Extrasolar planet population synthesis (original) (raw)
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Protostars and Planets VI, 2014
With the increasing number of exoplanets discovered, statistical properties of the population as a whole become unique constraints on planet formation models provided a link between the description of the detailed processes playing a role in this formation and the observed population can be established. Planet population synthesis provides such a link. The approach allows to study how different physical models of individual processes (e.g., proto-planetary disc structure and evolution, planetesimal formation, gas accretion, migration, etc.) affect the overall properties of the population of emerging planets. By necessity, planet population synthesis relies on simplified descriptions of complex processes. These descriptions can be obtained from more detailed specialised simulations of these processes. The objective of this chapter is twofold: 1) provide an overview of the physics entering in the two main approaches to planet population synthesis and 2) present some of the results achieved as well as illustrate how it can be used to extract constraints on the models and to help interpret observations.
The Astrophysical Journal, 2013
The rapid growth in the number of known exoplanets has revealed the existence of several distinct planetary populations in the observed mass-period diagram. Two of the most surprising are, (1) the concentration of gas giants around 1AU and (2) the accumulation of a large number of low-mass planets with tight orbits, also known as super-Earths and hot Neptunes. We have recently shown that protoplanetary disks have multiple planet traps that are characterized by orbital radii in the disks and halt rapid type I planetary migration. By coupling planet traps with the standard core accretion scenario, we showed that one can account for the positions of planets in the mass-period diagram. In this paper, we demonstrate quantitatively that most gas giants formed at planet traps tend to end up around 1 AU with most of these being contributed by dead zones and ice lines. In addition, we show that a large fraction of super-Earths and hot Neptunes are formed as "failed" cores of gas giants-this population being constituted by comparable contributions from dead zone and heat transition traps. Our results are based on the evolution of forming planets in an ensemble of disks where we vary only the lifetimes of disks as well as their mass accretion rates onto the host star. We show that a statistical treatment of the evolution of a large population of planetary cores initially caught in planet traps accounts for the existence of three distinct exoplantary populations-the hot Jupiters, the more massive planets at roughly orbital radii around 1 AU orbital, and the short period SuperEarths and hot Neptunes. There are very few evolutionary tracks that feed into the large orbital radii characteristic of the imaged Jovian planet and this is in accord with the result of recent surveys that find a paucity of Jovian planets beyond 10 AU. Finally, we find that low-mass planets in tight orbits become the dominant planetary population for low mass stars (M * ≤ 0.7M ⊙), in agreement with the previous studies which show that the formation of gas giants is preferred for massive stars.
Diverse outcomes of planet formation and composition around low-mass stars and brown dwarfs
Monthly Notices of the Royal Astronomical Society, 2019
The detection of Earth-size exoplanets around low-mass stars –in stars such as Proxima Centauri and TRAPPIST-1– provide an exceptional chance to improve our understanding of the formation of planets around M stars and brown dwarfs. We explore the formation of such planets with a population synthesis code based on a planetesimal-driven model previously used to study the formation of the Jovian satellites. Because the discs have low mass and the stars are cool, the formation is an inefficient process that happens at short periods, generating compact planetary systems. Planets can be trapped in resonances and we follow the evolution of the planets after the gas has dissipated and they undergo orbit crossings and possible mergers. We find that formation of planets above Mars mass and in the planetesimal accretion scenario, is only possible around stars with masses M⋆ ≥ 0.07Msun and discs of Mdisc ≥ 10−2 Msun. We find that planets above Earth-mass form around stars with masses larger tha...
Theoretical models of planetary system formation: mass vs. semi-major axis
Astronomy & Astrophysics, 2013
Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods. We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results. We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ∼5 M ⊕ , simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.
2011
The planetary mass-radius diagram is an observational result of central importance to understand planet formation. We present an updated version of our planet formation model based on the core accretion paradigm which allows us to calculate planetary radii and luminosities during the entire formation and evolution of the planets. We first study with it the formation of Jupiter, and compare with previous works. Then we conduct planetary population synthesis calculations to obtain a synthetic mass-radius diagram which we compare with the observed one. Except for bloated Hot Jupiters which can be explained only with additional mechanisms related to their proximity to the star, we find a good agreement of the general shape of the observed and the synthetic M - R diagram. This shape can be understood with basic concepts of the core accretion model.
Theory of planet formation and comparison with observation
EPJ Web of Conferences, 2011
The planetary mass-radius diagram is an observational result of central importance to understand planet formation. We present an updated version of our planet formation model based on the core accretion paradigm which allows us to calculate planetary radii and luminosities during the entire formation and evolution of the planets. We first study with it the formation of Jupiter, and compare with previous works. Then we conduct planetary population synthesis calculations to obtain a synthetic mass-radius diagram which we compare with the observed one. Except for bloated Hot Jupiters which can be explained only with additional mechanisms related to their proximity to the star, we find a good agreement of the general shape of the observed and the synthetic M − R diagram. This shape can be understood with basic concepts of the core accretion model.
A Decreased Probability of Habitable Planet Formation around Low‐Mass Stars
The Astrophysical Journal, 2007
Smaller terrestrial planets (0.3 M ⊕) are less likely to retain the substantial atmospheres and ongoing tectonic activity probably required to support life. A key element in determining if sufficiently massive "sustainably habitable" planets can form is the availability of solid planet-forming material. We use dynamical simulations of terrestrial planet formation from planetary embryos and simple scaling arguments to explore the implications of correlations between terrestrial planet mass, disk mass, and the mass of the parent star. We assume that the protoplanetary disk mass scales with stellar mass as M disk ∝ f M h ⋆ , where f measures the relative disk mass, and 1/2 < h < 2, so that disk mass decreases with decreasing stellar mass. We consider systems without Jovian planets, based on current models and observations for M stars. We assume the mass of a planet formed in some annulus of a disk with given parameters is proportional to the disk mass in that annulus, and show with a suite of simulations of late-stage accretion that the adopted prescription is surprisingly accurate. Our results suggest that the fraction of systems with sufficient disk mass to form > 0.3 M ⊕ habitable planets decreases for low-mass stars for every realistic combination of parameters. This "habitable fraction" is small for stellar masses below a mass in the interval 0.5 to 0.8 M ⊙ , depending on disk parameters, an interval that excludes most M stars. Radial mixing and therefore water delivery are inefficient in lower-mass disks commonly found around low-mass stars, such that terrestrial planets in the habitable zones of most low-mass stars are likely to be small and dry.
Formation of planetary populations − II. Effects of initial disc size and radial dust drift
Monthly Notices of the Royal Astronomical Society
Recent ALMA observations indicate that while a range of disc sizes exist, typical disc radii are small, and that radial dust drift affects the distribution of solids in discs. Here, we explore the consequences of these features in planet population synthesis models. A key feature of our model is planet traps – barriers to otherwise rapid type-I migration of forming planets – for which we include the ice line, heat transition, and outer edge of the dead zone. We find that the ice line plays a fundamental role in the formation of warm Jupiters. In particular, the ratio of super Earths to warm Jupiters formed at the ice line depends sensitively on the initial disc radius. Initial gas disc radii of ∼50 au results in the largest super Earth populations, while both larger and smaller disc sizes result in the ice line producing more gas giants near 1 au. This transition between typical planet class formed at the ice line at various disc radii confirms that planet formation is fundamentally...
Planet formation models: the interplay with the planetesimal disc
Astronomy & Astrophysics, 2012
Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims. We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods. We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M ⊕ or above several Jupiter masses. Conclusions. To form giant planets before the dissipation of the disc, small planetesimals (∼0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.
Hybrid methods in planetesimal dynamics: formation of protoplanetary systems and the mill condition
Monthly Notices of the Royal Astronomical Society, 2014
The formation and evolution of protoplanetary discs remains a challenge from both a theoretical and numerical standpoint. In this work we first perform a series of tests of our new hybrid algorithm presented in Glaschke, Amaro-Seoane and Spurzem 2011 (henceforth Paper I) that combines the advantages of high accuracy of directsummation N −body methods with a statistical description for the planetesimal disc based on Fokker-Planck techniques. We then address the formation of planets, with a focus on the formation of protoplanets out of planetesimals. We find that the evolution of the system is driven by encounters as well as direct collisions and requires a careful modelling of the evolution of the velocity dispersion and the size distribution over a large range of sizes. The simulations show no termination of the protoplanetary accretion due to gap formation, since the distribution of the planetesimals is only subjected to small fluctuations. We also show that these features are weakly correlated with the positions of the protoplanets. The exploration of different impact strengths indicates that fragmentation mainly controls the overall mass loss, which is less pronounced during the early runaway growth. We prove that the fragmentation in combination with the effective removal of collisional fragments by gas drag sets an universal upper limit of the protoplanetary mass as a function of the distance to the host star, which we refer to as the mill condition. (RS) 1 http://exoplanet.eu/catalog-all.php Understanding planet formation comprises many challenges, such as hydrodynamics of the protoplanetary disc, chemical evolution of the embedded dust grains, migration of planets and planetesimals and even star-star interactions in dense young star clusters (see Armitage 2010,for a review and references therein, and also the introduction of Paper I, for a brief summary). All these components constitute the frame for the essential process of planet formation: An enormous growth from dust-sized particles to the final planets, accompanied by a steady decrease of the number of particles which contain most of the mass over many orders of magnitude. The particle number changes over many orders of magnitude as planetary growth proceeds. There is active research on each of the different aspects of planet formation, but the current efforts are far from a unified model of planet formation .