Transcript Numerical modelling of Debris Discs

« Debris » discs
A crash course in numerical
methods
Philippe Thébault
Paris Observatory/Stockholm Observatory
« debris disc », what are they?
•Definition (Lagrange et al., 2000)
• Around Main Sequence Stars
• Ldust/L*<<1
• M(dust+gas)<0.01M*
• Mgas<<10Mdust (dust dynamics not controled by gas)
• Grain Lifetime << Age of the Star
•Which means
• Evolved System  ProtoPlanetary discs
• Planet formation already over
• Collisionally eroding system (what we see is NOT primordial stuff)
What do we see?
DUST !
(<1cm)
• Total flux = photometry
• One wavelength shows disk is there
• Two wavelengths determines dust temperature
• Model fitting with multiple wavelengths (Spectral Energy Distribution)
• Composition = spectroscopy
• Can be used like multiple photometry
• Also detects gas and compositional features
• Structure = imaging
Scattered light: UV, visible,near-IR
Thermal emission:mid-IR,far-IR,mm
• Give radial structure directly and detects asymmetries
• But rare as high resolution and stellar suppression required
« protoplanetary »
discs
Debris discs
Is there a M(t) evolution?
b-Pictoris: the crowned queen of debris discs
0.5µm
10-20µm
0.5µm
850µm
1-2µm
« debris discs » around MSS
Numerical Simulations, why?
•What are discs made of?
• Size Distribution
• Total mass
• “hidden” bigger parent bodies (>1cm)
OR
AND
•What is going on?
• Explain the Observed Spatial Structures
• Presence of Planets?
Numerical simulations are
about making the right
approximations
Size Distribution/Evolution:
the basic problem
~observational limit
~radiation pressure cutoff
collisional cascade
size
distribution
???
Size Distributions
derived from
observations are
model dependent
(Li & Greenberg 1998)
Theoretical collisionalequilibrium law dN R-3.5dR
What we don’t see
What we see
?
Size Distribution/Evolution:
Statistical “Particle in a box” Models
•Principle
• Dust grains distributed in Size Bins (and possibly spatial/velocity bins)
• “Collision” rates between all size-bins
• Each bini-binj interaction produces a distribution of binl<max(i,j) fragment
•Approximations/Simplifications
• No (or poor) dynamical Evolution
• No (or poor) spatial resolution
How to do it
•« Particle in a box » Principle
•Collision Outcome prescription (lab.experiments)
 q1i M lfq(1ii) 1q1i 


M1i 
M lf(i) M sl1(i)q1i   M lf(i) 
 1q1i 

1i
C2i  3C
C1i 3q1i Rlf3(qi1)i
q1i  q2i 
Rsl(i)
C2i R 3q2i  M i M1i
33q2i  sl(i) M sl(i)
EXAMPLE: Collisional dust production in debris discs
Thébault & Augereau (2006)
Numerical model
•Extended Disc: 0-120AU
•Size range: 1μm – 50km
103yrs
104yrs
105yrs
106yrs
107yrs
•Cratering, fragmentation, etc...
da a
3
a1 a2
High e orbits of grains close to the
RPR limit
a4
a5
strong departure from the
”equilibrium” distribution
in dN R-3.5dR
Dynamical Evolution Models
GOAL: explain the observed structures
Warps
Spirals
Offsets
Brightness
asymmetries
Rings & Clumps
•Structures could be caused by:
• Companion Star perturbation
• Encounter with a passing star
• Embedded planet(s): torques, resonances,…
• Isolated violent event: Cometary breakup?
• Complex dust/gas interactions
•…
Dynamical Evolution:
Deterministic “N-Body” models
•Principle
• Dust grains represented by “test particles”
• Forces: FG-Star(s), FG-planet(s),FRad-Pres, FGas-Drag,…
• Step-by-Step Equation of motion integatror:Runge-Kutta, Swift,…
•Approximations/Simplifications
• Nnumerical~104-105 <<<< Nreal
• No Size Distribution
Integrator Example:
Runge-Kutta
Equation of motion
An Example:
HD141569
350AU
observations
Wyatt (2005)
Augereau & Papaloizou (2004)
simulations
0.2MJup planet at 250AU
Passing star
Another one:
Fomalhaut
133AU
observations
simulations
warps:
A way to get a warp, is to introduce a
planet into the disk on an orbit inclined to
the disc midplane
This causes disc near planet to become aligned with the planet, but
that far away keeping the initial symmetry plane
HST image of b Pic
Model
Augereau et al.
(2001)
Heap et al. (2000)
Indirect detection of planets through
debris disc structures (?)
Theory tells us: debris discs and (proto)-planets should co-exist…
Wyatt (2006)
An attempt at coupling both approach:
“Super-Particles”
(Grigorieva, Artymowicz&Thebault,2006)
Collisionnal cascade after planetesimal/cometary breakup