6 Concluding remarks

We have presented for the first time a uniform and unbiased comparison between the metallicity distributions of a sample of stars with planets and a sample of stars "without'' planets. The main results can be summarized as follows:

• The currently known stars with planets are substantially metal-rich when compared with non-planetary host dwarfs. The mean difference in [Fe/H] is $\sim$0.25 dex and is clearly significant.

• The shape of the metallicity distribution of stars with planets has a very clear rise with [Fe/H], i.e. with Z, the mass fraction of heavy elements. This result, although still based upon "only'' 44 objects, may help put constraints on the models and conditions leading to giant-planet formation.

• The clear cut-off seen for the star-with-planet distribution at [Fe/H] $\ge$ +0.5 may be interpreted as a "limit'' for the metallicity of solar-type dwarf stars in the solar neighbourhood; it is very difficult to explain it in terms of a convective envelope "pollution'' scenario.

• The metallicity of stars with planets cannot be explained by a simple "pollution'' model. The differences in [Fe/H] between stars with planets and field stars does not seem to be explained by such mechanisms, but needs an original (cloud) metallicity "excess''. Otherwise huge quantities of iron-rich material would have to be engulfed, which is not easy to explain in face of the current observations. Our results do not rule out, however, planet accretion as an ongoing process in the early stages of planetary formation (during which the convective envelopes are more massive).

• An analysis of the planetary orbital parameters does not reveal any clear trends with [Fe/H]. This point might give further support to the "primordial'' origin of the high metallicity of stars with planets (e.g. Gonzalez 1998; Del Popolo et al. 2001). On the other hand, we cannot exclude the possibility that some trend may appear in the future, e.g. when some real solar system analogues are found.

The current result concerning the high metallicity of stars with planets may represent the simple fact that the higher the metallicity of the star, the higher will be the probability that planet formation will occur.

Recently, Israelian et al. (2001) have discovered that the planet host star HD 82943 has ⁶Li in its atmosphere. This discovery is interpreted as evidence of the infall of a planet into the star, most probably by planet disruption (Rasio & Ford 1996). As discussed by the authors, however, the high [Fe/H] value of this star is not necessarily related to the infall of a planet, as this would not be able to enhance the [Fe/H] value by more than a few hundredths of a dex. This is exactly what was found for the pair 16 Cyg A and B (Laws & Gonzalez 2001).

In fact, the present results do not exclude the possibility that pollution may play a role (eventually important in some cases, such as for the most massive dwarfs), but rather that it is not the key process leading to the observed high metallicity of the planet host stars. Recent work by Murray et al. (2001) supports the idea that pollution, on a small scale, is very common among the stars of the solar neighbourhood. If confirmed, however, this result does not change in any way the conclusions of this paper, since their models predict "pollution'' of the order of 0.4 Earth masses of iron, only noticeable in stars with M>1.5 $M_{\odot}$.

One remarkable point that becames evident from the current work is the fact that our Sun occupies a "modest'' position in the low [Fe/H] tail of the metallicity distribution of stars with planets. A look at the orbital parameters in Table 4, however, tells us that, to date, no "real'' Solar System analogs were found. This lead us to speculate about possible different formation histories for these systems. Note, however, that we cannot draw any conclusions until other Solar System analogs are found.

The future addition of more stars in both samples studied here, and the detailed analysis of other chemical elements (in particular the light elements Li, Be and B) are of particular interest for the future, both to consolidate current results, and to understand better the multitude of different planetary systems known today. The direct comparison of other elemental abundances (e.g. $\alpha$-elements, C, or O) between stars with planets and "single'' field dwarfs will, on the other hand, not be an easy task given the apparent lack of stars with high [Fe/H] having no giant planet companions. Meanwhile, we expect that theoretical models of disc evolution and (giant) planetary formation will be constructed to explain in a detailed way the physics beyond the current results.

Acknowledgements

We wish to thank the Swiss National Science Foundation (FNSRS) for the continuous support for this project. We would also like to thank Nami Mowlavi for help computing masses for the stars, and to Terry Mahoney for the useful english comments. Support from Fundação para a Ciência e Tecnologia, Portugal, to N.C.S. in the form of a scholarship is gratefully acknowledged.