AQUA: A Collection of H2_2O Equations of State for Planetary Models

Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state cover often only parts of the pressure - temperature space needed in planetary modelling. We construct an equation of state of H$_2$O spanning a very wide range from 0.1 Pa to 400 TPa and 150 K to $10^{5}$ K, which can be used to model the interior of planets. We combine equations of state valid in localised regions to form a continuous equation of state spanning over said pressure and temperature range. We provide tabulated values for the most important thermodynamic quantities, i.e., density, adiabatic temperature gradient, entropy, internal energy and bulk speed of sound of water over this pressure and temperature range. For better usability we also calculated density - temperature and density - internal energy grids. We discuss further the impact of this equation of state on the mass radius relation of planets compared to other popular equation of states like ANEOS and QEOS. AQUA is a combination of existing equation of state useful for planetary models. We show that AQUA is in most regions a thermodynamic consistent description of water. At pressures above 10 GPa AQUA predicts systematic larger densities than ANEOS or QEOS. A feature which was already present in a previously proposed equation of state, which is the main underlying equation of this work. We show that the choice of the equation of state can have a large impact on the mass-radius relation, which highlights the importance of future developments in the field of equation of states and regarding experimental data of water at high pressures.Comment: 20 pages, 12 Figures, Accepted for publication in A&

Exoplanet characterization using conditional invertible neural networks

The characterization of an exoplanet's interior is an inverse problem, which requires statistical methods such as Bayesian inference in order to be solved. Current methods employ Markov Chain Monte Carlo (MCMC) sampling to infer the posterior probability of planetary structure parameters for a given exoplanet. These methods are time consuming since they require the calculation of a large number of planetary structure models. To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks (cINNs) to calculate the posterior probability of the internal structure parameters. cINNs are a special type of neural network which excel in solving inverse problems. We constructed a cINN using FrEIA, which was then trained on a database of $5.6\cdot 10^6$ internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius and composition of the host star). The cINN method was compared to a Metropolis-Hastings MCMC. For that we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability of the internal structure parameters from both methods are very similar, with the biggest differences seen in the exoplanet's water content. Thus cINNs are a possible alternative to the standard time-consuming sampling methods. Indeed, using cINNs allows for orders of magnitude faster inference of an exoplanet's composition than what is possible using an MCMC method, however, it still requires the computation of a large database of internal structures to train the cINN. Since this database is only computed once, we found that using a cINN is more efficient than an MCMC, when more than 10 exoplanets are characterized using the same cINN.Comment: 15 pages, 13 figures, submitted to Astronomy & Astrophysic

The Nominal Range of Rocky Planet Masses, Radii, Surface Gravities and Bulk Densities

The two primary observable quantities of an exoplanet--its mass and radius--alone are not sufficient to probe a rocky exoplanet's interior composition and mineralogy. To overcome this, host-star abundances of the primary planet-building elements (Mg, Si, Fe) are typically used as a proxy for the planet's bulk composition. The majority of small exoplanet hosts, however, do not have available abundance data. Here we present the open-source ExoPlex mass-radius-composition solver. Unlike previous open-source mass-radius solvers, ExoPlex calculates the core chemistry and equilibrium mantle mineralogy for a bulk composition, including effects of mantle FeO content, core light elements and surface water/ice. We utilize ExoPlex to calculate the planetary radii, surface gravities and bulk densities for 10$^6$ model planets up to 2 R$_\oplus$ across these geochemistries, adopting the distribution of FGK stellar abundances to estimate of the range of bulk exoplanet compositions. We outline the $99.7\%$ distribution of radii, surface gravity and bulk densities that define planets as "nominally rocky." Planets outside this range require compositions outside those expected from stellar abundance data, likely making them either Fe-enriched super-Mercuries, or volatile-enriched mini-Neptunes. We apply our classification scheme to a sample of 85 well-resolved exoplanets without available host-star abundances. We estimate only 9 planets are within the "nominally rocky planet zone" at $>70\%$ confidence, while $\sim20\%$ and $\sim30\%$ of this sample can be reasonably classified as super-Mercuries or volatile-rich, respectively. Our results provide observers with a self-consistent way to broadly classify a planet as likely rocky, Mercury-like or volatile-enriched, using mass and radius measurements alone.Comment: 41 pages, 21 figures, 2 tables. Accepted to Ap

A pair of Sub-Neptunes transiting the bright K-dwarf TOI-1064 characterised with CHEOPS

Funding: TGW, ACC, and KH acknowledge support from STFC consolidated grant numbers ST/R000824/1 and ST/V000861/1, and UKSA grant ST/R003203/1.We report the discovery and characterization of a pair of sub-Neptunes transiting the bright K-dwarf TOI-1064 (TIC 79748331), initially detected in the Transiting Exoplanet Survey Satellite (TESS) photometry. To characterize the system, we performed and retrieved the CHaracterising ExOPlanets Satellite (CHEOPS), TESS, and ground-based photometry, the High Accuracy Radial velocity Planet Searcher (HARPS) high-resolution spectroscopy, and Gemini speckle imaging. We characterize the host star and determine Teff,⋆=4734±67K⁠, R⋆=0.726±0.007R⊙⁠, and M⋆=0.748±0.032M⊙⁠. We present a novel detrending method based on point spread function shape-change modelling and demonstrate its suitability to correct flux variations in CHEOPS data. We confirm the planetary nature of both bodies and find that TOI-1064 b has an orbital period of Pb = 6.44387 ± 0.00003 d, a radius of Rb = 2.59 ± 0.04 R⊕, and a mass of Mb=13.5+1.7−1.8 M⊕, whilst TOI-1064 c has an orbital period of Pc=12.22657+0.00005−0.00004 d, a radius of Rc = 2.65 ± 0.04 R⊕, and a 3σ upper mass limit of 8.5 M⊕. From the high-precision photometry we obtain radius uncertainties of ∼1.6 per cent, allowing us to conduct internal structure and atmospheric escape modelling. TOI-1064 b is one of the densest, well-characterized sub-Neptunes, with a tenuous atmosphere that can be explained by the loss of a primordial envelope following migration through the protoplanetary disc. It is likely that TOI-1064 c has an extended atmosphere due to the tentative low density, however further radial velocities are needed to confirm this scenario and the similar radii, different masses nature of this system. The high-precision data and modelling of TOI-1064 b are important for planets in this region of mass–radius space, and it allow us to identify a trend in bulk density–stellar metallicity for massive sub-Neptunes that may hint at the formation of this population of planets.Publisher PDFPeer reviewe

The nature of the radius valley

The existence of a radius valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between those of Earth and Neptune. In this work we provide insights into the existence of the radius valley, first from a pure formation point of view and then from a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift, and fragmentation, and the evolution of the gaseous disc by viscous accretion and photoevaporation. A planet grows from a moon-mass embryo by either silicate or icy pebble accretion, depending on its position with respect to the water ice line. We include gas accretion, type I–II migration, and photoevaporation driven mass-loss after formation. We perform an extensive parameter study evaluating a wide range of disc properties and initial locations of the embryo. We find that due to the change in dust properties at the water ice line, rocky cores form typically with ∼3 M⊕ and have a maximum mass of ∼5 M⊕, while icy cores peak at ∼10 M⊕, with masses lower than 5 M⊕ being scarce. When neglecting the gaseous envelope, the formed rocky and icy cores account naturally for the two peaks of the Kepler size distribution. The presence of massive envelopes yields planets more massive than ∼10 M⊕ with radii above 4 R⊕. While the first peak of the Kepler size distribution is undoubtedly populated by bare rocky cores, as shown extensively in the past, the second peak can host half-rock–half-water planets with thin or non-existent H-He atmospheres, as suggested by a few previous studies. Some additional mechanisms inhibiting gas accretion or promoting envelope mass-loss should operate at short orbital periods to explain the presence of ∼10–40 M⊕ planets falling in the second peak of the size distribution

TESS Reveals a Short-period Sub-Neptune Sibling (HD 86226c) to a Known Long-period Giant Planet

The Transiting Exoplanet Survey Satellite mission was designed to find transiting planets around bright, nearby stars. Here, we present the detection and mass measurement of a small, short-period (≈4 days) transiting planet around the bright (V = 7.9), solar-type star HD 86226 (TOI-652, TIC 22221375), previously known to host a long-period (~1600 days) giant planet. HD 86226c (TOI-652.01) has a radius of 2.16 ± 0.08 R ⊕ and a mass of ${7.25}_{-1.12}^{+1.19}$ M ⊕, based on archival and new radial velocity data. We also update the parameters of the longer-period, not-known-to-transit planet, and find it to be less eccentric and less massive than previously reported. The density of the transiting planet is 3.97 g cm−3, which is low enough to suggest that the planet has at least a small volatile envelope, but the mass fractions of rock, iron, and water are not well-constrained. Given the host star brightness, planet period, and location of the planet near both the "radius gap" and the "hot Neptune desert," HD 86226c is an interesting candidate for transmission spectroscopy to further refine its composition

TOI-178: a window into the formation and evolution of planetary systems

International audienceLaplacian resonant chains — where astronomical bodies are in mean motion resonance with two or more other bodies — are rare phenomena observed in systems such as the TRAPPIST-1 exoplanets and the Galilean moons of Jupiter. Laplacian chains are an important tool to study the history of planetary systems occupying this configuration, as the fragility of the chain significantly constrains the possible pathways through which the planets can form and evolve. Whilst initial TESS observations suggested that TOI-178 — a nearby system of exoplanets orbiting a relatively cool K-dwarf — hosted the first known planets occupying a horseshoe-coorbital configuration, follow-up observations by CHEOPS, NGTS and SPECULOOS revealed a compact system of six transiting exoplanets all smaller than Neptune: five of which form a chain of Laplacian resonance. Precise measurements of the host's radial velocity using the ESPRESSO spectrograph revealed uncommon planet-to-planet density variations: a stark departure from the monotonic decrease in density with orbital separation common to most systems. JWST time awarded in Cycle 1 to acquire transmission spectroscopy of planets b, d and g promises to make the evolution of the TOI-178 planets amongst the best-understood of any planetary system for the foreseeable future

TESS Reveals a Short-period Sub-Neptune Sibling (HD 86226c) to a Known Long-period Giant Planet

The Transiting Exoplanet Survey Satellite mission was designed to find transiting planets around bright, nearby stars. Here we present the detection and mass measurement of a small, short-period ($\approx\,4$\,days) transiting planet around the bright ($V=7.9$), solar-type star HD 86226 (TOI-652, TIC 22221375), previously known to host a long-period ($\sim$1600 days) giant planet. HD 86226c (TOI-652.01) has a radius of $2.16\pm0.08$ $R_{\oplus}$ and a mass of 7.25$^{+1.19}_{-1.12}$ $M_{\oplus}$ based on archival and new radial velocity data. We also update the parameters of the longer-period, not-known-to-transit planet, and find it to be less eccentric and less massive than previously reported. The density of the transiting planet is $3.97$ g cm$^{-3}$, which is low enough to suggest that the planet has at least a small volatile envelope, but the mass fractions of rock, iron, and water are not well-constrained. Given the host star brightness, planet period, and location of the planet near both the ``radius gap'' and the ``hot Neptune desert'', HD 86226c is an interesting candidate for transmission spectroscopy to further refine its composition.Comment: Accepted in AJ on 22 June 202