Info

** Ratio of the period of the planet with respect to the period of the planet closest to the star

** Ratio of the period of the planet with respect to the period of the planet closest to the star frequently (but not always) to increasing distance from the star, which may cause some confusion.

Planets in multiple systems have similar orbital characteristics to those of isolated planets close to their star, and with very eccentric orbits (Table 6.1). But apart from the planets themselves, the systems, taken overall, have orbital properties that reveal a turbulent past and major interactions between the planets. In particular, several systems exhibit mean-motion resonances, i.e., the periods of the planets are rational ratios (Fig. 6.4). The periods of planets in a 2:1 resonance have a ratio of 2. These resonances are believed to be the result of a single phenomenon: the migration of planets (see Sect. 6.2). The observations do not allow us to know if these planets are still in the process of evolution. But because theoretical models frequently associate migration with the stage at which planets form within a disk, and most of the systems observed do not have a disk, we may assume that the orbits of the planets have stabilized.

The migration process leads to very stable configurations where the periapses are aligned (or anti-aligned). This configuration, which is observed in several systems, whether resonant or not, may be explained only if the planets have migrated and have passed through configurations in which they were in resonance. A system may then remain frozen, or may continue to evolve, but the orbits will retain this property. The system of v Andromedae is the best example of planets whose orbits are aligned without being in resonance.

Fig. 6.4 Multiple systems. The diameter of the points is proportional to m.sin i of the planet. Systems in resonance are indicated at left by the type of resonance (After Marcy et al., 2005)

Our knowledge of multiple systems is still very incomplete, with some twenty known systems. The orbital parameters are still subject to large error bars. However, exploration of this field is full of promise: A full knowledge of the orbits in a multiple system, together with studies of the dynamics of the system is very rewarding in imposing constraints on the formation, or at least the evolution, of the planets.

6.1.5 Rotation of the Planets

An important dynamical characteristic of planets is their rotation. It is not possible, at present, to know the rotation periods of exoplanets. However, it is possible to predict them for planets whose orbits have evolved through tidal effects.

Tidal effects are a well-known phenomenon in the Solar System, in particular those between a planet and a satellite. Gravitational attraction, coupled with deformation of the two bodies, results in circularization of the orbit of the satellite and evolution towards a rate of rotation that is synchronized with the rate of revolution around the planet. In the Solar System, the Moon and all the regular satellites are in synchronous rotation about their respective planets. Over a longer timescale, the system evolves towards synchronizing the revolution period of the satellite with the rotation period of the planet. This tidal effect on the rotation of bodies is also known to occur between the two stars in a close binary system.

When an exoplanet approaches the star, the star's tidal effect will perturb its orbit. The most important consequence is circularization of the orbit. This is why the 'hot Jupiters', lying at distances of less than 0.05 AU, have circular orbits. It is often assumed that these planets have reached a state of equilibrium, co-rotating with their stars (Fig. 6.5). Models show, however, that the effects of atmospheric tides may lead to other limiting solutions, and even to retrograde rotation like that which may have occurred with Venus.

semi-major axis (AU)

Fig. 6.5 Dissipation through tidal effects. The curves represent the time (109 years) required to reach a state of equilibrium, as a function of the characteristics of the orbit: semi-major axis and eccentricity. The circles are exoplanets. This study has been made, assuming a dissipation coefficient and an initial rotation period similar to those of Jupiter. Exoplanets to the right of the curve for 10 (x 109) years may be considered not to have undergone tidal effects. The planets to the left of this curve, and particularly the planets at 0.05 AU, have reached a state of equilibrium determined by the star's tidal effects (After Laskar and Correia, 2008)

semi-major axis (AU)

Fig. 6.5 Dissipation through tidal effects. The curves represent the time (109 years) required to reach a state of equilibrium, as a function of the characteristics of the orbit: semi-major axis and eccentricity. The circles are exoplanets. This study has been made, assuming a dissipation coefficient and an initial rotation period similar to those of Jupiter. Exoplanets to the right of the curve for 10 (x 109) years may be considered not to have undergone tidal effects. The planets to the left of this curve, and particularly the planets at 0.05 AU, have reached a state of equilibrium determined by the star's tidal effects (After Laskar and Correia, 2008)

Was this article helpful?

0 0

Post a comment