formation of planetesimals in evolving accretion discs · bertram bitsch formation of planetesimals...
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Formation of planetesimals in evolving accretiondiscs
Bertram Bitsch
Lund Observatory
31.07.2014
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 2: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/2.jpg)
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
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 3: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/3.jpg)
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
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 4: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/4.jpg)
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)
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 5: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/5.jpg)
In this talk:
What determines the disc structure?
Implications how to form planetesimals via the streaminginstability?
How does the disc evolve in time?
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 6: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/6.jpg)
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
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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.
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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 = 3πνΣ = 3παH2ΩKΣ
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
Bitsch et al., 2014, in prep.
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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.
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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!
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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
M = 3πνΣ = 3παH2ΩKΣ
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
Bitsch et al., 2014, in prep.
Bertram Bitsch Formation of planetesimals in evolving accretion discs
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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
Bitsch et al., 2014, in prep.
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 14: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/14.jpg)
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!
Bertram Bitsch Formation of planetesimals in evolving accretion discs
![Page 15: Formation of planetesimals in evolving accretion discs · Bertram Bitsch Formation of planetesimals in evolving accretion discs. Time evolution of the star and the disc Accretion](https://reader033.vdocuments.mx/reader033/viewer/2022041813/5e59692dcbc0054368478b11/html5/thumbnails/15.jpg)
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!
Bertram Bitsch Formation of planetesimals in evolving accretion discs