High inclination orbits in the secular quadrupolar three-body problem

The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which correspond to the population of stable particles that Verrier & Evans (2008,2009) find in stable, high inclination circumbinary orbits around one of the components of the quadruple star HD 98800. We provide a simple analytical framework using a vectorial formalism for these situations. We also look at the evolution of these high inclination equilibria in the non restricted case.Comment: 11 pages, 6 figures. Accepted by MNRAS 2009 September 1

High Inclination Planets in Multistellar Systems

The Kozai mechanism often destabilises high inclination orbits. It couples changes in the eccentricity and inclination, and drives high inclination, circular orbits to low inclination, eccentric orbits. In a recent study of the dynamics of planetesimals in the quadruple star system HD98800 (Verrier & Evans 2008), there were significant numbers of stable particles in circumbinary polar orbits about the inner binary pair which are apparently able to evade the Kozai instability. Here, we isolate this feature and investigate the dynamics through numerical and analytical models. The results show that the Kozai mechanism of the outer star is disrupted by a nodal libration induced by the inner binary pair on a shorter timescale. By empirically modelling the period of the libration, a criteria for determining the high inclination stability limits in general triple systems is derived. The nodal libration feature is interesting and, although effecting inclination and node only, shows many parallels to the Kozai mechanism. This raises the possibility that high inclination planets and asteroids may be able to survive in multistellar systems.Comment: MNRAS, submitte

Symplectic integration of space debris motion considering several Earth's shadowing models

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones. Indeed, it has already been demonstrated that such objects could stay there for hundreds of years. Our model takes into account the Earth's gravitational potential, luni-solar and planetary gravitational perturbations and direct solar radiation pressure. Based on the analysis of the energy conservation and on a comparison with a high order non-symplectic integrator, we show that our algorithm allows us to use large time steps and keep accurate results. We also propose an innovative method to model Earth's shadow crossings by means of a smooth shadow function. In the particular framework of symplectic integration, such a function needs to be included analytically in the equations of motion in order to prevent numerical drifts of the energy. For the sake of completeness, both cylindrical shadows and penumbra transitions models are considered. We show that both models are not equivalent and that big discrepancies actually appear between associated orbits, especially for high area-to-mass ratios

Interesting dynamics at high mutual inclination in the framework of the Kozai problem with an eccentric perturber

We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric orbit of the outer perturber on the dynamics of a small highly inclined inner body. Our analytical study of the secular perturbations relies on the classical octupole hamiltonian expansion (third-order theory in the ratio of the semi-major axes), as third-order terms are needed to consider the secular variations of the outer perturber and potential secular resonances between the arguments of the pericenter and/or longitudes of the node of both bodies. Short-period averaging and node reduction (Laplace plane) reduce the problem to two degrees of freedom. The four-dimensional dynamics is analyzed through representative planes which identify the main equilibria of the problem. As in the circular problem (i.e. perturber on a circular orbit), the "Kozai-bifurcated" equilibria play a major role in the dynamics of an inner body on quasi-circular orbit: its eccentricity variations are very limited for mutual inclination between the orbital planes smaller than ~40^{\deg}, while they become large and chaotic for higher mutual inclination. Particular attention is also given to a region around 35^{\deg} of mutual inclination, detected numerically by Funk et al. (2011) and consisting of long-time stable and particularly low eccentric orbits of the small body. Using a 12th-order Hamiltonian expansion in eccentricities and inclinations, in particular its action-angle formulation obtained by Lie transforms in Libert & Henrard (2008), we show that this region presents an equality of two fundamental frequencies and can be regarded as a secular resonance. Our results also apply to binary star systems where a planet is revolving around one of the two stars.Comment: 12 pages, 9 figures, accepted for publication in MNRA

Cosmic ray short burst observed with the Global Muon Detector Network (GMDN) on June 22, 2015

We analyze the short cosmic ray intensity increase ("cosmic ray burst": CRB) on June 22, 2015 utilizing a global network of muon detectors and derive the global anisotropy of cosmic ray intensity and the density (i.e. the omnidirectional intensity) with 10-minute time resolution. We find that the CRB was caused by a local density maximum and an enhanced anisotropy of cosmic rays both of which appeared in association with Earth's crossing of the heliospheric current sheet (HCS). This enhanced anisotropy was normal to the HCS and consistent with a diamagnetic drift arising from the spatial gradient of cosmic ray density, which indicates that cosmic rays were drifting along the HCS from the north of Earth. We also find a significant anisotropy along the HCS, lasting a few hours after the HCS crossing, indicating that cosmic rays penetrated into the inner heliosphere along the HCS. Based on the latest geomagnetic field model, we quantitatively evaluate the reduction of the geomagnetic cut-off rigidity and the variation of the asymptotic viewing direction of cosmic rays due to a major geomagnetic storm which occurred during the CRB and conclude that the CRB is not caused by the geomagnetic storm, but by a rapid change in the cosmic ray anisotropy and density outside the magnetosphere.Comment: accepted for the publication in the Astrophysical Journa

Fuzzy Characterization of Near-Earth-Asteroids

Due to close encounters with the inner planets, Near-Earth-Asteroids (NEAs) can have very chaotic orbits. Because of this chaoticity, a statistical treatment of the dynamical properties of NEAs becomes difficult or even impossible. We propose a new way to classify NEAs by using methods from Fuzzy Logic. We demonstrate how a fuzzy characterization of NEAs can be obtained and how a subsequent analysis can deliver valid and quantitative results concerning the long-term dynamics of NEAs.Comment: 11 pages, presented at the 7th Alexander von Humboldt Colloquium on Celestial Mechanics (2008), accepted for publication in "Celestial Mechanics and Dynamical Astronomy

The CORALIE survey for southern extra-solar planets XV. Discovery of two eccentric planets orbiting HD4113 and HD156846

We report the detection of two very eccentric planets orbiting HD4113 and HD156846 with the CORALIE Echelle spectrograph mounted on the 1.2-m Euler Swiss telescope at La Silla. The first planet, HD4113b, has minimum mass of $m\sin{i}=1.6\pm0.2 M_{\rm Jup}$, a period of $P=526.59\pm0.21$ days and an eccentricity of $e=0.903\pm0.02$. It orbits a metal rich G5V star at $a=1.28$ AU which displays an additional radial velocity drift of 28 m s$^{-1}$/yr observed during 8 years. The combination of the radial-velocity data and the non-detection of any main sequence stellar companion in our high contrast images taken at the VLT with NACO/SDI, characterizes the companion as a probable brown dwarf or as a faint white dwarf. The second planet, \object{HD 156846 b}, has minimum mass of $m\sin{i}=10.45\pm0.05$ M$_{\rm Jup}$, a period of $P=359.51\pm0.09$ days, an eccentricity of $e=0.847\pm0.002$ and is located at $a=1.0$ AU from its parent star. HD156846 is a metal rich G0 dwarf and is also the primary of a wide binary system ($a>250$ AU, $P>4000$ years). Its stellar companion, \object{IDS 17147-1914 B}, is a M4 dwarf. The very high eccentricities of both planets can be explained by Kozai oscillations induced by the presence of a third object.Comment: 4 pages, 5 figures, A&A Letter accepte

Modeling of the Super-Eddington Phase for Classical Novae: Five IUE Novae

We present a light curve model for the super-Eddington luminosity phase of five classical novae observed with IUE. Optical and UV light curves are calculated based on the optically thick wind theory with a reduced effective opacity for a porous atmosphere. Fitting a model light curve with the UV 1455 \AA light curve, we determine the white dwarf mass and distance to be (1.3 M_sun, 4.4 kpc) for V693 CrA, (1.05 M_sun, 1.8 kpc) for V1974 Cyg, (0.95 M_sun, 4.1 kpc) for V1668 Cyg, (1.0 M_sun, 2.1 kpc) for V351 Pup, and (1.0 M_sun, 4.3 kpc) for OS And.Comment: 9 pages including 8 figures, to appear in the Astrophysical Journa