CAUP Researchers: Annelies Mortier, Nuno C. Santos, Sérgio A. G. Sousa
Team at CAUP: Origin and Evolution of Stars and Planets
Other Researchers: Garik Israelian (SP), Michel Mayor (CH), Stéphane Udry (CH)

On the functional form of the metallicity-giant planet correlation,
Astronomy and Astrophysics, Volume 551, pp. A112 (2013)

It is generally accepted that the presence of a giant planet is strongly dependent on the stellar metallicity. A stellar mass dependence has also been investigated, but this dependence does not seem as strong as the metallicity dependence. Even for metallicity, however, the exact form of the correlation has not been established. In this paper, we test several scenarios for describing the frequency of giant planets as a function of its host parameters. We perform this test on two volume-limited samples (from CORALIE and HARPS) and, by using a Bayesian analysis, we quantitatively compared the different scenarios. We confirm that giant planet frequency is indeed a function of metallicity. However, there is no statistical difference between a constant or an exponential function for stars with subsolar metallicities contrary to what has been previously stated in the literature. The dependence on stellar mass could neither be confirmed nor be discarded.

Figure 1 | Frequency of giant planets as a function of metallicity and mass of the HARPS and the CORALIE sample. Three different functional forms are shown: a complete exponential with linear mass (blue curve), an exponential and a constant (green curve), and an exponential, a constant plus a drop (red curve). The stellar mass is fixed to M = 1.0 Mʘ.

Although a large number of exoplanets has already been detected, astronomers have not yet achieved consensus regarding the theoretical models of giant planets formation. The two major possibilities are the core accretion and the disk instability models. While the first model predicts that planets form by accretion of gas from the protoplanetary disk into icy or rocky cores, the latter expects gravitational instabilities to develop directly in the disk, thus triggering planetary formation.

The key to establish the importance of each formation process could lie in the host stars. For instance, the core-accretion theory predicts an increasing correlation between the presence of a giant planet and the host metallicity, while the gravitational instability model does not. And while it is already well established the existence of an exponential relationship between the host star metallicity and the probability of harbouring a planet for solar and supersolar metallicites, no conclusive results have been found for subsolar metallicity stars yet. If this metallicity relation is proven not to be valid for subsolar metallicities, it could mean that the formation theory of gravitational instability may be more important for these stars.

Now, this team used two volume-limited samples of stars which included several planet-hosts to study the functional form of such relation. From the CORALIE sample 1216 stars had the required data available and were considered for this analysis while the HARPS sample yielded 582 stars. These stars’ masses and metallicities were then determined and the data was analyzed using a Bayesian inference method to find the best relationship between stellar mass and metallicity and likelihood of being orbited by a giant planet.

Seven different functional forms for the giant planet frequency function were tested, including dependency in mass alone and in metallicity alone. Only the functional form with dependence on the mass alone could be ruled out and Figure 1 represents the results obtained with the 3 functional forms which provided the best results for the samples used in this work.

The results obtained proved that the frequency of giant planets does have a dependence on metallicity and that a dependence also on the stellar mass could neither be confirmed nor ruled out. The functional form of such dependences for subsolar metallicity, however, could not be established with the samples used here. Thus, larger samples, of the order of 5000 stars – which should become available in the near future with results from Gaia and Kepler – are needed in order to firmly establish the functional form of this dependence.

Anellies Mortier, CAUP member and lead author of this paper, performed the Bayesian tests and Sérgio Sousa derived the stellar parameters. The remaining CAUP author, Nuno Santos, led the observations used in this work together with the remaining researchers.