NEW POPULATION SYNTHESIS MODEL FOR EXOPLANETS Sergei Nayakshin, - PowerPoint PPT Presentation

NEW POPULATION SYNTHESIS MODEL FOR EXOPLANETS Sergei Nayakshin, University of Leicester Seung-Hoon Cha, Mark Fletcher

Dominant view: both CA and GI needed 1.<----- -- CA -- -----> GI --> ✤ GI is probably needed at tens of AU and beyond ✤ However it can’t work closer in — need CA ✤ Also need planet migration for hot Jupiters

GI PLANET MIGRATION 1. GI gives birth to fragments in the outer disc 2. Fragments migrate inward in ~ 10 orbits Boley+ 2010 Vorobyov & Basu 06 Cha & Nayakshin 11

Migration of GI planets may explain all giant planets, including hot Jupiters

CORE FORMATION INSIDE GI FRAGMENTS Kuiper 51, McCrea Williams 65, Cameron+ 82, Boss 98 Grain sedimentation Envelope disruption

Migration and disruption of GI planets may explain all planets 1.“Tidal Downsizing” 2.Boley et al 2010, Nayakshin 2010 4.Note: parts of this were suggested by Kuiper 1951, McCrea & Williams 1965, Boss 1998

PLANET FORMATION DEBRIS Incomplete grain/planetesimal sedimentation into the core creates a core and planetesimal debris ring

DEBRIS DISCS MADE BY GI Nayakshin & Cha 2012 — Alternative to Safronov 1969

TIDAL DOWNSIZING (MODERN GI) 1.GI gives birth to fragments in the outer disc 2./3. Fragments migrate in/Cores form inside 4a. Disrupted fragments — rocky planets + debris discs 4b. Collapsed fragments — gas giants

TD = GI + MANY “ CA PROCESSES” •Fragment formation by GI (Rice, Forgan, Stamatellos, L. Mayer, Meru, Z. Zhu, Boley, Durisen…) •Fragment contraction, grain growth, core growth (Bodenheimer et al 1970-is; Helled et al 2008, 2010, 2011; N 2010, 2011, 2014) •Fragment migration in the disc (Crida, Baruteau, Paardekooper….) •Disc evolution in 1D (Shakura, Sunyaev … Clarke, Armitage, Alexander) •Population synthesis — Ida, Lin, Mordasini, Alibert (CA context); Forgan & Rice, Galvagni & Mayer (TD context) •Pebble accretion (Johanson, Lambrechts….) •Massive atmosphere formation around the core (Mizuno, Stevenson…)

Pebble accretion also applies to TD planets ✤ Johansen & Lacerda 2010, Ormel and Klarh 2010, … Lambrechts & J 2012— CA context ✤ Nayakshin (2015a,b) — TD context Planet embedded in a disc Pebbles of a few mm in size tend to decouple from gas and sink towards and into massive objects

Giant planets collapse faster due to pebble accretion 0 5 10 15 (a) accretion of grains at low velocities brings mass but not ✤ kinetic energy --> effective cooling 1000 T [K] = − L rad − GM p ˙ dE p M z dt R p γ = 1.37 γ = 1.37 γ = 1.37 γ = 1.37 γ = 1.37 1.40 1.40 1.40 1.40 1.40 P = K ρ 1+ 1 1.46 1.46 1.46 1.46 1.46 Considering a polytropic sphere ( ), 1.58 1.58 1.58 1.58 1.58 ✤ n 5/3 5/3 5/3 5/3 5/3 and exact solution for metal loading is found (b) Planet metallicity � 6 / (3 − n )  1 − z 0 T c = T 0 0.10 1 − z for H2 gas n=2.5, so the exponent is 12 Nayakshin 2015a ✤ 0.01 Adding ~10% of mass in metals can make the fragment 0 5 10 15 ✤ time [kyr] collapse

A detailed TD pop synthesis model 1. Planet-disc (migration) model (Nayakshin & Lodato 2012) • 1D viscous disc evolution • type II + type I migration 2. Planet contraction + grain physics • radiative cooling/external irradiation from the disc • grain (3 species) growth, sedimentation, vaporisation • core formation and energy release 3. Planet disruption (R_pl > R_hill) 4. Pebble accretion on GI planets (Nayakshin 2015a,b). Note: Forgan & Rice 2013, Calvagni & Mayer 2014 presented semi-analytical population synthesis models.

Example: formation of a Hot Super Earth Disc evolution 1. Fragment forms at 110 AU 1000 t= 0.18 Myr t= 0.18 Myr 0.23 Myr 0.23 Myr 1.20 Myr 1.20 Myr 1.50 Myr 1.50 Myr Σ [g cm -2 ] 2. Fragment migrates to ~3 AU 100 Tidal disruption Tidal disruption Gap closed Gap closed 3. Tidal forces destroy the envelope 10 4. A core of ~ 6 Earth masses remains 0.1 1.0 10.0 100.0 R, AU Super Earth planet formation 5. The core migrates to 0.23 AU 100.0 Separation and radii [AU] Gap openned Gap openned before the disc dissipates 10.0 Tidal disruption Tidal disruption Gap closed Gap closed 6. Need ~ 4 CPU hours per run 1.0 Separation, a Radius, R p (a) 0.1 Hill’s radius, R H Core mass [M Earth ] Total Core mass 1.0 Rocks CHON Nayakshin 2015c, subm. 0.1 0 100 200 300 400 500 600 time [10 3 years]

20,000 planet formation experiments 1/20 sample 1/20 sample Planet Mass vs Separation 1/2 sample 1/2 sample 10.000 1000 1.000 100 Mass [M Earth ] M p [M Jup ] 0.100 10 0.010 1 Z l < -0.25 Z l < -0.25 -0.25 < Z l < 0 -0.25 < Z l < 0 1/20 sample 1/20 sample 0 < Z l < 0.25 0 < Z l < 0.25 0.001 Nayakshin & Fletcher, Z l > 0.25 Z l > 0.25 2015, subm. 0.1 1.0 10.0 100.0 a [AU]

Planet Mass Function Simulated Planets, a < 5 AU (a) Planet disruption outcomes No selection v * = 1 m/s selection All 300 1500 Metal rich Initial Fragments Metal poor Number of planets Number of planets Tidal disruption desert 200 1000 100 500 0 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1 2 -1 0 1 2 3 4 N & Fletcher 2015 log Planet mass, M Earth log Planet mass, M Earth • PMF desert at ~ 20 to 100 Mearth predicted by Ida & Lin 2004 (also Mordasini et al 2009) • TD also has the desert, for a physically opposite reason • M_gas ~ M_core planets are rare no matter how you make them

z-correlations in Core Accretion ✤ Planetesimals form more efficiently in higher z discs (Johanson, Carrera, Drazkowska, ) ✤ Debris discs should correlate with z ✤ More massive cores at high z ✤ More gas giants at high z (Ida & Lin 04, Mordasini + 09) ✤ Positive giant planet -- metallicity correlation is observed (Fischer & Valenti 2005)

Metallicity Correlations Observed CA TD Gas giants Y es Y es Sub - Neptunes Y es ( ? ) Debris Discs Y es

metallicity correlations 0.6 0.4 0.2 Fe/H [dex] 0.0 Metallicity 0.0 –0.2 –0.4 − 0.5 Buchhave et al (2012) Mayor et al 2011 –0.6 10.0 100.0 1000. 0 5 10 15 M2sini [Earth Mass] Radius of planet ( R ⊕ ) • Gas giants correlate with Z, sub-Neptunes do not. • Maldonado et al 2012: Debris discs do not correlate with Z. • Contradicts original Ida & Lin 2004 suggestion

Metallicity Correlations Observed CA TD Gas giants Y es Y es Sub - Neptunes No Y es ( ? ) Debris Discs No Y es

TD z-correlations: as observed Cores and low mass giants vs Z l Simulated Planets, hot region 1.00 1.0 0.1400 Giants, moderate mass Super Earths 0.1200 0.8 Cumulative Probability Frequency of planets Fractional outcome 0.1000 0.10 0.6 0.0800 0.0600 0.4 0.0400 0.01 0.2 Giants, a = R in Giants, a = R in 0.0200 Giants, R in < a < 5 Giants, R in < a < 5 Super Earths Super Earths All cores All cores 0.0000 0.0 -0.4 -0.2 0.0 0.2 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 [Z/H] N & Fletcher 2015 Z l • At low z, most fragments are destroyed — few giants but lots of cores • At high z, very few fragments are disrupted — few massive cores • Peak of massive core production — intermediate z

Metallicity Correlations Observed CA TD Gas giants Y es Y es Y es Sub - Neptunes No Y es ( ? ) No Debris Discs No Y es

Z-CORRELATIONS OF SMALL THINGS Sub - Neptune planets and debris disc are created when gas giants are destroyed — > They cannot correlate same way with z as giants!

Debris disc correlations Number of tidal disruptions with Mz > 0.1 Mj Fletcher & N, in prep. -0.6 [Fe/H] 0.6

Metallicity Correlations Observed CA TD Gas giants Y es Y es Y es Sub - Neptunes No Y es ( ? ) No Debris Discs No Y es No

Prevalence of ~ 10 M_Earth cores ✤ Abrupt drop above ~ 10-20 M_Earths (Mayor et al 2011, Howard et al 2012) ✤ Cores of ~ 10 M_Earth are rare because more massive ones become gas giant by gas accretion [Planet desert — Ida, Lin 2004; Mordasini et al 2009] ✤ CA: Massive cores are predecessors of giant planets

TD: Massive cores are killers of giant planets Cores allowed No cores No cores 10.000 10.000 1000 1000 1.000 1.000 100 100 Mass [M Earth ] M p [M Jup ] M p [M Jup ] 0.100 0.100 10 10 0.010 0.010 1 1 Z l < -0.25 Z l < -0.25 Z l < -0.25 Z l < -0.25 Nayakshin, in prep. -0.25 < Z l < 0 -0.25 < Z l < 0 -0.25 < Z l < 0 -0.25 < Z l < 0 0 < Z l < 0.25 0 < Z l < 0.25 0 < Z l < 0.25 0 < Z l < 0.25 0.001 0.001 Z l > 0.25 Z l > 0.25 Z l > 0.25 Z l > 0.25 0.1 1.0 10.0 100.0 0.1 1.0 10.0 100.0 a [AU] a [AU] ✤ Massive cores are luminous ✤ They puff up gas fragments ✤ The envelope is expelled by the core — exactly like the cores destroy Red Giant stars!

Prevalence of ~ 10 M_Earth cores ✤ CA: Massive cores run away to become giants ✤ TD: Cores more massive than ~ 10 M_E destroy their planets Nayakshin, in prep.