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

✤ 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 --> 1.<----- -- CA -- ----->

GI PLANET MIGRATION

• 1. GI gives birth to fragments in the outer disc
• 2. Fragments migrate inward in ~ 10 orbits

Boley+ 2010 Cha & Nayakshin 11 Vorobyov & Basu 06

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

• bjects

Giant planets collapse faster due to pebble accretion

✤

accretion of grains at low velocities brings mass but not kinetic energy --> effective cooling

Tc = T0 1 − z0 1 − z 6/(3−n)

dEp dt = −Lrad − GMp ˙ Mz Rp

✤

Considering a polytropic sphere ( ), and exact solution for metal loading is found

P = Kρ1+ 1

n

✤

for H2 gas n=2.5, so the exponent is 12

✤

Adding ~10% of mass in metals can make the fragment collapse

5 10 15 time [kyr] 0.01 0.10 Planet metallicity (b) 1000 T [K] 5 10 15 (a)

5/3 1.58 1.46 1.40 γ = 1.37 5/3 1.58 1.46 1.40 γ = 1.37 5/3 1.58 1.46 1.40 γ = 1.37 5/3 1.58 1.46 1.40 γ = 1.37 5/3 1.58 1.46 1.40 γ = 1.37

Nayakshin 2015a

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

1. Fragment forms at 110 AU

• 2. Fragment migrates to ~3 AU
• 3. Tidal forces destroy the envelope
• 4. A core of ~ 6 Earth masses remains
• 5. The core migrates to 0.23 AU

before the disc dissipates

• 6. Need ~ 4 CPU hours per run

Disc evolution

0.1 1.0 10.0 100.0 R, AU 10 100 1000 Σ [g cm-2] t= 0.18 Myr 0.23 Myr 1.20 Myr 1.50 Myr t= 0.18 Myr 0.23 Myr 1.20 Myr 1.50 Myr

Tidal disruption Gap closed Tidal disruption Gap closed

Super Earth planet formation

0.1 1.0 10.0 100.0 Separation and radii [AU]

Tidal disruption Gap closed Tidal disruption Gap closed Gap openned Gap openned

(a)

Hill’s radius, RH Radius, Rp Separation, a

100 200 300 400 500 600 time [103 years] 0.1 1.0 Core mass [MEarth ]

Total Core mass Rocks CHON

Nayakshin 2015c, subm.

20,000 planet formation experiments

Nayakshin & Fletcher, 2015, subm.

Planet Mass vs Separation

0.1 1.0 10.0 100.0 a [AU] 0.001 0.010 0.100 1.000 10.000 Mp [MJup] 1 10 100 1000 Mass [MEarth]

Zl > 0.25 0 < Zl < 0.25

• 0.25 < Zl < 0

Zl < -0.25 Zl > 0.25 0 < Zl < 0.25

• 0.25 < Zl < 0

Zl < -0.25

1/20 sample 1/20 sample 1/20 sample 1/20 sample 1/2 sample 1/2 sample

Planet Mass Function

• 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

N & Fletcher 2015 Planet disruption outcomes

• 1

1 2 3 4 log Planet mass, MEarth 500 1000 1500 Number of planets

Initial Fragments

(a)

All Metal rich Metal poor

Simulated Planets, a < 5 AU

1.0 1.5 2.0 2.5 3.0 3.5 4.0 100 200 300 Number of planets

No selection v* = 1 m/s selection

Tidal disruption desert

1 2 log Planet mass, MEarth

✤ 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)

z-correlations in Core Accretion

Metallicity Correlations

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

metallicity correlations

5 10 15 Radius of planet (R⊕) –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6 Metallicity

Buchhave et al (2012)

• 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

Mayor et al 2011

10.0 100.0 1000. −0.5 0.0

Fe/H [dex] M2sini [Earth Mass]

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

• At low z, most fragments are destroyed — few giants but lots
• f cores
• At high z, very few fragments are disrupted — few massive

cores

• Peak of massive core production — intermediate z

Simulated Planets, hot region

• 0.4
• 0.2

0.0 0.2 0.4 [Z/H] 0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 Frequency of planets 0.0 0.2 0.4 0.6 0.8 1.0 Cumulative Probability

Giants, moderate mass Super Earths

N & Fletcher 2015

Cores and low mass giants vs Zl

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 0.6 Zl 0.01 0.10 1.00 Fractional outcome

Giants, a = Rin Giants, Rin < a < 5 Super Earths All cores Giants, a = Rin Giants, Rin < a < 5 Super Earths All cores

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

[Fe/H] 0.6

• 0.6

Number of tidal disruptions with Mz > 0.1 Mj

Fletcher & N, in prep.

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

✤ Massive cores are luminous ✤ They puff up gas fragments ✤ The envelope is expelled by the core — exactly like the cores destroy Red Giant stars!

No cores

0.1 1.0 10.0 100.0 a [AU] 0.001 0.010 0.100 1.000 10.000 Mp [MJup] 1 10 100 1000 Mass [MEarth]

Zl > 0.25 0 < Zl < 0.25

• 0.25 < Zl < 0

Zl < -0.25 Zl > 0.25 0 < Zl < 0.25

• 0.25 < Zl < 0

Zl < -0.25

No cores

0.1 1.0 10.0 100.0 a [AU] 0.001 0.010 0.100 1.000 10.000 Mp [MJup] 1 10 100 1000

Zl > 0.25 0 < Zl < 0.25

• 0.25 < Zl < 0

Zl < -0.25 Zl > 0.25 0 < Zl < 0.25

• 0.25 < Zl < 0

Zl < -0.25

Cores allowed

Nayakshin, in prep.

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.

Massive cores are made at all separations, and rapidly

✤ It takes < 1Myr to make a massive core at any

separation in TD. Better than CA, pebbles or not.

• 1.0 -0.5

0.0 0.5 1.0 1.5 2.0 log a [AU] 50 100 150 200 Number of cores

Disruption Final Disruption Final

Core separation Core separation

5.0 5.5 6.0 6.5 7.0 log tdisr [yrs] 50 100 150 Number of cores

Disruption time Disruption time

Nayakshin, in prep.

✤ TD — a promising alternative to CA in every aspect

• f planet formation.

Conclusion

Additional slides

More results from N & Fletcher 2015

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 log a [AU]

100 200 300 400 500 600 Number of Earths

0.3 < Mp < 2 ME 0.3 < Mp < 2 ME All Zl > 0 Zl < 0 All Zl > 0 Zl < 0

(a)

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 log a [AU]

500 1000 1500 2000 Super Earths

2 < Mp < 15 ME 2 < Mp < 15 ME

• Obs. (Silburt et al)
• Obs. (Silburt et al)

(b)

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 log a [AU]

50 100 150 200 250 Giants

50 ME < Mp < 5 MJ 50 ME < Mp < 5 MJ

(c)

Obs. Obs.

• 1.0
• 0.5

0.0 0.5 1.0 log a [AU]

10 20 30 40 50 Giants

• Obs. x 0.1
• Obs. x 0.1

(d)

50 ME < Mp < 5 MJ 50 ME < Mp < 5 MJ

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 log a [AU]

10 20 30 40 50 Super Giants

Mp > 5 MJ Mp > 5 MJ

(e)

0.1 1.0 10.0 1 10 100

Planet to Star metallicity ratio

0.1 1.0 10.0 Mp [MJup] 1 10 100 Zpl/Zstar

Zl < -0.25

• 0.25 < Zl < 0

0 < Zl < 0.25 Zl > 0.25 Zl < -0.25

• 0.25 < Zl < 0

0 < Zl < 0.25 Zl > 0.25

✤ Observed planets are over-abundant in metals (Miller & Fortney 2011). ✤ GI clumps are disrupted too easily (Zhu et al 12, Vazan & Helled 12). ✤ Negative giant planet -- metallicity correlation is expected (Helled &

Bodenheimer 2011), but a positive one is observed (Fischer & Valenti 2005)

✤ Cores made inside GI fragments are < 1 M_Earth (Helled et al 2008).

Pebble accretion solves GI “problems”

dEp dt = −Lrad − GMp ˙ Mz Rp

Pebble accretion: game changer for TD

tz ∼ 5000 0.1 fpeb a3/2

100

years

✤ In CA, massive bodies (M > Lunar mass) accrete grains (pebbles) but not gas (Johansen

and Lacerda 10, Ormel & Klarh 10)

✤ Same must happen for molecular GI clumps (N 2015a,b). Gas accretion on low mass (M

< few Jupiter mass) clumps in outer discs is inefficient (N & Cha 2013).

✤ Grain accretion occurs in “Hills regime”,

where

dMz dt = zMp tz

GI planets contract when accreting pebbles

✤

Isolated GI clump, no grain growth. Metallicity z=const on the left, dz/ dt > 0 on the right

✤

z=const confirms Helled & Bodenhemier’s results

✤

But dz/dt > 0 planets contract faster than z=z_0 one!

2 4 6 8 10 12 time [kyr] 0.01 0.10 Planet metallicity (b) 100 1000 T [K] 2 4 6 8 10 12 (a)

2 ZSol 0.5 ZSol Z=ZSol

2 4 6 8 time [kyr] 0.01 0.10 Planet metallicity (d) 100 1000 T [K] 2 4 6 8 (c)

4000 2000 1000 500 tz=250 Z=ZSol

1.Nayakshin 2014b, subm.