Analytic orbit propagation for transiting circumbinary planets

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 NASA's 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.Comment: Accepted for publication in Ap

Sublimation-induced orbital perturbations of extrasolar active asteroids and comets: application to white dwarf systems

The metal budgets in some white dwarf (WD) atmospheres reveal that volatile-rich circumstellar bodies must both exist in extrasolar systems and survive the giant branch phases of stellar evolution. The resulting behaviour of these active asteroids or comets which orbit WDs is not well-understood, but may be be strongly influenced by sublimation due to stellar radiation. Here we develop a model, generally applicable to any extrasolar system with a main sequence or WD star, that traces sublimation-induced orbital element changes in approximately km-sized extrasolar minor planets and comets traveling within hundreds of au. We derive evolution equations on orbital timescales and for arbitrarily steep power-law sublimation dependencies on distance, and place our model in a Solar system context. We also demonstrate the importance of coupling sublimation and general relativity, and the orbital consequences of outgassing in arbitrary directions. We prove that nongravitational accelerations alone cannot result in orbit crossing with the WD disruption radius, but may shrink or expand the orbit by up to several au after a single pericentre passage, potentially affecting subsequent interactions with remnant debris and planets. Our analysis suggests that extant planets must exist in polluted WD systems.Comment: Accepted for publication in MNRA

Detectability of Earth-like Planets in Circumstellar Habitable Zones of Binary Star Systems with Sun-like Components

Given the considerable percentage of stars that are members of binaries or stellar multiples in the Solar neighborhood, it is expected that many of these binaries host planets, possibly even habitable ones. The discovery of a terrestrial planet in the alpha Centauri system supports this notion. Due to the potentially strong gravitational interaction that an Earth-like planet may experience in such systems, classical approaches to determining habitable zones, especially in close S-Type binary systems, can be rather inaccurate. Recent progress in this field, however, allows to identify regions around the star permitting permanent habitability. While the discovery of alpha Cen Bb has shown that terrestrial planets can be detected in solar-type binary stars using current observational facilities, it remains to be shown whether this is also the case for Earth analogues in habitable zones. We provide analytical expressions for the maximum and RMS values of radial velocity and astrometric signals, as well as transit probabilities of terrestrial planets in such systems, showing that the dynamical interaction of the second star with the planet may indeed facilitate the planets detection. As an example, we discuss the detectability of additional Earth-like planets in the averaged, extended, and permanent habitable zones around both stars of the alpha Centauri system.Comment: accepted for publication in The Astrophysical Journa

The orbital evolution of asteroids, pebbles and planets from giant branch stellar radiation and winds

The discovery of over 50 planets around evolved stars and more than 35 debris discs orbiting white dwarfs highlight the increasing need to understand small body evolution around both early and asymptotic giant branch (GB) stars. Pebbles and asteroids are susceptible to strong accelerations from the intense luminosity and winds of GB stars. Here, we establish equations that can model time-varying GB stellar radiation, wind drag and mass loss. We derive the complete three-dimensional equations of motion in orbital elements due to (1) the Epstein and Stokes regimes of stellar wind drag, (2) Poynting-Robertson drag, and (3) the Yarkovsky drift with seasonal and diurnal components. We prove through averaging that the potential secular eccentricity and inclination excitation due to Yarkovsky drift can exceed that from Poynting-Robertson drag and radiation pressure by at least three orders of magnitude, possibly flinging asteroids which survive YORP spin-up into a widely dispersed cloud around the resulting white dwarf. The GB Yarkovsky effect alone may change an asteroid's orbital eccentricity by ten per cent in just one Myr. Damping perturbations from stellar wind drag can be just as extreme, but are strongly dependent on the highly uncertain local gas density and mean free path length. We conclude that GB radiative and wind effects must be considered when modelling the post-main-sequence evolution of bodies smaller than about 1000 km.Comment: Corrected Fig. 3 and Eq. 14 (In Press, MNRAS

Adjoint-based mixing enhancement for binary fluids

Mixing is a fundamental fluid process that dominates {a} great many natural phenomena and is present in a wide variety of industrial applications. Therefore, studying the characteristics and optimisation of this process may lead to a significant impact in many fields. This thesis presents an analytical and computational framework for optimising fluid mixing processes using embedded stirrers based on a non-linear direct-adjoint looping approach. The governing equations are the non-linear Navier-Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a Fourier-based spectral method. Stirrers are embedded in the computational domain by a Brinkman-penalisation technique, and shape and path gradients for the stirrers are computed from the adjoint solution. The relationship between this penalisation approach and the adjoint will be examined through the derivation of a dual system of equations, and three different optimisation scenarios of increasing complexity, each focusing on different optimisation parameters, are considered. Within the limits of the parameterisations of the geometry and the externally imposed bounds, significant improvements in mixing efficiency are achieved in all cases.Open Acces

Impact flux of asteroids and water transport to the habitable zone in binary star systems

By now, observations of exoplanets have found more than 50 binary star systems hosting 71 planets. We expect these numbers to increase as more than 70% of the main sequence stars in the solar neighborhood are members of binary or multiple systems. The planetary motion in such systems depends strongly on both the parameters of the stellar system (stellar separation and eccentricity) and the architecture of the planetary system (number of planets and their orbital behaviour). In case a terrestrial planet moves in the so-called habitable zone (HZ) of its host star, the habitability of this planet depends on many parameters. A crucial factor is certainly the amount of water. We investigate in this work the transport of water from beyond the snow-line to the HZ in a binary star system and compare it to a single star system

Prediction of transits of solar system objects in Kepler/K2 images: An extension of the Virtual Observatory service SkyBoT

All the fields of the extended space mission Kepler/K2 are located within the ecliptic. Many solar system objects thus cross the K2 stellar masks on a regular basis. We aim at providing to the entire community a simple tool to search and identify solar system objects serendipitously observed by Kepler. The SkyBoT service hosted at IMCCE provides a Virtual Observatory (VO) compliant cone-search that lists all solar system objects present within a field of view at a given epoch. To generate such a list in a timely manner, ephemerides are pre-computed, updated weekly, and stored in a relational database to ensure a fast access. The SkyBoT Web service can now be used with Kepler. Solar system objects within a small (few arcminutes) field of view are identified and listed in less than 10 sec. Generating object data for the entire K2 field of view (14{\deg}) takes about a minute. This extension of the SkyBot service opens new possibilities with respect to mining K2 data for solar system science, as well as removing solar system objects from stellar photometric time-series

The shape evolution of cometary nuclei via anisotropic mass loss

Context. Breathtaking imagery recorded during the European Space Agency's Rosetta mission confirmed the bilobate nature of comet 67P/Churyumov-Gerasimenko's nucleus. Its peculiar appearance is not unique among comets. The majority of cometary cores imaged at high resolution exhibit a similar build. Various theories have been brought forward as to how cometary nuclei attain such peculiar shapes. Aims. We illustrate that anisotropic mass loss and local collapse of subsurface structures caused by non-uniform exposure of the nucleus to solar irradiation can transform initially spherical comet cores into bilobed ones. Methods. A mathematical framework to describe the changes in morphology resulting from non-uniform insolation during a nucleus' spin-orbit evolution is derived. The resulting partial differential equations that govern the change in the shape of a nucleus subject to mass loss and consequent collapse of depleted subsurface structures are solved analytically for simple insolation configurations and numerically for more realistic scenarios. Results. The here proposed mechanism is capable of explaining why a large fraction of periodic comets appear to have peanut-shaped cores and why light-curve amplitudes of comet nuclei are on average larger than those of typical main belt asteroids of the same size.Comment: 4 pages of the main text, 2 pages of appendix, 4 figure