arXiv subjects

Barbara Funk

Publications and source records attributed to Barbara Funk.

10 recordsLinked to original sources

arXiv2017

Exchange orbits - an interesting case of co-orbital motion

In this investigation we treat a special configuration of two celestial bodies in 1:1 mean motion resonance namely the so-called exchange orbits. There exist -- at least -- theoretically -- two different types: the exchange-a orbits and the exchange-e orbits. The first one is the following: two celestial bodies are in orbit around a central body with almost the same semi-major axes on circular orbits. Because of the relatively small differences in semi-major axes they meet from time to time and exchange their semi-major axes. The inner one then moves outside the other planet and vice versa. The second configuration one is the following: two planets are moving on nearly the same orbit with respect to the semi-major axes, one on a circular orbit and the other one on an eccentric one. During their dynamical evolution they change the characteristics of the orbit, the circular one becomes an elliptic one whereas the elliptic one changes its shape to a circle. This 'game' repeats periodically. In this new study we extend the numerical computations for both of these exchange orbits to the three dimensional case and in another extension treat also the problem when these orbits are perturbed from a fourth body. Our results in form of graphs show quite well that for a large variety of initial conditions both configurations are stable and stay in this exchange orbits.

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arXiv2017

Stability and secondary resonances in the spatial restricted three-body problem for small mass ratios

This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L4 in the spatial restricted three-body problem for moderate mass ratios (mu), meaning that mu is smaller than 0.0045. However, we concentrated our investigations on small mass ratios for mu smaller than 0.001, which represent the mass ratios for stable configurations of tadpole orbits in the Solar system. The stability is investigated by numerical methods, computing stability maps in different parameter planes. We started investigating the mass of the secondary; from Earth-mass bodies up to Jupiter-mass bodies. In addition we changed the orbital elements (eccentricity and inclination) of the secondary and Trojan body. For this parameter space we found high order secondary resonances, which are present for various inclinations. To determine secondary resonances we used Rabe's equation and the frequency analysis. In addition we investigated the stability in and around these secondary resonances.

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arXiv2017

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

In the spatial circular restricted three-body problem librational motion around the Lagrangian points $L_4$ and $L_5$ exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability of this librational motion for systematic variations in the inclination of the Trojan and the mass-ratio $\mu$ of the two massive bodies. We show that stable motion prevails for inclinations below 60 degrees and mass-ratios $\mu < 0.04$ for typical integration times up to $10^6$ revolution periods. At even higher mass-ratios -- beyond the critical mass-ratio for the planar case -- stable orbits were found to exist for up to $10^7$ periods at moderate inclinations. We extracted the librational frequencies on a grid in the parameter space from the Fourier spectra and traced their variation. Several resonances between the short and long period librational frequency as well as the vertical frequency lie inside the investigated region. The application of the Lyapunov characteristic indicator and spectral number methods also reveals the chaotic regions. This simple model is equally applicable in the Solar system for low mass ratios for Trojans of the planets, as well as to Trojan-type exoplanets in binary star systems at high mass-ratios.

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arXiv2016

On the possibility of habitable Trojan planets in binary star systems

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky Way) are members of binary or multiple star systems. This fact led to the speculations that many more planets may exist in binary systems than are currently known. To estimate the habitability of exoplanetary systems, we have to define the so-called habitable zone (HZ). The HZ is defined as a region around a star where a planet would receive enough radiation to maintain liquid water on its surface and to be able to build a stable atmosphere. We search for new dynamical configurations - where planets may stay in stable orbits - to increase the probability to find a planet like the Earth. Therefore we investigated five candidates and found that two systems (HD 41004 and HD 196885) which have small stable regions.

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arXiv2016

A quick method to identify secular resonances in multi-planet systems with a binary companion

Gravitational perturbations in multi-planet systems caused by an accompanying star are the subject of this investigation. Our dynamical model is based on the binary star HD41004 AB where a giant planet orbits HD41004 A. We modify the orbital parameters of this system and analyze the motion of a hypothetical test-planet surrounding HD41004 A on an interior orbit to the detected giant planet. Our numerical computations indicate perturbations due to mean motion and secular resonances. The locations of these resonances are usually connected to high eccentricity and highly inclined motion depending strongly on the binary-planet architecture.As the positions of mean motion resonances can easily be determined, the main purpose of this study is to present a new semi-analytical method to determine the location of a secular resonance without huge computational effort.

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arXiv2016

Dynamics and habitability in circumstellar planetary systems of known binary stars

We present a survey on exoplanetary systems of binary stars with stellar separations less than 100 au. For a sample of 11 binaries that harbour detected circumstellar giant planets we investigate the frequency of systems with secular resonances (SR) affecting the habitable zone (HZ). Secular resonances are connected to dynamically unstable or chaotic regions by enforcing highly eccentric motion. We apply a semi-analytical method to determine the locations of linear SR, which is based on finding the apsidal precession frequencies of the massive bodies. For configurations where the giant planet is located exterior to the HZ we find that there is always a SR interior to its orbit, the exact location of the SR strongly depends on the system's architecture. In systems with the giant planet interior to the HZ no SR can occur in the Newtonian framework. Taking into account the general relativistic precession of the perihelion, which increases the precession frequencies, planets with $a < 0.1$ au can cause SR in the HZ. We find two cases where the SR is located inside the HZ, and some more where it is close to the HZ. Generally, giant planets interior to the HZ are more favourable than exterior planets to avoid SR in the HZ. Around the location of the SR weaker mean-motion resonances are excited, and resonance overlap is possible. Existing analytical models are not as accurate as the semi-analytical method in locating the SR and deviate by $\sim 0.1$ au or more.

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arXiv2015

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

Locating planets in HabitableZones (HZs) around other stars is a growing field in contemporary astronomy. Since a large percentage of all G-M stars in the solar neighbourhood are expected to be part of binary or multiple stellar systems, investigations of whether habitable planets are likely to be discovered in such environments are of prime interest to the scientific community. As current exoplanet statistics predicts that the chances are higher to find new worlds in systems that are already known to have planets, we examine four known extrasolar planetary systems in tight binaries in order to determine their capacity to host additional habitable terrestrial planets. Those systems are Gliese 86, gamma Cephei, HD 41004 and HD 196885. In the case of gamma Cephei, our results suggest that only the M dwarf companion could host additional potentially habitable worlds. Neither could we identify stable, potentially habitable regions around HD 196885 A. HD 196885 B can be considered a slightly more promising target in the search for Earth-twins. Gliese 86 A turned out to be a very good candidate, assuming that the systems history has not been excessively violent. For HD 41004, we have identified admissible stable orbits for habitable planets, but those strongly depend on the parameters of the system. A more detailed investigation shows that for some initial conditions stable planetary motion is possible in the HZ of HD 41004 A. In spite of the massive companion HD 41004 Bb, we found that HD 41004 B, too, could host additional habitable worlds.

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arXiv2012

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 and 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 alpha Centauri 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.

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arXiv2012

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 binary's eccentricity, as well as a possible extension of Habitable Zones towards the secondary in close binary systems.

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arXiv2009

Dynamics of the TrES-2 system

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.

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