* Astronomy

Blobrana · L

RE: Circumbinary Planetary Systems

Blobrana · L

Title: "Winter is coming"
Authors: Veselin Kostov, Daniel Allan, Nikolaus Hartman, Scott Guzewich, Justin Rogers

Those that do not sow care little about such mundane things as equinoxes or planting seasons, or even crop rotation for that matter. Wherever and whenever the reavers reave, the mood is always foul and the nights are never warm or pleasant. For the rest of the good folks of Westeros, however, a decent grasp of the long-term weather forecast is a necessity. Many a maester have tried to play the Game of Weather Patterns and foretell when to plant those last turnip seeds, hoping for a few more years of balmy respite. Tried and failed. For other than the somewhat vague (if not outright meaningless) omens of "Winter is Coming", their meteorological efforts have been worse than useless. To right that appalling wrong, here we attempt to explain the apparently erratic seasonal changes in the world of G.R.R.M. A natural explanation for such phenomena is the unique behaviour of a circumbinary planet. Thus, by speculating that the planet under scrutiny is orbiting a pair of stars, we utilise the power of numerical three-body dynamics to predict that, unfortunately, it is not possible to predict either the length, or the severity of any coming winter. We conclude that, alas, the Maesters were right -- one can only throw their hands in the air in frustration and, defeated by non-analytic solutions, mumble "Coming winter? May be long and nasty (~850 days, T<268K) or may be short and sweet (~600 days, T~273K). Who knows..."

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Title: An Analytic Theory for the Orbits of Circumbinary Planets
Authors: Gene C. K. Leung, Man Hoi Lee (HKU)

Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions. The largest forced oscillation term corresponds to a forced eccentricity (which is an explicit function of the parameters of the binary and of the guiding center radius of the planet), and the amplitude of the epicyclic motion (which is a free parameter of the theory) is the free eccentricity. Comparisons with direct numerical orbit integrations show that this analytic theory gives an accurate description of the planetary motion for all three Kepler systems. We find that all three Kepler circumbinary planets have nonzero free eccentricities.

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Blobrana · L

Title: On the Habitable Zones of Circumbinary Planetary Systems
Authors: Stephen R. Kane, Natalie R. Hinkel

The effect of the stellar flux on exoplanetary systems is becoming an increasingly important property as more planets are discovered in the Habitable Zone (HZ). The Kepler mission has recently uncovered circumbinary planets with relatively complex HZs due to the combined flux from the binary host stars. Here we derive HZ boundaries for circumbinary systems and show their dependence on the stellar masses, separation, and time while accounting for binary orbital motion and the orbit of the planet. We include stability regimes for planetary orbits in binary systems with respect to the HZ. These methods are applied to several of the known circumbinary planetary systems such as Kepler-16, 34, 35, and 47. We also quantitatively show the circumstances under which single-star approximations break down for HZ calculations.

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