Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals...

Formation of planetesimals in evolving accretiondiscs

Bertram Bitsch

Lund Observatory

31.07.2014

Bertram Bitsch Formation of planetesimals in evolving accretion discs

Standard disc: MMSN

MMSN uses:

Spread appropriate mass of solids around the orbit of eachplanet and multiply by 100 (add gas)Power law through data (Weidenschilling, 1997; Hayashi,1981):

ΣG (r) = 1700( r

1AU

)−3/2g/cm2

MMSN assumptions:

The planets accreted all solids (hence ”Minimum”)The planets formed on their present orbits


Importance of the disc structure

Growth and formation of planetary cores relies on the discstructure:

Growth of dust particles to pebbles (Zsom et al., 2010;Birnstiel et al., 2012)

Movements of pebbles inside the gas disc (Brauer et al., 2008)

Formation of planetesimals via streaming instability (Johansen& Youdin, 2007)

Formation of planetary cores from embryos and planetesimals(Levison et al., 2010) or pebble accretion (Lambrechts &Johansen, 2012)

Migration of planetary cores in the disc (Ward, 1997;Paardekooper & Mellema, 2006; Kley et al., 2009)


In this talk:

What determines the disc structure?

Implications how to form planetesimals via the streaminginstability?

How does the disc evolve in time?


Disc Model

2D hydrodynamical disc model with viscous heating, radiativecooling and stellar irradiation with S ∝ L?(following Bitsch et al. 2013):

1 2 3 4 5 6 7 8 9

r [aJup]

0

0.5

1

1.5

2

2.5

3

z in [

aJu

p]

-13-12.5-12-11.5-11-10.5-10-9.5-9

log (

ρ in

g/c

m3 )

Mass flux through disc: M disc with constant α viscosity:

M = 3πνΣ = 3παH2ΩKΣ

Change of M-rate by changing Σ


Influence of opacity on cooling

Grey area marks transitionin opacity at the ice line

Cooling of the disc:

F = − λc

ρκR∇ER

Change of gradient inopacity:⇒ change of Cooling

Change of Temperature:bump in T (r)

log (

κ in c

m2/g

)

T in K

TransitionκR = κP

κ*-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

10 100 1000

Tin

K

r [AU]

TransitionM = 3.5× 10−8M⊙/yr

MMSN

50

200

500

1

10

100

2 3 4 5 201 10

Bitsch et al., 2014, in prep.


Influence of viscosity and M

Hydrostatic equilibrium:

T =

(H

r

)2 GM?

r

µ

R

bump in T : bump in H/r

M disc:


M constant at each r :⇒ dip in Σ

What does that imply for the for-mation of planetesimals?

Σin

g/cm

2

r [AU]

H/r

M = 3.5× 10−8M⊙/yrMMSN

50

200

500

10

100

1000

2 3 4 5 10 201

M = 3.5× 10−8M⊙/yrMMSN

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08



Streaming Instability

Gas orbits slightly slower than Keplerian

Particles loose angular momentum due to headwind

Particle clumps locally reduce headwind and are fed byisolated particles

Youdin and Goodman (2005): ”streaming instability”

Streaming instabilities feed on velocity difference between twocomponents (gas and particles) at the same location


Streaming instability in disc

Reduction of velocitiescaused by the effectivegravitational force by theradially outwards pointingforce of the radial pressuregradient:

∆ = ηvKcs

= −1

2

H

r

∂ ln(P)

∂ ln(r)

Reduced ∆ helps theformation of large clumpsvia streaming instability(Bai & Stone, 2010b)

∆

r [AU]

H/r

M = 3.5× 10−8M⊙/yrMMSN

0

0.02

0.04

0.06

0.08

0.1

0.12

2 3 4 5 10 201

M = 3.5× 10−8M⊙/yrMMSN

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

⇒ Planetesimal formation easier in shadowed regions of the disc!Bitsch et al., 2014, in prep.


Time evolution of the star and the disc

Accretion rate M changes with time (Hartmann et al., 1998)⇒ Accretion rate changes by a factor of 100 in 5Myr!

Star changes luminosity in time (Baraffe et al., 1998)⇒ Stellar luminosity changes by a factor of 3 in 5Myr!

0

0.5

1

1.5

2

2 50.1 1 10

10−9

5× 10−9

10−8

5× 10−8

10−7

Lin

L⊙

Min

M⊙/yr

t in Myr

LM

⇒ The disc is subject to massive changes in its lifetime!


Change of Mdot in timeT

inK

r [AU]

TransitionM = 1.0× 10−7

M = 7.0× 10−8

M = 3.5× 10−8

M = 1.75× 10−8

M = 8.75× 10−9

M = 4.375× 10−9

50

200

500

10

100

2 3 4 5 201 10

M decreases withdecreasing Σ


Inner disc dominated byviscous heating for high M,dominated by stellarheating for low M

ΣG

ing/cm

2

r [AU]

H/r

M = 1.0× 10−7

M = 7.0× 10−8

M = 3.5× 10−8

M = 1.75× 10−8

M = 8.75× 10−9

M = 4.375× 10−9

1

10

50

100

200

500

1000

2 3 4 5 10 201

M = 1.0× 10−7

M = 7.0× 10−8

M = 3.5× 10−8

M = 1.75× 10−8

M = 8.75× 10−9

M = 4.375× 10−9

0

0.01

0.02

0.03

0.04

0.05

0.06



Implications to planetesimal formation

∆ decreases with decreasingM, as H/r decreases:

∆ = ηvKcs

= −1

2

H

r

∂ ln(P)

∂ ln(r)

Planetesimal Formation:

Minimum of ∆ movesinwards as M decreases∆ fairly constant in outerdisc through all M stages

∆

r [AU]

H/r

M = 1.0× 10−7

M = 7.0× 10−8

M = 3.5× 10−8

M = 1.75× 10−8

M = 8.75× 10−9

M = 4.375× 10−9

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

2 3 4 5 10 201

M = 1.0× 10−7

M = 7.0× 10−8

M = 3.5× 10−8

M = 1.75× 10−8

M = 8.75× 10−9

M = 4.375× 10−9

0.01

0.02

0.03

0.04

0.05

0.06



Different regions of the disc: fit

Viscous heating dominated inner region

Stellar irradiated outer region

Shadowed middle region

Tin

K

r in AU

M = 3.5× 10−8

r−6/7

r−8/7

r−4/7

50

200

500

10

100

2 5 201 10

⇒ The upcoming paper will contain a 3-power law fit for thedisc structure as a function of the disc evolution time!


Summary

Realistic discs are not uniform power-laws, but show somebumps and dips caused by opacity transitions

Planetesimal formation is more likely in shadowed regions ofthe discs (minimum of H/r)

As M reduces in time, the shadowed regions shrink anddisappear in the late stages of the disc evolution

⇒ Formation of planetesimals and also planet migrationdepend on the evolutionary state of the disc!


Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals...

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