Sta%s%cal Proper%es of Exoplanets Mordasini et al. 2009, A&A, 501, 1139 Next: Popula%on Synthesis 1
Goals of Population Synthesis: incorporate essential planet formation processes, with simplifying approximation simulate thousands of planets (formation + evolution) compare synthetic population to observed population
Basic Flow of Pop. Syn. Model From Mordasini (2012), See Benz et al. PPVI (2014) for detailed char + references 3
Formation Model (many coupled steps) Key Issues: growth/accretion migration planet-planet interactions planet structure (composition & envelope) disk evolution Benz et al. (2014) underlying planetesimal population
Initial, Boundary, Arbitrary Conditions Metallicity Distribution (as observed in stars) Disk masses and lifetimes (as observed) Initial distribution of seeds embryos (from theory and simulation) Stellar mass disk T inner edge migration damping
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Planet Forma,on: Core Accre,on total gas solids Simulated forma%on of Jupiter (standard Pollack et al. 1996 mul%- step model)
Planet Forma,on: Core Accre,on total gas Slow growth of the core solids
Planet Forma,on: Core Accre,on total gas Core grows to 10 M earth and gas accre%on starts solids
Planet Forma,on: Core Accre,on total gas Hydrodynamic flow results in runaway accre%on solids
Planet Forma,on: Core Accre,on total gas Gas in the neighborhood decreases, a gap in the disk is opened, and growth eventually stops at about 1 M Jup in about 3 Myr solids
Type 1 migration: small planets (no gap), very short timescales (~ 10 4 years!) and is usually damped, (See Tanaka et al. 2002) Type 2 migration: large planets (with a gap) two sub-types (disk or planetdominant interaction). Pop. Syn. models usually only consider gravitational interaction with gas disk (e.g., planetesimal interactions ignored)
Transi%on between Type I and II as planet mass increase For small planets, density waves propagate through the disk, while massive planets open a gap. leading waves (density enhancements) pull planet forward, while trailings waves pull planet backwards. Net- torque determines direc%on of migra%on (usually leading to inward mo%on). Gap size depends on planet mass, but also disk proper%es. Simula%on by P. Armitage 13
planet-disk resonances establish location of wave excitation. One co-rotation resonance (near planet) and series of Lindblad resonances located at natural frequencies of radial disk oscillations. Spiral density waves are excited by the planet at Lindblad resonances -- net torque determines direction of migration.
common example - - net torque < 0, inward migra%on 15
See Kley & Nelson (2012) for review of planet- disk interac%ons 16
Failed Cores: (stopping a_er phase 2 of CA model) %ny gas envelope planetesimal accre%on Note: Type- 1 migra%on damped to avoid a pile up of hot- Jupiters. Thus, these planets undergo damped type- I migra%on and more or less stay put. For most embryos, this is it! Disk life%mes are too short for substan%al growth at fixed r. Note: mass increases as you approach the ice line Average M ~ 3.6 Mearth with 0.1 Mearth of gas Mordasini et al. (2009) 17
horizontal branch disk- dominated Type- 2 migra%on These cores grow massive enough to experience Type- 2 migra%on (not damped). Migra%on is happening as fast or faster than accre%on. These planets begin near or beyond ice- line (but depends on star, Fe/H, etc.) Growth decrease when migra%on passes inside the ice line. Produces the popula%on of hot- Neptunes. Mordasini et al. (2009) 18
Many make it through the horizontal branch For star%ng posi%ons between 4 and 7 AU, cores can reach run- away accre%on mass before disk life%me / accre%on limit (and reduced accre%on a_er being within the ice- line). This produces hot super- Jupiters, for example. Mordasini et al. (2009) 19
Massive Planets late- stage planetesimal acc. very uncertain. For in massive, metal rich, long- lived disks, can produce small popula%on of very massive planets (the tail of the distribu%on). Mordasini et al. (2009) 20
Synthetic a-m diagram Type II Migration Limit Giants Timescale Limit Mainly icy core Mainly rocky core Menv / Mheavy > 10 1< Menv / Mheavy < 10 Menv / Mheavy < 1 Iceline upturn Planetary Desert See Ida & Lin (2004) Inner boundary comp. disk 0.1 AU From Mordasini (2012) Failed cores (Proto-terrestrial planets) Mstar=1 M, alpha=7x10-3 Irradiated disk. Σ(0.1)=0 non-isothermal migration 0.3% interstellar grain opacity 21
Planetary Initial Mass Function PIMF Mordasini et al. 2009b Peak at low masses Neptunian Bump Minimum: Planetary desert Flat Giant s Plateau Superjupiter Tail MStar=1 MSun Nominal Model Type Mass (MEarth) % (Super)-Earth < 7 58 Neptunian 7-30 17 Intermediate 30-100 6 Jovian 100-1000 14 Super-Jupiter > 1000 4 Model incompleteness Complex structure, dominated by low mass planets Consistent w. non-detection of Jupiters around 90% stars. Maxima at masses similar to Solar System planets. From Mordasini (2012) Model predicts that planets with M < 30 MEarth account for over 75% of all planets 22
Mass distribution: low RV precision Using a synthetic observational bias for a RV survey of 10 years at 10 m/s precision, find sub-population of detectable synthetic planets. Number of Planets 20 15 10 5 Planet Mass Distribution dn/dm M 1.05 104 Planets Keck, Lick, AAT Marcy et al. 2005 0 0 2 4 6 8 10 12 14 M sin i (M JUP ) The mass distribution is very well reproduced. Forming really massive planets is hard (insufficient mass & time) From Mordasini (2012) 23
Towards the underlying mass distribution Observation Udry & Santos 2007 All instruments HARPS (1 m/s) Observational bias Synthetic Mordasini et al. 2009 10 m/s 1m/s 0.1 m/s Full Population? Hints of the Neptunian bump and the minimum at 30 ME? Mordasini et al. (2009, 2014) Very strong sign of core accretion (all models - Ida & Lin, Mordasini et al, Miguel et al.) 24
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