Properties of Observed Extrasolar Planets

So many planets have now been found that it is possible to consider the statistics of the mass and orbital parameter distributions, as has been done by Collier Cameron (2002), and Marcy et al. (2003). Radial velocity measurements can only provide information on the distribution of Mp sin i. However, it can be shown (Jorissen et al., 2001) that for a random distribution of planetary systems, the distribution of Mp sin i is very close to the distribution of Mp and thus statistical conclusions on the overall mass distribution can be inferred from the distribution of Mp sin i for known exoplanets, shown in Fig. 1.4.

Considering the selection effects of radial velocity measurements, a predominance of heavy planets might be expected. However, most of the planets discovered so far have Mp sin i < 10Mj, and the distribution of planets rises rapidly for smaller masses. A power law fit to the distribution is also plotted in Fig. 1.4, where the number of planets N has been assumed to vary with planetary mass as N = a(Mp sin i)3. Fitting only to the well sampled distribution where Mp sin i < 4Mj, values of a = 44.98 and ยก3 = โ€”0.95 are derived, which are found to reasonably well ap-

Minimum mass Msini (Mj)

Fig. 1.4. Distribution of Mp sin i of currently known exoplanets. Also plotted is the curve N = a(Mp sin , where a = 44.98 and 3 = โ€”0.95, which is described in the text

Minimum mass Msini (Mj)

Fig. 1.4. Distribution of Mp sin i of currently known exoplanets. Also plotted is the curve N = a(Mp sin , where a = 44.98 and 3 = โ€”0.95, which is described in the text proxinate the rest of the distribution. Hence, to first order it would appear that the number of planets falls approximately linearly with the planetary mass.

The smallest exoplanets discovered to date are OGLE-05-390L b and GJ 876 d (Rivera et al., 2005) which have estimated masses of only ~ 5.5MEarth and ~ 7.5MEarth, respectively. In contrast, there is an apparent absence of heavy extrasolar planets with mass above the deuterium-burning limit for brown dwarfs of ~ 13.6Mj (Lewis, 2004). This apparent absence of very large mass planets has become known as the 'Brown Dwarf Desert' and it has been suggested that brown dwarfs might be formed by a different process from planets, leading to them orbiting at much greater distances than is currently detectable with the radial velocity technique. However, very recently a few heavy mass exoplanets have been discovered, the heaviest being GQ Lup b and HD 41004 B b which have an estimated Mp sin i of 21.5Mj and 18.4MJ (Zucker et al., 2004) respectively. Hence, the 'Brown Dwarf Desert' may prove not to be quite so barren as has been previously thought, supporting the suggestion of Jorissen et al. (2001) that there is no reason to ascribe the transition between giant planets and brown dwarfs to the threshold mass of deuterium ignition.

The distribution of exoplanet orbital periods is shown in Fig. 1.5, which appears to have a slight bimodal distribution, with peaks at 3 days and 500 days.

The distribution of exoplanet orbit radii is shown in Fig. 1.6 and it is found that a large fraction of known exoplanets orbit within 1 AU. However, given that planets with larger orbital distances take longer to orbit and current observation programmes have only been running for 10 years or so and are becoming more

100 1000 Period(days)

10000

Fig. 1.5. Orbital period distribution of known exoplanets.

100 1000 Period(days)

10000

Fig. 1.5. Orbital period distribution of known exoplanets.

100.00

1.00

Orbital radius (AU)

10.00

Fig. 1.6. Orbital radius distribution of known exoplanets.

1.00

Orbital radius (AU)

10.00

100.00

Fig. 1.6. Orbital radius distribution of known exoplanets.

100.0000 10.0000 3 1.0000

g 0.1000

E 0.0100 0.0010 0.0001

Radius (AU)

Fig. 1.7. Distribution of mass and radius for known exoplanets. Solar System planets are indicated by letter.

precise all the time, there is good reason to suspect that there is a large population of planets orbiting beyond 3 AU (Marcy et al., 2003) which will soon be detected.

Fig. 1.7 shows Mp sin i for known exoplanets plotted against their orbital distance and there can be seen to be a general decrease in the number of massive planets (Mp > 4MJ) orbiting within 0.3 AU. Such planets would be eminently detectable using the radial velocity method so we can be confident that they are really not there. A possible explanation for this is that the migration mechanism of massive planets is either inefficient within 0.3 AU or too efficient and thus that massive planets straying within 1 AU fall all the way into the star (Marcy et al., 2003). Alternatively, as discussed in Sect. 1.2.3 it may be that planets closer than this quickly evaporate (Vidal-Madjar et al., 2003).

There is a massive and uniform spread in the eccentricities of exoplanets between 0 and 0.9 (Fig. 1.8), which suggests that there is a common mechanism for pumping the eccentricity of extrasolar planets. It can also be seen from Fig. 1.8 that the eccentricity distribution for planets in multiple-planet systems is indistinguishable from that for single planet systems. For the multiple planet systems known, eccentricity pumping may result from planets migrating in their circumstellar disc, leading to occasional mutual capture and resonance. Subsequent close encounters may lead to scattering and ejection of planets. This scenario explains the orbital resonances commonly seen in multiple-planet systems and also the occurrence of 'hierarchical' systems (ones with only a few, widely separated planets), where some of the planets have presumably been ejected. Single planet systems may be the end result of such interactions, where all other giant planets have been lost through ejec-

JUUN

0.01

0.10

1.00

10.00

Radius (AU)

Fig. 1.8. Distribution of eccentricity and radius for known exoplanets. In this plot Solar System planets are indicated by letter and planets in multi-planet systems are indicated by diamonds.

tion. Alternatively it could just be that single planet systems actually have other planets which have just not been detected yet.

An intriguing discovery is of a multiple planet system around the star HD 69830 which comprises three Neptune mass planets (Lovis et al., 2006) and possibly also an asteroid belt (Beichman et al., 2005).

It has been pointed out by Charbonneau (2006) that the precision achieved by Lovis et al. (2006) means that it is now more likely that terrestrial-type planets may be detected by the radial-velocity method, since the Sun is unusually hot and massive compared to other nearby stars. The 'habitable zone' of other stars is likely to be closer to the star and coupled with their lower mass the 'wobble' introduced by a terrestrial planet's mass may now be just about detectable.

The analysis of the metallicity of stars which have planetary companions is very revealing (Fig. 1.9). The [Fe/H] ratio is defined as the abundance of iron in a star to that found in the Sun, expressed on a logarithmic scale. Thus a star with [Fe/H]=1 has 10 times the abundance of iron (and other metals) as the Sun. From Fig. 1.9 it can be seen that, as found by Fischer and Valenti (2003) and Santos et al. (2004), the distribution rises rapidly at the high metallicity end and thus the great majority of known exoplanets orbit stars with a metallicity equal to, or greater than that of our Sun (Sudarsky et al., 2003). These observations strongly suggest that the presence of dust in proto-stellar nebulas is very important for the formation of planets and thus favours the core-accretion model of planetary formation (Pollack et al., 1996).

Fig. 1.9. Distribution of star metallicity for known exoplanetary systems.

Fig. 1.9. Distribution of star metallicity for known exoplanetary systems.

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