This is the second paper in a series of papers showing the results of extrasolar planet population synthesis calculations. In the companion paper (Paper I), we have presented in detail our methods. By applying an observational detection bias for radial velocity surveys, we identify the potentially detectable synthetic planets. The properties of these planets are compared in quantitative statistical tests with the properties of a carefully selected sub-population of actual exoplanets. We use a two dimensional Kolmogorov-Smirnov test to compare the mass-distance distributions of synthetic and observed planets, as well as 1D KS tests to compare the mass, the semimajor axis and the [Fe/H] distributions. We find that some models can account to a reasonable degree of significance for the observed properties. We concurrently account for many other observed features, e.g. the "metallicity effect". This gives us confidence that our model captures several essential features of giant planet formation. Our simulations allow us also to extract the properties of the underlying exoplanet population that are not yet detectable. For example, we have derived the planetary initial mass function (PIMF) and have been led to conclude that the planets detected so far represent only the tip of the iceberg. The PIMF can also be used to predict how the detectable extrasolar planet population will change as the precision of radial velocity surveys improves to an extreme precision of 0.1 m/s.
Deep Dive into Extrasolar planet population synthesis II: Statistical comparison with observation.
This is the second paper in a series of papers showing the results of extrasolar planet population synthesis calculations. In the companion paper (Paper I), we have presented in detail our methods. By applying an observational detection bias for radial velocity surveys, we identify the potentially detectable synthetic planets. The properties of these planets are compared in quantitative statistical tests with the properties of a carefully selected sub-population of actual exoplanets. We use a two dimensional Kolmogorov-Smirnov test to compare the mass-distance distributions of synthetic and observed planets, as well as 1D KS tests to compare the mass, the semimajor axis and the [Fe/H] distributions. We find that some models can account to a reasonable degree of significance for the observed properties. We concurrently account for many other observed features, e.g. the “metallicity effect”. This gives us confidence that our model captures several essential features of giant planet forma
In the first paper of this series (Mordasini et al. 2008, hereafter Paper I), we have presented our methods to synthesize populations of extrasolar planets. We have explained how we use our extended core accretion model (Alibert et al. 2005a) to generate synthetic planetary populations by varying in a Monte Carlo fashion four key variables describing the initial conditions in our planet formation model. As shown in Paper I, we have tried in deriving the probability distribution of these four variables to stay as close as possible to actual observations.
We have found that the large spread of initial conditions resulting from the variation of the characteristics of the protoplanetary disk (abundance of heavy elements, mass and lifetime) and their relative probability of occurrence leads to the formation of a synthetic population of planets characterized by a large diversity. Hence, we argued that, within the core accre-tion paradigm, the observed diversity of exoplanets is a natural consequence of the diversity of disk properties.
In Paper I, we have also identified a number of typical phases planets undergo during their formation, and found that these phases lead to characteristic planetary formation tracks. These tracks determine the final position of each planet in the distance to star versus planetary mass diagram (a-M) and therefore can be used in order to interpret the corresponding observational diagram.
Unfortunately, not all model parameters can be constrained by observations of proto-stellar disks. To circumvent this problem, we present in this paper an approach that consists in comparing statistically the overall characteristics of our synthetic planets with those of a carefully selected sub-population of actually detected exoplanets. This approach has been made possible by the large number of exoplanets that have been detected over the recent years which has allowed to go beyond the characteristics of individual objects and define the characteristics of the ensemble population. Many studies have discussed from a observational point of view the statistical properties of the extrasolar arXiv:0904.2542v1 [astro-ph.EP] 16 Apr 2009 planets, analyzing various distributions and correlations in order to address the following (and many more) issues, as recently reviewed by Udry & Santos (2007).
(1) Before the detection of 51 Peg b 13 years ago by Mayor & Queloz (1995) it was not clear if planets outside our own Solar System existed, although from a theoretical point of view, there was no reason to doubt it. Nowadays we know that roughly 5-10 % (e.g. Marcy et al. 2005;Cumming et al. 2008) of solar-like star in the solar neighborhood harbor a giant planet within a few AU in distance.
(2) Detection biases still hinder the exploration of the full planetary mass domain. It is however clear that the mass distribution increases towards small mass planets (e.g. Butler et al. 2006;Jorissen et al. 2001), which points towards the existence of a large number of yet undetected low mass planets. It is also known that there are very few objects with masses larger than ∼ 15 Jupiter masses inside a few AU (e.g. Marcy & Butler 2000) defining the “brown dwarf desert”. With the detection of smaller and smaller mass planets, new, finer structures in the mass distribution, like a bimodal shape at very low masses (Mayor et al. 2009) have recently been suggested.
(3) The distribution of semimajor axes consists of a pile up of Hot Jupiters at about 0.03 AU, followed by a relative depletion (the “period valley”) and finally an increase in frequency further out at about 1 AU (e.g. Udry et al. 2003). Outside a few AU the limited time duration of the surveys does not allow definitive statements yet.
(4) The combination of mass and distance has shown that there is an absence of massive planets at small orbital distances (e.g. Zucker & Mazeh 2002), and a positive correlation of planetary mass and distance (e.g. Jiang et al. 2007). Low mass, Neptunian planets seem to be characterized by a different distribution than giant planets (Udry & Santos 2007).
(5) Soon after the first discoveries of extrasolar planets it was noticed that the detection probability of giant planets increases with stellar metallicity (Gonzalez 1997). This “metallicity effect” is now very well established (e.g. Fischer & Valenti 2005;Santos et al. 2003). Also correlations between stellar metallicity and the planetary semimajor axis have been discussed (e.g. Sozzetti 2004), but no definitive conclusions can be drawn at this time. The stellar mass certainly also plays a role for planet formation. Observations of stellar types other than FGK underly certain complications, but a positive correlation between stellar mass and frequency of massive planets seems now to be clear (e.g. Lovis & Mayor 2007).
(6) It was found that planets in relatively tight binary systems have statistically different properties (e.g. Eggenberger et al. 2004;Desidera & Barbieri 2007). F
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