Fig. 6.15 Plot of stability close to planet c in the PSR 1257+12 system. The dark areas correspond to unstable orbits. The resonances with the other planets in the system are indicated at the top of the diagram (After Beauge et al., 2005)

The existence of planetary systems around pulsars is an enigma: How could the planets have survived the supernova phase that gave birth to the pulsar? Their composition must be very different from that of a planet of a Main-Sequence star.

According to one hypothesis, these objects did not form in the circumstellar disk of the pulsar's parent star. It is possible that these planets may have formed after the supernova phase, in a disk of 'circumpulsar' material. Few studies have been made of this process, but searches have been made to detect the sites at which such planets might form, using infrared observations of millisecond pulsars.

It should be noted that the low number of pulsar planetary systems detected is because of the low number of millisecond pulsars known to date (about one hundred).

6.5 The Dynamics of Debris Disks

The formation of stars is accompanied by the formation of circumstellar disks, known as 'primary' disks. These disks have the same composition as the local interstellar medium. The mass of these primary disks decreases with the age of the star as a result of the clumping of dust in the disk into larger bodies and through the disk being swept the very violent stellar wind from the protostar (see Chap. 6).

A significant number of Main-Sequence stars are still surrounded by disks of dust. These disks, more evolved, as known as debris disks (see Sect. 6.3). They are detected from the infrared excess in the star's spectrum. Analysis of the infrared spectrum provides information on the radial structure of the disk and on the size of the particles. The characteristics of these disks are different from those of primary disks; in particular, they do not contain any gas, or very little, and have a low optical depth.

The properties of these disks of dust give cause to suspect that they are hosts to more massive bodies, which might be planets or planetesimals. Because dust grains are rapidly ejected by radiation pressure, there must be a source that re-supplies the population. Two processes may generate the dust: collisions between planetesimals or degassing like that found in comets. The dust detected in debris disks is therefore the visible portion of disks that also contain more massive bodies. Other indications prove the existence of cometary bodies in some of these disks, and in particular in the disk of P Pictoris. The spectrum of this star shows variable absorption lines cause by the passage of cometary tails in front of the disk of the star. Models indicate that to explain these observations, these comets must be perturbed by one (or several) planets.

Another characteristic, common to several disks, may also be the signature of the presence of one or more planets. This is a gap, several astronomical units wide, near the star, which could have been cleared by planetary perturbations. Only a few of the disks detected in the infrared have been imaged (Fig. 6.16), but all these disks clearly show complex structures, rings, spirals, arcs (HD 141569), concentrations of material (P Pictoris, e Eridani, Vega, Fomalhaut), asymmetries in azimuth (HD 141569, HR 4796), braiding, or vertical asymmetries (Table 6.4). Debris disks, particularly those of P Pictoris and HR 4796 have also been discussed in Sect. 6.3.

These structures may be compared with those observed in planetary rings, in particular with Saturn's rings: The presence of sharp boundaries or narrow rings is associated with resonances with the satellites. The satellites also generate vertical undulations, or gravity waves. The stability of arcs is also explained by specific configurations of satellites in inclined or eccentric orbits (or both). Small satellites close to the rings may be involved, or more distant and massive satellites, which create perturbations in regions where the ring particles are in resonance with them.

Fig. 6.16 Resolved disks of Main-Sequence stars
Table 6.4 Characteristics of resolved disks: age, distance, star's spectral type, distance at which the disk has a density peak, typical width of the ring, inclination of the disk, and resolution of the observations [After Augereau, 2004]

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