Global dynamics and stability limits for planetary systems around HD 12661, HD 38529, HD 37124 and HD 160691

In order to distinguish between regular and chaotic planetary orbits we apply a new technique called MEGNO in a wide neighbourhood of orbital parameters determined using standard two-body Keplerian fits for HD 12661, HD 38529, HD 37124 and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system.Comment: 12 pages, 3 figures, accepted ApJ, revised version following the referee's repor

Conditions of Dynamical Stability for the HD 160691 Planetary System

The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to its existence. In order to be dynamically stable, the HD 160691 planetary system has to satisfy the following conditions: (1) a 2:1 mean motion resonance, combined with (2) an apsidal secular resonance in (3) a configuration $P_{c}(ap) - S - P_{b}(ap)$ where the two apsidal lines are anti-aligned, and (4) specific conditions on the respective sizes of the eccentricities (high eccentricity for the outer orbit is in particular the most probable necessary condition). More generally, in this original orbital topology, where the resonance variables $\theta_{1}$ and $\theta_{3}$ librate about $180^{\circ}$ while $\theta_{2}$ librates about $0^{\circ}$, the HD 160691 system and its mechanism have revealed aspects of the 2:1 orbital resonances that have not been observed nor analyzed before. The present topology combined with the 2:1 resonance is indeed more wide-ranging than the particular case of the HD 160691 planetary system. It is a new theoretical possibility suitable for a stable regime despite relatively small semi-major axes with respect to the important masses in interactions.Comment: 21 pages, 8 figures, 1 table, accepted version to ApJ (31 Jul 2003

Evolution in Binary and Triple Stars, with an application to SS Lac

We present equations governing the way in which both the orbit and the intrinsic spins of stars in a close binary should evolve subject to a number of perturbing forces, including the effect of a third body in a possibly inclined wider orbit. We illustrate the solutions in some binary-star and triple-star situations: tidal friction in a wide but eccentric orbit of a radio pulsar about a B star, the Darwin and eccentricity instabilities in a more massive but shorter-period massive X-ray binary, and the interaction of tidal friction with Kozai cycles in a triple such as Algol (beta-Per), at an early stage in that star's life when all 3 components were ZAMS stars. We also attempt to model in some detail the interesting triple system SS Lac, which stopped eclipsing in about 1950. We find that our model of SS Lac is quite constrained by the relatively good observational data of this system, and leads to a specific inclination (29 deg) of the outer orbit relative to the inner orbit at epoch zero (1912). Although the intrinsic spins of the stars have little effect on the orbit, the converse is not true: the spin axes can vary their orientation relative to the close binary by up to 120 deg on a timescale of about a century.Comment: 30 pages, 6 figure

The Evolution of Cool Algols

We apply a model of dynamo-driven mass loss, magnetic braking and tidal friction to the evolution of stars with cool convective envelopes; in particular we apply it to binary stars where the combination of magnetic braking and tidal friction can cause angular-momentum loss from the {\it orbit}. For the present we consider the simplification that only one component of a binary is subject to these non-conservative effects, but we emphasise the need in some circumstances to permit such effects in {\it both} components. The model is applied to examples of (i) the Sun, (ii) BY Dra binaries, (iii) Am binaries, (iv) RS CVn binaries, (v) Algols, (vi) post-Algols. A number of problems regarding some of these systems appear to find a natural explanation in our model. There are indications from other systems that some coefficients in our model may vary by a factor of 2 or so from system to system; this may be a result of the chaotic nature of dynamo activity