arXiv subjects

Tadahiro Kimura

Publications and source records attributed to Tadahiro Kimura.

18 recordsLinked to original sources

arXiv2026

Super-Earth Interiors Shrink by About 10% as They Crystallise

Super-Earth exoplanets are among the most abundant planets known, yet their bulk densities leave the interior state degenerate. The static structure models used to interpret them, and the interior retrievals built on them, typically describe the cold, solidified end state of an evolution that begins hot and molten. During this magma ocean stage the interior, the outgassed atmosphere, and the surface co-evolve and set the long-term climate and geophysics of super-Earths. We develop and validate a fully coupled model for the structural and thermal evolution of super-Earth exoplanets within the PROTEUS framework, including new and upgraded models of the interior structure, mantle energetics, and volatile outgassing. In volatile-poor super-Earths of 1 to 10 Earth masses, the silicate interior contracts by about 10 % of its molten radius through cooling and crystallisation, nearly independent of planet mass and driven by the thinning silicate shell alone. The solidified radius is set by planetary mass and core fraction, insensitive to the host star, irradiation, and initial thermal state. In contrast, volatile-rich super-Earths at and above about 5 Earth masses may not solidify: their thick outgassed atmospheres throttle the surface heat loss until the interior settles into a deep magma ocean, keeping the planet inflated and limiting the contraction to about half its volatile-poor value. Mantle contraction alone thus shapes the low-mass exoplanet transit population, motivating joint interpretation of atmospheric and geophysical signatures in upcoming exoplanet surveys.

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arXiv2026

A Search for helium in the atmospheres of three sub-Neptunes and a super-Earth around M-dwarfs

Thousands of sub-Neptunes have been discovered mainly through space-based surveys such as Kepler and TESS. Their bulk compositions and internal structures are thought to reflect their formation and evolutionary pathways, and atmospheric observations provide constraints on these processes. The near-infrared helium triplet is a potential tracer of extended, escaping H/He atmospheres. Recent models that include geometric effects suggest that planets orbiting nearby late M dwarfs may offer favorable conditions for detecting this signal. Nevertheless, helium has been reported for only three planets around M dwarfs to date. We conducted high-resolution transmission spectroscopy of three sub-Neptunes (TOI-2136b, TOI-654b, and LP 791-18c) and a super-Earth (TOI-1634b) orbiting M dwarfs with the InfraRed Doppler (IRD) spectrograph on the Subaru Telescope. We find no statistically significant helium absorption in any target; accordingly, we derive 95% confidence upper limits on the helium line depth of 1.36%, 0.60%, 2.07%, and 3.00%, and on the equivalent width of 7.3, 2.1, 7.4, and 9.1 mÅ, for TOI-2136b, TOI-1634b, TOI-654b, and LP 791-18c, respectively. We further explored constraints on the upper-atmospheric temperature and mass-loss rate by comparing these results with isothermal Parker-wind models. While we have compared with self-consistent ATES models of primordial H/He atmospheres spanning a range of assumed X-ray luminosities, changes in the assumed XUV flux do not appear to account for the non-detections. The results suggest that these planets have metal-enriched H/He primary atmospheres or non-primordial atmospheres, such as water-rich envelopes. Future observations of other absorption lines, such as Lyman-$α$, H-$α$, and H$_2$O, may provide further constraints on these atmospheres.

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arXiv2026

The mass of TOI-1883 b: A low density super-Neptune in the ridge regime transiting an early-M dwarf

Recent large-scale transit surveys conducted by space telescopes such as Kepler and TESS have revealed a vast number of exoplanets, uncovering the diversity of their population. One of the remarkable findings is the presence of a deficiency region in the period-radius distribution of short-period (< 10 days) Neptune-sized planets (4-8 Earth radii). This region is classified into the Neptune desert (< 3.2 days), the ridge (3.2-5.7 days), and the savanna (> 5.7 days) based on orbital period, each likely reflecting distinct evolutionary pathways. In this study, we used the InfraRed Doppler (IRD) instrument on the Subaru Telescope to determine the mass of the super-Neptune TOI-1883 b, which resides in the ridge region (P ~ 4.51 days) orbiting an M dwarf. We measured a planetary mass of Mp = 13.7 +6.8/-6.5 Earth masses and a mean density of 0.4 +0.3/-0.2 g cm^-3, with 3-sigma upper limits of 34.1 Earth masses, and 5-sigma upper limits of 47.7 Earth masses. These results suggest that TOI-1883 b is likely a low density super-Neptune. We also find that the boundary of the Neptune desert defined by planets orbiting FGK-type stars exhibits a similar distribution for planets around M-type stars. According to the population-based argument of Bourrier et al. (2025), this suggests that TOI-1883 b may have undergone disk-driven migration to reach its current orbit and experienced early atmospheric photoevaporation driven by strong stellar XUV irradiation. The derived planetary mass is comparable to or exceeds the conventional critical core mass. We suggest that the high metallicity of the host star ([Fe/H] = 0.32 +/- 0.18) may have suppressed the onset of runaway gas accretion. Furthermore, TOI-1883 b has a high Transmission Spectroscopy Metric (TSM > 140), making it an excellent target for future atmospheric characterization via transmission spectroscopy.

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arXiv2026

Rapid and Predictive Planet Population Synthesis Model (RAPPS) I. Upgraded model and resulting synthetic populations

Exoplanet surveys have revealed a wide diversity of planetary systems, requiring integrated models of planet formation to explain their origin. Planet population synthesis (PPS) modelling is a key tool for linking theory with the statistical properties of observed exoplanets. In the coming decade, the number of known exoplanets is expected to increase ten-fold, with a significant expansion in the range of planetary parameters probed by upcoming missions. We aim to develop a new PPS model capable of predicting planetary masses, radii, orbits, and atmospheric properties across diverse stellar hosts, while maintaining high computational efficiency for statistical comparison with observations. We build upon our previous model, which included water enrichment of primordial atmospheres via magma-gas interactions, and extend it by incorporating a semi-analytical treatment of post-disc dynamical evolution in multiplanet systems. Additional updates include revised prescriptions for disc evolution, resonance trapping, and atmospheric escape. The updated model produces planetary distributions that differ from our previous results, particularly in the abundance of Earth- and sub-Earth-mass planets. These differences arise mainly from the new dynamical evolution model and show improved agreement with simulations based on direct N-body integrations. Atmospheric enrichment is also found to strongly influence both the occurrence of gas giants and the radius distribution of close-in super-Earths and sub-Neptunes. The upgraded model provides a computationally efficient and physically comprehensive framework for predicting planetary populations across a wide range of stellar environments, enabling large parameter surveys and robust statistical comparisons with observations.

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arXiv2026

Water enrichment of forming sub-Neptune envelopes limited by oxygen exhaustion

The interaction between a magma ocean and a primordial atmosphere is increasingly recognized as a key process in shaping planetary envelope compositions. This coupling should strongly influence gas accretion, yet its role during the disk-embedded stage remains poorly constrained. We develop a time-dependent model that couples solid accretion, nebular-gas accretion, and water enrichment and partitioning through magma-atmosphere interactions, along with post-disk thermal evolution and escape. We find that, for super-Earth-mass planets, water production is generally limited by the magma oxygen budget and typically ceases before disk dispersal. Subsequent nebular-gas accretion dilutes the envelope toward hydrogen-dominated compositions, largely independent of the initial magma redox state. This establishes an upper bound on the envelope water fraction -- the oxygen exhaustion limit -- primarily set by the reactive-oxygen inventory and the planet mass. After disk dispersal, degassing increases the water fraction only in Earth-mass planets undergoing strong escape, while super-Earths exhibit little change because surface pressures are hardly affected by escape. Magma-atmosphere coupling alone therefore cannot maintain water-rich envelopes in sub-Neptunes and produces a strong mass-composition relation imposed by the oxygen exhaustion limit. Highly enriched sub-Neptunes would therefore imply additional mechanisms such as late volatile delivery or post-disk giant impacts. The relation between planetary radius and envelope composition offers a means to infer magma properties, providing a pathway to connect present-day observables with early formation histories.

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arXiv2026

A Dichotomy of the Mass-Metallicity Relation of Exoplanetary Atmospheres Demarcated by their Birthplace

Atmospheric observations by JWST raise a growing evidence that atmospheric metallicity exhibits an anti-correlation with masses of giant exoplanets. While such a trend was anticipated by planetesimal-based planet formation models, it remains unclear what kind of atmospheric metallicity trends emerge from pebble-based planet formation. Moreover, while recent studies of solar system Jupiter suggest that uppermost observable atmosphere may not represent the bulk envelope composition, it remains uncertain how the envelope inhomogeneity influences the atmospheric metallicity trend. In this study, we develop disk evolution and planet formation models to investigate the possible atmospheric metallicity trends of giant exoplanets formed via pebble accretion and how they depend on the metallicity inhomogeneity within the envelope. We find that pebble-based planet formation produces two distinct mass-metallicity relations depending on planetary birthplace. Planets formed beyond the H2O snowline exhibit a mass-metallicity anti-correlation similar to that predicted by planetesimal-based models if their atmospheres are fully convective. This anti-correlation disappears if the convective mixing is inefficient. In contrast, planets formed inside the H2O snowline show a shallower mass-metallicity anti-correlation, regardless of the efficiency of atmospheric mixing. Many gas giants observed by JWST observations lie around the mass-metallicity relation predicted for formation at close-in orbits, although some planets with sub-stellar atmospheric metallicity appear to require unmixed envelopes and formation beyond the H2O snowline. We also examine the relationship between bulk and atmospheric metallicity and find a clear correlation that closely follows atmospheric metallicity that is comparable to bulk metallicity.

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arXiv2025

The mass of TOI-654 b: A short-period sub-Neptune transiting a mid-M dwarf

Sub-Neptunes are small planets between the size of the Earth and Neptune. The orbital and bulk properties of transiting sub-Neptunes can provide clues for their formation and evolution of small planets. In this paper, we report on follow-up observations of a planetary system around the mid-M dwarf TOI-654, whose transiting sub-Neptune TOI-654 b ($P=1.53$ day) is validated as a suitable target for the atmospheric observation. We measure the planetary mass and stellar properties with the InfraRed Doppler instrument (IRD) mounted on the Subaru telescope and obtain the stellar and planetary properties from additional transit observations by the Transit Exoplanetary Survey Satellite (TESS) and a series of the Multicolor Simultaneous Camera for studying Atmospheres of Transiting exoplanets (MuSCAT). As a result, the planetary mass of TOI-654 b is determined to be $M_{\rm p} = 8.71 \pm 1.25 M_{\oplus}$, and the radius is updated to be $R_{\rm p} = 2.378 \pm 0.089 R_{\oplus}$. The bulk density suggests that the planet is composed of a rocky and volatile-rich core or a rocky core surrounded by a small amount of H/He envelope.TOI-654 b is one of unique planets located around the radius valley and and also on the outer edge of the Neptune desert. The precise mass determination enables us to constrain the atmospheric properties with future spectroscopic observations especially for the emission by the James Webb Space Telescope and Ariel.

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arXiv2025

Semi-analytical model for the dynamical evolution of planetary system II: Application to systems formed by a planet formation model

The standard formation model of close-in low-mass planets involves efficient inward migration followed by growth through giant impacts after the protoplanetary gas disk disperses. While detailed N-body simulations have enhanced our understanding, their high computational cost limits statistical comparisons with observations. In our previous work, we introduced a semi-analytical model to track the dynamical evolution of multiple planets through gravitational scattering and giant impacts after the gas disk dispersal. Although this model successfully reproduced N -body simulation results under various initial conditions, our validation was still limited to cases with compact, equally-spaced planetary systems. In this paper, we improve our model to handle more diverse planetary systems characterized by broader variations in planetary masses, semi-major axes, and orbital separations and validate it against recent planet population synthesis results. Our enhanced model accurately reproduces the mass distribution and orbital architectures of the final planetary systems. Thus, we confirm that the model can predict the outcomes of post-gas disk dynamical evolution across a wide range of planetary system architectures, which is crucial for reducing the computational cost of planet formation simulations.

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arXiv2025

Semi-analytical model for the dynamical evolution of planetary systems via giant impacts

In the standard model of terrestrial planet formation, planets are formed through giant impacts of planetary embryos after the dispersal of the protoplanetary gas disc. Traditionally, $N$-body simulations have been used to investigate this process. However, they are computationally too expensive to generate sufficient planetary populations for statistical comparisons with observational data. A previous study introduced a semi-analytical model that incorporates the orbital and accretionary evolution of planets due to giant impacts and gravitational scattering. This model succeeded in reproducing the statistical features of planets in $N$-body simulations near 1 au around solar-mass stars. However, this model is not applicable to close-in regions (around 0.1 au) or low-mass stars because the dynamical evolution of planetary systems depends on the orbital radius and stellar mass. This study presents a new semi-analytical model applicable to close-in orbits around stars of various masses, validated through comparison with $N$-body simulations. The model accurately predicts the final distributions of planetary mass, semi-major axis, and eccentricity for the wide ranges of orbital radius, initial planetary mass, and stellar mass, with significantly reduced computation time compared to $N$-body simulations. By integrating this model with other planet-forming processes, a computationally low-cost planetary population synthesis model can be developed.

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arXiv2025

Monosilane Worlds: Sub-Neptunes with Atmospheres Shaped by Reduced Magma Oceans

High-precision infrared spectroscopic measurements now enable detailed characterization of sub-Neptune atmospheres, potentially providing constraints on their interiors. Motivated by this, atmospheric models have been developed to explore chemical interactions between hydrogen-dominated atmospheres and possibly underlying magma oceans with various redox states. Recent models have predicted monosilane (SiH$_4$) as a potential atmospheric species derived from magma oceans in sub-Neptunes, but suggested that it is highly depleted in the observable atmospheric layers. Here, we propose that SiH$_4$ can persist throughout the atmospheres of sub-Neptunes with FeO-free reduced magma oceans by considering the dissolution of H$_2$O into the magma oceans, a factor not accounted for in previous models. We construct a one-dimensional atmospheric model to simulate the chemical equilibrium composition of hydrogen-dominated atmospheres overlying FeO-free magma oceans, incorporating H-O-Si chemistry. Our results show that the dissolution of H$_2$O enhances the SiH$_4$ molar fraction to levels of 0.1--10~\%, preventing it from reverting to silicates in the upper atmospheric layers. We find that SiH$_4$-rich atmospheres can exist across a broad parameter space with ground temperatures of 2000--6000~K and hydrogen pressures of 10$^2$--10$^5$~bar. We discuss that SiH$_4$-rich atmospheres could contain the other silanes but lack C-/N-/O-bearing species. The detection of SiH$_4$ in future observations of sub-Neptunes would provide compelling evidence for the presence of a rocky core with a reduced magma ocean. However, the accuracy of our model is limited by the lack of data on the non-ideal behavior and radiative properties of SiH$_4$, highlighting the need for further numerical and laboratory investigations.

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arXiv2023

The mass determination of TOI-519 b: a close-in giant planet transiting a metal-rich mid-M dwarf

We report the mass determination of TOI-519 b, a transiting substellar object around a mid-M dwarf. We carried out radial velocity measurements using Subaru / InfraRed Doppler (IRD), revealing that TOI-519 b is a planet with a mass of $0.463^{+0.082}_{-0.088}~M_{\rm Jup}$. We also find that the host star is metal rich ($\rm [Fe/H] = 0.27 \pm 0.09$ dex) and has the lowest effective temperature ($T_{\rm eff}=3322 \pm 49$ K) among all stars hosting known close-in giant planets based on the IRD spectra and mid-resolution infrared spectra obtained with NASA Infrared Telescope Facility / SpeX. The core mass of TOI-519 b inferred from a thermal evolution model ranges from $0$ to $\sim30~M_\oplus$, which can be explained by both the core accretion and disk instability models as the formation origins of this planet. However, TOI-519 is in line with the emerging trend that M dwarfs with close-in giant planets tend to have high metallicity, which may indicate that they formed in the core accretion model. The system is also consistent with the potential trend that close-in giant planets around M dwarfs tend to be less massive than those around FGK dwarfs.

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arXiv2023

An Earth-sized Planet around an M5 Dwarf Star at 22 pc

We report on the discovery of an Earth-sized transiting planet ($R_p=1.015\pm0.051\,R_\oplus$) in a $P=4.02$ day orbit around K2-415 (EPIC 211414619), an M5V star at 22 pc. The planet candidate was first identified by analyzing the light curve data by the K2 mission, and is here shown to exist in the most recent data from TESS. Combining the light curves with the data secured by our follow-up observations including high-resolution imaging and near infrared spectroscopy with IRD, we rule out false positive scenarios, finding a low false positive probability of $2\times 10^{-4}$. Based on IRD's radial velocities of K2-415, which were sparsely taken over three years, we obtain the planet mass of $3.0\pm 2.7\,M_\oplus$ ($M_p<7.5\,M_\oplus$ at $95\,\%$ confidence) for K2-415b. Being one of the lowest mass stars ($\approx 0.16\,M_\odot$) known to host an Earth-sized transiting planet, K2-415 will be an interesting target for further follow-up observations, including additional radial velocity monitoring and transit spectroscopy.

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arXiv2022

Predicted diversity in water content of terrestrial exoplanets orbiting M dwarfs

Exoplanet surveys around M dwarfs have detected a growing number of exoplanets with Earth-like insolation. It is expected that some of those planets are rocky planets with the potential for temperate climates favourable to surface liquid water. However, various models predict that terrestrial planets orbiting in the classical habitable zone around M dwarfs have no water or too much water, suggesting that habitable planets around M dwarfs might be rare. Here we present the results of an updated planetary population synthesis model, which includes the effects of water enrichment in the primordial atmosphere, caused by the oxidation of atmospheric hydrogen by rocky materials from incoming planetesimals and from the magma ocean. We find that this water production in the primordial atmosphere is found to significantly impact the occurrence of terrestrial rocky aqua planets, yielding ones with diverse water content. We estimate that 5-10% of the planets with a size $<1.3 R_\oplus$ orbiting early-to-mid M dwarfs have appropriate amounts of seawater for habitability. Such an occurrence rate would be high enough to detect potentially habitable planets by ongoing and near-future M-dwarf planet survey missions.

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arXiv2022

TOI-1696: a nearby M4 dwarf with a $3R_\oplus$ planet in the Neptunian desert

We present the discovery and validation of a temperate sub-Neptune around the nearby mid-M dwarf TIC 470381900 (TOI-1696), with a radius of $3.09 \pm 0.11 \,R_\oplus$ and an orbital period of $2.5 \,\rm{days}$, using a combination of TESS and follow-up observations using ground-based telescopes. Joint analysis of multi-band photometry from TESS, MuSCAT, MuSCAT3, Sinistro, and KeplerCam confirmed the transit signal to be achromatic as well as refined the orbital ephemeris. High-resolution imaging with Gemini/'Alopeke and high-resolution spectroscopy with the Subaru/IRD confirmed that there are no stellar companions or background sources to the star. The spectroscopic observations with IRD and IRTF/SpeX were used to determine the stellar parameters, and found the host star is an M4 dwarf with an effective temperature of $T_{eff} = 3185 \pm 76\,\rm{K}$ and a metallicity of [Fe/H] $=0.336 \pm 0.060 \,\rm{dex}$. The radial velocities measured from IRD set a $2$-$σ$ upper limit on the planetary mass to be $48.8 \,M_\oplus$. The large radius ratio ($R_p/R_\star \sim 0.1$) and the relatively bright NIR magnitude ($J=12.2 \,\rm{mag}$) make this planet an attractive target for further followup observations. TOI-1696b is one of the planets belonging to the Neptunian desert with the highest transmission spectroscopy metric discovered to date, making it an interesting candidate for atmospheric characterizations with JWST.

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arXiv2021

TOI-2285b: A 1.7 Earth-radius Planet Near the Habitable Zone around a Nearby M Dwarf

We report the discovery of TOI-2285b, a sub-Neptune-sized planet transiting a nearby (42 pc) M dwarf with a period of 27.3 days. We identified the transit signal from the Transiting Exoplanet Survey Satellite photometric data, which we confirmed with ground-based photometric observations using the multiband imagers MuSCAT2 and MuSCAT3. Combining these data with other follow-up observations including high resolution spectroscopy with the Tillinghast Reflector Echelle Spectrograph, high resolution imaging with the SPeckle Polarimeter, and radial velocity (RV) measurements with the InfraRed Doppler instrument, we find that the planet has a radius of 1.74 $\pm$ 0.08 $R_\oplus$, a mass of $<$ 19.5 $M_\oplus$ (95\% c.l.), and an insolation flux of 1.54 $\pm$ 0.14 times that of the Earth. Although the planet resides just outside the habitable zone for a rocky planet, if the planet harbors an H$_2$O layer under a hydrogen-rich atmosphere, then liquid water could exist on the surface of the H$_2$O layer depending on the planetary mass and water mass fraction. The bright host star in the near infrared ($K_s=9.0$) makes this planet an excellent target for further RV and atmospheric observations to improve our understanding on the composition, formation, and habitability of sub-Neptune-sized planets.

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arXiv2021

Exploring the link between star and planet formation with Ariel

The goal of the Ariel space mission is to observe a large and diversified population of transiting planets around a range of host star types to collect information on their atmospheric composition. The planetary bulk and atmospheric compositions bear the marks of the way the planets formed: Ariel's observations will therefore provide an unprecedented wealth of data to advance our understanding of planet formation in our Galaxy. A number of environmental and evolutionary factors, however, can affect the final atmospheric composition. Here we provide a concise overview of which factors and effects of the star and planet formation processes can shape the atmospheric compositions that will be observed by Ariel, and highlight how Ariel's characteristics make this mission optimally suited to address this very complex problem.

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arXiv2021

Two Bright M Dwarfs Hosting Ultra-Short-Period Super-Earths with Earth-like Compositions

We present observations of two bright M dwarfs (TOI-1634 and TOI-1685: $J=9.5-9.6$) hosting ultra-short period (USP) planets, identified by the TESS mission. The two stars are similar in temperature, mass, and radius ($T_\mathrm{eff}\,\approx\,3500$ K, $M_\star\,\approx\,0.45-0.46\,M_\odot$, and $R_\star\approx 0.45-0.46\,R_\odot$), and the planets are both super-Earth-sized ($1.25\,R_\oplus<R_p<2.0\,R_\oplus$). For both systems, light curves from the ground-based photometry exhibit planetary transits, whose depths are consistent with those by the TESS photometry. We also refine the transit ephemerides based on the ground-based photometry, finding the orbital periods of $P=0.9893436\pm0.0000020$ day and $P=0.6691416\pm0.0000019$ day for TOI-1634b and TOI-1685b, respectively. Through intensive radial velocity (RV) observations using IRD on the Subaru 8.2m telescope, we confirm the planetary nature of the TOIs, and measure their masses: $10.14\pm0.95\,M_\oplus$ and $3.43\pm0.93\,M_\oplus$ for TOI-1634b and TOI-1685b, respectively, when the observed RVs are fitted with a single-planet circular-orbit model. Combining those with the planet radii of $R_p=1.749\pm 0.079\,R_\oplus$ (TOI-1634b) and $1.459\pm0.065\,R_\oplus$ (TOI-1685b), we find that both USP planets have mean densities consistent with an Earth-like internal composition, which is typical for small USP planets. TOI-1634b is currently the most massive USP planet in this category, and it resides near the radius valley, which makes it a benchmark planet in the context of discussing the size limit of rocky planet cores as well as testing the formation scenarios for USP planets. Excess scatter in the RV residuals for TOI-1685 suggests the presence of a possible secondary planet or unknown activity/instrumental noise in the RV data, but further observations are required to check those possibilities.

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arXiv2020

Formation of aqua planets with water of nebular origin: Effects of water enrichment on the structure and mass of captured atmospheres of terrestrial planets

Recent detection of exoplanets with Earth-like insolation attracts growing interest in how common Earth-like aqua planets are beyond the solar system. While terrestrial planets are often assumed to capture icy or water-rich planetesimals, a primordial atmosphere of nebular origin itself can produce water through oxidation of the atmospheric hydrogen with oxidising minerals from incoming planetesimals or the magma ocean. Thermodynamically, normal oxygen buffers produce water comparable in mole number to or more than hydrogen. Thus, the primordial atmosphere would likely be highly enriched with water vapour; however, the primordial atmosphereshave been always assumed to have the solar abundances. Here we integrate the 1D structure of such an enriched atmosphere of sub-Earths embedded in a protoplanetary disc around an M dwarf of 0.3$M_\odot$ and investigate the effects of water enrichment on the atmospheric properties with focus on water amount. We find that the well-mixed, highly-enriched atmosphere is more massive by a few orders of magnitude than the solar-abundance atmosphere, and that even a Mars-mass planet can obtain water comparable to the present Earth's oceans. Although close-in Mars-mass planets likely lose the captured water via disc dispersal and photo-evaporation, these results suggest that there are more sub-Earths with Earth-like water contents than previously predicted. How much water terrestrial planets really obtain and retain against subsequent loss, however, depends on efficiencies of water production, mixing in the atmosphere and magma ocean, and photo-evaporation, detailed investigation for which should be made in the future.

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