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Register a new userAnalytic orbit propagation for transiting circumbinary planets
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Added by
Nikolaos Georgakarakos Ph.D.
Publication date
2015
fields
Physics
and research's language is
English
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The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are used to derive short period evolution of the system, while octupole secular theory is applied to describe its long term behaviour. A post Newtonian correction on the stellar orbit is included. The planetary orbit is initially circular and the theory developed here assumes that the planetary eccentricity remains relatively small (e_2<0.2). Our model is tested against results from numerical integrations of the full equations of motion and is then applied to investigate the dynamical history of some of the circumbinary planetary systems discovered by NASAs Kepler satellite. Our results suggest that the formation history of the systems Kepler-34 and Kepler-413 has most likely been different from the one of Kepler-16, Kepler-35, Kepler-38 and Kepler-64, since the observed planetary eccentricities for those systems are not compatible with the assumption of initially circular orbits.
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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.
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
Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while in transit. These propertied make the popular transit finding algorithm BLS almost ineffective so a modified version of BLS for the identification of CB planets was developed - CB-BLS. We show that using this algorithm it is possible to find CB planets in the residuals of light curves of eclipsing binaries that have noise levels of 1% and more - quality that is routinely achieved by current ground-based transit surveys. Previous searches for CB planets using variation of eclipse times minima of CM Dra and elsewhere are more closely related to radial velocity than to transit searches and so are quite distinct from CB-BLS. Detecting CB planets is expected to have significant impact on our understanding of exoplanets in general, and exoplanet formation in particular. Using CB-BLS will allow to easily harness the massive ground- and space- based photometric surveys in operation to look for these hard-to-find objects.
Because the planets of a system form in a flattened disk, they are expected to share similar orbital inclinations at the end of their formation. The high-precision photometric monitoring of stars known to host a transiting planet could thus reveal the transits of one or more other planets. We investigate here the potential of this approach for the M dwarf GJ 1214 that hosts a transiting super-Earth. For this system, we infer the transit probabilities as a function of orbital periods. Using Monte-Carlo simulations we address both the cases for fully coplanar and for non-coplanar orbits, with three different choices of inclinations distribution for the non-coplanar case. GJ 1214 reveals to be a very promising target for the considered approach. Because of its small size, a ground-based photometric monitoring of this star could detect the transit of a habitable planet as small as the Earth, while a space-based monitoring could detect any transiting habitable planet down to the size of Mars. The mass measurement of such a small planet would be out of reach for current facilities, but we emphasize that a planet mass would not be needed to confirm the planetary nature of the transiting object. Furthermore, the radius measurement combined with theoretical arguments would help us to constrain the structure of the planet.
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