Info

log10{D}

Fig. 6.13 The dynamics of the HD 202206 system for variations of the semi-major axis and of the longitude of periapsis of the outer planet. The greyscale represents the stability index: the darkest zone is the most stable. The lines correspond to the residuals of the correlation between the system and observations (After Correia et al., 2005)

The model also shows that modifications in the orbits of the planets will be detectable in future. Measurements of them will give the inclination of the system and thus the true masses of the planets.

This system poses the question of the formation of such objects. If the outer planet formed within the circumstellar disk, it is similar to the inner planet, which is not, therefore, a brown dwarf (formed like a star), but a 'super-planet' (formed from a solid core). On the other hand, if the inner object is a brown dwarf, it formed like a star and the planet formed within a circumbinary disk. Such circumbinary disks have been observed, as, for example, around the binary system GG Tau A and B.

6.3.6 The HD 69830 System: Three Neptunes and a Ring of Dust

The HD 69830 system consists of three low-mass planets, between 5 and 20 times the mass of the Earth. The semi-major axes of the orbits are 0.08, 0.2, and 0.6 AU. The spectrum of HD 69830 shows an infrared emission excess, which indicates the presence of a disk of dust that is less than one micrometre in size. This thin disk lies less than 1 AU from the star. The observations exclude the presence of a planet with a mass greater than that of Saturn less than 4 AU from the star. Dynamical models of the system assume that the orbits are coplanar, and use two hypothetical values for the inclination of the system relative to the plane of the sky (and thus about the masses). These two values lead to stable systems.

Modelling of the system also allows us to say that the stability zones for the disk of dust lie either between 0.3 and 0.5 AU or beyond 0.8 AU (Fig. 6.14).

Comparison between the characteristics of the planets and formation models indicates that the inner planets should be rocky, while the outer planet probably has a gaseous envelope surrounding a rocky and icy core. It may also be noted that the outer planet lies within the habitable zone, that is, water at the surface of any solid body, a satellite of this planet, for example, is in the liquid state.

6.4 Planetary Systems Around Pulsars

In 1992, Wolszczan and Frail detected modulations in the arrival time of pulses from the millisecond pulsar PSR 1257+12, at a distance of 300 parsecs from the Sun. From this they deduced the presence of two planets orbiting the pulsar. Two years later, a third planet was announced, on an inner orbit. The planets remain the least massive exoplanets so far discovered, with one of them having a mass similar to that of the Moon (Table 6.3).

From the point of view of exobiology, planets around a pulsar are of little interest, because the electromagnetic environment leaves little chance of the possible development of any form of life on those planets. However, the dynamics of these systems, particularly that of the multiple system around PSR 1257+12 is extremely

192 a

192 a

Fig. 6.14 (a): Examination of the stability of the three planets in the HD 69830 system. The points are the positions of the planets every 50 000 years. The system remains stable over a period of 109 years. (b): The stability zone for mass-less particles. The mid-grey zones correspond to unstable orbits; the light-grey and very dark zones correspond to stable orbits where the ring of dust, detected in the infrared, may be located (After Lovis et al., 2006)

Fig. 6.14 (a): Examination of the stability of the three planets in the HD 69830 system. The points are the positions of the planets every 50 000 years. The system remains stable over a period of 109 years. (b): The stability zone for mass-less particles. The mid-grey zones correspond to unstable orbits; the light-grey and very dark zones correspond to stable orbits where the ring of dust, detected in the infrared, may be located (After Lovis et al., 2006)

interesting (Fig. 6.15). It is one of the rare systems where the planets interact grav-itationally and where the orbital eccentricities are low, as in the Solar System. The ratio of the periods of planets d and c is close to 3/2. This proximity to a mean-motion resonance produces perturbations that are observable from Earth.

Table 6.3 Characteristic of planets around pulsars

Planet

M. sin i (MJUP)

Period (days)

Semi-major

Ecc.

Incl. (deg)

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