In Situ and Ex Situ Formation Models of Kepler 11 Planets

In Situ and Ex Situ Formation Models of Kepler 11 Planets

Authors:

D'Angelo et al

Abstract:

We present formation simulations of the six Kepler 11 planets. Models assume either in situ or ex situ assembly, the latter with migration, and are evolved to the estimated age of the system, 8 Gyr. Models combine detailed calculations of both the gaseous envelope and the condensed core structures, including accretion of gas and solids, of the disk's viscous and thermal evolution, including photo-evaporation and disk-planet interactions, and of the planets' evaporative mass loss after disk dispersal. Planet-planet interactions are neglected. Both sets of simulations successfully reproduce measured radii, masses, and orbital distances of the planets, except for the radius of Kepler 11b, which loses its entire gaseous envelope shortly after formation. Gaseous (H+He) envelopes account for < 18% of the planet masses, and between 35 and 60% of the planet radii. In situ models predict a very massive inner disk, whose solids' surface density (sigma_Z) varies from over 1e4 to 1e3 g/cm2 at stellocentric distances 0.1 < r < 0.5 AU. Initial gas densities would be in excess of 1e5 g/cm2 if solids formed locally. Given the high disk temperatures (> 1000 K), planetary interiors can only be composed of metals and highly refractory materials. Sequestration of hydrogen by the core and subsequent outgassing is required to account for the observed radius of Kepler 11b. Ex situ models predict a relatively low-mass disk, whose initial sigma_Z varies from 10 to 5 g/cm2 at 0.5 < r < 7 AU and whose initial gas density ranges from 1e3 to 100 g/cm2. All planetary interiors are expected to be rich in H2O, as core assembly mostly occurs exterior to the ice condensation front. Kepler 11b is expected to have a steam atmosphere, and H2O is likely mixed with H+He in the envelopes of the other planets. Results indicate that Kepler 11g may not be more massive than Kepler 11e.

Orbital Dynamics of Exoplanetary Systems Kepler-62, HD 200964 and Kepler-11

Orbital Dynamics of Exoplanetary Systems Kepler-62, HD 200964 and Kepler-11

Authors:

Mia et al

Abstract:

The presence of mean-motion resonances (MMR) in exoplanetary systems is a new exciting field of celestial mechanics which motivate us to consider the present work to study the dynamical behaviour of exoplanetary systems by time evolution of the orbital elements of the planets. Mainly we study the influence of planetary perturbations on semi-major axis and eccentricity. We identify (r+1):r mean-motion resonance terms in the expression of disturbing function and obtain the perturbations from the truncated disturbing function. Using the expansion of the disturbing function of three body problem and an analytical approach, we solve the equations of motion. The solution which is obtained analytically is compared with that of obtained by numerical method to validate our analytical result. In the present work we consider three exoplanetary systems namely Kepler-62, HD 200964 and Kepler-11. We have plotted the evolution of the resonant angles and found that they librate around constant value. In view of this, our opinion is that two planets of each system Kepler-62, HD 200964 and Kepler-11 are in 2:1, 4:3 and 5:4 mean motion resonances respectively.

Stellar Extreme Ultraviolet Spectral Energy Distribution's Impact on hot Jupiter Atmospheres

The influence of the Extreme Ultraviolet spectral energy distribution on the structure and composition of the upper atmosphere of exoplanets

Authors:

Guo et al

Abstract:

By varying the profiles of stellar extreme ultraviolet (EUV) spectral energy distribution (SED), we tested the influences of stellar EUV SEDs on the physical and chemical properties of the escaping atmosphere. We apply our model to study four exoplanets, HD 189733b, HD 209458b, GJ 436b, and Kepler-11b. We found that the total mass loss rates of an exoplanet, which are determined mainly by the integrated fluxes, are moderately affected by the profiles of the EUV SED, but the composition and species distributions in the atmosphere can be dramatically modified by the different profiles of the EUV SED. For exoplanets with a high hydrodynamic escape parameter (λ), the amount of atomic hydrogen produced by photoionization at different altitudes can vary by one to two orders of magnitude with the variation of stellar EUV SEDs. The effect of photoionization of H is prominent when the EUV SED is dominated by the low-energy spectral region (400-900${\AA}$), which pushes the transition of H/H+ to low altitudes. On the contrary, the transitions of H/H+ move to higher altitudes when most photons concentrate in the high-energy spectral region (50-400${\AA}$). For exoplanets with a low λ, the lower temperatures of the atmosphere make many chemical reactions so important that photoionization alone can no longer determine the composition of the escaping atmosphere. For HD 189733b, it is possible to explain the time variability of \lya\ between 2010 and 2011 by a change in the EUV SED of the host K star, yet invoking only thermal H\,I in the atmosphere.

Are Tightly Packed Exoplanet Systems Shaped by Unseen Gas Giants?

There might be giants: unseen Jupiter-mass planets as sculptors of tightly-packed planetary systems

Authors:

Hands et al

Abstract:

The limited completeness of the Kepler sample for planets with orbital periods ≳ 1 yr leaves open the possibility that exoplanetary systems may host undetected giant planets. Should such planets exist, their dynamical interactions with the inner planets may prove vital in sculpting the final orbital configurations of these systems. Using an N-body code with additional forces to emulate the effects of a protoplanetary disc, we perform simulations of the assembly of compact systems of super-Earth-mass planets with unseen giant companions. The simulated systems are analogous to Kepler-11 or Kepler-32 in that they contain 4 or 5 inner super-Earths, but our systems also contain longer-period giant companions which are unlikely to have been detected by Kepler. We find that giant companions tend to break widely-spaced, first-order mean-motion resonances, allowing the inner planets to migrate into tighter resonances. This leads to more compact architectures and increases the occurrence rate of Laplace resonant chains.

A Model for the Evolution of SuperEarths & MiniNeptunes Applied to the Kepler-11 System

Evolutionary Models of Super-Earths and Mini-Neptunes Incorporating Cooling and Mass Loss

Authors:

Howe et al

Abstract:

We construct models of the structural evolution of super-Earth- and mini-Neptune-type exoplanets with hydrogen-helium envelopes, incorporating radiative cooling and XUV-driven mass loss. We conduct a parameter study of these models, focusing on initial mass, radius, and envelope mass fractions, as well as orbital distance, metallicity, and the specific prescription for mass loss. From these calculations, we investigate how the observed masses and radii of exoplanets today relate to the distribution of their initial conditions. Orbital distance and initial envelope mass fraction are the most important factors determining planetary evolution, particular radius evolution. Initial mass also becomes important below a "turnoff mass," which varies with orbital distance, with mass-radius curves being approximately flat for higher masses. Initial radius is the least important parameter we study, with very little difference between the hot start and cold start limits after an age of 100 Myr. Model sets with no mass loss fail to produce results consistent with observations, but a plausible range of mass loss scenarios is allowed. In addition, we present scenarios for the formation of the Kepler-11 planets. Our best fit to observations Kepler-11b and Kepler-11c involves formation beyond the snow line, after which they moved inward, circularized, and underwent a reduced degree mass loss.

Stability of the Kepler-11 System and its Origin

Stability of the Kepler-11 System and its Origin

Author:

Mahajan et al

Abstract:

A significant fraction of Kepler systems are closely-packed, largely coplanar and circular. We study the stability of a 6-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique called `frequency maps' as fast indicators for long-term stability, we explore the stability of Kepler-11 system by analyzing the neighbourhood space around its orbital parameters. Frequency maps provide a visual representation of chaos and stability, and their dependence on orbital parameters. We find that the current system is stable, but lies within a few percent of several dynamically dangerous 2-body mean-motion resonances. Planet eccentricities are restricted below a small value, ∼0.04, for long-term stability, but planet masses can be more than twice their reported values (thus, allowing for the possibility of mass-loss by past photoevaporation). Based on our frequency maps, we speculate on the origin for instability in closely-packed systems. We then proceed to investigate how the system can have been assembled. The stability constraints on Kepler-11 (mainly, eccentricity constraints) suggest that if the system were assembled in-situ, a dissipation mechanism must have been at work to neutralize eccentricity excitation. On the other hand, if migration was responsible for assembling the planets, there has to be little differential migration among the planets, to avoid them either getting trapped into mean motion resonances, or crashing into each other.

Understanding the Formation & Assembly of Kepler's Compact Exoplanetary Systems

Understanding the assembly of Kepler's compact planetary systems

Authors:

Hands et al

Abstract:

The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler-11 and Kepler-32, in which ensembles of several planets are found in very closely packed orbits (often within a few percent of an AU of one another). These compact configurations present a challenge for traditional planet formation and migration scenarios. We present a dynamical study of the assembly of these systems, using an N-body method which incorporates a parametrized model of planet migration in a turbulent protoplanetary disc. We explore a wide parameter space, and find that under suitable conditions it is possible to form compact, close-packed planetary systems via traditional disc-driven migration. We find that simultaneous migration of multiple planets is a viable mechanism for the assembly of tightly-packed planetary systems, as long as the disc provides significant eccentricity damping and the level of turbulence in the disc is modest. We discuss the implications of our preferred parameters for the protoplanetary discs in which these systems formed, and comment on the occurrence and significance of mean-motion resonances in our simulations.

TRAnsits and Dynamics of Exoplanetary Systems Software for Detecting, Refining Transit Detections

TRADES: a new software to derive orbital parameters from observed Transit Times and Radial Velocities. Revisiting Kepler-11 and Kepler-9

Authors:

Borsato et al

Abstract:

Aims.

With the purpose of determining the orbital parameters of exoplanetary systems from observational data, we have developed a software, named TRADES (TRAnsits and Dynamics of Exoplanetary Systems) to simultaneously fit observed radial velocities and transit times data.

Methods.

We implemented a dynamical simulator for N-body system which also fits the available data during the orbital integration and determines the best combination of the orbital parameters using grid search, χ2 minimization, genetic algorithms, particle swarm optimization, and bootstrap analysis.

Results.

To validate TRADES, we tested the code on a synthetic three-body system and on two real systems discovered by the Kepler mission: Kepler-9 and Kepler-11. These systems are good benchmarks to test multiple exoplanet systems showing transit time variations (TTVs) due to the gravitational interaction among planets. We have found orbital parameters of Kepler-11 planets in good agreement with the values proposed in the discovery paper and with a a recent work from the same authors. We analyzed the first three quarters of Kepler-9 system and found parameters in partial agreement with discovery paper. Analyzing transit times (T0s) covering 12 quarters of Kepler data we have found a new best-fit solution. This solution outputs masses that are about the 55% of the values proposed in the discovery paper; this leads to a reduced semi-amplitude of the radial velocities of about 12.80 m/s.

Did Kepler-11f Form Farther out and Migrate in?

Accretion and Evolution of ~2.5 Earth-mass Planets with Voluminous H/He Envelopes

Authors:

Bodenheimer et al

Abstract:

Formation of planets in the Neptune size range with low-mass, but voluminous, H_2/He gaseous envelopes is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. Formation locations ranging from 0.5 to 4 AU from a star of 1 solar mass are considered. The final planets have heavy-element cores of 2.2--2.5 Earth masses and envelopes in the range 0.037--0.16 Earth masses. After the formation process, which lasts 2 Myr or less, the planets evolve at constant mass up to an age of several Gyr. For assumed equilibrium temperatures of 250, 500, and 1000 K, their calculated final radii are compared with those observed by the Kepler spacecraft. For the particular case of Kepler-11 f, we address the question whether it could have formed in situ or whether migration from a formation location farther out in the disk is required.

Reexamining the Kepler-11 Multi Exoplanetary System

Phase Curves of the Kepler-11 Multi-Planet System

Authors:

Gelino et al

Abstract:

The Kepler mission has allowed the detection of numerous multi-planet exosystems where the planetary orbits are relatively compact. The first such system detected was Kepler-11 which has six known planets at the present time. These kinds of systems offer unique opportunities to study constraints on planetary albedos by taking advantage of both the precision timing and photometry provided by Kepler data to monitor possible phase variations. Here we present a case study of the Kepler-11 system in which we investigate the phase modulation of the system as the planets orbit the host star. We provide predictions of maximum phase modulation where the planets are simultaneously close to superior conjunction. We use corrected Kepler data for Q1-Q17 to determine the significance of these phase peaks. We find that data quarters where maximum phase peaks occur are better fit by a phase model than a "null hypothesis" model.