Richard Schwarz

Extrasolar Trojan planets close to habitable zones

We investigate the stability regions of hypothetical terrestrial planets around the Lagrangian equilibrium points L4 and L5 in some specific extrasolar planetary systems. The problem of their stability can be treated in the framework of the restricted three body problem where the host star and a massive Jupiter-like planet are the primary bodies and the terrestrial planet is regarded as being massless. From these theoretical investigations one cannot determine the extension of the stable zones around the equilibrium points. Using numerical experiments we determined their largeness for three test systems chosen from the table of the know extrasolar planets, where a giant planet is moving close to the so-called habitable zone around the host star in low eccentric orbits. The results show the dependence of the size and structure of this region, which shrinks significantly with the eccentricity of the known gas giant.

Pathways to Earth-like atmospheres. Extreme ultraviolet (EUV)-powered escape of hydrogen-rich protoatmospheres.

We discuss the evolution of the atmosphere of early Earth and of terrestrial exoplanets which may be capable of sustaining liquid water oceans and continents where life may originate. The formation age of a terrestrial planet, its mass and size, as well as the lifetime in the EUV-saturated early phase of its host star play a significant role in its atmosphere evolution. We show that planets even in orbits within the habitable zone of their host stars might not lose nebular- or catastrophically outgassed initial protoatmospheres completely and could end up as water worlds with CO2 and hydrogen- or oxygen-rich upper atmospheres. If an atmosphere of a terrestrial planet evolves to an N2-rich atmosphere too early in its lifetime, the atmosphere may be lost. We show that the initial conditions set up by the formation of a terrestrial planet and by the evolution of the host star’s EUV and plasma environment are very important factors owing to which a planet may evolve to a habitable world. Finally we present a method for studying the discussed atmosphere evolution hypotheses by future UV transit observations of terrestrial exoplanets.

Survey of the stability region of hypothetical habitable Trojan planets

Aims. In this work we study the dynamical possibility in extrasolar planetary systems that a terrestrial planet can exist in 1:1 mean motion resonance with a Jovian-like planet. We compiled a catalogue of hypothetical habitable Trojan planets, to be able to make a stability forecast for further extrasolar planetary systems discovered in the future. When speaking of habitability we also took the influence of the spectral type of the central star into account. Methods. We integrated some 10 6 orbits of fictitious Trojans around the Lagrangian points for up to 10 7 orbital periods of the primary bodies and checked the stability of the orbital elements and their chaoticity with the aid of the Lyapunov characteristic indicator and maximum eccentricity. The computations were carried out using the dynamical model of the elliptic, restricted three-body problem that consists of a central star, a gas giant moving in the habitable zone, and a hypothetical (massless) terrestrial planet. Results. Our investigations have shown that 7 exoplanetary systems can harbour habitable Trojan planets with stable orbits (HD 93083, HD 17051, HD 28185, HD 27442, HD 188015, HD 99109, and HD 221287, which is a recently discovered system). The comparison of the investigated systems with our catalogue showed matching results, so that we can use the catalogue in practice.

Prospects of the detection of circumbinary planets with Kepler and CoRoT using the variations of eclipse timing

In close eclipsing binaries, measurements of the variations in binarys eclipse timing may be used to infer information about the existence of circumbinary objects. To determine the possibility of the detection of such variations with CoRoT and Kepler space telescopes, we have carried out an extensive study of the dynamics of a binary star system with a circumbinary planet, and calculated its eclipse timing variations (ETVs) for different values of the mass ratio and orbital elements of the binary and the perturbing body. Here, we present the results of our study and assess the detectability of the planet by comparing the resulting values of ETVs with the temporal sensitivity of CoRoT and Kepler. Results point to extended regions in the parameter space where the perturbation of a planet may be large enough to create measurable variations in the eclipse timing of the secondary star. Many of these variations point to potentially detectable ETVs and the possible inference of Jovian-type planets.

The stability of ultra-compact planetary systems

Aims. We investigate the dynamical stability of compact planetary systems in the CoRoT discovery space, i.e., with orbital periods of less than 50 days, including a detailed study of the stability of systems, which are spaced according to Hill’s criteria. Methods. The innermost fictitious planet was placed close to the Roche limit from the star (MStar = 1 MSun) and all other fictitious planets are lined up according to Hill’s criteria up to a distance of 0.26 AU, which corresponds to a 50 day period for a Sun-massed star. For the masses of the fictitious planets, we chose a range of 0.33–17 mEarth, where in each simulation all fictitious planets have the same mass. Additionally, we tested the influence of both the semi-major axis of the innermost planet and of the number of planets. In a next step we also included a gas giant in our calculations, which perturbs the inner ones and investigated their stability. Results. With numerous integrations of many different configurations we could show that long-time stable motion is possible for up to 10 planets with 17 mEarth within a distance of 0.26 AU. Further investigations show that the fictitious planets remain stable under certain circumstances even if a close-in gas giant is present.

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.

The Hungaria region as a possible source of Trojans and satellites in the inner Solar system

The Hungaria Family (the closest region of the Main Belt to Mars) is an important source of Planet-Crossing-Asteroids and even impactors of terrestrial planets. We present the possibility that asteroids coming from the Hungaria Family get captured into co-orbital motion with the terrestrial planets in the inner solar system. Therefore we carried out long term numerical integrations (up to 100 Myr) to analyze the migrations from their original location - the Hungaria family region- into the inner solar system. During the integration time we observed whether or not the Hungarias get captured into a co-orbital motion with the terrestrial planets. Our results show that 5.5% of 200 Hungarias, selected as a sample of the whole group, escape from the Hungaria region and the probability from that to become co-orbital objects (Trojans, satellites or horseshoes) turns out to be about 3.3%: 1.8% for Mars and 1.5% for the Earth. In addition, we distinguished in which classes of co-orbital motion the asteroids get captured and for how long they stay there in stable motion. Most of the escaped Hungarias become Quasi-satellites and the ones captured as Trojans favor the L_5 lagrangian point. This work highlights that the Hungaria region is a source of Mars and also Earth co-orbital objects.

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

Stability of librational motion in the spatial circular restricted three-body problem for high inclinations and mass ratios

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