The metallicity of stars with planets

The discussion about the origin of the metal-rich stars in our Galaxy is nowadays intimately related to the study of stars with giant planets. Soon after the discovery of the first extra-Solar planets, it was noticed that planet-host stars are particularly metal-rich compared with "single" field dwarfs (Gonzalez 1998; Gonzalez et al. 2001; Santos et al. 2001, 2004a, 2005b; Fischer & Valenti 2005), i.e. on average they present a metal content greater than that found in stars not known to be orbited by any planetary-mass companion. This result, which has clearly been confirmed by a uniform spectroscopic analysis of large samples of stars with and without detected giant planets (Santos et al. 2001) is obtained by using various kinds of techniques to derive the stellar metallicity (e.g. Reid 2002). Furthermore, it is found both for Solar-neighborhood planet-hosts and for their most distant counterparts (Santos et al. 2006b), such as the ones found by the OGLE photometric transit campaign.

It was shown that the metallicity excess observed cannot be explained by any sampling or observational biases (Santos et al. 2003). Planet-host stars are indeed significantly more metal-rich than stars without known giant planets. The average metallicity difference between the two samples is ~0.25 dex.

Furthermore, and most importantly, the results show that the probability of finding a planet is proportional to the metallicity of the star: more metal-rich stars have a higher probability of harboring a planet than do objects of lower metallicity (e.g. Santos et al. 2001, 2003, 2004a; Reid 2002; Fischer & Valenti 2005) - see the lower right panel of Figure 2.1. About 3% of Solar-metallicity stars seem to harbor a planetary-mass companion, while more than 20% of stars with twice the Solar metallicity have been detected to have orbiting planets.

This result is probably telling us that the probability of forming a giant planet depends strongly on the metallicity of the cloud of gas and dust that gave rise to the star and planetary system. Although it is unwise to draw any strong conclusions on the basis of just one point, it is also worth noticing that our own Sun is in the "metal-poor" tail of the planet-host [Fe/H] distribution.

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Figure 2.1. Upper panels: [Fe/H] distributions for planet-host stars (hashed histogram) and for a volume-limited comparison sample of stars not known to harbor any planetary-mass companion (open bars). The average difference between the [Fe/H] of the two samples is ~0.25 dex. A Kolgomorov-Smirnov test showed that the probability that the two samples are parts of the same population is of the order of 10-8. Lower panel, left: [Fe/H] distributions for planet-host stars (hashed histogram) included in the CORALIE planet-search sample, compared with the same distribution for ~900 stars in the whole CORALIE program (solid-line open histogram). Lower panel, right: the percentage of planet-hosts found among the stars in the CORALIE sample as a function of stellar metallicity. From Santos et al. (2004a).

It is important to remember at this point that the metallicities for the two samples of stars plotted in Figure 2.1 were derived using exactly the same techniques, and are thus to the same scale.

2.1 The origin of the high metallicity

All the conclusions discussed above are true under the assumption that the metallicity excess observed is original to the cloud of gas and dust that gave rise to the star and its planetary system. In other words, we are supposing that the higher prevalence of planets around metal-rich stars is reflecting a higher probability of forming a planet around such a star before the disk dissipates.

However, one other interpretation has been discussed in the literature to explain the [Fe/H] excess observed for stars with planets. In fact, it has been suggested that the high metal content is the result of the accretion of planets and/or planetary material into the star (e.g. Gonzalez 1998). In such a case, the observed metallicity excess would itself be a by-product of planet formation.

There are multiple ways of deciding between the two scenarios above, and in particular to try to see whether "pollution" might indeed have played an important role in increasing the metal content of the planet-host stars relative to that of their non-planet-host counterparts. Probably the clearest argument is based on stellar internal structure. Material falling onto a star's surface would induce a different increase in [Fe/H] depending on the depth of its convective envelope, which is where mixing can occur. However, no correlation between the metallicity of the planethost stars and their convective-envelope mass has been found (e.g. Pinsonneault etal. 2001; Santos etal. 2003).

Some doubts have recently been advanced against the contention that this lack of correlation is a good reason to exclude the possibility that stellar pollution could have caused the observed [Fe/H] "excess" (Vauclair 2004). Furthermore, it has been shown that in a few cases stellar pollution may have played some role (Israelian etal. 2001, 2003; Laws & Gonzalez 2001), although not a strong enough role for it to be responsible for a large variation in [Fe/H]. However, the evidence for an "original" source is further supported by the huge quantities of "pollution" by hydrogen-poor (planetary) material needed to explain the metallicity excess observed for a few late-type very-metal-rich dwarfs known to harbor giant-planets, as well as for a few sub-giant-planet-host stars (Santos et al. 2003). Recent asteroseismological measurements were also not conclusive regarding this issue (Bazot et al. 2005). In other words, the bulk metallicity "excess" observed most probably has a "primordial" origin.

The study of kinematic properties of planet-host stars has also given some interesting information. In particular, recent results suggest that the planet-host stars have kinematics typical of metal-rich stars in the Solar neighborhood (Ecuvillon et al. 2007). This comes as no surprise if we accept that pollution did not play an important role in defining the metallicities for these stars. The results also indicate that planet-hosts may have originated in the inner regions of the Galaxy.

2.2 Implications for the models

These conclusions have many important implications for theories of planet formation. In this respect, two main proposals are now being debated in the literature.

On the one side, the traditional core-accretion scenario (e.g. Pollack et al. 1996; Alibert et al. 2004) tells us that giant planets are formed as the result of the runaway accretion of gas around a previously formed icy core with about 10-20 times the mass of the Earth. In contrast to this idea, some authors have proposed that giant planets may form by a disk-instability process (Boss 1997).

According to the instability model, the efficiency of planet formation should not be dependent on the metallicity of the star/disk (Boss 2002). This is opposite to what is expected from the traditional core-accretion scenario (Ida & Lin 2004), since the higher the grain content of the disk, the easier it should be for the "metal" cores that will later on accrete gas to form before the gas disk dissipates.

The results presented above, showing that the probability of finding a planet is a strong function of the stellar metallicity, thus favor the core-accretion model as the main mechanism responsible for the formation of giant planets, although they do not completely exclude the disk-instability model). Indeed, it has even been shown that according to the core-accretion model it is possible to predict the observed [Fe/H] distribution of planet-host stars (e.g. Ida & Lin 2004).

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