Fig. 6.8 Top: minimal mass as a function of period for exoplanets. On the left the filled squares indicate the planets orbiting binary stars and the circles indicate planets orbiting single stars. The circle within parentheses indicates HD 162020, which is probably a brown dwarf. On the right, just planets of single stars are shown. In this diagram the symbols represent the mass of the planets: filled circles are the massive planets (> 2Mj), open circles intermediate masses (between 0.75 and 2 Mj) and the triangles, light planets (< 0.75 Mj). The components of the HD 168443 system are joined by a dotted line. Bottom: distribution of periods of planets for different masses: the grey, white and red histograms are those for light, intermediate, and massive planets, respectively. The masses delimiting the three populations differ on the left (0.75 and 4 Mj) and on the right (0.75 and 2 MJ) (After Udry et al., 2003)

If we ignore multiple star systems, where the mechanisms governing formation may be different, there is no planet with a mass greater than 2 Mj and a period less than 100 days (Fig. 6.8, top right). This is not an observational bias, because these planets are the easiest to detect.

It seems that the maximum mass increases with distance from the central star. There are no light planets (M.sin i < 0.75Mj) with periods above 100 days.

6.2.5 The End of the Migration and Tidal Effects

Several of the migration mechanisms that have been suggested go through a phase where the planet has a very eccentric orbit, with periapsis very close to the star. Dynamical models show that successive passes of a gaseous planet close to a star leads to the eventual re-circularization of the orbit at an equilibrium distance that is about twice the Roche limit. This agrees with observations (Fig. 6.9). The maximum loss of energy by the planet occurs when periapsis is close to the Roche limit1. If the planet passes closer to the star, it loses material and moves farther away from the star. It may even be ejected from the system. It is therefore possible that the migration of a planet ends more often in its ejection from the planetary system than by falling into the star. Tidal effects also affect the rotation of a planet (see Sect. 6.1.5).

Gaseous planets that pass close to their star may lose all their hydrogen by thermal or non-thermal effects. They may create a new atmosphere by evaporation from their icy core, and thus create new terrestrial-type planets. Two possible candidates are shown in Fig. 6.9.

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