FORMATION OF CLOSE-IN PLANETS IN AN EVOLVING DISC WITH N-BODY SIMULATIONS

Masahiro Ogihara (National Astronomical Observatory of Japan)

Eiichiro Kokubo (NAOJ), Takeru Suzuki (Univ. Tokyo), Alessandro Morbidelli (OCA)

Acknowledgments:

seealsoOgiharaetal.(2018,A&A)

1

Masahiro Ogihara (NAOJ) / 14

Barrier in planet formation: Type I migration

0.3 M⊕

�2

(Suzuki et al.)

1 M⊕

5 M⊕

r (au

) 1

0.1

10

t (Myr)0.1 1 10

Rapid migration may cause several problems

Masahiro Ogihara (NAOJ) / 14

Key questions in this talk

�3

Q1: Is type I migration really problematic in close-in super-Earth formation?

Q2: If so, how can we overcome the migration problem?

Masahiro Ogihara (NAOJ) / 14

Close-in super-Earths

�4

Close-in super-Earths ・2401 planets (confirmed)

Multiple close-in super-Earth systems (N≧2) ・432 systems ・1082 planets (confirmed)

Mas

s (Ea

rth M

ass)

as of Aug. 2017

Masahiro Ogihara (NAOJ) / 14

Formation of super-Earths in a power-law disc

0.1

1

10

100

0.01 0.1 1

Mas

s (M

Earth

)

Semimajor Axis (AU)

(b)

0.1

1

10

100

0.01 0.1 1

Mas

s (M

Earth

)

Semimajor Axis (AU)

(a)

10-3

10-2

10-1

103

104

105103 yr

10-3

10-2

10-1

103

104

105104 yr

10-3

10-2

10-1

103

104

105105 yr

10-3

10-2

10-1

103

104

105106 yr

10-3

10-2

10-1

0.1 1103

104

105

Semimajor Axis (AU)

107 yr

Ecce

ntric

ity

Gas Surface D

ensity (g cm-2)

0.05 0.3

10-3

10-2

10-1

103

104

105103 yr

10-3

10-2

10-1

103

104

105104 yr

10-3

10-2

10-1

103

104

105105 yr

10-3

10-2

10-1

103

104

105106 yr

10-3

10-2

10-1

0.1 1103

104

105

Semimajor Axis (AU)

107 yr

Ecce

ntric

ity

Gas Surface D

ensity (g cm-2)

0.05 0.3

tacc ⇠ 103✓

⌃d

150 g/cm3

◆�1 ⇣ a

0.3 au

⌘27/10✓

M

M�

◆1/3

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inner edge MMSN

10 simulations observation

short growth timescale ↓ rapid type I migration

Mtot = 50 M⊕

pileup at disc edge

�5

(Ogihara, Morbidelli, Guillot 2015)

tmig~104yr

Masahiro Ogihara (NAOJ) / 14

2:13:24:35:4

6:5

Formation of super-Earths in a power-law disc

・observation: not in MMRs (mean motion resonances)・simulation: compact systems in MMRs (←rapid inward migration)

�6

observation

results of 10 runs of simulations

0 5

10 15 20 25 30

Num

ber

Period ratio (Pout/Pin) of adjacent pair

1 102 3 5

Masahiro Ogihara (NAOJ) / 14

Key questions in this talk

�7

Q1: Is type I migration really problematic in close-in super-Earth formation?

Q2: If so, how can we overcome the migration problem?

Yes. Due to rapid inward migration, results of simulations are inconsistent with observed distributions (e.g., period ratio).

Disc model.

Masahiro Ogihara (NAOJ) / 14

Disc evolution including disc winds

@⌃

@t=

1

r

@

@r

⇢2

r⌦

@

@r(r2⌃↵c2s ) + r

2↵w

⌃p⇡H

c2s

��+ Cw

⌃p⇡H

cs

viscous accretion(turbulence-driven)

wind-driven accretion(magnetic braking)

wind mass loss

MHD simulation (by T. Suzuki; X. Bai)

viscousaccretion

wind-driven accretion

wind mass loss

disc profiles can be altered from MMSN (r < 1 au) ・flat surface density slope ・decrease in density

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10MyrMMSN

type I migration would change

(Suzuki, Ogihara, Morbidelli et al. 2016)

�8

Masahiro Ogihara (NAOJ) / 14

Formation of super-Earths including disc winds

Planets do not undergo significant migration

(Ogihara, Kokubo, Suzuki, Morbidelli 2018)

�9

initial total mass: Mtot = 40 M⊕

Masahiro Ogihara (NAOJ) / 14

Formation of super-Earths including disc winds

FORMATION PROCESSES

MMR chaingas dissipation

late orbital instability

not in mean-motion resonances

・instability→giant impacts

・gas dissipation (~a few Myr)

・slow migration → formation of MMRs

�10

(Ogihara, Kokubo, Suzuki, Morbidelli 2018)

Masahiro Ogihara (NAOJ) / 14

Formation of super-Earths including disc winds

Mtot = 40 M⊕Mtot = 20 M⊕ Mtot = 80 M⊕

0 0.2 0.4 0.6 0.8

1

1 10

Cum

ulativ

e dis

tribu

tion

Period ratio

2:13:24:35:46:5

7:6

2 3 5(10 simulations each)

0 0.2 0.4 0.6 0.8

1

1 10

Cum

ulativ

e dis

tribu

tion

Period ratio

2:13:24:35:46:5

7:6

2 3 5 0

0.2 0.4 0.6 0.8

1

1 10

Cum

ulativ

e dis

tribu

tion

Period ratio

2:13:24:35:46:5

7:6

2 3 5

�11

(Ogihara, Kokubo, Suzuki, Morbidelli 2018)

Observed distribution can be reproduced when the migration is slow

Masahiro Ogihara (NAOJ) / 14

Key questions in this talk

�12

Q1: Is type I migration really problematic in close-in super-Earth formation?

Q2: If so, how can we overcome the migration problem?

Yes. Due to rapid inward migration, results of simulations are inconsistent with observed distributions (e.g., period ratio).

Type I migration can be slowed down if the disc is depleted (→slope, Σg) in the close-in region

Masahiro Ogihara (NAOJ) / 14

Comment on different approach

�13

10−1

100

105 106 107

Sem

imaj

or a

xis

(au)

Time (yr)

/Users/ogihara/home/m000/run−Aug18/run459/fig

10−2

10−1

100

101

102

103

105 106 107

Mco

re (M

Earth

)

Time (yr)

/Users/ogihara/home/m000/run−Aug18/run459/fig

101

102

103

104

105

0.01 0.1 1 10 100

Σ g (g

cm-2

)

r (au)

initial0.1Myr

1Myr

❏ Model・disc model (Bitsch et al. 2015)

・initial total solid: 1M⊕・pebble accretion

Slow migration is favored

・Slow migration (~Myr)・Planets reach SE-mass in the late phase・Planets are not in MMRs

(see also Lambrechts et al. 2019)

Masahiro Ogihara (NAOJ) / 14

Summary

❏ N-body simulations of formation of close-in super-Earths

❏ Rapid type I migration results in compact systems in MMRs

❏ If the gas density is depleted in the close-in region (e.g., Suzuki et al. 2016), type I migration can be slowed down

❏ Observed properties of close-in super-Earths can be reproduced (ie, not in MMRs)

0 0.2 0.4 0.6 0.8

1

1 10Cu

mula

tive

distri

butio

nPeriod ratio

2:13:24:35:46:5

7:6

2 3 510-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)

Radial distance (au)

initial1Myr

10Myr

�14

seealsoOgiharaetal.(2018,A&A)