us to pinpoint their global formation and evolution. We searched for additional substellar companions by using direct imaging in systems known to host close-in small planets. The use of direct imaging complemented by radial velocity and astrometric detection limits enabled us to explore the giant planet and brown dwarf demographics around these hosts to investigate the potential connection between both populations. We carried out a direct imaging survey with VLT/SPHERE to look for outer giant planets and brown dwarf companions in 27 systems hosting close-in low-mass planets discovered by radial velocity. Our sample is composed of very nearby (<20pc) planetary systems, orbiting G-, K-, and M-type mature (0.5-10Gyr) stellar hosts. We performed homogeneous direct imaging data reduction and analysis to search for and characterize point sources, and derived robust statistical detection limits. Of 337 point-source detections, we do not find any new bound companions. We recovered the emblematic very cool T-type brown dwarf GJ229B. Our typical sensitivities in direct imaging range from 5 to 30 MJup beyond 2 au. The non-detection of massive companions is consistent with predictions based on models of planet formation by core accretion. Our pilot study opens the way to a multi-technique approach for the exploration of very nearby exoplanetary systems with future ground-based and space observatories.

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Composition of giant planets: the roles of pebbles and planetesimals

One of the current challenges of planet formation theory is to explain the enrichment of observed exoplanetary atmospheres. Past studies have focused on scenarios where either pebbles or planetesimals were the heavy element enrichment's drivers, we combine here both approaches to understand whether the composition of a planet can constrain its formation pathway. We study three different formation scenarios: pebble accretion, pebble accretion with planetesimal formation, combined pebble and planetesimal accretion. We use the chemcomp code to perform semi-analytical 1D simulations of protoplanetary discs, including viscous evolution, pebble drift, and simple chemistry to simulate the growth of planets from planetary embryos to gas giants as they migrate through the disc, while tracking their composition. Our simulations confirm that the composition of the planetary atmosphere is dominated by the accretion of gas enriched by inward drifting and evaporating pebbles. Including planetesimal formation hinders the enrichment, because the pebbles locked into planetesimals cannot evaporate and enrich the disc. This results in a big drop of the accreted heavy elements both in the planetesimal formation and accretion case, proving that planetesimal formation needs to be inefficient in order to explain planets with high heavy element content. Accretion of planetesimals enhances the refractory component of the atmosphere, leading to low volatile to refractory ratios, contrary to the pure pebble scenario. Such low volatile to refractory ratios can also be achieved by planets migrating in the inner disc in pure pebble scenario. Distinguishing these two scenarios requires knowledge about the planet's atmospheric C/H and O/H ratios, which are higher for pure pebble accretion. Therefore, a detailed knowledge of the composition of planetary atmospheres could help to constrain the planet's formation pathway.

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Enriching inner discs and giant planets with heavy elements

Giant exoplanets seem to have on average a much larger heavy element content than the solar system giants. Past attempts to explain these heavy element contents include collisions between planets, accretion of volatile rich gas and accretion of gas enriched in micro-metre sized solids. However, these different theories individually could not explain the heavy element content of giants and the volatile to refractory ratios in atmospheres of giant planets at the same time. Here we combine the approaches of gas accretion enhanced with vapor and small micro-meter sized dust grains. As pebbles drift inwards, the volatile component evaporates and enriches the disc, while the smaller silicate core of the pebble continues to move inwards. The smaller silicate pebbles drift slower, leading to a pile-up of material interior to the water ice line, increasing the dust-to-gas ratio interior to the ice line. Under the assumption that these small dust grains follow the motion of the gas, gas accreting giants accrete large fractions of small solids in addition to the volatile vapor. The effectiveness of the solid enrichment requires a large disc radius to maintain the pebble flux for a long time and a large viscosity that reduces the size and inward drift of the small dust grains. However, this process depends crucially on the debated size difference of the pebbles interior and exterior of the water ice line. On the other hand, the volatile component released by the inward drifting pebbles can lead to a large enrichment with heavy element vapor, independently of a size difference of pebbles interior and exterior to the water ice line. Our model stresses the importance of the disc's radius and viscosity on the enrichment of dust and vapor. Consequently we show how our model could explain the heavy element content of the majority of giant planets by using combined estimates of dust and vapor enrichment.

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How to make giant planets via pebble accretion

Planet formation is directly linked to the birthing environment that protoplanetary disks provide. The disk properties determine whether a giant planet will form and how it evolves. The number of exoplanet and disk observations is consistently rising, however, it is not yet possible to directly link these two populations. Therefore, a deep theoretical understanding of how planets form is crucial. We performed numerical simulations of planet formation via pebble and gas accretion, while including migration, in a viscously evolving protoplanetary disk, with dust growing, drifting, and evaporating at the ice lines. In our investigation of the most favorable conditions for giant planet formation, we find that these are high disk masses, early formation, and a large enough disk to host a long-lasting pebble flux. However, small disks with the same mass allow more efficient gas accretion onto planetary cores, leading to more massive gas giants. Given the right conditions, high viscosity leads to more massive cores and it enhances gas accretion. It also causes faster type II migration rates, so the giants have a decreasing final position for increasing viscosity. Intermediate dust fragmentation velocities provide the necessary pebble sizes and radial drift velocities for maximized pebble accretion and pebble flux. An enhanced dust-to-gas ratio can compensate for lower disk masses, but early formation is still crucial. We conclude that there is no specific initial parameter that leads to giant planet formation; rather, it is the outcome of a combination of complementary factors. This also implies that the diversity of the exoplanet systems is the product of the intrinsic diversity of the protoplanetary disks and it is crucial to take advantage of the increasing number and quality of observations to constrain the disk population properties and ultimately devise planet formation theories.

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C3PO: Towards a complete census of co-moving pairs of stars. I. High precision stellar parameters for 250 stars

We conduct a line-by-line differential analysis of a sample of 125 co-moving pairs of stars (dwarfs and subgiants near solar metallicity). We obtain high precision stellar parameters with average uncertainties in effective temperature, surface gravity and metallicity of 16.5 K, 0.033 dex and 0.014 dex, respectively. We classify the co-moving pairs of stars into two groups, chemically homogeneous (conatal; |Delta[Fe/H]| $\le$ 0.04 dex) and inhomogeneous (non-conatal), and examine the fraction of chemically homogeneous pairs as a function of separation and effective temperature. The four main conclusions from this study are: (1) A spatial separation of \ds = 10$^6$ AU is an approximate boundary between homogeneous and inhomogeneous pairs of stars, and we restrict our conclusions to only consider the 91 pairs with \ds $\le$ 10$^6$ AU; (2) There is no trend between velocity separation and the fraction of chemically homogeneous pairs in the range \dv $\le$ 4 \kms; (3) We confirm that the fraction of chemically inhomogeneous pairs increases with increasing \teff\ and the trend matches a toy model of that expected from planet ingestion; (4) Atomic diffusion is not the main cause of the chemical inhomogeneity. A major outcome from this study is a sample of 56 bright co-moving pairs of stars with chemical abundance differences $\leq$ 0.02 dex (5\%) which is a level of chemical homogeneity comparable to that of the Hyades open cluster. These important objects can be used, in conjunction with star clusters and the \gaia\ ``benchmark'' stars, to calibrate stellar abundances from large-scale spectroscopic surveys.

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Do all gaps in protoplanetary discs host planets?

Following the assumption that the disc substructures observed in protoplanetary discs originate from the interaction between the disc and the forming planets embedded therein, we aim to test if these putative planets could represent the progenitors of the currently observed giant exoplanets. We performed N-body simulations assuming initially three, four, five or seven planets. Our model includes pebble and gas accretion, migration, damping of eccentricities and inclinations, disc-planet interaction and disc evolution. We locate the planets in the positions where the gaps in protoplanetary discs have been observed and we evolve the systems for 100Myr including a few Myr of gas disc evolution, while also testing three values of $α$ viscosity. For planetary systems with initially three and four planets we find that most of the growing planets lie beyond the RV detection limit of 5AU and only a small fraction of them migrate into the inner region. We also find that these systems have too low final eccentricities to be in agreement with the observed giant planet population. Systems initially consisting of five or seven planets become unstable after $\approx$40Kyr of integration time. This clearly shows that not every gap can host a planet. The general outcome of our simulations - too low eccentricities - is independent of the disc's viscosity and surface density. Further observations could either confirm the existence of an undetected population of wide-orbit giants or exclude the presence of such undetected population to constrain how many planets hide in gaps even further.

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