#55 formation of close-in super-earths in evolving ... · #55 formation of close-in super-earths in...

#55 Formation of close-in super-Earths in evolving protoplanetary disks via disk windsMasahiro Ogihara1, Eiichiro Kokubo1, Takeru K. Suzuki2, Alessandro Morbidelli3

1 National Astronomical Observatory of Japan, 2 University of Tokyo, 3 Observatoire de la Côte d’Azur

3. Disk evolution 4. In situ formation from embryos in a disk evolving via disk winds(Suzuki, Ogihara, et al. 2016)

5. Resonant chain 6. A limit on gas accretion onto cores 7. Summary

• We focus on the period-ratio distribution of close-in super-Earths (SEs)

• Close-in SEs are generally not in mean-motion resonances (MMRs), which should be reproduced by simulation

❏ Results of N-body simulation • We perform N-body simulations in a power-law disk based on

MMSN• Accretion of SEs is quite rapid in the close-in region because of

high solid surface density• SEs undergo rapid migration in a power-law disk• SEs form in a compact configuration captured in MMRs• The system is stable even after gas depletion• Period-ratio distribution is not matched to observed distribution

@⌃

@t=

1

r

@

@r

⇢2

r⌦

@

@r(r2⌃↵c2s ) + r

2↵w

⌃p⇡H

c2s

��+ Cw

⌃p⇡H

cs

• Magnetically driven disk winds are observed in 3D-MHD simulations

(e.g., Suzuki & Inutsuka 2009, Fromang et al. 2013)

• Disk winds cause wind mass loss and wind-driven accretion

• Suzuki et al. (2016) derived global viscous disk evolution including disk winds by solving the diffusion equation

• Disk profiles can be altered from the power-law disk

❏ Results of N-body simulation • We perform N-body simulations from embryos in disk evolving via disk winds• Type I migration is significantly suppressed owing to small gas density and flat slope in the close-in region• No pileup near the disk inner edge is observed• Planets are captured in MMRs before the disk depletion, which is destroyed by the late orbital instability• Final orbits are not in MMRs, which is consistent with observed period-ratio distribution

• Some systems do not undergo late orbital instability

• Resonant chain can also form

• SE cores should undergo runaway gas accretion based on evolution models of a planetary atmosphere (e.g., Ikoma & Hori 2012)

• We propose that rapid radial accretion near the surface due to wind-driven accretion slips out of the core and regulates the gas supply onto the core

• Planets undergo rapid inward migration in a power-law disk

• Type I migration can be suppressed in a disk evolving via disk winds

• Close-in SEs form in a non-resonant configuration after late orbital instability

• Observed period-ratio distribution can be reproduced

• The gas accretion onto cores can be limited depending on the vertical structure of the radial gas accretion

(Ogihara et al. 2018)

Schematic picture of disk evolution

MHD simulation by Suzuki & Inutsuka (2009)

Evolution of gas surface density

Comparison of period-ratio distribution

Examples of systems with MMRs

Comparison of period-ratio distribution

0.01 0.1 1 10

103

100

10

1

0.1

Semi-Major Axis [Astronomical Units (AU)]

Plan

et M

ass

[Ear

th M

ass]

exoplanets.org | 6/27/2018

0 5

10 15 20 25 30

Num

ber

Period ratio (Pout/Pin) of adjacent pair

2:13:24:35:46:5

7:6

1 102 3 5

0 0.2 0.4 0.6 0.8

1

1 10

Cum

ulativ

e dis

tribu

tion

2:13:24:35:46:5

7:6

2 3 5Period ratio (Pout/Pin) of adjacent pair

0.1

1

103 104 105 106 107 108

Sem

imajo

r axis

(au)

Time (yr)

-2

-1.5

-1

-0.5

0

0.5

1

log(M/M

⊕)

5

0 0.2 0.4 0.6 0.8

1

1 10

Cum

ulativ

e dis

tribu

tion

2:13:24:35:46:5

7:6

2 3 5Period ratio (Pout/Pin) of adjacent pair

10-3

10-2

10-1 1000 yr

0.1 Myr

1 Myr

0.1 1

10 Myr

0.05

Radial distance (au)

Ecce

ntric

ity

Gas surface density (g cm-2)

103

104

105

10-3

10-2

10-1

103

104

105

10-3

10-2

10-1

103

104

105

10-3

10-2

10-1

103

104

105


Ecce

ntric

ity

Gas surface density (g cm-2)

100 Myr

1 Myr

100 yr10-3

10-2

10-1

10-210-1100101102103104105

10-3

10-2

10-1

10-210-1100101102103104105

10-3

10-2

10-1

0.1 110-210-1100101102103104105

viscousaccretion

wind-driven accretion

viscousaccretion

wind-driven accretion

wind mass loss

wind mass loss

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

10-210-1100101102103104105

0.01 0.1 1 10 100Gas s

urfa

ce d

ensit

y (g

cm-2

)


initial1Myr

10Myr

1.60 1.67 1.50(3:2)1.50(3:2)1.34(4:3)

1.25(5:4)1.33(4:3)

1.33(4:3) 1.50(3:2)1.33(4:3)

1.67 3:2 3:2 3:2

4:3 3:2 4:3 5:4

observation

simulation

1 10P/Pinnermost

TRAPPIST-1

Kepler-60

Kepler-223

model5-1

model6-1

model6-2

4:3 7:6

3:2 5:4 5:4 7:65:4 4:3

rz

Rapid gas flow due to wind-driven accretionmay slips out of the core

close-in super-Earths

rapid migration

MMRs stable after gas depletion

observation

10 runs of simulation

MMSN

late orbital instability

late orbital instability

results with Mtotal = 80 M⊕



blended results of 3 sets of simulations

1. Close-in super-Earths 2. In situ formation in a power-law disk (Ogihara, Morbidelli, Guillot 2015)

#55 formation of close-in super-earths in evolving ... · #55 formation of close-in super-earths in...

Documents