[Paper Review] Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution

C. Mordasini, Y. Alibert+1 more|Apr 16, 2009

Stellar, planetary, and galactic studiesPhysics and Astronomy109 references306 citations

TL;DR

This paper introduces a population synthesis framework within the core accretion model to simulate extrasolar planet formation, using observed disk and stellar properties as initial conditions. It reveals distinct formation tracks in the mass-semimajor axis diagram, identifying key sub-populations: 'failed cores' (low-mass, core-dominated planets), a 'horizontal branch' of Neptune-mass planets (10–30 M⊕ up to 6 AU), and a 'main clump' of giant planets (100 M⊕ to 3 M_Jup) at 0.3–2 AU, with predictions matching observed planetary distributions and correlations.

ABSTRACT

With the high number of extrasolar planets discovered by now, it becomes possible to constrain theoretical formation models in a statistical sense. This paper is the first in a series in which we carry out a large number of planet population synthesis calculations. We begin the series with a paper mainly dedicated to the presentation of our approach, but also the discussion of a representative synthetic planetary population of solar like stars. Based as tightly as possible on observational data, we have derived probability distributions for the most important initial conditions for the planetary formation process. We then draw sets of initial conditions from these distributions and obtain the corresponding synthetic planets with our formation model. Although the main purpose of this paper is the description of our methods, we present some key results: We find that the variation of the initial conditions in the limits occurring in nature leads to the formation of planets of large diversity. This formation process is best visualized in planetary formation tracks, where different phases of concurrent growth and migration can be identified. These phases lead to the emergence of sub-populations of planets distinguishable in a mass-semimajor axis diagram. The most important ones are the "failed cores", a vast group of core-dominated low mass planets, the "horizontal branch", a sub-population of Neptune mass planets extending out to 6 AU, and the "main clump", a concentration of giant gaseous giants planets at around 0.3-2 AU.

Motivation & Objective

• To develop a statistical, population-based approach to test planet formation models using the growing sample of extrasolar planets.
• To address the limitations of single-system modeling by leveraging the statistical power of large planetary populations.
• To simulate synthetic planetary systems based on observed initial conditions for protoplanetary disks and stellar systems.
• To identify key formation pathways and sub-populations in the mass-semimajor axis plane.
• To provide a foundation for statistical comparison with observed exoplanet distributions in follow-up studies.

Proposed method

• The method draws initial conditions—such as disk mass, metallicity, and core mass—from empirically derived probability distributions based on observational constraints.
• A detailed planet formation model simulates core growth, gas runaway accretion, and type I and type II migration over time.
• The model computes formation tracks in the mass-semimajor axis plane, tracking how planets evolve through distinct phases of growth and migration.
• Synthetic planetary populations are generated by repeating the simulation with randomly drawn initial conditions from the observed distributions.
• The model incorporates disk evolution, including disk lifetime and viscosity, and accounts for migration timescales relative to accretion timescales.
• Non-nominal simulations test the sensitivity of results to key parameters like core formation timescale, disk lifetime, and migration regime transitions.

Experimental results

Research questions

• RQ1 What are the dominant formation pathways that lead to the observed diversity in exoplanet masses and orbital distances?
• RQ2 How do variations in initial disk and core conditions produce distinct sub-populations in the mass-semimajor axis diagram?
• RQ3 To what extent can the core accretion model reproduce the observed distribution of planets, including the 'planetary desert' and the concentration of giant planets at 0.3–2 AU?
• RQ4 What role do migration and accretion timescales play in shaping the final planetary population?
• RQ5 How do model assumptions—such as core formation speed or disk lifetime—affect the synthetic population's statistical properties?

Key findings

• The formation process produces a diverse planetary population, with distinct sub-populations clearly visible in the mass-semimajor axis diagram.
• The 'failed cores' sub-population dominates, consisting of low-mass, core-dominated planets formed when gas accretion is suppressed, consistent with the 90–95% of FGK stars without giant planets.
• The 'horizontal branch' comprises Neptune-mass planets (10–30 M⊕) that grow to critical mass but do not undergo runaway gas accretion, extending up to 6 AU.
• The 'main clump' forms from giant planets (100 M⊕ to 3 M_Jup) that undergo runaway gas accretion and migrate inward via type II migration, concentrating at 0.3–2 AU.
• The model predicts a depletion of planets between 30–100 M⊕ (a factor of 2–3 lower than giant planets), consistent with the observed 'planetary desert' but not as strong.
• The absence of massive planets (≳10 M_Jup) at both very close (≲0.5 AU) and very wide (≳10 AU) orbits is reproduced, indicating physical limits in formation and migration.