We use an end-to-end model of planet formation, thermodynamic evolution, and atmospheric escape to investigate how the statistical imprints of evaporation depend on the bulk composition of planetary ...cores (rocky versus icy). We find that the population-wide imprints like the location of the "evaporation valley" in the distance-radius plane and the corresponding bimodal radius distribution clearly differ depending on the bulk composition of the cores. Comparison with the observed position of the valley suggests that close-in low-mass Kepler planets have a predominantly Earth-like rocky composition. Combined with the excess of period ratios outside of MMR, this suggests that low-mass Kepler planets formed inside of the water iceline but were still undergoing orbital migration. The core radius becomes visible for planets losing all primordial H/He. For planets in this "triangle of evaporation" in the distance-radius plane, the degeneracy in composition is reduced. In the observed planetary mass-mean density diagram, we identify a trend to more volatile-rich compositions with an increasing radius (R/R⊕ 1.6 rocky; 1.6-3.0 ices, and/or H/He; 3: H/He). The mass-density diagram contains important information about formation and evolution. Its characteristic broken V-shape reveals the transitions from solid planets to low-mass core-dominated planets with H/He and finally to gas-dominated giants. Evaporation causes the density and orbital distance to be anticorrelated for low-mass planets in contrast to giants, where closer-in planets are less dense, likely due to inflation. The temporal evolution of the statistical properties reported here will be of interest for the PLATO 2.0 mission, which will observe the temporal dimension.
Context. Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state often only cover parts of the pressure-temperature space ...needed in planetary modelling. Aims. We aim to construct an equation of state of H2O spanning a very wide range, from 0.1 Pa to 400 TPa and 150 to 105 K, which can be used to model the interior of planets. Methods. We combined equations of state valid in localised regions to form a continuous equation of state spanning over the above-mentioned pressure and temperature range. Results. We provide tabulated values for the most important thermodynamic quantities: the 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 equations of state like ANEOS and QEOS. Conclusions. AQUA is a combination of existing equations of state useful for planetary models. We show that, in most regions, AQUA is a thermodynamic consistent description of water. At pressures above 10 GPa, AQUA predicts systematic larger densities than ANEOS or QEOS. This is a feature that 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 equations of state and regarding experimental data of water at high pressures.
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Today, with the large number of detected exoplanets and improved measurements, we can reach the next step of planetary characterization. Classifying different populations of planets is not only ...important for our understanding of the demographics of various planetary types in the galaxy, but also for our understanding of planet formation. We explore the nature of two regimes in the planetary mass-radius (M-R) relation. We suggest that the transition between the two regimes of “small” and “large” planets occurs at a mass of 124 ± 7M⊕ and a radius of 12.1 ± 0.5R⊕. Furthermore, the M-R relation is R ∝ M0.55 ± 0.02 and R ∝ M0.01 ± 0.02 for small and large planets, respectively. We suggest that the location of the breakpoint is linked to the onset of electron degeneracy in hydrogen, and therefore to the planetary bulk composition. Specifically, it is the characteristic minimal mass of a planet that consists of mostly hydrogen and helium, and therefore its M-R relation is determined by the equation of state of these materials. We compare the M-R relation from observational data with the relation derived by population synthesis calculations and show that there is a good qualitative agreement between the two samples.
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The orbital distribution of giant planets is crucial for understanding how terrestrial planets form and predicting yields of exoplanet surveys. Here, we derive giant planets occurrence rates as a ...function of orbital period by taking into account the detection efficiency of the Kepler and radial velocity (RV) surveys. The giant planet occurrence rates for Kepler and RV show the same rising trend with increasing distance from the star. We identify a break in the RV giant planet distribution between ∼2 and 3 au-close to the location of the snow line in the solar system-after which the occurrence rate decreases with distance from the star. Extrapolating a broken power-law distribution to larger semimajor axes, we find good agreement with the ∼1% planet occurrence rates from direct imaging surveys. Assuming a symmetric power law, we also estimate that the occurrence of giant planets between 0.1 and 100 au is for planets with masses 0.1-20 MJ and decreases to for planets more massive than Jupiter. This implies that only a fraction of the structures detected in disks around young stars can be attributed to giant planets. Various planet population synthesis models show good agreement with the observed distribution, and we show how a quantitative comparison between model and data can be used to constrain planet formation and migration mechanisms.
In the core-accretion formation scenario of gas giants, most of the gas accreting onto a planet is processed through an accretion shock. In this series of papers we study this shock because it is key ...in setting the structure of the forming planet and thus its postformation luminosity, with dramatic observational consequences. We perform one-dimensional gray radiation-hydrodynamical simulations with nonequilibrium (two-temperature) radiation transport and up-to-date opacities. We survey the parameter space of accretion rate, planet mass, and planet radius and obtain postshock temperatures, pressures, and entropies, as well as global radiation efficiencies. We find that the shock temperature is usually given by the "free-streaming" limit. At low temperatures the dust opacity can make the shock hotter but not significantly so. We corroborate this with an original semianalytical derivation of . We also estimate the change in luminosity between the shock and the nebula. Neither nor the luminosity profile depend directly on the optical depth between the shock and the nebula. Rather, depends on the immediate preshock opacity, and the luminosity change on the equation of state. We find quite high immediate postshock entropies ( -20 ), which makes it seem unlikely that the shock can cool the planet. The global radiation efficiencies are high ( ), but the remainder of the total incoming energy, which is brought into the planet, exceeds the internal luminosity of classical cold starts by orders of magnitude. Overall, these findings suggest that warm or hot starts are more plausible.
Abstract
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.
The key aspect determining the postformation luminosity of gas giants has long been considered to be the energetics of the accretion shock at the surface of the planet. We use one-dimensional ...radiation-hydrodynamical simulations to study the radiative loss efficiency and to obtain postshock temperatures and pressures and thus entropies. The efficiency is defined as the fraction of the total incoming energy flux that escapes the system (roughly the Hill sphere), taking into account the energy recycling that occurs ahead of the shock in a radiative precursor. We focus in this paper on a constant equation of state (EOS) to isolate the shock physics but use constant and tabulated opacities. While robust quantitative results will have to await a self-consistent treatment including hydrogen dissociation and ionization, the results presented here show the correct qualitative behavior and can be understood from semianalytical calculations. The shock is found to be isothermal and supercritical for a range of conditions relevant to the core accretion formation scenario (CA), with Mach numbers . Across the shock, the entropy decreases significantly by a few times . While nearly 100% of the incoming kinetic energy is converted to radiation locally, the efficiencies are found to be as low as roughly 40%, implying that a significant fraction of the total accretion energy is brought into the planet. However, for realistic parameter combinations in the CA scenario, we find that a nonzero fraction of the luminosity always escapes the Hill sphere. This luminosity could explain, at least in part, recent observations in the young LkCa 15 and HD 100546 systems.
Aims.
The goal of this work is to study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim to compute the maximum core mass of a ...rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the
Kepler
size distribution.
Methods.
We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection–diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation, and sublimation at the water ice line are included. The disc evolution is computed solving the vertical and radial structure for standard
α
-discs with photoevaporation from the central star. The planets grow from a moon-mass embryo by silicate pebble accretion and gas accretion. We perform a parameter study to analyse the effect of a different initial disc mass,
α
-viscosity, disc metallicity, and embryo location. We also test the effect of considering migration versus an in situ scenario. Finally, we compute atmospheric mass loss due to evaporation over 5 Gyr of evolution.
Results.
We find that inside the ice line, the fragmentation barrier determines the size of pebbles, which leads to different planetary growth patterns for different disc viscosities. We also find that in this inner disc region, the pebble isolation mass typically decays to values below 5
M
⊕
within the first million years of disc evolution, limiting the core masses to that value. After computing atmospheric mass loss, we find that planets with cores below ~4
M
⊕
become completely stripped of their atmospheres, and a few 4–5
M
⊕
cores retain a thin atmosphere that places them in the “gap” or second peak of the
Kepler
size distribution. In addition, a few rare objects that form in extremely low-viscosity discs accrete a core of 7
M
⊕
and equal envelope mass, which is reduced to 3–5
M
⊕
after evaporation. These objects end up with radii of ~6–7
R
⊕
.
Conclusions.
Overall, we find that rocky planets form only in low-viscosity discs (
α
≲ 10
−4
). When
α
≥ 10
−3
, rocky objects do not grow beyond 1 Mars mass. For the successful low-viscosity cases, the most typical outcome of dry pebble accretion is terrestrial planets with masses spanning from that of Mars to ~4
M
⊕
.
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The collection of planetary system properties derived from large surveys such as Kepler provides critical constraints on planet formation and evolution. These constraints can only be applied to ...planet formation models, however, if the observational biases and selection effects are properly accounted for. Here we show how epos, the Exoplanet Population Observation Simulator, can be used to constrain planet formation models by comparing the Bern planet population synthesis models to the Kepler exoplanetary systems. We compile a series of diagnostics, based on occurrence rates of different classes of planets and the architectures of multiplanet systems within 1 au, that can be used as benchmarks for future and current modeling efforts. Overall, we find that a model with 100-seed planetary cores per protoplanetary disk provides a reasonable match to most diagnostics. Based on these diagnostics we identify physical properties and processes that would result in the Bern model more closely matching the known planetary systems. These are as follows: moving the planet trap at the inner disk edge outward; increasing the formation efficiency of mini-Neptunes; and reducing the fraction of stars that form observable planets. We conclude with an outlook on the composition of planets in the habitable zone, and highlight that the majority of simulated planets smaller than 1.7 Earth radii in this zone are predicted to have substantial hydrogen atmospheres. The software used in this paper is available online for public scrutiny at https://github.com/GijsMulders/epos.
We present an open-source retrieval code named HELIOS-RETRIEVAL, designed to obtain chemical abundances and temperature-pressure profiles by inverting the measured spectra of exoplanetary ...atmospheres. In our forward model, we use an exact solution of the radiative transfer equation, in the pure absorption limit, which allows us to analytically integrate over all of the outgoing rays. Two chemistry models are considered: unconstrained chemistry and equilibrium chemistry (enforced via analytical formulae). The nested sampling algorithm allows us to formally implement Occam's Razor based on a comparison of the Bayesian evidence between models. We perform a retrieval analysis on the measured spectra of the four HR 8799 directly imaged exoplanets. Chemical equilibrium is disfavored for HR 8799b and c. We find supersolar C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have a range of C/H and O/H values. The C/O values range from being superstellar for HR 8799b to being consistent with stellar for HR 8799c and being substellar for HR 8799d and e. If these retrieved properties are representative of the bulk compositions of the exoplanets, then they are inconsistent with formation via gravitational instability (without late-time accretion) and consistent with a core accretion scenario in which late-time accretion of ices occurred differently for the inner and outer exoplanets. For HR 8799e, we find that spectroscopy in the K band is crucial for constraining C/O and C/H. HELIOS-RETRIEVAL is publicly available as part of the Exoclimes Simulation Platform (http://www.exoclime.org).
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