planetesimal accretion in binary systems
DESCRIPTION
Planetesimal Accretion in Binary Systems. Philippe Thébault Stockholm/Paris Observatory(ies). Marzari, Scholl,2000, ApJ Thébault, Marzari, Scholl, 2002, A&A Thébault, Marzari, Scholl,Turrini, Barbieri, 2004, A&A Thébault, Marzari, Scholl, 2006, Icarus - PowerPoint PPT PresentationTRANSCRIPT
Planetesimal Accretion inBinary Systems
Philippe Thébault
Stockholm/Paris Observatory(ies)
•Marzari, Scholl,2000, ApJ•Thébault, Marzari, Scholl, 2002, A&A•Thébault, Marzari, Scholl,Turrini, Barbieri, 2004, A&A•Thébault, Marzari, Scholl, 2006, Icarus •Marzari, Thebault, Kortenkamp, Scholl, 2007 (« planets in binaries » book chapter)•Scholl, Thébault, Marzari, 2007, Icarus (to be submitted)
Extrasolar planets in Binary systems
(Udry et al., 2004)HD 188753 12.6 0.04 1.14 0.0 (Konaki, 2005)
~40 planets in binaries (jan.2007)
(Desidera & Barbieri, 2007)
(Raghavan et al., 2006)
Extrasolar planets in Binary systems
Gliese 86
HD 41004A
γ Cephei
Companion star
Planet M mini. : 1,7 MJupiter, a=2,13AU e=0,2
M : 0,25 Mprimary, a=18,5 AU.e=0,36
The -Cephei system
Extrasolar planets in Binary systems
~23% of detected extrasolar planets in multiple systems
But...
~2-3% (3-4 systems) in binaries with ab<30AU
(Raghavan et al., 2006, Desidera&Barbieri, 2007)
Statistical analysisAre planets-in-binaries different?
short period planets
long period planets
all planets•Zucker & Mazeh, 2002•Eggenberger et al., 2004•Desidera&Barbieri, 2007
Only correlation (?): more massive planets on short-period orbits around close-in (<75AU) binaries
Long-term stability analysis
22 20.015.059.063.038.046.0 bbbbb
crit eeeea
a
(Holman&Wiegert, 1999)
Q: In which regions of a given (ab, eb, mb) binary system can a (Earth-like) planet survive for ~109years ?
A:
(David et al., 2003)
Long-term stability analysis
Estimating the ejection timescale
Long-term stability analysis
(Fatuzzo et al., 2006)
Role of mutual inclinations
Long-term stability analysis
(Mudryk & Wu., 2006)
Physical mechansim for orbital ejection:
overlapping resonances
μ=1
eb=0μ=0.5
eb=0
μ=0.5
eb=0.3
μ=0.1
eb=0.7
Stability regions, a few examples…
Statistical distribution of binary systems
(Duquennoy&Mayor, 1991)
a0 ~30 AU ~50% binaries wide enough for stable Earths on S-type orbits
~10% close enough for stable Earths on P-type orbits
Stability analysis for γ Cephei
(Dvorak et al. 2003)
The « standard » model of planetary formation to what extent is it affected by binarity?
•Step by Step scenario:
2-Grain condensation
3-formation of planetesimals
4-Planetesimal accretion
5-Embryo accretion (Quintana 2004, Lissauer et al.2004,Quintana&Lissauer, 2006,…)
1-protoplanetary disc formation (Artymowicz&Lubow 1994, Pichardo et al.2005)
√
√√√√
xx
6-Later evolution, resonances, migration: (Wu&Murray 2003, Takeda&Rasio 2006,…)
√
Cloud collapse & disc formation
Tidal truncation of a circumstellar disc
(1994)
Protoplanetary discs in binaries
Depletion of mm-flux for binaries with 1<a<50AU(Jensen et al., 1996)
model fit with Rdisc<0.4ab
model fit with Rdisc<0.2ab
(Andrews & Williams, 2005)
Fondamental limit 1 : T ~ 1350°K condensation of silicates
Fondamental limit 2: T ~ 160°K condensation of water-ice
A protoplanetary disc
From grains to planetesimals…a miracle occurs
In a « quiet » disc: gravitational instabilities
In a turbulent disc: mutual sticking
In any case: formation of~ 1 km objects
Formation of a dense dust mid-plane: instability occurs when Toomre parameter Q = kcd/(Gd)<1
Crucial parameter: Δv, imposed by particle/gas interactions.2 components:- Δv differential vertical/radial drift- Δv due to turbulence•Small grains (μm-cm) are coupled to turbulent eddies of all sizes: Δv~0.1-1cm/s•Big grains (cm-m) decouple from the gas and turbulence, and Δvmax~10-50m/s for 1m bodies
Formation of planetesimals from dust…
gravitational instability
Concurent scenarios: pros and cons
- Requires extremely low turbulence and/or abundance enhancement of solids
Turbulence-induced sticking
- Particles with 1mm<R<10m might be broken up by dV>10-50m/s impacts
fierce debate going on…
Mutual planetesimal accretion: a tricky situation
high-e orbits: high encounter rate but
fragmentation instead of accretion
low-e orbits: low encounter rate but always accretion
Accretion criterion: dV<C.Vesc.
Planetesimal accretion
Runaway growth:astrophysical Darwinism
gravitational focusing factor: (vesc(R)/v)2
If v~ vesc(r) then things get out of hand…=> Runaway growth
2)2,1(2221 12 v
vRR RResc
Oligarchic growth
(Kokubo, 2004)
CRUCIAL PARAMETER:
ENCOUNTER VELOCITY DISTRIBUTION
•dV < Vesc => runaway accretion
•Vesc< dV < Verosion => accretion (non-runaway)
•Verosion < dV => erosion/no-accretion
Some figures to keep in mind
Accretion if V < k. Vescape
IF isotropic distribution : V ~ C.(e2 + i2)1/2 Vkeplerian
Vesc(R=5km) ~ 7 m.s-1 e ~ 0.0003 (!!!)Vesc(R=100km) ~ 150 m.s-1 e ~ 0.006 (!!)Vesc(R=500km) ~ 750 m.s-1 e ~ 0.03 (!)
For a body at 1AU of a solar-type star
It doesn’t take much to stop planetesimal accretion
Dynamical effect of a close-in stellar companion
Large e-oscillations
High dV??
M2=0.5M1 e2=0.3 a2=20AU
Orbital phasing => V C.(e2 + i2)1/2 VKep
Our numerical approach
Gravitational problem: analytical derivation
orbital crossing ac as a function of M2,e2,a2,tcross
Gas drag influence: numerical runs
simplified gas friction modelisation
differential orbital phasing effects
dV(R1,R2) as a function of a2,e2
interpret dV(R1,R2) in terms of accretion/erosion
=> Collision Outcome Prescriptions
(Davis et al., Housen&Holsapple, Benz et al.)
!!! Time Scales & Initial Conditions !!!
A typical example
revising the Secular Theory approximation
10% within accurate 2sin - 125
2
2
2
tu
ee
aae
• eccentricity oscillations (e0=0)
y)discrepenc 70% to (up unaccutare 1
1 23
32
2/3
2/322
2 aa
eMu
• oscillation frequency
2
232
2
232
2/3
2/322
2 132 1 11 2
3aa
eM
aa
eMu
analytical derivation of ac
•Orbital crossing occurs when phasing gradient becomes too strong within one wave
taaCa
aaC 1 4
22
2
2
2/11
322
22
222/52
2
21 13
224 1132
45 withe
MCa
MeeC
Accuracy of the analytical expression
eb=0.1
eb=0.3
eb=0.5
Results
M2=0.5M1 e2=0.5
Time dependancy
yrsAUa
AUa
Mm
eetcr
7.23.42
1.1
*
2
2
75.2222
1111104.3
Reaching a general empirical expression
AUyrt
AUa
Mm
eeacr
36.053.12
39.0
*
236.0
2
07.122
111130.0
Effect of gas drag
No Gas With Gas
Effect of gas drag
relreldgazg vvR
CF
83 -
•Modelisation
•Gas density profile: axisymmetric disc (??!!)
390
75.2
0g
.x104.1 1 :81)Hayashi(19 M.M.S.N
AU
cmg
a
•Planetesimal sizes
- « small planetesimals » run: 1<R<10km- « big planetesimals » run: 10<R<50km
N~104 particles
5km planetesimals1km planetesimals
Differential orbital alignement between objects of different sizes
typical gas drag run
dV increase!
Encounter velocity evolution between different
Target-Projectile pairs R1/R2
typical gas drag run
Orbital crossing occurrence in gas free case
Average dV for 0<t<2.104yrs
« Small » planetesimals
Average dV for 0<t<2.104yrs
« Big » planetesimals
Typical highly perturbed configuration:Mb=0.5 / ab=10AU / eb=0.3
Benz&Asphaug, 1999
Critical Fragmentation EnergyContradicting esimates
Typical moderately perturbed configuration:Mb=0.5 / ab=20AU / eb=0.4
Average dV for 0<t<2.104yrs
« Small » planetesimals
Average dV for 0<t<2.104yrs
« Big » planetesimals
Average dV(R1,R2) for 0<t<2.104yrs
« Small » Planetesimals: R1=2.5 km & R2=5 km
limit accretion/erosion
Unperturbed runaway
Type II runaway (?)
M2=0.5 M1
No accretion
Average dV(R1,R2) for 0<t<2.104yrs
« Big » Planetesimals: R1=15 km & R2=50 km
limit accretion/erosionOrbital crossing
M2=0.5 M1
Unperturbed runaway
Type II runaway (?)
M2=0.5 M1
No Accretion
so what?
•Gas drag increases dV for R1≠R2 pairs=> Friction works against accretion in « real »
systems
•For <10 km planetesimals: accretion inhibition for large fraction of the (a2,e2) space, type II runaway otherwise (?)
•For 10<R<50 km planetesimals: type II runaway (?) for most of the cases
is all of this too simple?
•Assume e=0 initially for all planetesimals bodies begin to « feel » perurbations at the same time tpl.form < trunaway & tpl.form < tsecular
how do planetesimals form??Progressive sticking or Gravitational instabiliies?
•Time scale for Runaway/Oligarchic growth?
• Phony gas drag modelisation?
• Migration of the planet? Can only make things worse
•Different initial configuration for the binary?
<e0> = 0
<e0> = eforced
100% orbital dephasing
What if all planetesimals do not « appear » at the same time?
Ciecielag (2005-?)
Gas streamlines in a binary system: Spiral waves!
Coupled dust-gas model
Effect of mutual collisions (« bouncing balls » model}
forced and proper eccentricities
Detection of debris discs in binaries
Trilling et al. (2007)