Planet Formation with Different Gas Depletion Timescales:Comparing with Observations

Huigen Liu, Ji-lin Zhou, Su Wanghuigen@nju.edu.cnDept. of AstronomyNanjing University

Nanjing 210093, China

Previous works:Core accretion scenario, Monte Carlo Method:Peering works:

Ida & Lin 2004a,2004b ， 2005 ， 2008

Albert et al. 2005a ， 2005b

Recent work: Mordasini et al. 2009

Only a-M diagram. Lack of gravitation between planets.

No information of eccentricity

Adding N-body interaction,

focus on the influence of disk

Outline: 1.Model

disk model Core accretion scenario initial conditions

2.Corelations with gas depletion timescale Eccentricity of planets hot or not hot Mass of planets

3.Comparing with observations Statistics of a, e, M deserts and peaks

4.Conclusion and discussion

Model: Modified MMNM: 2D, -disk

Choose an index -1 (K.R.Bell et al. 1997).

MRI effect: (Gammie 1996)Accumulation of small planets outside

The snow line: (Kennedy & Kenyon 2008)

Gravitational instability:

/2 1/ 2 1*4

280 ( )( ) ( )10 1

diskeff tg g

M agcm f e

M AU

0.1 1 10

0.26

10

100

1000

=--1

g(g

/cm2 )

a(AU)a

crit

=-1.5

(b)

0.1 1 10

10-4

10-3

10-2

DeadZone

eff

a(AU)a

crit

MRI

dead

activezone

(a)

0 exp( )disk

tM M

AUawhileG

CQ

g

Ks 1001

4/9crita M

crita

Gas accretion scenario: similar with Ida & Lin 2004

Critical mass (onset of gas accretion):

Gas accretion rate:(considering the replenishment of materials)

Asymptotic Mass:

4critM M

)1(,)()1

(120 2/1*4/3, hrM

M

M

AU

aM Hthg

),)(10min( 149disk

cc MyrM

M

MM

M/M

Eae

thT

onset of gas accretion

Asymptotic mass

Collision growth

Migrations:Type I: (Cresswell & Nelson 2006)

Scaling factor: C1=0.3

Outward if

Type II :(Albert et al. 2005)

a braking phase, inward only

Critical mass for gap-opening: (Armitage & Rice 2005)

Tidal damp of gas disk :Low mass: Cresswell & Nelson 2006

Others: Lee & Peale 2002

M

MaM

a

hM Star

p 5.7)( *22/1

2.7 1.1 0 0.1 1 10

-30

-25

-20

-15

-10

-5

0

5

a(AU)

2.7+1.1=0

2.7+1.1

migrate outward

damp

(log ) / (log )gd d r

Initial conditions:40 embryos >0.1MEarth

Location: 0.5~13AU(Zhou et al. 2007)

Uniform:Haischi et al. 2001:

Other parameters:

gas disk: 0.05-100AU:remove planets: a<0.04AU or a>100AU

20 runs for each220 runs totally Stop time: 10Myr

0.5 10

a(AU) aice

a~10RH

small embryos

The initial condition of our model:

icegdSung MMf 03.0/,1*,1

log( )disk

Myr

disk5~5.0:

disk

Corelations with

1 2 3 4 5 6 7100

200

300

400

1 52.5

3.0

3.5

4.0

4.5

0.5 1 1 3

1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

1 5

0.12

0.16

0.20

0.5 11 3

(d)

Mmean

=407.3*(0.85)Nleft

Mm

ean

Nleft

(b)

disk

(Myr)

Nm

ean

(c)

e mea

n

Nleft

emean

=0.65*(0.67)Nleft

e mea

n

disk

(Myr)

(a)

disk

meaneCorrelation between and disk

Eccentricity of planets: Damped before gas disk depletion

Smaller gas depleted fast larger e Excited via N-body interaction

scattering, resonance. Hill instability: ,

Due to different type I migration rates:

Hill instability: (Sensitive to C1)

Corresponding with the minimum e.

Correlations:

and : possibility of collisions

and : on average

)/exp()(/10 6disk

p tM

MyrAU

dt

ad

2 3 Ha R

disk

~ 2crit

Myr

meanMmeane leftN

leftN

Correlation between and

Hot or not hot?

Hot: period=1~20 day

Hot Earth:Come out:

Proportion: Ascending (Type I migration)

Decreasing (scattered)

Hot Jupiter: Come out:

Proportion: Ascending

(sufficient type II migration)

meana diskdecrease with

1 51

2

3

4

5

6

1 30.5 1

disk

(Myr)

a mea

n(AU

)

(a)

1 5

0.00

0.05

0.10

0.15

0.20

0.25

Hot-Earth Hot-Jupiter

pro

po

rtio

n

disk

(Myr)2 0.5

(b)

Myr2.1disk

Myr6.1disk

meana disk

10M

50M

1 50

100

200

300

400

0.5 11 3

disk

(Myr)

Mmean M

1

Mm

ean/M

Ear

th

(a)

)()1,min( ,1 meanisoggrow

disk aMM

diskCorrelation between and

Growth timescale:

For small :

gas depleted before

Insufficient gas accretion

meanM

grow

grow

1 50

2

4

6

1 30.5 1

grow

disk

disk

(Myr)

grow

(Myr

)

grow

disk

( b)

disk

is evaluated by gas accretion rategrow

),)(10min( 149disk

cc MyrM

M

MM

0.01 0.1 1

0.0

0.2

0.4

0.6

0.8

1.0

Vr>3m/s

Vr<3m/s

e

M/MJ

(b)

0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

e

Msin(i)/MJ

(a)

pdampM

Comparing with observations:M-e diagram: Assuming Vr < 3m/s: undetectableRV limited

Maximum e:

Observations: ~0.9 (single) ~0.67(multiple)

Simulations: ~0.88

Moderate mass:Larger M larger dispersion of e

Larger dispersion for small planets: scattering

0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

Vr>=3m/s

Vr<3m/s

e

a(AU)

a(1-e)=5Rsun

a(1-e)=10Rsun

(b) desert？

disk

pdampa

a-e diagram:

For outer planets,

Larger a larger M

larger dispersion of e

Few a~10AU and e>0.4:

a desert?

Scattering: Large e when a>10AU

Materials of Neptune and Uranus

0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

a(1-e)=5Rsun

a(1-e)=10Rsun

e

a(AU)

(a)

0.1 1 10

1

10

100

1000

Mg,iso

Vr=1m/s

Vr=10m/s

M/M

Ear

th

a(AU)

(b)

a-M diagram

RV limit：

<3m/s 21.7%, <1m/s 15.5%

Smaller mass in simulations:

No distribution of fg (0.25~5)

Comparing with Mordasini et al. 20090.01 0.1 1 10

1

10

100

1000

10000

1m/s

10m/s

Msi

ni/M

Ear

th

a(AU)

(a)

Peaks:1: inner boundary2: MRI effect3: Type II migration4: insufficient gas accretion

collision growth 5: Asymptotic Mass

Deserts: i, ii: peak 1, 2iii: onset of gas accretioniv: runaway gas accretion

0.04 0.1 1 100

20

40

60

80

N

<3m/s >3m/s

(b) 3

2

a(AU)

1

0.01 0.1 1 100

20

40

60

N

M/MJ

(c) 5

4

1E-3 0.01 0.1 10

40

80

120

160

N

<3m/s >3m/s

(a)

4

5

M/MJ

0.0 0.2 0.4 0.6 0.8 1.00

40

80

120 (e)

N

e0.0 0.2 0.4 0.6 0.80

100

200

300

400 (f) <3m/s >3m/s

Ne

0.016 0.1 1 100

20

40

60

N

a(AU)

(a) 3

2

1

i iii

iii

iv

iii iv

iii

Peaks and deserts

Cumulative distribution function (CDF):Observations:

e=0 (unkown)

More massiveScaling factor fg

Few planets with a>6AU0.1 1 10

0.00.20.40.60.81.0

0.01 0.1 1 10

0.00.20.40.60.81.0

0.0 0.2 0.4 0.6 0.8 1.0

0.00.20.40.60.81.0

(c)

CD

F

a(AU)

simulationsobservations

(b) simulationsobservations

CD

F

M/MJ

CD

F

e

simulationsobservations

(a)

Conclusions: Reproduce the distribution of eccentricity The influence of (a, e, M) Proportion of Hot-Earth and Hot-Jupiter Deserts and peaks of a, M Indicate the of our solar systems for different Type I migration rates

consistent with the result from geochemistry

2 ~ 3solar Myr

disk

disk

3solar Myr

Discussion: Excluded effects:

Gravitation of gas disk.

tidal damp of host star

Dynamical friction of small planetesimalsDamp of e, difficulty: time costing ， uncertain model

Comparing with observations:Distribution of

Uncertainty of initial conditions:a, M of embryos.

, ,[ / ]g diskf M Fe H

The EndThank You!

North Building

Symbol of Nanjing University

email: huigen@nju.edu.cn

105 106 1070.0

0.1

0.2

0.3

a(A

U)

T(yr)

disk

=0.5Myr

disk

=1Myr

disk

=2Myr

disk

=5Myr

crita

disk)exp(0

dept

tMM 9/4

18)

10(

yrM

Macrit

Peaks around 0.2AU due to MRI effect

inward migration of with differentcrita

Halting round ~0.2AU：

small planets (Type I migration)

Larger

unconspicuous

Not found in observations

disk

Back

Peak around 5 AU:

Type II migration of giantsBraking phase,

Less massive planets with larger inner position

The final position of giants: 1~10AU duo to different

MMAUa p 100,70

disk

0 2 4 6 8 102

4

6

8

2

4

6

8

a(A

U)

t(Myr)

disk

=0.5Myr

disk

=1Myr

disk

=5Myr)/exp()1(2

107

2

5,

diskp

g

IImig

tM

AU

yr

a

dt

da

0 , ,p diska M

Back

diskM

disk

~ 20M M

0.0 2.0x106 4.0x106 6.0x106 8.0x106 1.0x107

5

10

15

20

M/M

Ear

th

T

0.0 2.0x106 4.0x106 6.0x106 8.0x106 1.0x107

0

5

10

15

20

25

30

M/M

Eae

th

TBack

Gas accretion growth for small

Gas depleted too fast, limited by

replenishment of materials

Collision growth for large

Migrate to inner range, limited by small asymptotic mass

Example for Myrdisk 5.0

Peak at

Example for

disk

Myrdisk 5