Barbara Funk

Planets in habitable zones: A study of the binary Gamma Cephei

The recently discovered planetary system in the binary y Cep was studied concerning its dynamical evolution. We confirm that the orbital parameters found by the observers are in a stable configuration. The primary aim of this study was to find stable planetary orbits in a habitable region in this system, which consists of a double star (a = 21.36 AU) and a relatively close (a = 2.15 AU) massive (1.7 m j u p sin i) planet. We did straightforward numerical integrations of the equations of motion in different dynamical models and determined the stability regions for a fictitious massless planet in the interval of the semimajor axis 0.5 AU < a < 1.85 AU around the more massive primary. To confirm the results we used the Fast Lyapunov Indicators (FLI) in separate computations, which are a common tool for determining the chaoticity of an orbit. Both results are in good agreement and unveiled a small island of stable motions close to I AU up to an inclination of about 15° (which corresponds to the 3:1 mean motion resonance between the two planets). Additionally we computed the orbits of earthlike planets (up to 90 earthmasses) in the small stable island and found out, that there exists a small window of stable orbits on the inner edge of the habitable zone in γ Cep even for massive planets.

AN ANALYTIC METHOD TO DETERMINE HABITABLE ZONES FOR S-TYPE PLANETARY ORBITS IN BINARY STAR SYSTEMS

With more and more extrasolar planets discovered in and around binary star systems, questions concerning the determination of the classical Habitable Zone arise. Do the radiative and gravitational perturbations of the second star influence the extent of the Habitable Zone significantly, or is it sufficient to consider the host-star only? In this article we investigate the implications of stellar companions with different spectral types on the insolation a terrestrial planet receives orbiting a Sun-like primary. We present time independent analytical estimates and compare these to insolation statistics gained via high precision numerical orbit calculations. Results suggest a strong dependence of permanent habitability on the binarys eccentricity, as well as a possible extension of Habitable Zones towards the secondary in close binary systems.

Circumstellar Habitable Zones of Binary Star Systems in the Solar Neighborhood

Binary and multiple systems constitute more than half of the total stellar population in the Solar neighborhood (Kiseleva-Eggleton & Eggleton 2001). Their frequent occurrence as well as the fact that more than 70 (Schneider et al. 2011) planets have already been discovered in such configurations - most noteably the telluric companion of α Cen B (Dumusque et al. 2012) - make them interesting targets in the search for habitable worlds. Recent studies (Eggl et al. 2012b; Forgan 2012) have shown, that despite the variations in gravitational and radiative environment, there are indeed circumstellar regions where planets can stay within habitable insolation limits on secular dynamical timescales. In this article we provide habitable zones for 19 near S-Type binary systems from the Hipparchos and WDS catalogues with semimajor axes between 1 and 100 AU. Hereby, we accounted for the combined dynamical and radiative influence of the second star on the Earth-like planet. Out of the 19 systems presented, 17 offer dynamically stable habitable zones around at least one component. The 17 potentially habitable systems contain 5 F, 3 G, 7 K and 16 M class stars. As their proximity to the Solar System (d < 31 pc) makes the selected binary stars exquisite targets for observational campaigns, we offer estimates on radial velocity, astrometric and transit signatures produced by habitable Earth-like planets in eccentric circumstellar orbits.

Dynamical habitability of planetary systems

The problem of the stability of planetary systems, a question that concerns only multiplanetary systems that host at least two planets, is discussed. The problem of mean motion resonances is addressed prior to discussion of the dynamical structure of the more than 350 known planets. The difference with regard to our own Solar System with eight planets on low eccentricity is evident in that 60% of the known extrasolar planets have orbits with eccentricity e > 0.2. We theoretically highlight the studies concerning possible terrestrial planets in systems with a Jupiter-like planet. We emphasize that an orbit of a particular nature only will keep a planet within the habitable zone around a host star with respect to the semimajor axis and its eccentricity. In addition, some results are given for individual systems (e.g., Gl777A) with regard to the stability of orbits within habitable zones. We also review what is known about the orbits of planets in double-star systems around only one component (e.g., gamma Cephei) and around both stars (e.g., eclipsing binaries).

New prospects for observing and cataloguing exoplanets in well-detached binaries

This paper is devoted to study the circumstances favourable to detect circumstellar and circumbinary planets in well detached binary-star-systems using eclipse timing variations (ETVs). We investigated the dynamics of well detached binary star systems with a star separation from 0.5 to 3~AU, to determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions Plato, Tess and Cheops). For the chosen star separations both dynamical configurations (circumstellar and circumbinary) may be observable. We performed numerical simulations by using the full three-body problem as dynamical model. The dynamical stability and the ETVs are investigated by computing ETV maps for different masses of the secondary star and the exoplanet (Earth, Neptune and Jupiter size). In addition we changed the planets and binarys eccentricities. We conclude that many amplitudes of ETVs are large enough to detect exoplanets in binary star systems. As an application, we prepared statistics of the catalogue of exoplanets in binary star systems which we introduce in this article and compared the statistics with our parameter-space which we used for our calculations. In addition to these statistics of the catalogue we enlarged them by the investigation of well detached binary star systems from several catalogues and discussed the possibility of further candidates.

On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis - inclination plane. The gas giants initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 10 5 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.

Eclipse timing variations to detect possible Trojan planets in binary systems

This paper is devoted to study the circumstances favourable to detect Trojan planets in close binary-star-systems by the help of eclipse timing variations (ETVs). To determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions like Plato, Tess and Cheops), we investigated the dynamics of binary star systems with a planet in tadpole motion. We did numerical simulations by using the full three-body problem as dynamical model. The stability and the ETVs are investigated by computing stability/ETV maps for different masses of the secondary star and the Trojan planet. In addition we changed the eccentricity of the possible Trojan planet. By the help of the libration amplitude

Dynamics of the TrES-2 system

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Dynamics and habitability in circumstellar planetary systems of known binary stars

we could show whether or not all stable objects are moving in tadpole orbits. We can conclude that many amplitudes of ETVs are large enough to detect Earth-like Trojan planets in binary star systems. As an application, we prepared a list of possible candidates.

Can there be additional rocky planets in the Habitable Zone of tight binary stars with a known gas giant

The TrES-2 system harbors one planet which was discovered with the transit technique. In this work we investigate the dynamical behavior of possible additional, lower-mass planets. We identify the regions where such planets can move on stable orbits and show how they depend on the initial eccentricity and inclination. We find, that there are stable regions inside and outside the orbit of TrES-2b where additional, smaller planets can move. We also show that those planets can have a large orbital inclination which makes a detection with the transit technique very difficult (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)