3 The metallicity distributions

In Fig. 1 we present the [Fe/H] distributions of both samples described above. For the stars with planets we included both the objects presented in Tables 2 and 3. As is clear from the plot, stars with planets are significantly more metal rich than field stars without giant planet companions. While the stars-with-planets sample has a mean metallicity of +0.15 $\pm$ 0.23 the mean [Fe/H] for the field star sample is -0.10 $\pm$ 0.18 (here the errors represent the rms around the mean [Fe/H]). A Kolmogorov-Smirnov test (Fig. 1, right) shows that the probability that both samples belong to the same population is about $\sim$10^-7.

At this point it is important to discuss possible sources of bias. Is the star-with-planet sample completely unbiased? If we make the same plot using only the stars forming part of the CORALIE sample (from which the comparison stars were taken), the result is exactly the same (dotted histogram in Fig. 1): the same general shape and difference is found. In fact, this result cannot be related to a selection bias since, as discussed above, the most important planet search programmes make use of volume-limited samples of stars. The only exception is BD-10 3166 (Butler et al. 2000), chosen for its high metallicity. This star was not included in our analysis. It is worthy of note that the five planet-host stars that were included in our volume-limited sample (HD 1237, HD 13445, HD 17051, HD 22049 and HD 217107) have a mean [Fe/H] of +0.10.

No important systematics are expected concerning the magnitudes of the objects. On the one hand, for a given colour higher [Fe/H] stars are more luminous. Also, higher metallicity implies more and deeper lines, and thus a more precise determination of the velocity. But a star with more metals is also, for a given mass, cooler and fainter. For example, doubling the metallicity of the Sun (i.e. increasing [Fe/H] to $\sim$0.30) would make its temperature decrease by more than 150 K, and its luminosity by a factor of $\sim$1.2 (Schaller et al. 1992; Schaerer et al. 1993). As we shall see below, for the mass intervals for which we have a good representation of both samples, stars with planets are always significantly more metal-rich. Furthermore, at least in the CORALIE survey, exposure times are computed in order to have a photon-noise error at least as low as the instrumental errors.

Figure 3: Panel a): Metallicity distribution of stars with planets (dashed histogram) compared with the distribution of a volume limited sample of field dwarfs (empty histogram) - see text for more details; panel b): correcting the distribution of stars with planets from the same distribution for stars in the volume-limited sample results in a even more steep rise of the planet host star distribution as a function of [Fe/H]. Note that the last bin in the planet distribution has no counterpart in the field star distribution; panel c): same as a) but for a field distribution computed using a calibration of the CORALIE cross-correlation dip to obtain the metallicity for $\sim$1000 stars; panel d): same as b) when correcting from the field distribution presented in c).

Figure 4: Distribution for the field star sample (empty histogram) if we add 15 earth masses of iron (left) or a quantity of iron proportional to Z (right) - in the latter case, 0.003$\times$Z. The distributions peak at about the same value as the distribution of stars with planets (dashed histogram), but have completely distinct forms and extents in [Fe/H]. See the text for more details.

Given the uniformity of the study, we may conclude that the plot in Fig. 1 represents a proof that the stars now observed with giant planets are, on average, more metal-rich than field stars. For the record, it is also interesting to verify that the mean value of [Fe/H] obtained by Favata et al. (1997) for their volume-limited sample of G-dwarfs is -0.12, which means that there are almost no systematics between the method used by these authors and that used for the current study.

Also remarkable in Fig. 1 is the interesting position of the three low-mass ( $10~M_{\rm Jup}<M\,\sin{i}<20~M_{\rm Jup}$) brown-dwarf candidates. Although it is too early to arrive at any firm conclusions, the position of one of them (HD 202206), with [Fe/H] = +0.37 is strongly suggestive of a common origin with the lower-mass planets. On the opposite side of the distribution there is HD 114762 ([Fe/H] = -0.60), the most metal-poor object among all those studied in this paper. This "dispersion'' might be interpreted as a sign that the frontier between brown dwarfs and massive giant planets is very tenuous (and probably overlaps) with regard to the mass limit; we are possibly looking at results of different formation processes (e.g. Boss 2000).