Orbital Stability of Planets in Binary Systems: A New Look at Old Results

About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical research, including the derivation of mathematically stringent criteria for the orbital stability of planets in stellar binary systems, valid for the "coplanar circular restricted three-body problem". In the following, we use these criteria to explore the validity of results from previous theoretical studies.Comment: 3 pages, 1 figure; submitted to: Exoplanets: Detection, Formation and Dynamics, IAU Symposium 249, eds. Y.-S. Sun, S. Ferraz-Mello, and J.-L. Zhou (Cambridge: Cambridge University Press

Case Studies of Habitable Trojan Planets in the System of HD 23079

We investigate the possibility of habitable Trojan planets in the HD 23079 star-planet system. This system consists of a solar-type star and a Jupiter-type planet, which orbits the star near the outer edge of the stellar habitable zone in an orbit of low eccentricity. We find that in agreement with previous studies Earth-mass habitable Trojan planets are possible in this system, although the success of staying within the zone of habitability is significantly affected by the orbital parameters of the giant planet and by the initial condition of the theoretical Earth-mass planet. In one of our simulations, the Earth-mass planet is captured by the giant planet and thus becomes a habitable moon.Comment: 24 pages, 8 figures, 3 tables; International Journal of Astrobiology (in press

The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio of the binary components and the initial distance ratio of the planet relative to the stellar separation distance. Our theoretical results allow us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.Comment: 10 pages, 8 figures, 3 tables; accepted by Astronomy and Astrophysic

Forced oscillations of coronal loops driven by external EIT waves

Aims. We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modelling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature of the driver, and the type of interaction between the two systems. Methods. We consider the oscillations of a magnetic straight cylinder with fixed-ends under the influence of an external driver modelling the force due to the global EIT wave. Given the uncertainties related to the nature of EIT waves, we first approximate the driver by an oscillatory force in time and later by a shock with a finite width. Results. Results show that for a harmonic driver the dominant period in the generated oscillation belongs to the driver. Depending on the period of driver, compared to the natural periods of the loop, a mixture of standing modes harmonics can be initiated. In the case of a non-harmonic driver (modelling a shock wave), the generated oscillations in the loop are the natural periods only. The amplitude of oscillations is determined by the position of the driver along the tube. The full diagnosis of generated oscillations is achieved using simple numerical methods

Forced oscillations of coronal loops driven by external EIT waves

Aims. We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modelling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature of the driver, and the type of interaction between the two systems. Methods. We consider the oscillations of a magnetic straight cylinder with fixed-ends under the influence of an external driver modelling the force due to the global EIT wave. Given the uncertainties related to the nature of EIT waves, we first approximate the driver by an oscillatory force in time and later by a shock with a finite width. Results. Results show that for a harmonic driver the dominant period in the generated oscillation belongs to the driver. Depending on the period of driver, compared to the natural periods of the loop, a mixture of standing modes harmonics can be initiated. In the case of a non-harmonic driver (modelling a shock wave), the generated oscillations in the loop are the natural periods only. The amplitude of oscillations is determined by the position of the driver along the tube. The full diagnosis of generated oscillations is achieved using simple numerical methods

ROSAT Pointed Observations of Cool Magnetic White Dwarfs

Observational evidence for the existence of a chromosphere on the cool magnetic white dwarf GD 356 has been reported. In addition, there has been theoretical speculations that cool magnetic white dwarfs may be sources of coronal X-ray emission. This emission, if it exists, would be distinct from the two types of X-ray emission (deep photospheric and shocked wind) that have already been observed from hot white dwarfs. We have used the PSPC instrument on ROSAT to observe three of the most prominent DA white dwarf candidates for coronal X-ray emission: GD 356, KUV 2316+123, and GD 90. The data show no significant emission for these stars. The derived upper limits for the X-ray luminosities provide constraints for a revision of current theories of the generation of nonradiative energy in white dwarfs

The Stability of the Suggested Planet in the nu Octantis System: A Numerical and Statistical Study

We provide a detailed theoretical study aimed at the observational finding about the nu Octantis binary system that indicates the possible existence of a Jupiter-type planet in this system. If a prograde planetary orbit is assumed, it has earlier been argued that the planet, if existing, should be located outside the zone of orbital stability. However, a previous study by Eberle & Cuntz (2010) [ApJ 721, L168] concludes that the planet is most likely stable if assumed to be in a retrograde orbit with respect to the secondary system component. In the present work, we significantly augment this study by taking into account the observationally deduced uncertainty ranges of the orbital parameters for the stellar components and the suggested planet. Furthermore, our study employs additional mathematical methods, which include monitoring the Jacobi constant, the zero velocity function, and the maximum Lyapunov exponent. We again find that the suggested planet is indeed possible if assumed to be in a retrograde orbit, but it is virtually impossible if assumed in a prograde orbit. Its existence is found to be consistent with the deduced system parameters of the binary components and of the suggested planet, including the associated uncertainty bars given by observations.Comment: 11 pages, 10 figures, 3 tables; Monthly Notices of the Royal Astronomical Society (in press

On reflection of Alfven waves in the solar wind

We have revisited the problem of propagation of toroidal and linear Alfven waves formulated by Heinemann and Olbert (1980) to compare WKB and non-WKB waves and their effects on the solar wind. They considered two solar wind models and showed that reflection is important for Alfven waves with periods of the order of one day and longer, and that non-WKB Alfven waves are no more effective in accelerating the solar wind than WKB waves. There are several recently published papers which seem to indicate that Alfven waves with periods of the order of several minutes should be treated as non-WKB waves and that these non-WKB waves exert a stronger acceleration force than WKB waves. The purpose of this paper is to study the origin of these discrepancies by performing parametric studies of the behavior of the waves under a variety of different conditions. In addition, we want to investigate two problems that have not been addressed by Heinemann and Olbert, namely, calculate the efficiency of Alfven wave reflection by using the reflection coefficient and identify the region of strongest wave reflection in different wind models. To achieve these goals, we investigated the influence of temperature, electron density distribution, wind velocity and magnetic field strength on the waves. The obtained results clearly demonstrate that Alfven wave reflection is strongly model dependent and that the strongest reflection can be expected in models with the base temperatures higher than 10(exp 6) K and with the base densities lower than 7 x 10(exp 7) cm(exp -3). In these models as well as in the models with lower temperatures and higher densities, Alfven waves with periods as short as several minutes have negligible reflection so that they can be treated as WKB waves; however, for Alfven waves with periods of the order of one hour or longer reflection is significant, requiring a non-WKB treatment. We also show that non-WKB, linear Alfven waves are always less effective in accelerating the plasma than WKB Alfven waves. Finally, it is evident from our results that the region of strongest wave reflection is usually located at the base of the models, and hence that interpretation of wave reflection based solely on the reflection coefficient can be misleading