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Register a new userOn the Detection of Habitable Trojan Planets in the Kepler Circumbinary Systems
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We present the results of a study of the prospect of detecting habitable Trojan planets in the Kepler Habitable Zone circumbinary planetary systems (Kepler-16, -47, -453, -1647, -1661). We integrated the orbits of 10,000 separate N-body systems (N=4,6), each with a one Earth-mass body in a randomly selected orbit near the L4 and L5 Lagrangian points of the host HZ circumbinary planet. We find that stable Trojan planets are restricted to a narrow range of semimajor axes in all five systems and limited to small eccentricities in Kepler-16, -47, and -1661. To assess the prospect of the detection of these habitable Trojan planets, we calculated the amplitudes of the variations they cause in the transit timing of their host bodies. Results show that the mean amplitudes of the transit timing variations (TTVs) correlate with the mass of the transiting planet and range from 70 minutes for Kepler-16b to 390 minutes for Kepler-47c. Our analysis indicates that the TTVs of the circumbinary planets caused by these Trojan bodies fall within the detectable range of timing precision obtained from the Kepler telescopes long-cadence data. The latter points to Kepler data as a viable source to search for habitable Trojan planets.
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The discovery of many planets using the Kepler telescope includes ten planets orbiting eight binary stars. Three binaries, Kepler-16, Kepler-47, and Kepler-453, have at least one planet in the circumbinary habitable-zone (BHZ). We constrain the level of high-energy radiation and the plasma environment in the BHZ of these systems. With this aim, BHZ limits in these Kepler binaries are calculated as a function of time, and the habitability lifetimes are estimated for hypothetical terrestrial planets and/or moons within the BHZ. With the time-dependent BHZ limits established, a self-consistent model is developed describing the evolution of stellar activity and radiation properties as proxies for stellar aggression toward planetary atmospheres. Modeling binary stellar rotation evolution, including the effect of tidal interaction between stars in binaries is key to establishing the environment around these systems. We find that Kepler-16 and its binary analogs provide a plasma environment favorable for the survival of atmospheres of putative Mars-sized planets and exomoons. Tides have modified the rotation of the stars in Kepler-47 making its radiation environment less harsh in comparison to the solar system. This is a good example of the mechanism first proposed by Mason et al. Kepler-453 has an environment similar to that of the solar system with slightly better than Earth radiation conditions at the inner edge of the BHZ. These results can be reproduced and even reparametrized as stellar evolution and binary tidal models progress, using our online tool http://bhmcalc.net.
The Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple) secular resonances emerging in the disk. We derive analytic results for size-dependent planetesimal eccentricity, and demonstrate the key role of the disk gravity for circumbinary dynamics. We then combine these results with a simple model for collisional outcomes and find that in systems like Kepler 16, planetesimal growth starting with 10-100 m planetesimals is possible outside a few AU. The exact location exterior to which this happens is sensitive to disk eccentricity, density and precession rate, as well as to the size of the first generation of planetesimals. Strong perturbations from the binary in the inner part of the disk, combined with a secular resonance at a few AU inhibit the growth of km-sized planetesimals within 2 - 4 AU of the binary. In situ planetesimal growth in the Kepler circumbinary systems is possible only starting from large (few-km-sized) bodies in a low-mass disk with surface density less than 500 g/cm^2 at 1 AU.
We use a one-dimensional (1-D) cloud-free climate model to estimate habitable zone (HZ) boundaries for terrestrial planets of masses 0.1 M$_{E}$ and 5 M$_{E}$ around circumbinary stars of various spectral type combinations. Specifically, we consider binary systems with host spectral types F-F, F-G, F-K, F-M, G-G, G-K, G-M, K-K, K-M and M-M. Scaling the background N2 atmospheric pressure with the radius of the planet, we find that the inner edge of the HZ moves inwards towards the star for 5ME compared to 0.1ME planets for all spectral types. This is because the water-vapor column depth is smaller for larger planets and higher temperatures are needed before water vapor completely dominates the outgoing longwave radiation. The outer edge of the HZ changes little due to competing effects of the albedo and greenhouse effect. While these results are broadly consistent with the trend of single star HZ results for different mass planets, there are significant differences between single star and binary star systems for the inner edge of the HZ. Interesting combinations of stellar pairs from our 1-D model results can be used to explore for in-depth climate studies with 3-D climate models. We identify a common HZ stellar flux domain for all circumbinary spectral types
Most Sun-like stars in the Galaxy reside in gravitationally-bound pairs of stars called binary stars. While long anticipated, the existence of a circumbinary planet orbiting such a pair of normal stars was not definitively established until the discovery of Kepler-16. Incontrovertible evidence was provided by the miniature eclipses (transits) of the stars by the planet. However, questions remain about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we present two additional transiting circumbinary planets, Kepler-34 and Kepler-35. Each is a low-density gas giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 orbits two Sun-like stars every 289 days, while Kepler-35 orbits a pair of smaller stars (89% and 81% of the Suns mass) every 131 days. Due to the orbital motion of the stars, the planets experience large multi-periodic variations in incident stellar radiation. The observed rate of circumbinary planets implies > ~1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.
The Kepler mission has detected a number of transiting circumbinary planets (CBPs). Although currently not detected, exomoons could be orbiting some of these CBPs, and they might be suitable for harboring life. A necessary condition for the existence of such exomoons is their long-term dynamical stability. Here, we investigate the stability of exomoons around the Kepler CBPs using numerical $N$-body integrations. We determine regions of stability and obtain stability maps in the (a_m,i_pm) plane, where a_m is the initial exolunar semimajor axis with respect to the CBP, and i_pm is the initial inclination of the orbit of the exomoon around the planet with respect to the orbit of the planet around the stellar binary. Ignoring any dependence on i_pm, for most Kepler CBPs the stability regions are well described by the location of the 1:1 mean motion commensurability of the binary orbit with the orbit of the moon around the CBP. This is related to a destabilizing effect of the binary compared to the case if the binary were replaced by a single body, and which is borne out by corresponding 3-body integrations. For high inclinations, the evolution is dominated by Lidov-Kozai oscillations, which can bring moons in dynamically stable orbits to close proximity within the CBP, triggering strong interactions such as tidal evolution, tidal disruption, or direct collisions. This suggests that there is a dearth of highly-inclined exomoons around the Kepler CBPs, whereas coplanar exomoons are dynamically allowed.
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