6 Concluding remarks

In this article we present a detailed spectroscopic analysis of more than 50 extra-solar planet host stars (to be added to the previously derived results), with the main goal of looking for correlations between the stellar metallicity and the planetary orbital properties. We have further tried to verify if planet host stars have any anomaly concerning the space velocities. The main conclusions of the article can be summarized in the following way:

• We confirm previous results that have shown that planet host stars are metal-rich when compared to the average local field dwarfs. The addition of the new data, and the comparison of the planet host star metallicity with the one for a large volume limited sample of field dwarfs, even strengthens the statistical significance of the result. Furthermore, it is shown that this result is still true if we compare planet and non-planet host stars within a given stellar mass regime.
• Stars with companions in the mass regime 20  $M_{{\rm Jup}}$ > M > 10  $M_{{\rm Jup}}$ present a wide variety of metallicities, and are up to now indistinguishable from the stars having lower mass companions. This result might be telling us that these "higher'' mass companions were formed in the same way as their lower mass counterparts. The same situation is found for systems with more than one planet, and for planets in stellar binaries.
• We also confirm previous results suggesting that the probability of finding a planet increases with the metallicity of the star. At least 7% of the stars in the CORALIE planet-search sample having [Fe/H] between 0.3 and 0.4 dex have a planetary companion. This frequency falls to a value of less then 1% for stars with solar metallicity. We have also shown that this result cannot be related to any observational bias.
• Our results also strongly support the "primordial'' source as the key parameter controlling the high metal content of the planet host stars. "Pollution'' does not seem to be an "important'' mechanism.
• We have explored the relation between the metallicity of the host stars and the orbital parameters of the planets. We have found some indications (not statistically significant) that metal-poor stars might be mainly able to form low mass planets, a result previously discussed by Udry et al. (2002a). In an even less significant sense, the low [Fe/H] stars seem to be orbited (in average) by planets having intermediate eccentricities. As for the orbital period, very short period planets also seem to orbit preferentially metal-rich stars, but the difference with respect to their longer period counterparts is clearly not significant. In any case, the results seem to be telling us that the metallicity is not playing a very important role in determining the final orbital characteristics of the discovered exoplanets. The metal content of the disk does not seem to be a crucial parameter controlling the migration processes. But it will be very interesting to follow the results as more low mass and long period planets, more similar to the Solar System giants, become common in the planet discovery lists.
• No significant differences are found when comparing planet hosts and non-planet hosts in plots relating U, V, W and [Fe/H]. In general, planet host stars seem to occupy the metal-rich envelope of the plots.

The results presented above seem to support a scenario where the formation of giant planets, or at least of the type we are finding now, is particularly dependent on the [Fe/H] of the primordial cloud. In other words, and as already discussed in Paper II, the metallicity seems to play a crucial role in the formation of giant planets, as it is indicated by the shape of the metallicity distribution.

Our results further support the core accretion scenario (e.g. Pollack et al. 1996) against the disk instability model (Boss 2000) as the "main'' mechanism of giant-planetary formation. In fact, Boss (2002) has shown that contrarily to the core-accretion models, the efficiency of planetary formation in the case of the disk instability should not strongly depend on the metallicity of the disk. In other words, if that were the case, we should probably not see an increase in the frequency of planets as a function of the metallicity: such a trend is clearly seen in our data. We note, however, that the current data does not discard that both situations can occur.

In the future, it is important to try to explore and compare the abundances of other metals (besides light elements) in planet and non-planet host stars. In this context, there are already a few results published (Santos et al. 2000; Smith et al. 2001; Gonzalez et al. 2001; Takeda et al. 2001; Sadakane et al. 2002), but up to now there have been no published uniform studies, a matter that clearly makes a comparison difficult. We are currently working on this problem, in order to offer a uniform comparison between planet and non-planet hosts for other elements in a similar way as was done here for [Fe/H].

As seen in the current work, the increase in the number of known exoplanets is permitting the development of different sorts of statistical studies. However, in face of the number of variables that might be interrelated (e.g. metallicity, and the various orbital parameters) it is still difficult to take any statistically significant conclusions. A clear improvement of the current situation can only be achieved if the kind of studies presented here are continued as new planets are found.

Acknowledgements

We would like to thank Nami Mowlavi for the important help in determining the stellar masses, and C. Perrier for obtaining ELODIE spectra for two of the stars. We wish to thank the Swiss National Science Foundation (Swiss NSF) for the continuous support to this project. Support from Fundação para a Ciência e Tecnologia (Portugal) to N.C.S. in the form of a scholarship is gratefully acknowledged.