3 Confirming the excess metallicity

In Fig. 1 we plot the metallicity distribution for all the stars known to have companions with minimum masses lower than $\sim$18  $M_{{\rm Jup}}$ (hashed histogram) when compared to the same distribution for a volume limited sample of stars with no (known) planetary companions (open histogram) - see Paper II.

For the planet host stars, most of the metallicity values ([Fe/H]) were taken from Table 2 and from Table 2 of Paper II. HD 39091, a star that was included in the "single'' star comparison sample in Paper II, was recently discovered to harbor a brown dwarf companion (Jones et al. 2002). This star was thus taken out from this latter sample, and included in the planet sample. For 4 other stars for which we could not obtain spectra, values that were computed using the same technique (and are thus compatible with ours) are available. These are for BD -10 3166 (Gonzalez et al. 2001), HD 89744 (Gonzalez et al. 2001), HD 120136 (Gonzalez & Laws 2000), and HD 178911 B (Zucker et al. 2002b). The parameters (T $_{{\rm eff}}$, $\log{g}$, $\xi _t$, [Fe/H]) listed by these authors are (5320, 4.38, 0.85, 0.33), (6338, 4.17, 1.55, 0.30), (6420, 4.18, 1.25, 0.32), and (5650, 4.65, 0.85, 0.28), respectively.

We note that from the 89 stars known to harbor low mass (planetary or brown dwarf) companions, only 7 lack a metallicity determination.

It is important to remember that the metallicity for the two samples of stars plotted in Fig. 1 was derived using exactly the same method, and are thus both in the same scale (Paper II). This plot thus clearly confirms the already known trend that stars with planetary companions are more metal-rich (in average) that field dwarfs. The average metallicity difference between the two samples is about 0.24 dex, and the probability that the two distributions belong to the same sample is of the order of 10^-7.

In Fig. 1, stars having "planetary'' companions with masses higher than 10  $M_{{\rm Jup}}$are denoted by the vertical lines. Given the still low number, it is impossible to do any statistical study of this group. It is interesting though to mention that two of the stars having companions in this mass regime (HD 202206 and HD 38529) have very high metallicities ([Fe/H] = 0.39 and 0.37, respectively), while one other (HD 114762) has the lowest metallicity of all the objects in the sample ([Fe/H] = -0.72). This large dispersion might be seen as an evidence that (at least part of) the higher mass objects were formed by the same physical mechanisms as their lower mass counterparts; the 13  $M_{{\rm Jup}}$ deuterium burning limit has no role in this matter. Furthermore, this represents a good example to show that the metallicity by itself cannot be used as a planetary identification argument, contrarily to what has been used by Chen & Zhao (2001).

We have tried to see if there were any differences between those stars having multiple planetary systems and stars having one single planet. The analysis revealed no significant trend. This negative result is probably not only due to the low number of points used, but most of all to the fact that as can be seen in the literature (e.g. Fischer et al. 2001), many planet host stars do present long term trends, some of them that might be induced by other planetary companions.

Figure 2: Left: metallicity distribution of stars with planets making part of the CORALIE planet search sample (shaded histogram) compared with the same distribution for the about 1000 non binary stars in the CORALIE volume-limited sample (see text for more details). Right: the percentage of stars belonging to the CORALIE search sample that have been discovered to harbor planetary mass companions plotted as a function of the metallicity. The vertical axis represents the percentage of planet hosts with respect to the total CORALIE sample.

   
3.1 The probability of planet formation

More interesting conclusions can be taken by looking at the shape of the distribution of stars with planets. As it as been discussed in Paper II, this distribution is rising with [Fe/H], up to a value of $\sim$0.4, after which we see a sharp cutoff. This cutoff suggests that we may be looking at the approximate limit on the metallicity of the stars in the solar neighborhood.

Here we have repeated the analysis presented in Paper II, but using only the planet host stars included in the well defined CORALIE sample. This sub-sample has a total of 41 objects, $\sim$60% of them having planets discovered in the context of the CORALIE survey itself. Here we have included all stars known to have companions with minimum masses lower than $\sim$18  $M_{{\rm Jup}}$; changing this limit to e.g. 10  $M_{{\rm Jup}}$ does not change any of the results presented below.

The fact that planets seem to orbit the most metal-rich stars in the solar neighborhood has led some groups to build planet search samples based on the high metal content of their host stars. Examples of these are the stars BD-10 3166 (Butler et al. 2000), HD 4203 (Vogt et al. 2002), and HD 73526, HD 76700, HD 30177, and HD 2039 (Tinney et al. 2002). Although clearly increasing the planet detection rate, these kind of metallicity biased samples completely spoil any statistical study. Using only stars being surveyed for planets in the context of the CORALIE survey (none of these 6 stars is included), a survey that has never used the metallicity as a favoring quantity for looking for planets, has thus the advantage of minimizing this bias.

As we can see from Fig. 2 (left panel), the metallicity distribution for the planet host stars included in the CORALIE sample does show an increasing trend with [Fe/H]. In the figure, the empty histogram represents the [Fe/H] distribution for a large volume limited sample of stars included in the CORALIE survey (Udry et al. 2000). The metallicities for this latter sample were computed from a precise calibration of the CORALIE Cross-Correlation Function (see Santos et al. 2002a); since the calibrators used were the stars presented in Paper I, Paper II, and this paper, the final results are in the very same scale.

The knowledge of the metallicity distribution for stars in the solar neighborhood (and included in the CORALIE sample) permits us to determine the percentage of planet host stars per metallicity bin. The result is seen in Fig. 2 (right panel). As we can perfectly see, the probability of finding a planet host is a strong function of its metallicity. This result confirms former analysis done in Paper II and by Reid (2002). For example, here we can see that about 7% of the stars in the CORALIE sample having metallicity between 0.3 and 0.4 dex have been discovered to harbor a planet. On the other hand, less than 1% of the stars having solar metallicity seem to have a planet. This result is thus probably telling us that the probability of forming a giant planet, or at least a planet of the kind we are finding now, depends strongly on the metallicity of the gas that gave origin to the star and planetary system. This might be simple explained if we consider that the higher the metallicity (i.e. dust density of the disk) the higher might be the probability of forming a core (and an higher mass core) before the disk dissipates (Pollack et al. 1996; Kokubo & Ida 2002).

Although it is unwise to draw any strong conclusions based on only one point, it is worth noticing that our own Sun is in the "metal-poor'' tail of the planet host [Fe/H] distribution. Other stars having very long period systems (more similar to the Solar System case) do also present an iron abundance above solar. If we take all stars having companions with periods longer than 1000 days and eccentricities lower than 0.3 we obtain an average <[Fe/H]> of +0.21. A lower (but still high) value of +0.12 is achieved if we do not introduce any eccentricity limit into this sample. We caution, however, that these systems are not necessarily real Solar System analogs.

It is important to discuss the implications of this result on the planetary formation scenarios. Boss (2002) has shown that the formation of a giant planet as a result of disk instabilities is almost independent of the metallicity; this is contrary to what is expected from a process based in the core accretion scenario. The results presented here, suggesting that the probability of forming a planet (at least of the kind we are finding now) is strongly dependent on the metallicity of the host star, can thus be seen as an argument for the former (traditional) core accretion scenario (Pollack et al. 1996). We note that here we are talking about a probabilistic effect: the fact that the metallicity enhances the probability of forming a planet does not mean one cannot form a planet in a lower metallicity environment. This is mostly due to the fact that other important and unknown parameters, like the proto-planetary disk mass and lifetime, do control the efficiency of planetary formation as well. Furthermore, these results do not exclude that an overlap might exist between the two planetary formation scenarios.

Finally, the small increase seen in the distribution of Fig. 2 (right panel) for low metallicities is clearly not statistically significant, since only one planet host per bin exists in this region of the plot.

   
3.1.1 Measurement precision and [Fe/H]

As discussed in Papers I and II, the rise of the percentage of planets found as a function of the increasing metallicity cannot be the result of any observational bias.

In this sense, particular concern has been shown by the community regarding the fact that a higher metallicity will imply that the spectral lines are better defined. This could mean that the the final precision in radial-velocity could be better for the more "metallic'' objects. However, in the CORALIE survey we always set the exposure times in order to have a statistical precision better than the former 7 m s^-1 instrumental long-term error.

Figure 3: Plot of the mean-photon noise error for the CORALIE measurements of stars having magnitude V between 6 and 7, as a function of the metallicity. This latter quantity was computed using the calibration presented in Santos et al. (2002a). Only a very few planet host stars present radial-velocity variations with an amplitude smaller than 30 m s-1 (dotted line).

A look at Fig. 3, where we plot the mean photon noise error for stars with different [Fe/H] having V magnitudes between 6 and 7, shows us exactly that there is no clear trend in the data. The very slight tendency (metal-rich stars have, in average, measurements with only about 1-2 m s^-1 better precision than metal poor stars) is definitely not able to induce the strong tendency seen in the [Fe/H] distribution in Fig. 2, specially when we compare it with the usual velocity amplitude induced by the known planetary companions (a few tens of meters-per-second). This also seems to be the case concerning the Lick/Keck planet search programs (D. Fischer, private communication).

   
3.1.2 Primary mass bias

The currently used planet-search surveys are based (in most cases) on samples chosen as volume-limited. However, the criteria to "cut'' the sample was usually also based on stellar temperature (i.e. B-V colour).

For a given B-V (i.e. $T_{{\rm eff}}$), varying the metallicity implies also changing the derived stellar mass. This means that we will have missed in our samples stars with very high [Fe/H] and low mass (they have too high B-V), as well as "high'' mass objects with low [Fe/H] (too small B-V). For example, a 1.3 $M_{\odot}$ dwarf with [Fe/H] = -0.4 has a temperature of $\sim$7000 K (Schaller et al. 1992), clearly outside the B-V limits imposed by the CORALIE survey (Udry et al. 2000). On the other side of the mass regime, a 6 Gyr old, 0.6 $M_{\odot}$ star with solar metallicity has a temperature of only $\sim$4150 K (Charbonnel et al. 1999); a star of this temperature not only is close to the border of our samples, but it is intrinsically very faint, and thus much more difficult to follow at very high precision.

In other words, the current samples are not really uniform in stellar masses. That fact is well illustrated in Fig. 4: there is clearly a trend that results from the definition of the sample, implying that this latter is constituted (in average) of more metal-poor stars as we go toward a lower mass regime.

Figure 4: Metallicity vs. stellar mass for planet (open circles) and non-planet host stars (filled dots) included in the CORALIE survey. As we can see from the plot, there is a strong bias related with the cutoff in colour of the sample. The two dashed lines represent simply approximate sampling limits, while the box represents a mass region with no strong biases.

This strong bias makes it difficult to study the probability of planetary formation as a function of the stellar mass. It would be very interesting to understand e.g. if higher mass stars, that might have slightly higher disk masses, may eventually form planets more readily. Such studies might be very important to test the planetary formation scenarios.

We can be quite sure, however, that the frequency of planetary formation for a given stellar mass is still increasing with [Fe/H]. If we look at the plot, the region inside the box is quite clean from the biases discussed above. And as it can be easily seen, in this region planet hosts are still dominating the upper part of the plot. This is true even if for a given mass the higher metallicity stars are also fainter and thus more difficult to measure.

3.2 Primordial source as the best explanation

Two main different interpretations have been given to the [Fe/H] "excess'' observed for stars with planets. One suggests that the high metal content is the result of the accretion of planets and/or planetary material into the star (e.g. Gonzalez 1998). Another simply states that the planetary formation mechanism is dependent on the metallicity of the proto-planetary disk: according to the "traditional'' view, a gas giant planet is formed by runaway accretion of gas by a $\sim$10 earth-mass planetesimal. The higher the metallicity (and thus the number of dust particles) the faster a planetesimal can grow, and the higher the probability of forming a giant planet before the gas in the disk dissipates.

A third possibility is that the metallicity is in fact favoring the formation of the currently found (in general short period when compared to the Solar System giant planets) exoplanets (Gonzalez 1998). This could fit e.g. into the idea of planetary migration induced by the interaction of the giant planet with a swarm of planetesimals: the higher the metallicity, the higher the number of those minor bodies, and thus the more effective the migration could be. However, the migration mechanisms are not very well understood, and probably more than with the number of planetesimals or the metallicity, the migration rate seems to be related with the disk lifetimes, and to the (gas) disk and planetary masses (Trilling et al. Trilling et al.(2002)). These variables are, however, very poorly known (do they depend e.g. on stellar mass or on the metallicity itself?).

There are multiple ways of deciding between the two former scenarios (see discussion in Paper II), and in particular to try to see if pollution might indeed have played an important role in increasing the metal content of the planet host stars relative to their non-planet host counterparts. Probably the most clear and strong argument is based on stellar internal structure, and in particular on the fact that material falling into a star's surface would induce a different increase in [Fe/H] depending on the depth of its convective envelope (where mixing can occur). This approach, already used by several authors (Laughlin 2000; Santos et al. 2000; Gonzalez et al. 2001; Pinsonneault et al. 2001; Santos et al. 2001a,b; Murray & Chaboyer 2002; Reid 2002), has led to somewhat opposite conclusions.

In Fig. 5 we plot the metallicity for the planet host stars having surface gravity higher than 4.1 dex (to avoid sub-giant stars) against their convective envelope mass (open symbols) as well as for the stars in the comparison sample of Paper II (points). The dashed line represents the mean metallicity for this latter group. The curved line represents the results of adding 8 earth masses of pure iron in the convective envelopes of stars having an initial metallicity similar to the average metallicity of the field star sample.

A look at the points reveals no trend comparable to the one expected if the metallicity excess were mainly a result of the infall of planetary material. In particular, a quick look indicates that the upper envelope of the points is extremely constant. Furthermore, there are no stars with [Fe/H] $\ge$ +0.5; this should not be the case if pollution were the main cause of the excess metallicity. As shown by Pinsonneault et al. (2001), a similar result is achieved if we replace $M_{{\rm conv}}$ by $T_{{\rm eff}}$, since this latter quantity is well correlated with the convective envelope mass. These authors have further shown that even non-standard models of convection and diffusion cannot explain the lack of a trend and thus sustain "pollution'' as the source of the high-[Fe/H].

The analysis of Fig. 5 strongly suggests that the high metal content of stars with planets is of "primordial'' origin. This is further supported by the fact that the 7 planet host stars which have $\log{g}$ values lower than 4.1 dex (probably already evolved stars, that have deepened their convective envelopes, diluting every metallicity excess that could be present at the beginning) have a mean metallicity of 0.17 dex, even higher than the 0.13 dex mean value found for all the planet hosts. This result, together with Fig. 2, implies that the metallicity is a key parameter controlling planet formation and evolution, and may have enormous implications on theoretical models (as discussed in Sect. 3.1).

Figure 5: Metallicity vs. convective envelope mass for stars with planets (open symbols) and field dwarfs (points). The [Fe/H] = constant line represents the mean [Fe/H] for the non-planet hosts stars of Fig. 1. The curved line represents the result of adding 8 earth masses of iron to the convective envelope of stars having an initial metallicity equal to the non-planet hosts mean [Fe/H]. The resulting trend has no relation with the distribution of the stars with planets.

An explanation to the absence of "important'' pollution traces can indeed come from arguments based on the timescales of planetary formation. Although still a matter of debate, near-infrared observations suggest that circumstellar (proto-planetary) disks have lifetimes shorter than 10 Myr (e.g. Haisch et al. 2001, and references therein). Considering that the disappearance of a near-IR disk (i.e. a dust disk) also means that the gas has disappeared (a reasonable assumption), then all the processes connected to the formation of a giant planet must happen before 10 Myr. Taking the example of the Sun, after 10 Myr its convective envelope has $\sim$0.3 $M_{\odot}$ of material. In an extreme case where all the solid material from the disk falls into the star (i.e. about 1  $M_{{\rm Jup}}$ considering a very massive disk with 0.1 $M_{\odot}$ of gas and dust - Beckwith et al. 1990) but none H and He is accreted, the solar iron abundance would increase by only $\sim$0.1 dex. Even in this case, the pollution would induce a [Fe/H] variation that is still $\sim$0.15 dex lower than the average difference between planet hosts and non-planet hosts. We can thus state that after all pollution is probably not expected to make an important contribution to the total metallicity excess. This is even stressed by the fact that higher mass stars evolve faster, and attain a shallow convective envelope before their lower mass counterparts. This would even strengthen the expected slope in Fig. 5: nothing is seen.

It should be noted however, that we are not excluding that, in some isolated cases, pollution might have been able to alter more or less significantly the global metallicity of the stars. There are some examples supporting that some planet host stars might have suffered a limited amount of "pollution'' (e.g. Gonzalez 1998; Smith et al. 2001; Israelian et al. 2001; Laws & Gonzalez 2001; Israelian et al. 2002), although not necessarily able to change considerably the overall metal content (see e.g. Israelian et al. 2001; Pinsonneault et al. 2001; Santos et al. 2002b; Sandquist et al. 2002).

It is also important to mention that here we are interested in discussing the origin of the high metallicity of planet host stars, something that has strong implications into the theories of planetary formation and evolution. The current results do not pretend to discuss the general question of "pollution'' in the solar neighborhood, a subject that has seen some results recently published (e.g. Murray et al. 2001; Gratton et al. 2001; Quillen 2002; Gaidos & Gonzalez 2002). In particular, the discovery of possible non-planet host main-sequence binaries with different chemical compositions (Gratton et al. 2001) does not permit to say much regarding the planetary "pollution'' problem.