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Planetary Population Synthesis

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Abstract

In stellar astrophysics, the technique of population synthesis has been successfully used for several decades. For planets, it is in contrast still a young method which only became important in recent years because of the rapid increase of the number of known extrasolar planets and the associated growth of statistical observational constraints. With planetary population synthesis, the theory of planet formation and evolution can be put to the test against these constraints. In this review of planetary population synthesis, we first briefly list key observational constraints. Then, the workflow in the method and its two main components are presented, namely, global end-to-end models that predict planetary system properties directly from protoplanetary disk properties and probability distributions for these initial conditions. An overview of various population synthesis models in the literature is given. The sub-models for the physical processes considered in global models are described: the evolution of the protoplanetary disk, planets’ accretion of solids and gas, orbital migration, and N-body interactions among concurrently growing protoplanets. Next, typical population synthesis results are illustrated in the form of new syntheses obtained with the latest generation of the Bern model. Planetary formation tracks, the distribution of planets in the mass-distance and radius-distance plane, the planetary mass function, and the distributions of planetary radii, semimajor axes, and luminosities are shown, linked to underlying physical processes, and compared with their observational counterparts. We finish by highlighting the most important predictions made by population synthesis models and discuss the lessons learned from these predictions – both those later observationally confirmed and those rejected.

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References

  • Alessi M, Pudritz RE, Cridland AJ (2017) On the formation and chemical composition of super Earths. MNRAS 464:428

    ADS  Google Scholar 

  • Alexander RD, Armitage PJ (2009) Giant planet migration, disk evolution, and the origin of transitional disks. ApJ 704:989

    ADS  Google Scholar 

  • Alexander R, Pascucci I, Andrews S, Armitage P, Cieza L (2014) Protostars and planets VI. University of Arizona Press, Tucson, pp 475–496

    Google Scholar 

  • Alibert Y, Mordasini C, Benz W (2004) Migration and giant planet formation. A&A 417:L25

    ADS  Google Scholar 

  • Alibert Y, Mordasini C, Benz W, Winisdoerffer C (2005) Models of giant planet formation with migration and disc evolution. A&A 434:343

    ADS  Google Scholar 

  • Alibert Y, Carron F, Fortier A et al (2013) Theoretical models of planetary system formation: mass vs. semi-major axis. A&A 558:A109

    ADS  Google Scholar 

  • Andrews SM, Wilner DJ, Hughes AM, Qi C, Dullemond CP (2010) Protoplanetary disk structures in ophiuchus. II. Extension to fainter sources. ApJ 723:1241

    ADS  Google Scholar 

  • Bai X-N (2016) Towards a global evolutionary model of protoplanetary disks. ApJ 821:80

    ADS  Google Scholar 

  • Baruteau C, Masset FS (2008) On the corotation torque in a radiatively inefficient disk. ApJ 672:1054

    ADS  Google Scholar 

  • Baruteau C, Bai X, Mordasini C, Mollière P (2016) Formation, orbital and internal evolutions of young planetary systems. Space Sci Rev 205:77

    ADS  Google Scholar 

  • Benítez-Llambay P, Masset F, Koenigsberger G, Szulágyi J (2015) Planet heating prevents inward migration of planetary cores. Nature 520:63

    ADS  Google Scholar 

  • Benz W, Ida S, Alibert Y, Lin D, Mordasini C (2014) Protostars and planets VI. University of Arizona Press, Tucson, pp 691–713

    Google Scholar 

  • Birnstiel T, Andrews SM (2014) On the outer edges of protoplanetary dust disks. ApJ 780:153

    ADS  Google Scholar 

  • Birnstiel T, Klahr H, Ercolano B (2012) A simple model for the evolution of the dust population in protoplanetary disks. A&A 539:148

    ADS  MATH  Google Scholar 

  • Bitsch B, Johansen A, Lambrechts M, Morbidelli A (2015a) The structure of protoplanetary discs around evolving young stars. A&A 575:A28

    ADS  Google Scholar 

  • Bitsch B, Lambrechts M, Johansen A (2015b) The growth of planets by pebble accretion in evolving protoplanetary discs. A&A 582:A112

    ADS  Google Scholar 

  • Bodenheimer PH, Pollack JB (1986) Calculations of the accretion and evolution of giant planets: the effects of solid cores. Icarus 67:391

    ADS  Google Scholar 

  • Bodenheimer PH, Hubickyj O, Lissauer JJ (2000) Models of the in situ formation of detected extrasolar giant planets. Icarus 143:2

    ADS  Google Scholar 

  • Bonfils X, Delfosse X, Udry S et al (2013) The HARPS search for southern extra-solar planets. XXXI. The M-dwarf sample. A&A 549:A109

    Google Scholar 

  • Borucki WJ, Koch DG, Basri G et al (2011) Characteristics of kepler planetary candidates based on the first data set. ApJ 728:117

    ADS  Google Scholar 

  • Boss AP (1995) Proximity of jupiter-like planets to low-mass stars. Science 267:360

    ADS  Google Scholar 

  • Boss AP (1997) Giant planet formation by gravitational instability. Science 276:1836

    ADS  Google Scholar 

  • Bowler BP (2016) Imaging extrasolar giant planets. PASP 128:102001

    ADS  Google Scholar 

  • Brauer F, Dullemond CP, Henning T (2008) Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks. A&A 480:859

    ADS  MATH  Google Scholar 

  • Bruzual G, Charlot S (2003) Stellar population synthesis at the resolution of 2003. MNRAS 344:1000

    ADS  Google Scholar 

  • Bryan ML, Knutson HA, Howard AW et al (2016) Statistics of long period gas giant planets in known planetary systems. ApJ 821:89

    ADS  Google Scholar 

  • Burke CJ, Christiansen JL, Mullally F et al (2015) Terrestrial planet occurrence rates for the Kepler GK dwarf sample. ApJ 809:8

    ADS  Google Scholar 

  • Burrows A, Hubeny I, Budaj J, Hubbard WB (2007) Possible solutions to the radius anomalies of transiting giant planets. ApJ 661:502

    ADS  Google Scholar 

  • Cameron AGW (1978) Physics of the primitive solar accretion disk. Moon Planets. 18:5

    ADS  Google Scholar 

  • Casoli J, Masset FS (2009) On the horseshoe drag of a low-mass planet. II. Migration in adiabatic disks. ApJ 703:845

    Google Scholar 

  • Cassan A, Kubas D, Beaulieu J et al (2012) One or more bound planets per Milky Way star from microlensing observations. Nature 481:167

    ADS  Google Scholar 

  • Chabrier G (2003) Evolutionary models for cool brown dwarfs and extrasolar giant planets. The case of HD 209458. Publ Astron Soc Pac 115:763

    Google Scholar 

  • Chabrier G, Baraffe I, Leconte J, Gallardo J, Barman TS (2009) The mass-radius relationship from solar-type stars to terrestrial planets: a review. Cool Stars 1094:102

    Google Scholar 

  • Chambers JE (1999) A hybrid symplectic integrator that permits close encounters between massive bodies. MNRAS 304:793

    ADS  Google Scholar 

  • Chambers JE (2009) An analytic model for the evolution of a viscous, irradiated disk. ApJ 705:1206

    ADS  Google Scholar 

  • Chiang E, Laughlin G (2013) The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths. MNRAS 431:3444–3455. https://doi.org/10.1093/mnras/stt424_MNRAS

    ADS  Google Scholar 

  • Cimerman NP, Kuiper R, Ormel CW (2017) Hydrodynamics of embedded planets’ first atmospheres – III. The role of radiation transport for super-Earth planets. MNRAS 471:4662

    ADS  Google Scholar 

  • Coleman GAL, Nelson RP (2014) On the formation of planetary systems via oligarchic growth in thermally evolving viscous discs. MNRAS 445:479

    ADS  Google Scholar 

  • Coleman GAL, Nelson RP (2016a) MNRAS 457:2480

    ADS  Google Scholar 

  • Coleman GAL, Nelson RP (2016b) Giant planet formation in radially structured protoplanetary discs. MNRAS 460:2779–2795. https://doi.org/10.1093/mnras/stw1177

    ADS  Google Scholar 

  • Coleman GAL, Papaloizou JCB, Nelson RP (2017) In situ accretion of gaseous envelopes on to planetary cores embedded in evolving protoplanetary discs. MNRAS 470:3206

    ADS  Google Scholar 

  • Coughlin JL, Mullally F, Thompson SE et al (2016) Planetary candidates observed by Kepler. VII. The first fully uniform catalog based on the entire 48-month data set (Q1-Q17 DR24). ApJS 224:12

    ADS  Google Scholar 

  • Cresswell P, Nelson RP (2008) Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc. A&A 482:677

    ADS  Google Scholar 

  • Crida A, Morbidelli A, Masset FS (2006) On the width and shape of gaps in protoplanetary disks. Icarus 181:587

    ADS  Google Scholar 

  • Cridland AJ, Pudritz RE, Alessi M (2016) Composition of early planetary atmospheres - I. Connecting disc astrochemistry to the formation of planetary atmospheres. MNRAS 461:3274

    ADS  Google Scholar 

  • Cridland AJ, Pudritz RE, Birnstiel T, Cleeves LI, Bergin EA (2017) Composition of early planetary atmospheres II: coupled dust and chemical evolution in protoplanetary disks. MNRAS. http://adsabs.harvard.edu/abs/2017arXiv170502381C

  • Cumming A, Butler RP, Marcy GW et al (2008) The Keck planet search: detectability and the minimum mass and orbital period distribution of extrasolar planets. PASP 120:531

    ADS  Google Scholar 

  • D’Angelo G, Lubow SH (2008) Evolution of migrating planets undergoing gas accretion. ApJ 685:560

    ADS  Google Scholar 

  • David TJ, Hillenbrand LA, Petigura EA et al (2016) A Neptune-sized transiting planet closely orbiting a 5-10-million-year-old star. Nature 534:658

    ADS  Google Scholar 

  • Dell’Omodarme M, Valle G, Degl’Innocenti S, Prada Moroni PG (2012) The Pisa stellar evolution data base for low-mass stars. A&A 540:A26

    ADS  Google Scholar 

  • Dittkrist K-M, Mordasini C, Klahr H, Alibert Y, Henning T (2014) Impacts of planet migration models on planetary populations. Effects of saturation, cooling and stellar irradiation. A&A 567:A121

    Google Scholar 

  • Donati JF, Moutou C, Malo L et al (2016) A hot Jupiter orbiting a 2-million-year-old solar-mass T Tauri star. Nature 534:662

    ADS  Google Scholar 

  • Dong S, Xie J-W, Zhou J-L, Zheng Z, Luo A (2018) LAMOST telescope reveals that Neptunian cousins of hot Jupiters are mostly single offspring of stars that are rich in heavy elements. Proc Natl Acad Sci 115:266–271. https://doi.org/10.1073/pnas.1711406115

    ADS  Google Scholar 

  • Dra̧żkowska J, Alibert Y, Moore B (2016) Close-in planetesimal formation by pile-up of drifting pebbles. A&A 594:A105

    ADS  Google Scholar 

  • Duffell PC, Haiman Z, MacFadyen AI, D’Orazio DJ, Farris BD (2014) The migration of gap-opening planets is not locked to viscous disk evolution. ApJ 792:L10

    ADS  Google Scholar 

  • Dürmann C, Kley W (2015) Migration of massive planets in accreting disks. A&A 574:A52

    ADS  Google Scholar 

  • Fabrycky DC, Tremaine S (2007) Shrinking binary and planetary orbits by kozai cycles with tidal friction. ApJ 669:1298

    ADS  Google Scholar 

  • Figueira P, Pont F, Mordasini C et al (2009) Bulk composition of the transiting hot Neptune around GJ 436. A&A 493:671

    ADS  Google Scholar 

  • Fischer DA, Valenti JA (2005) The planet-metallicity correlation. ApJ 622:1102

    ADS  Google Scholar 

  • Forgan D, Rice K (2013) Towards a population synthesis model of objects formed by self-gravitating disc fragmentation and tidal downsizing. MNRAS 432:3168

    ADS  Google Scholar 

  • Forgan DH, Hall C, Meru F, Rice WKM (2018) Towards a population synthesis model of self-gravitating disc fragmentation and tidal downsizing II: the effect of fragment-fragment interactions. MNRAS 474:5036

    ADS  Google Scholar 

  • Fortier A, Alibert Y, Carron F, Benz W, Dittkrist K-M (2013) Planet formation models: the interplay with the planetesimal disc. A&A 549:44

    ADS  Google Scholar 

  • Fouchet L, Alibert Y, Mordasini C, Benz W (2012) Effects of disk irradiation on planet population synthesis. A&A 540:107

    ADS  Google Scholar 

  • Freedman RS, Lustig-Yaeger J, Fortney JJ et al (2014) Gaseous mean opacities for giant planet and ultracool dwarf atmospheres over a range of metallicities and temperatures. ApJS 214:25

    ADS  Google Scholar 

  • Fressin F, Torres G, Charbonneau D et al (2013) The false positive rate of Kepler and the occurrence of planets. ApJ 766:81

    ADS  Google Scholar 

  • Fulton BJ, Petigura EA, Howard AW et al (2017) The California-Kepler survey. III. A gap in the radius distribution of small planets. AJ 154:109

    ADS  Google Scholar 

  • Goldreich P, Tremaine S (1979) The excitation of density waves at the Lindblad and corotation resonances by an external potential. ApJ 233:857

    ADS  MathSciNet  Google Scholar 

  • Gomes R, Levison HF, Tsiganis K, Morbidelli A (2005) Origin of the cataclysmic late heavy bombardment period of the terrestrial planets. Nature 435:466

    ADS  Google Scholar 

  • Gonzalez G (1997) The stellar metallicity-giant planet connection. MNRAS 285:403

    ADS  Google Scholar 

  • Greenzweig Y, Lissauer JL (1992) Accretion rates of protoplanets II. Icarus 100:440

    ADS  Google Scholar 

  • Haisch KE, Lada EA, Lada CJ (2001) Disk frequencies and lifetimes in young clusters. ApJ 553:L153

    ADS  Google Scholar 

  • Hasegawa Y, Pudritz RE (2011) The origin of planetary system architectures – I. Multiple planet traps in gaseous discs. MNRAS 417:1236

    ADS  Google Scholar 

  • Hasegawa Y, Pudritz RE (2012) Evolutionary tracks of trapped, accreting protoplanets: the origin of the observed mass-period relation. ApJ 760:117

    ADS  Google Scholar 

  • Hasegawa Y, Pudritz RE (2013) Planetary populations in the mass-period diagram: a statistical treatment of exoplanet formation and the role of planet traps. ApJ 778:78

    ADS  Google Scholar 

  • Hayashi C (1981) Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Prog Theor Phys Suppl 70:35

    ADS  Google Scholar 

  • Hellary P, Nelson RP (2012) Global models of planetary system formation in radiatively-inefficient protoplanetary discs. MNRAS 419:2737

    ADS  Google Scholar 

  • Horn B, Lyra W, Mac Low M-M, Sándor Z (2012) Orbital migration of interacting low-mass planets in evolutionary radiative turbulent models. ApJ 750:34

    ADS  Google Scholar 

  • Howard AW, Marcy GW, Johnson JA et al (2010) The occurrence and mass distribution of close-in super-Earths, neptunes, and jupiters. Science 330:653

    ADS  Google Scholar 

  • Howard AW, Marcy GW, Bryson ST et al (2012) Planet occurrence within 0.25 AU of solar-type stars from Kepler. ApJS 201:15

    Google Scholar 

  • Hueso R, Guillot T (2005) Evolution of protoplanetary disks: constraints from DM Tauri and GM Aurigae. A&A 442:703

    ADS  Google Scholar 

  • Ida S, Lin DNC (2004a) Toward a deterministic model of planetary formation. I. A desert in the mass and semimajor axis distributions of extrasolar planets. ApJ 604:388

    ADS  Google Scholar 

  • Ida S, Lin DNC (2004b) Toward a deterministic model of planetary formation. II. The formation and retention of gas giant planets around stars with a range of metallicities. ApJ 616:567

    ADS  Google Scholar 

  • Ida S, Lin DNC (2008a) Toward a deterministic model of planetary formation. IV. Effects of type I migration. ApJ 673:487

    ADS  Google Scholar 

  • Ida S, Lin DNC (2008b) Toward a deterministic model of planetary formation. V. Accumulation near the ice line and super-earths. ApJ 685:584

    ADS  Google Scholar 

  • Ida S, Lin DNC (2010) Toward a deterministic model of planetary formation. VI. Dynamical interaction and coagulation of multiple rocky embryos and super-earth systems around solar-type stars. ApJ 719:810

    ADS  Google Scholar 

  • Ida S, Makino J (1993) Scattering of planetesimals by a protoplanet: slowing down of runaway growth. Icarus 106:210

    ADS  Google Scholar 

  • Ida S, Lin DNC, Nagasawa M (2013) Toward a deterministic model of planetary formation. VII. Eccentricity distribution of gas giants. ApJ 775:42

    ADS  Google Scholar 

  • Ikoma M, Nakazawa K, Emori H (2000) Formation of giant planets: dependences on core accretion rate and grain opacity. ApJ 537:1013

    ADS  Google Scholar 

  • Jin S, Mordasini C (2018) Compositional imprints in density-distance-time: a rocky composition for close-in low-mass exoplanets from the location of the valley of evaporation. ApJ 853:163

    ADS  Google Scholar 

  • Jin S, Mordasini C, Parmentier V et al (2014) Planetary population synthesis coupled with atmospheric escape: a statistical view of evaporation. ApJ 795:65

    ADS  Google Scholar 

  • Johansen A, Lambrechts M (2017) Forming planets via pebble accretion. Annu Rev Earth Planet Sci 45:359

    ADS  Google Scholar 

  • Jurić M, Tremaine S (2008) Dynamical origin of extrasolar planet eccentricity distribution. ApJ 686:603

    ADS  Google Scholar 

  • Kasting JF, Whitmire DP, Reynolds RT (1993) Habitable zones around main sequence stars. Icarus 101:108

    ADS  Google Scholar 

  • Kley W, Nelson RP (2012) Planet-disk interaction and orbital evolution. ARA&A 50:211

    ADS  Google Scholar 

  • Kley W, Bitsch B, Klahr H (2009) Structure and evolution of the first CoRoT exoplanets: probing the brown dwarf/planet overlapping mass regime. A&A 506:971

    ADS  MATH  Google Scholar 

  • Kokubo E, Ida S (2000) Formation of protoplanets from planetesimals in the solar nebula. Icarus 143:15

    ADS  Google Scholar 

  • Kokubo E, Ida S (2002) Formation of protoplanet systems and diversity of planetary systems. ApJ 581:666

    ADS  Google Scholar 

  • Kokubo E, Ida S (2012) Dynamics and accretion of planetesimals. Prog Theor Exp Phys 2012:01A308. https://doi.org/10.1093/ptep/pts032

    Google Scholar 

  • Kornet K, Stepinski TF, Rozyczka M (2001) Diversity of planetary systems from evolution of solids in protoplanetary disks. A&A 378:180

    ADS  Google Scholar 

  • Kozai Y (1962) Secular perturbations of asteroids with high inclination and eccentricity. AJ 67:591

    ADS  MathSciNet  Google Scholar 

  • Kretke KA, Lin DNC (2012) The importance of disk structure in stalling type I migration. ApJ 755:74

    ADS  Google Scholar 

  • Kuiper GP (1951) On the origin of the solar system. Proc Natl Acad Sci 37:1

    ADS  Google Scholar 

  • Lambrechts M, Johansen A (2012) Rapid growth of gas-giant cores by pebble accretion. A&A 544:32

    ADS  Google Scholar 

  • Lambrechts M, Johansen A (2014) Forming the cores of giant planets from the radial pebble flux in protoplanetary discs. A&A 572:A107

    ADS  Google Scholar 

  • Levison HF, Thommes EW, Duncan MJ (2010) Modeling the formation of giant planet cores. I. Evaluating key processes. ApJ 139:1297

    Google Scholar 

  • Lin DNC, Papaloizou JCB (1986a) On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction. ApJ 307:395

    ADS  Google Scholar 

  • Lin DNC, Papaloizou JCB (1986b) On the tidal interaction between protoplanets and the protoplanetary disk. III - Orbital migration of protoplanets. ApJ 309:846

    ADS  Google Scholar 

  • Lodders K (2003) Solar system abundances and condensation temperatures of the elements. ApJ 591:1220

    ADS  Google Scholar 

  • Lopez ED, Fortney JJ (2013) The role of core mass in controlling evaporation: the Kepler radius distribution and the Kepler-36 density dichotomy. ApJ 776:2

    ADS  Google Scholar 

  • Lubow SH, Seibert M, Artymowicz P (1999) Disk accretion onto high-mass planets. ApJ 526:1001

    ADS  Google Scholar 

  • Lüst R (1952) Die Entwicklung einer um einen Zentralkörper rotierenden Gasmasse. I. Lösungen der hydrodynamischen Gleichungen mit turbulenter Reibung. Z Naturforsch A 7:87

    Google Scholar 

  • Lynden-Bell D, Pringle JE (1974) The evolution of viscous discs and the origin of the nebular variables. MNRAS 168:603

    ADS  Google Scholar 

  • Lyra W, Paardekooper S-J, Mac Low M-M (2010) Orbital migration of low-mass planets in evolutionary radiative models: avoiding catastrophic infall. ApJ 715:L68

    ADS  Google Scholar 

  • Madhusudhan N, Amin MA, Kennedy GM (2014) Toward chemical constraints on hot Jupiter migration. ApJ 794:L12

    ADS  Google Scholar 

  • Mamajek EE (2009) Initial conditions of planet formation: lifetimes of primordial disks. In: Usuda T, Tamura M, Ishii M (eds) American institute of physics conference series, vol 1158, pp 3–10. http://adsabs.harvard.edu/abs/2009AIPC.1158....3M

  • Manara CF, Rosotti G, Testi L et al (2016) Evidence for a correlation between mass accretion rates onto young stars and the mass of their protoplanetary disks. A&A 591:L3

    ADS  Google Scholar 

  • Mann AW, Newton ER, Rizzuto AC et al (2016) Zodiacal exoplanets in time (ZEIT). III. A short-period planet orbiting a pre-main-sequence star in the upper scorpius OB association. AJ 152:61

    ADS  Google Scholar 

  • Marboeuf U, Thiabaud A, Alibert Y, Cabral N, Benz W (2014) From planetesimals to planets: volatile molecules. A&A 570:A36

    ADS  Google Scholar 

  • Marcy GW, Butler RP, Fischer D, Vogt S, Wright JT, Tinney CG, Jones HRA (2005) Observed properties of exoplanets: masses, orbits, and metallicities. Prog Theor Phys Suppl 158:24–42. https://doi.org/10.1143/PTPS.158.24

    ADS  Google Scholar 

  • Marcy GW, Weiss LM, Petigura EA et al (2014) Occurrence and core-envelope structure of 1-4 x Earth-size planets around Sun-like stars. Proc Natl Acad Sci 111:12655

    ADS  Google Scholar 

  • Masset F, Snellgrove M (2001) Reversing type II migration: resonance trapping of a lighter giant protoplanet. MNRAS 320:L55

    ADS  Google Scholar 

  • Masset FS, Casoli J (2010) Saturated torque formula for planetary migration in viscous disks with thermal diffusion: recipe for protoplanet population synthesis. ApJ 723:1393

    ADS  Google Scholar 

  • Mayor M, Queloz D (1995) A Jupiter-mass companion to a solar-type star. Nature 378:355

    ADS  Google Scholar 

  • Mayor M, Marmier M, Lovis C, Udry S, Segransan D, Pepe FA, Benz W, Bertaux J-L, Bouchy F, Dumusque X, Lo Curto G, Mordasini C, Queloz D, Santos NC et al (2011) The HARPS search for southern extra-solar planets XXXIV. Occurrence, mass distribution and orbital properties of super-Earths and Neptune-mass planets. arXiv, astro-ph 1109.2497

    Google Scholar 

  • Mizuno H (1980) Formation of the giant planets. Prog Theor Phys 64:544

    ADS  Google Scholar 

  • Mollière P, Mordasini C (2012) Deuterium burning in objects forming via the core accretion scenario. A&A 547:A105

    ADS  Google Scholar 

  • Mordasini C (2014) Grain opacity and the bulk composition of extrasolar planets. II. An analytical model for grain opacity in protoplanetary atmospheres. A&A 572:A118

    ADS  Google Scholar 

  • Mordasini C, Alibert Y, Benz W (2006) Destruction of planetesimals in protoplanetry atmospheres. In: Arnold L, Bouchy F, Moutou C (eds) Tenth anniversary of 51 peg-b: status of and prospects for hot Jupiter studies. Frontier Group, Paris, pp 84–86

    Google Scholar 

  • Mordasini C, Alibert Y, Benz W (2009a) Extrasolar planet population synthesis. I. Method, formation tracks, and mass-distance distribution. A&A 501:1139

    ADS  Google Scholar 

  • Mordasini C, Alibert Y, Benz W, Naef D (2009b) Extrasolar planet population synthesis. II. Statistical comparison with observations. A&A 501:1161

    ADS  Google Scholar 

  • Mordasini C, Alibert Y, Benz W, Klahr H, Henning T (2012a) Extrasolar planet population synthesis. IV. Correlations with disk metallicity, mass, and lifetime. A&A 541:97

    ADS  Google Scholar 

  • Mordasini C, Alibert Y, Georgy C et al (2012b) Characterization of exoplanets from their formation. II. The planetary mass-radius relationship. A&A 547:112

    ADS  Google Scholar 

  • Mordasini C, Alibert Y, Klahr H, Henning T (2012c) Characterization of exoplanets from their formation. I. Models of combined planet formation and evolution. A&A 547:111

    ADS  Google Scholar 

  • Mordasini C, Klahr H, Alibert Y, Miller N, Henning T (2014) A&A 566:A141

    ADS  Google Scholar 

  • Mordasini C, Mollière P, Dittkrist K-M, Jin S, Alibert Y (2015) Global models of planet formation and evolution. Int J Astrobiol 14:201

    Google Scholar 

  • Mordasini C, van Boekel R, Mollière P, Henning T, Benneke B (2016) The imprint of exoplanet formation history on observable present-day spectra of hot jupiters. ApJ 832:41

    ADS  Google Scholar 

  • Mordasini C, Marleau G-D, Mollière P (2017) Characterization of exoplanets from their formation. III. The statistics of planetary luminosities. A&A 608:A72

    Google Scholar 

  • Mortier A, Santos NC, Sousa S et al (2013) On the functional form of the metallicity-giant planet correlation. A&A 551:A112

    ADS  Google Scholar 

  • Moutou C, Deleuil M, Guillot T et al (2013) CoRoT: harvest of the exoplanet program. Icarus 226:1625

    ADS  Google Scholar 

  • Movshovitz N, Bodenheimer PH, Podolak M, Lissauer JJ (2010) Formation of Jupiter using opacities based on detailed grain physics. Icarus 209:616

    ADS  Google Scholar 

  • Mulders GD, Pascucci I, Apai D (2015) An increase in the mass of planetary systems around lower-mass stars. ApJ 814:130

    ADS  Google Scholar 

  • Müller S, Helled R, Mayer L (2018) On the diversity in mass and orbital radius of giant planets formed via disk instability. APJ 854:112. https://doi.org/10.3847/1538-4357/aaa840

    ADS  Google Scholar 

  • Nakazawa K, Ida S, Nakagawa Y (1989) Collisional probability of planetesimals revolving in the solar gravitational field. I basic formulation. A&A 220:293

    Google Scholar 

  • Nayakshin S (2010) Formation of planets by tidal downsizing of giant planet embryos. MNRAS 408:L36

    ADS  Google Scholar 

  • Nayakshin S, Fletcher M (2015) Tidal Downsizing model – III. Planets from sub-Earths to brown dwarfs: structure and metallicity preferences. MNRAS 452:1654

    ADS  Google Scholar 

  • Ndugu N, Bitsch B, Jurua E (2018) Planet population synthesis driven by pebble accretion in cluster environments. MNRAS 474:886

    ADS  Google Scholar 

  • Ogihara M, Morbidelli A, Guillot T (2015) Suppression of type I migration by disk winds. A&A 584:L1

    ADS  Google Scholar 

  • Ormel CW (2014) An atmospheric structure equation for grain growth. ApJ 789:L18

    ADS  Google Scholar 

  • Ormel CW (2017) The emerging paradigm of pebble accretion. In: Pessah M, Gressel O (eds) Astrophysics and space science library, vol 445. Springer International Publishing, p 197. http://adsabs.harvard.edu/abs/2017ASSL..445..197O

    Google Scholar 

  • Ormel CW, Klahr HH (2010) The effect of gas drag on the growth of protoplanets. Analytical expressions for the accretion of small bodies in laminar disks. A&A 520:A43

    ADS  Google Scholar 

  • Ormel CW, Dullemond CP, Spaans M (2010) Accretion among preplanetary bodies: the many faces of runaway growth. Icarus 210:507

    ADS  Google Scholar 

  • Ormel CW, Ida S, Tanaka H (2012) Migration rates of planets due to scattering of planetesimals. ApJ 758:80

    ADS  Google Scholar 

  • Ormel CW, Shi J-M, Kuiper R (2015) Hydrodynamics of embedded planets’ first atmospheres – II. A rapid recycling of atmospheric gas. MNRAS 447:3512

    ADS  Google Scholar 

  • Owen JE, Wu Y (2013) Kepler planets: a tale of evaporation. ApJ 775:105

    ADS  Google Scholar 

  • Owen JE, Wu Y (2017) The evaporation valley in the Kepler planets. ApJ 847:29

    ADS  Google Scholar 

  • Paardekooper S-J (2014) Dynamical corotation torques on low-mass planets. MNRAS 444:2031

    ADS  Google Scholar 

  • Paardekooper S-J, Baruteau C, Crida A, Kley W (2010) A torque formula for non-isothermal type I planetary migration I. Unsaturated horseshoe drag. MNRAS 401:1950

    ADS  Google Scholar 

  • Panić O, Hogerheijde MR, Wilner D, Qi C (2009) A break in the gas and dust surface density of the disc around the T Tauri star IM Lupi. A&A 501:269

    ADS  Google Scholar 

  • Perri F, Cameron AGW (1974) Hydrodynamic instability of the solar nebula in the presence of a planetary core. Icarus 22:416

    ADS  Google Scholar 

  • Petigura EA, Howard AW, Marcy GW (2013) Prevalence of Earth-size planets orbiting Sun-like stars. Proc Natl Acad Sci 110:19273

    ADS  Google Scholar 

  • Petigura EA, Marcy GW, Winn JN et al (2018) The California-Kepler survey. IV. Metal-rich stars host a greater diversity of planets. AJ 155:89

    ADS  Google Scholar 

  • Pierens A (2015) Fast migration of low-mass planets in radiative discs. MNRAS 454:2003

    ADS  Google Scholar 

  • Pinilla P, Birnstiel T, Walsh C (2015) Sequential planet formation in the HD 100546 protoplanetary disk? A&A 580:A105

    ADS  Google Scholar 

  • Piso A-MA, Youdin AN (2014) On the minimum core mass for giant planet formation at wide separations. ApJ 786:21

    ADS  Google Scholar 

  • Piso A-MA, Öberg KI, Birnstiel T, Murray-Clay RA (2015) C/O and snowline locations in protoplanetary disks: the effect of radial drift and viscous gas accretion. ApJ 815:109

    ADS  Google Scholar 

  • Podolak M, Pollack JB, Reynolds RT (1988) Interactions of planetesimals with protoplanetary atmospheres. Icarus 73:163

    ADS  Google Scholar 

  • Pollack JB, Hubickyj O, Bodenheimer PH et al (1996) Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124:62

    ADS  Google Scholar 

  • Reffert S, Bergmann C, Quirrenbach A, Trifonov T, Künstler A (2015) Precise radial velocities of giant stars. VII. Occurrence rate of giant extrasolar planets as a function of mass and metallicity. A&A 574:A116

    ADS  Google Scholar 

  • Safronov VS (1969) Evolution of the protoplanetary cloud and formation of the Earth and the planets. Nauka, Moscow

    Google Scholar 

  • Sahlmann J, Segransan D, Queloz D et al (2011) Search for brown-dwarf companions of stars. A&A 525:95

    Google Scholar 

  • Sallum S, Follette KB, Eisner JA et al (2015) Accreting protoplanets in the LkCa 15 transition disk. Nature 527:342

    ADS  Google Scholar 

  • Salpeter EE (1955) The luminosity function and Stellar evolution. ApJ 121:161

    ADS  Google Scholar 

  • Sándor Z, Lyra W, Dullemond CP (2011) Formation of planetary cores at type I migration traps. ApJ 728:L9

    ADS  Google Scholar 

  • Santos NC, Israelian G, Mayor M (2004) Spectroscopic [Fe/H] for 98 extra-solar planet-host stars. Exploring the probability of planet formation. A&A 415:1153

    Google Scholar 

  • Santos NC, Israelian G, Mayor M et al (2005) Spectroscopic metallicities for planet-host stars: extending the samples. A&A 437:1127

    ADS  Google Scholar 

  • Santos NC, Adibekyan V, Figueira P et al (2017) Observational evidence for two distinct giant planet populations. A&A 603:A30

    ADS  Google Scholar 

  • Schneider J, Dedieu C, Le Sidaner P, Savalle R, Zolotukhin I (2011) Defining and cataloging exoplanets: the exoplanet.eu database. A&A 532:A79

    ADS  Google Scholar 

  • Shakura NI, Sunyaev RA (1973) Black holes in binary systems. Observational appearance. A&A 24:337

    Google Scholar 

  • Shu FH (1977) Self-similar collapse of isothermal spheres and star formation. ApJ 214:488

    ADS  Google Scholar 

  • Shu FH, Tremaine S, Adams FC, Ruden SP (1990) Sling amplification and eccentric gravitational instabilities in gaseous disks. ApJ 358:495

    ADS  Google Scholar 

  • Tanaka H, Takeuchi T, Ward WR (2002) Three-dimensional interaction between a planet and an isothermal gaseous disk. I. corotation and lindblad torques and planet migration. ApJ 565:1257

    ADS  Google Scholar 

  • Thommes EW, Duncan MJ, Levison HF (2003) Oligarchic growth of giant planets. Icarus 161:431

    ADS  Google Scholar 

  • Thommes EW, Matsumura S, Rasio FA (2008) Gas disks to gas giants: simulating the birth of planetary systems. Supporting online material. Science 321:814

    ADS  Google Scholar 

  • Udry S, Santos NC (2007) Statistical properties of exoplanets. Annu Rev A&A 45:397

    ADS  Google Scholar 

  • Udry S, Mayor M, Santos NC (2003) Statistical properties of exoplanets. I. The period distribution: constraints for the migration scenario. A&A 407:369

    ADS  Google Scholar 

  • Van Eylen V, Agentoft C, Lundkvist MS, Kjeldsen H, Owen JE, Fulton BJ, Petigura E, Snellen I (2017) An asteroseismic view of the radius valley: stripped cores, not born rocky. arXiv:1710.05398. http://adsabs.harvard.edu/abs/2017arXiv171005398V

  • Veras D, Armitage PJ (2004) Outward migration of extrasolar planets to large orbital radii. MNRAS 347:613

    ADS  Google Scholar 

  • Visser RG, Ormel CW (2016) On the growth of pebble-accreting planetesimals. A&A 586:A66

    ADS  Google Scholar 

  • Walsh KJ, Morbidelli A, Raymond SN, O’Brien DP, Mandell AM (2011) A low mass for Mars from Jupiter’s early gas-driven migration. Nature 475:206

    ADS  Google Scholar 

  • Ward WR (1986) Density waves in the solar nebula–differential Lindblad torque. Icarus 67:164

    ADS  Google Scholar 

  • Weidenschilling S (1977) The distribution of mass in the planetary system and solar nebula. Astrophys Space Sci 51:153

    ADS  Google Scholar 

  • Winn JN, Fabrycky DC (2015) The occurrence and architecture of exoplanetary systems. ARA&A 53:409

    ADS  Google Scholar 

  • Wolfgang A, Rogers LA, Ford EB (2016) Probabilistic mass-radius relationship for sub-neptune-sized planets. ApJ 825:19

    ADS  Google Scholar 

  • Wright JT, Fakhouri O, Marcy GW et al (2011) The exoplanet orbit database. PASP 123:412

    ADS  Google Scholar 

  • Xie J-W, Dong S, Zhu Z, Huber D, Zheng Z, De Cat P, Fu J, Liu H-G, Luo A, Wu Y, Zhang H, Zhang H, Zhou J-L, Cao Z, Hou Y, Wang Y, Zhang Y (2016) Exoplanet orbital eccentricities derived from LAMOST-Kepler analysis. Proc Natl Acad Sci 113:11431–11435. https://doi.org/10.1073/pnas.1604692113

    ADS  Google Scholar 

  • Yu L, Donati J-F, Hébrard EM et al (2017) A hot Jupiter around the very active weak-line T Tauri star TAP 26. MNRAS 467:1342

    ADS  Google Scholar 

  • Zhu W, Petrovich C, Wu Y, Dong S, Xie J (2018) About 30% of sun-like stars Have Kepler-like planetary systems: a study of their intrinsic architecture. http://adsabs.harvard.edu/abs/2018arXiv180209526Z

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Acknowledgements

C.M. acknowledges the support from the Swiss National Science Foundation under grant BSSGI0_155816 “PlanetsInTime.” Parts of this work have been carried out within the frame of the National Center for Competence in Research PlanetS supported by the SNSF.

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Correspondence to Christoph Mordasini .

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Mordasini, C. (2018). Planetary Population Synthesis. In: Deeg, H., Belmonte, J. (eds) Handbook of Exoplanets . Springer, Cham. https://doi.org/10.1007/978-3-319-55333-7_143

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