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
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
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
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
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
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
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
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
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
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
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
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
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
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
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