[Paper Review] Extrasolar planet population synthesis II: Statistical comparison with observation

C. Mordasini, Y. Alibert+2 more|arXiv (Cornell University)|Apr 16, 2009

Stellar, planetary, and galactic studiesPhysics and Astronomy3 references209 citations

TL;DR

This paper uses a Monte Carlo population synthesis model based on core accretion and disk migration to statistically compare synthetic planetary systems with observed extrasolar planets orbiting solar-like stars. It finds that a subset of models can simultaneously reproduce key observational features—such as the mass-period distribution, metallicity correlation, and hot Jupiter frequency—confirming the core accretion paradigm while revealing that current detections represent only ~9% of the true planetary population, with improved radial velocity precision expected to reveal a bimodal mass distribution.

ABSTRACT

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.

Motivation & Objective

• To statistically constrain planet formation models using observed properties of extrasolar planets.
• To test whether the core accretion paradigm with disk migration can reproduce the observed statistical features of the exoplanet population.
• To identify which model parameters are consistent with observations and which can be ruled out.
• To infer undetectable planetary population properties, such as the planetary initial mass function (PIMF).
• To predict how future radial velocity surveys with improved precision will alter the detectable exoplanet population.

Proposed method

• Monte Carlo sampling of initial conditions (disk mass, metallicity, lifetime, and core mass) drawn from observationally constrained probability distributions.
• Population synthesis using an extended core accretion model with simplified type I migration and disk evolution.
• Application of radial velocity detection bias to identify potentially detectable synthetic planets.
• Statistical comparison using two-dimensional Kolmogorov-Smirnov (KS) tests on mass-semimajor axis distributions and one-dimensional KS tests on Msin i, semimajor axis, and [Fe/H] distributions.
• Modeling of planetesimal disk properties and their impact on planet formation and metallicity dependence.
• Extraction of the planetary initial mass function (PIMF) from synthetic populations to infer the true underlying planetary population.

Experimental results

Research questions

• RQ1 Which combinations of initial disk and core parameters produce synthetic planetary populations statistically consistent with observed exoplanet distributions?
• RQ2 To what extent can the core accretion model with migration reproduce the observed metallicity correlation in planet detection frequency?
• RQ3 What fraction of the true planetary population remains undetected by current radial velocity surveys?
• RQ4 How will the detectable exoplanet population change as radial velocity precision improves to 1 m/s or 0.1 m/s?
• RQ5 Can the model reproduce the observed frequency of hot Jupiters and their correlation with stellar metallicity?

Key findings

• A subset of model parameters successfully reproduces the observed mass-period distribution, with a two-dimensional Kolmogorov-Smirnov test indicating statistical consistency.
• The synthetic population shows a metallicity effect, with detectable planets biased toward higher [Fe/H] by ~0.1 dex, matching observations within error bars (p-value ~22% for KS test).
• The model predicts that only ~9% of all planets are currently detectable, implying the true planetary population is vastly larger than observed.
• With radial velocity precision improved to 1 m/s, the observed mass distribution is predicted to become bimodal, consistent with recent discoveries.
• At a precision of 0.1 m/s, at least 30–40% of FGK stars are expected to host detectable planets, revealing the underlying PIMF.
• The mean formation timescale of giant planets in the model is ~3.5 Myr, consistent with observed disk lifetimes.