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 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.

💡 Research Summary

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This paper presents the second installment of a series on extrasolar planet population synthesis, focusing on a statistical comparison between synthetic planetary populations generated by an extended core‑accretion model and the observed sample of planets detected by radial‑velocity (RV) surveys. Building on the methodological framework laid out in Paper I, the authors draw initial conditions for each simulation from probability distributions derived from observations of protoplanetary disks: (1) the dust‑to‑gas ratio (linked to stellar metallicity), (2) the initial gas surface density at 5.2 AU (constrained by disk mass surveys), (3) the photo‑evaporation rate (setting disk lifetimes), and (4) the starting location of the planetary embryo (restricted to regions where the isolation mass exceeds the seed mass). A Monte‑Carlo approach is used to generate thousands of planetary formation tracks, each solving the internal structure equations for the growing planet while simultaneously evolving the viscous α‑disk, including type I and type II migration, and tracking the accretion of solids and gas.

A crucial step is the implementation of a realistic detection bias that mimics the selection effects of RV surveys. Using the method of Naef et al. (2004, 2005), the authors compute a two‑dimensional detection‑probability grid as a function of planetary period (1–40 000 days) and mass (1–12 720 M⊕) for a representative instrumental precision of 10 m s⁻¹ and a survey duration of 10 years. For each synthetic planet, the detection probability is interpolated from this grid and compared with a random number to decide whether the planet would have been detected. This yields a sub‑sample of “observable” synthetic planets (N_obssynt) that can be directly compared with a carefully curated observational sample of RV‑detected planets around solar‑type stars.

Statistical comparison is performed using a two‑dimensional Kolmogorov‑Smirnov (KS) test on the mass–semimajor‑axis (M–a) distribution, and one‑dimensional KS tests on the distributions of M sin i, semimajor axis a, and stellar metallicity