4 Correlations with planetary orbital parameters and minimum masses

Some hints of trends between the metallicity of the host stars and the orbital parameters of the planet have been discussed already in the literature. The usually low number of points involved in the statistics did not permit, however, to extract any major conclusions (see Paper II). Today, we dispose of about 80 high-precision and uniform metallicity determinations for planet host stars, a sample that enables us to look for possible trends in [Fe/H] with planetary mass, semi-major axis or period, and eccentricity with a higher degree of confidence. Let us then see what is the current situation.

   
4.1 Planetary mass

In Fig. 6 (upper left panel) we plot the minimum mass for the "planetary'' companions as a function of the metallicity. A simple look at the plot gives us the impression that there is a lack of high mass companions to metal-poor stars. This fact, although not clearly significant, does deserve some discussion.

Figure 6: Upper panels: metallicity against minimum mass for the planetary companions known to date whose host stars have precise spectroscopic [Fe/H] determinations. The right plot is just a zoom of the upper plot in the region of $M_2~\sin{i}$ < 10  $M_{{\rm Jup}}$ (see text). Different symbols go for the planets with minimum mass above (circles) or below (squares) 0.75  $M_{{\rm Jup}}$. The filled dots represent planets in stellar systems (Eggenberger et al. 2002). Lower left: [Fe/H] distributions for stars with planets less and more massive than 0.75  $M_{{\rm Jup}}$ (the hashed and open bars, respectively). Lower right: cumulative functions of both distributions. A Kolmogorov-Smirnov test gives a probability of $\sim$0.98 that both samples belong to the same distribution.

If we concentrate in the region of $M_2~\sin{i}$ < 10  $M_{{\rm Jup}}$ (Fig. 6, upper right panel), the trend mentioned above still remains. As discussed in Udry et al. (2002a), this result can be seen as an evidence that to form a massive planet (at least up to a mass of $\sim$10  $M_{{\rm Jup}}$) we need more metal-rich disks. For example, the upper plots of Fig. 6 show that except for HD 114762 (a potential brown-dwarf host), all planets with masses above $\sim$4  $M_{{\rm Jup}}$ orbit stars having metallicities similar or above to solar. This tendency could have to do with the time needed to build the planet seeds before the disk dissipates (if you form more rapidly the cores, you have more time to accrete gas around), or with the mass of the "cores'' that will later on accrete gas to form a giant planet.

Figure 7: Upper panels: metallicity against orbital period for the planetary companions known to date and whose host stars have precise spectroscopic [Fe/H] determinations in linear (left) and log scales (right). Different symbols are used for planets in orbits having periods longer and smaller than 10 days. The filled dots represent planets in stellar systems (Eggenberger et al. 2002). Lower left: [Fe/H] distributions for stars with planets with orbital periods shorter and longer than 10 days (the hashed and open bars, respectively). Lower right: cumulative functions of both distributions. A Kolmogorov-Smirnov test gives a probability of $\sim$0.75 that both samples belong to the same distribution.

In the two upper panels, the filled symbols represent planets in multiple stellar systems (Eggenberger et al. 2002). We do not see any special trend for these particular cases.

In the lower panels of Fig. 6 we show the [Fe/H] distribution for the stars with low mass companions for two different companion mass regimes. The chosen limit of 0.75  $M_{{\rm Jup}}$ as a border takes into account the striking result found by Udry et al. (2002b), in the sense that planets with masses lower than about this value have all periods shorter than $\sim$100 days (these authors see this limit as a strong constraint for the planet migration scenarios). The Kolmogorov-Smirnov test shows that there is no statistically significant difference between these two distributions. Changing the limit from 0.75  $M_{{\rm Jup}}$ to some other value does not change the significance of the result (nor the shape of the distributions).

   
4.2 Period

Gonzalez (1998) and Queloz et al. (2000) have presented some evidences that stars with short-period planets (i.e. small semi-major axes) may be particularly metal-rich, even amongst the planetary hosts. This fact could be interpreted by considering that the migration process is able to pollute the stellar convective envelope (Murray et al. 1998), that the formation of close-in planets is favored by the metallicity, or that the subsequent inward orbital evolution of a newborn planet may be favored by the higher metallicity of the disk (e.g. by the presence of more planetesimals/planets with which the planet can interact). The number of planets that were known by that time was, however, not sufficient for us to take any definitive conclusion. In fact, in Paper II we have not found that this trend was very significant, although there was still a slight correlation.

In Fig. 7 (upper panels) we plot the metallicity against the orbital period for the planets whose stars have precise spectroscopic metallicity determinations. In the plot, the squares represent planet hosts having companions in orbits shorter than 10 days ("hot jupiters''), while circles represent planets with longer orbital period. As we can see from the plots, there seems to be a small tendency for short period planets to orbit more metal-rich stars (see also the two lower panels). Or, from another point of view, the distribution for longer period systems seems to have a low metallicity tail, not present for the shorter period case (see the lower left panels). This tendency is clearly not significant, however (the Kolmogorov-Smirnov probability that both samples belong to the same population is of 0.75).

Changing the limits does not bring further clues on any statistically significant trend. In particular, setting the border at around 100 days, a value that seems to have some physical sense (companions to stars having periods shorter than this limit have statistically lower masses - Udry et al. 2002b) does not change the conclusions. We have further tried to investigate if the shape of the metallicity distributions changes if we consider planet hosts having companions with a different range of orbital period. A very slight trend seems to appear if we separate stars having companions with periods longer and shorter than 1 year, in the sense that the former's [Fe/H] distribution seems to be a bit more flat. But at this moment this is far from being significant.

We note, however, that the two lowest metallicity stars in the samples are both in the <100 day period regime. These two points give us the impression (in the upper-left plot) that there do not seem to exist any long period systems around low metallicity stars. This impression disappears, however, if we plot the period in a logarithmic scale (upper-right panel). No further conclusions can be taken at this moment.

As before, in the two upper panels, the filled symbols represent planets in stellar systems (Eggenberger et al. 2002). We do not see any special trend for these particular cases.

The lack of a clear relation between orbital period and stellar metallicity might imply that the migration mechanisms are reasonably independent of the quantity of metals in the disk. This result might thus fit better into the scenarios based on the migration of the planet through a gas disk (e.g. Goldreich & Tremaine 1980; Lin et al. 1996) when compared to the scenarios of migration due to interaction with a disk of planetesimals (Murray et al. 1998).

On the other hand, lower mass planets are supposed to migrate faster than their more massive counterparts, since these latter open more easily a gap in the disk, thus halting their (type-II) migration (Trilling et al. Trilling et al.(2002)). This is observationally supported by the discovery that there are no massive planets in short period orbits (Zucker & Mazeh 2002; Udry et al. 2002a), and by the clear trend showing that planets less massive than $\sim$0.75  $M_{{\rm Jup}}$ all follow short period trajectories (Udry et al. 2002b). If the low metallicity stars are only able to form low-mass planets (a slight trend suggested in the last section), metal-poor stars should have preferentially "short'' period planets.

   
4.3 Eccentricity

It might also be interesting to explore whether there is any relation between the eccentricity of the planetary orbits and the stellar metallicity. Such an analysis is presented in Fig. 8.

Figure 8: Upper left: metallicity against orbital eccentricity for the known planetary companions whose host stars have precise spectroscopic [Fe/H] determinations. Different symbols are used for planets in orbits having eccentricity higher or smaller than 0.25. The filled dots represent planets in stellar systems (Eggenberger et al. 2002). Lower left: [Fe/H] distributions for stars with planets with eccentricities lower and higher than 0.25 (the hashed and open bars, respectively). Right: cumulative functions of both distributions. A Kolmogorov-Smirnov test gives a probability of $\sim$0.38 that both samples belong to the same distribution.

As it can be seen, no special trends seem to exist. There is a slight suggestion that all the low metallicity objects have intermediate eccentricities only. In other words, the more eccentric planets seem to orbit only stars with metallicity higher or comparable to solar, and on the opposite side of the eccentricity distribution, there seems also to be a lack of low eccentricity planets around metal-poor stars.

However, as can also be seen in Fig. 8 (histogram and cumulative functions), this result is not statistically significant. We have tried to change the limits of eccentricity for the two [Fe/H] distributions. No further conclusions can be taken.