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Register a new userEarths in Other Solar Systems N-body simulations: the Role of Orbital Damping in Reproducing the Kepler Planetary Systems
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The population of exoplanetary systems detected by Kepler provides opportunities to refine our understanding of planet formation. Unraveling the conditions needed to produce the observed exoplanets will sallow us to make informed predictions as to where habitable worlds exist within the galaxy. In this paper, we examine using N-body simulations how the properties of planetary systems are determined during the final stages of assembly. While accretion is a chaotic process, trends in the ensemble properties of planetary systems provide a memory of the initial distribution of solid mass around a star prior to accretion. We also use EPOS, the Exoplanet Population Observation Simulator, to account for detection biases and show that different accretion scenarios can be distinguished from observations of the Kepler systems. We show that the period of the innermost planet, the ratio of orbital periods of adjacent planets, and masses of the planets are determined by the total mass and radial distribution of embryos and planetesimals at the beginning of accretion. In general, some amount of orbital damping, either via planetesimals or gas, during accretion is needed to match the whole population of exoplanets. Surprisingly, all simulated planetary systems have planets that are similar in size, showing that the peas in a pod pattern can be consistent with both a giant impact scenario and a planet migration scenario. The inclusion of material at distances larger than what Kepler observes has a profound impact on the observed planetary architectures, and thus on the formation and delivery of volatiles to possible habitable worlds.
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A significant fraction of the hot Jupiters with final circularized orbital periods of less than 5 days are thought to form through the channel of high-eccentricity migration. Tidal dissipation at successive periastron passages removes orbital energy of the planet, which has the potential for changes in semi-major axis of a factor of ten to a thousand. In the equilibrium tide approximation we show that, in order for high-eccentricity migration to take place, the relative level of tidal dissipation in Jupiter analogues must be at least 10 times higher than the upper-limit attributed to the Jupiter-Io interaction. While this is not a severe problem for high-e migration, it contradicts the results of several previous calculations. We show that these calculations of high-e migration inadvertently over-estimated the strength of tidal dissipation by three to four orders of magnitude. These discrepancies were obscured by the use of various parameters, such as lag time tau, tidal quality factor Q and viscous time t_V. We provide the values of these parameters required for the Jupiter-Io interaction, tidal circularization and high-e migration. Implications for tidal theory as well as models of the inflated radii of hot Jupiters are discussed. Though the tidal Q is not, in general, well-defined, we derive a formula for it during high-eccentricity migration where Q is approximately constant throughout evolution.
Young stars are mostly found in dense stellar environments, and even our own Solar system may have formed in a star cluster. Here, we numerically explore the evolution of planetary systems similar to our own Solar system in star clusters. We investigate the evolution of planetary systems in star clusters. Most stellar encounters are tidal, hyperbolic, and adiabatic. A small fraction of the planetary systems escape from the star cluster within 50 Myr; those with low escape speeds often remain intact during and after the escape process. While most planetary systems inside the star cluster remain intact, a subset is strongly perturbed during the first 50 Myr. Over the course of time, 0.3 % - 5.3 % of the planets escape, sometimes up to tens of millions of years after a stellar encounter occurred. Survival rates are highest for Jupiter, while Uranus and Neptune have the highest escape rates. Unless directly affected by a stellar encounter itself, Jupiter frequently serves as a barrier that protects the terrestrial planets from perturbations in the outer planetary system. In low-density environments, Jupiter provides protection from perturbations in the outer planetary system, while in high-density environments, direct perturbations of Jupiter by neighbouring stars is disruptive to habitable-zone planets. The diversity amongst planetary systems that is present in the star clusters at 50 Myr, and amongst the escaping planetary systems, is high, which contributes to explaining the high diversity of observed exoplanet systems in star clusters and in the Galactic field
We simulate a Kepler-like observation of a theoretical exoplanet population and we show that the observed orbital period distribution of the Kepler giant planet candidates is best matched by an average stellar specific dissipation function Q_* in the interval 10^6 ~< Q_* ~< 10^7. In that situation, the few super-Earths that are driven to orbital periods P < 1 day by dynamical interactions in multiple-planet systems will survive tidal disruption for a significant fraction of the main-sequence lifetimes of their stellar hosts. Consequently, though these very-hot super-Earths are not characteristic of the overall super-Earth population, their substantial transit probability implies that they should be significant contributors to the full super-Earth population uncovered by Kepler. As a result, the CoRoT-7 system may be the first representative of a population of very-hot super-Earths that we suggest should be found in multiple-planet systems preferentially orbiting the least-dissipative stellar hosts in the Kepler sample.
We study the orbital evolution of a three planet system with masses in the super-Earth regime resulting from the action of tides on the planets induced by the central star which cause orbital circularization. We consider systems either in or near to a three body commensurability for which adjacent pairs of planets are in a first order commensurability. We develop a simple analytic solution, derived from a time averaged set of equations, that describes the expansion of the system away from strict commensurability as a function of time, once a state where relevant resonant angles undergo small amplitude librations has been attained. We perform numerical simulations that show the attainment of such resonant states focusing on the Kepler 60 system. The results of the simulations confirm many of the scalings predicted by the appropriate analytic solution. We go on to indicate how the results can be applied to put constraints on the amount of tidal dissipation that has occurred in the system. For example, if the system has been in a librating state since its formation, we find that its present period ratios imply an upper limit on the time average of 1/Q, with Q being the tidal dissipation parameter. On the other hand if a librating state has not been attained, a lower upper bound applies.
We determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting planet, which supplement our previous measurements of 66 planets in multi-planet systems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planet have a different eccentricity distribution than systems with multiple detected transiting planets. The eccentricity distribution of the single-transiting systems is well described by the positive half of a zero-mean Gaussian distribution with a dispersion $sigma_e = 0.32 pm 0.06$, while the multiple-transit systems are consistent with $sigma_e = 0.083^{+0.015}_{-0.020}$. A mixture model suggests a fraction of $0.76^{+0.21}_{-0.12}$ of single-transiting systems have a moderate eccentricity, represented by a Rayleigh distribution that peaks at $0.26^{+0.04}_{-0.06}$. This finding may reflect differences in the formation pathways of systems with different numbers of transiting planets. We investigate the possibility that eccentricities are self-excited in closely packed planetary systems, as well as the influence of long-period giant companion planets. We find that both mechanisms can qualitatively explain the observations. We do not find any evidence for a correlation between eccentricity and stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricity is linked to the detection of a companion star. Along with this paper we make available all of the parameters and uncertainties in the eccentricity distributions, as well as the properties of individual systems, for use in future studies.
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