Planet Formation - PowerPoint Presentation

Slide1

Planet Formation

Topic:

Formation of

gas giant planets

Lecture by: C.P. DullemondSlide2

Two main theoriesGravitational instability of the gas diskCore accretion scenarioSlide3

Giant Planet Formation byGravitational InstabilitySlide4

Image: Quinn et al.

From: http://www.psc.edu/science/quinn.html

Gravitational fragmentation of a gas disk

From earlier chapters we

know that a disk with

Q<1 will fragment into

clumps.Slide5

Will a clump stay bound?The big discussion: Can a clump cool quickly enough to stay bound?

Let‘s take a clump of polytropic gas of radius R and squeeze it:

If gravity increases faster than the opposing pressure forces:

it will continue to collapse. Slide6

Will a clump stay bound?

Approximate relation between mass and density:

So the gravity wins out over pressure acceleration upon contraction if:

Since most astrophysical gases have γ>4/3 they will be stable

against gravitational collapse, UNLESS the gas cools (and thus

the gas deviates from the strictly polytropic EOS)!Slide7

Will a clump stay bound?But cooling timescale must be shorter than 1 orbit, otherwise a

clump of gas will be quickly dispersed again.

Let‘s calculate the cooling time of a gravitationally unstable (Q=1)

protoplanetary disk at radial coordinate

R

:Slide8

Will a clump stay bound?

In outer

disk: Can

fragment

and form

Gas GiantSlide9

Exoplanets: Direct imaging

HR 8799

Credit: Marois et al (2010)Slide10

Which mass planets will form?Since the disk muss be massive to become self-gravitating, theodds are, that the planet will be massive too:

But many clumps can form

a planet:

Typically more massive than Jupiter!

M

clump

M

planetSlide11

Giant Planet Formation byCore accretionSlide12

Core accretion main ideaFirst form a rocky planet (a „core“)As the rocky core‘s mass increases, it will attract a

hydrogen

atmosphere from the disk. A given core mass yields a given atmosphere thickness.

The core mass can grow when the core+atmosphere accretes planetesimals or pebbles and/or when the atmosphere can cool and thus shrink.

As the core‘s mass increases further, the

mass of the

atmosphere will grow faster than linear with core mass.

Eventually become similar to the core‘s mass, so the additional mass of the gas will attract new gas, which will attract further gas etc: runaway gas accretion!Slide13

Attracting a hydrogen atmosphereSmallest core mass to attract a hydrogen atmosphere:

Bondi radius is the radius from the

planet (core) at which the escape

speed equals the sound speed of the gas

If R

Bondi

< R

core

, then no atmosphere can be kept bound to the

core.

Typically: 10

-3

...10

-2

M

earthSlide14

Atmosphere structureThe equations for the atmosphere are very similar to those forstellar structure, just with a fixed core mass added:

If the atmosphere is thick enough, and if it is continuously

bombarded with planetesimals (=heating), then to good

approximation it can be regarded as adiabatic:

Outer boundary: R=R

Bondi

. Boundary condition: density

and temperature equal to disk density and temperature.Slide15

Atmosphere structure

From: Bachelor thesis

Gianni Klesse

Varying the

mass of the

coreSlide16

Atmosphere structureFrom: Bachelor thesisGianni Klesse

Varying the rate

of accretion of

pebbles and/or

planetesimalsSlide17

Formation

of

a Gas Giant Planet

Original: Pollack et al. 1996;

Here

:

Mordasini

,

Alibert

,

Klahr

& Henning 2012

Total

Gas

SolidsSlide18

Formation

of

a Gas Giant Planet

Original: Pollack et al. 1996;

Here

:

Mordasini

,

Alibert

,

Klahr

& Henning 2012

G

rowth by accretion of planetesimals until

the local supply

runs out (isolation

mass).

Total

Gas

SolidsSlide19

Formation

of

a Gas Giant Planet

Original: Pollack et al. 1996;

Here

:

Mordasini

,

Alibert

,

Klahr

& Henning 2012

Total

Gas

Solids

Slow

accretion

of

gas (

slow

,

because

the

gas must

radiatively

cool

,

before

new

gas

can

be

added

).

Speed

is

limited

by

opacities

.

The

added

gas

increases

the

mass

,

and

thereby

the

size

of

the

feeding

zone

.

Hence

: New

solids

are

accreted

.

If

planet

migrates

,

it

can

sweep

up

more

solids

,

accellerating

this

phase

.Slide20

Formation

of

a Gas Giant Planet

Original: Pollack et al. 1996;

Here

:

Mordasini

,

Alibert

,

Klahr

& Henning 2012

Once

Mgas > Msolid, the core

instability sets in: accelerating

accretion of

more and more

gas

Total

Gas

SolidsSlide21

Formation

of

a Gas Giant Planet

Original: Pollack et al. 1996;

Here

:

Mordasini

,

Alibert

,

Klahr

& Henning 2012

A

hydrostatic envelope smoothly connecting core

with disk no longer

exists. Planet

envelope detaches from

the disk

.

Total

Gas

SolidsSlide22

Formation

of

a Gas Giant Planet

Original: Pollack et al. 1996;

Here

:

Mordasini

,

Alibert

,

Klahr

& Henning 2012

Something

ends the gas accretion phase, for example: strong

gap opening. „Normal“ planet evolution

starts.

Total

Gas

SolidsSlide23

Population synthesisPut

this

model

into

varying

disks

,

at varying positions (Monte Carlo)Allow the planet to migrate

(which means, incidently

, that it can sweep up more solids than before) Obtain a statistical

sample of exoplanets and compare

to observed

statistics.East-Asian Models: Ida & Lin

Toward

a Deterministic Model of Planetary Formation I...VI (2004...2010)

Bern Models:

Mordasini

,

Alibert

, Benz et al.

Extrasolar

planet

population

synthesis

I...IV

(2009...2012)

Kornet

et al. (2001...2005), Robinson et al. (2006)

Thommes

et al. (2008) [multi-planet:

with

full

N-body]Slide24

Predicted initial mass function

Mordasini

,

Alibert

, Benz &

Naef

2009

Runaway

gas

accretion

„

Failed

cores

“

Gas

giants

Ice

giants

G

rowth

by

accretion

of

planetesimals

until

the

local

supply

runs

out (

isolation

mass

).

Note:

effect

caused

by

reduced

type I

migration

rate.

Once

the

faster

type II

migration

sets

in,

the

core

can

sweep

up

fresh

material

from

further

inwardSlide25

Lots of added complexitiesAccretion of gas onto GP is a complex 3-D problem

Lubow, Seibert & Artymowics (1999)