2 The data

2.1 The samples

As mentioned above, the choice of a "comparison sample'' (as we shall call it from now on), free from giant planets and with the minimum bias possible, is of crucial importance. In order to be sure that we are not including any systematics when selecting the sample, we have taken all stars within the CORALIE sample (defined as volume-limited - Udry et al. 2000) having right ascensions between 20$^{\rm h}$ and 9$^{\rm h}$ (observable in mid November from La Silla). Since such a sample corresponds to more than half of the $\sim$1600 stars searched for planets, it is virtually impossible to make a precise spectroscopic analysis for all those stars in a reasonable amount time. We thus decided as a first step to limit our observations to all stars within 17 pc of the Sun having (B-V)<1.1 (determined from Hipparcos data - ESA 1997), and within 20 pc with (B-V)<0.9. This sample includes about 50 stars, most of which were observed. Some of the stars in this sample have known planetary systems, namely HD 1237, HD 13445, HD 17051, HD 22049 and HD 217107 (HD 192263, would also have been included if we had not imposed any limit on (B-V)). All these objects were excluded from our final sample (43 objects) presented in Table 1.

In what concerns the stars with planets, all known objects having precise spectroscopic iron abundance determinations using a similar technique were used. This excludes Gl 876 (Delfosse et al. 1998; Marcy et al. 1998), HD 195019 (Fischer et al. 1999) and the recently announced planets around HD 160691, HD 27442 and HD 179949 (Tinney et al. 2001; Butler et al. 2001). Also, from the set of 9 new planet host stars recently announced by the Geneva group (Mayor et al. 2001b) only two had available data (HD 28185 and HD 80606). The only exception was made respecting BD-10 3166, which was included in the planet surveys for its high [Fe/H] (Gonzalez et al. 1999). All the other stars were part of search programmes for planets in volume-limited samples (Udry et al. 2000; Marcy et al. 2000), and there is no particular reason to take out any of the targets (possible sources of bias are discussed below).

Figure 1: Left: distribution of stars with planets (shaded histogram) compared with the distribution of field dwarfs presented in this paper (empty histogram). The dashed histogram represents the planet host sample if we consider only stars forming part of the CORALIE survey (see text for details). The vertical lines represent stars with brown dwarf candidate companions having minimum masses between 10 and 20  $M_{\rm Jup}$. Right: The cumulative functions of both samples. A Kolmogorov-Smirnov test shows the probability of the stars' being part of the same sample is around 10-7.

2.2 Observations and data reduction

For the "comparison sample'', spectra of S/N between 150 and 350 were obtained using the CORALIE high-resolution spectrograph ( $R\equiv\Delta\lambda/\lambda\sim$ 50 000), at the Swiss 1.2-m Euler Swiss Telescope (La Silla, Chile) in 2000 mid November. The spectra were reduced using IRAF tools, and the equivalent widths were measured by fitting a Gaussian function to each of the lines using the "k'' key within splot.

Some planet host stars were also observed with CORALIE (adding a few objects to the study presented in Paper I), some of them with no previous spectroscopic abundance determinations (see Table 2). Observations of some stars with planets were also complemented with spectra of $S/N \sim 300$ taken with the FEROS spectrograph ($R\sim$ 48 000), at the ESO 1.52 m Telescope (La Silla), during the nights of 2000 November 8 and 9. The UES spectrograph ($R\sim$ 55 000) at the 4 m WHT (La Palma, Canary Islands) was also used to obtain a spectrum for the planet host star HD 190228.

2.3 Spectroscopic analysis

The technique used has already been described extensively in Paper I. Abundances and atmospheric parameters were determined using a standard local thermodynamic equilibrium (LTE) analysis with a revised version of the line abundance code MOOG (Sneden 1973), and a grid of Kurucz (1993) ATLAS9 atmospheres. As in Paper I, we used a set of iron lines taken from the list of Gonzalez & Laws (2000). Here, we added one more Fe II line (the 5991 Å presented in Gonzalez et al. 2001) and we excluded the previously used Fe II line at 6432 Å line, because it was giving systematically low values for most stars.

The atmospheric parameters were obtained from the Fe I and Fe II lines by iterating until the correlation coefficients between $\log{\epsilon}$(Fe I) and $\chi_l$, and between $\log{\epsilon}$(Fe I) and $\log{({W}_\lambda/\lambda)}$ were zero, and the mean abundance given by Fe I and Fe II lines were the same. This procedure gives very good results since the set of Fe I lines has a very wide range of excitation potentials. We used $\log{\epsilon_{\odot}}$(Fe) = 7.47.

The complete results obtained for the comparison sample are presented in Table 1. The errors in $T_{\rm eff}$, $\log{g}$, $\xi_t$ and [Fe/H] for a typical measure are of the order of 50 K, 0.15 dex, 0.10 dex, and 0.06 dex respectively. The number of lines used for each star, and the dispersions for Fe I and Fe II lines are also tabulated. The masses were determined from theoretical isochrones of Schaller et al. (1992), Schaerer et al. (1992) and Schaerer et al. (1993), using M_V computed from Hipparcos parallaxes and $T_{\rm eff}$ obtained from spectroscopy. Only for HD 222237 we do not present a mass, given the high error in its determination.

In Table 2 we present our results of the spectroscopic analysis for stars with low mass companions for which we have obtained spectra. Also included are the objects already presented in Paper I and Santos et al. (2001), since the values were revised; the differences are always perfectly within the uncertainties (usually lower than 0.02 dex for [Fe/H]). Errors in the parameters were computed as described in Paper I.

For a few stars in our sample we had both CORALIE and FEROS spectra. No important systematics are evident in the results from the two spectrographs (due to errors in flatfields or background subtraction), and we simply used a mean value of the results.

We compared our [Fe/H] determinations for the eight stars presented in this paper in common with the studies of Gonzalez et al. (1999), Gonzalez & Laws (2000), and Gonzalez et al. (2001) to look for any possible systematics. The stars and [Fe/H] obtained by these authors are HD 1237 (0.16), HD 16141 (0.15), HD 17051 (0.19), HD 38529 (0.37), HD 52265 (0.27), HD 75289 (0.28), HD 210277 (0.24) and HD 217107 (0.36). The comparison shows that the formal mean difference in [Fe/H] obtained by these authors and from the present work is virtually 0.00 dex; the rms of the differences is $\sim$0.01 dex. The atmospheric parameters for these stars are also usually the same within the errors. We thus conclude that we can include their determinations for stars with planets in our analysis (as expected since our studies were similar in all aspects to theirs) without introducing any systematics, thus increasing the number of available planetary host candidates used in the current study. The list of stars with planets whose determinations were made by other authors is presented in Table 3.

Figure 2: The shape of the distribution of metallicities for stars with planets increases with [Fe/H]. This represents also an increase with Z, the mass fraction of heavy elements.