Sta%s%cal Proper%es of Exoplanets

Transcription

1 Sta%s%cal Proper%es of Exoplanets Mordasini et al. 2009, A&A, 501, 1139 Next: Popula%on Synthesis 1

2 Goals of Population Synthesis: incorporate essential planet formation processes, with simplifying approximation simulate thousands of planets (formation + evolution) compare synthetic population to observed population

3 Basic Flow of Pop. Syn. Model From Mordasini (2012), See Benz et al. PPVI (2014) for detailed char + references 3

4 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

5 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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7 Planet Forma,on: Core Accre,on total gas solids Simulated forma%on of Jupiter (standard Pollack et al mul%- step model)

8 Planet Forma,on: Core Accre,on total gas Slow growth of the core solids

9 Planet Forma,on: Core Accre,on total gas Core grows to 10 M earth and gas accre%on starts solids

10 Planet Forma,on: Core Accre,on total gas Hydrodynamic flow results in runaway accre%on solids

11 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

12 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)

13 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

14 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.

15 common example - - net torque < 0, inward migra%on 15

16 See Kley & Nelson (2012) for review of planet- disk interac%ons 16

17 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

18 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

19 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

20 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

21 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

22 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 Intermediate Jovian Super-Jupiter > 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

23 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 Planet Mass Distribution dn/dm M Planets Keck, Lick, AAT Marcy et al 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

24 Towards the underlying mass distribution Observation Udry & Santos 2007 All instruments HARPS (1 m/s) Observational bias Synthetic Mordasini et al 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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