1. « Debris » discs A crash course in numerical methods Philippe Thébault Paris Observatory/Stockholm Observatory

2. « debris disc », what are they? Definition (Lagrange et al., 2000) Around Main Sequence Stars L dust /L * <<1 M (dust+gas) <0.01M * M gas <<10M dust (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)

3. 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 Give radial structure directly and detects asymmetries But rare as high resolution and stellar suppression required Scattered light: UV, visible,near-IR Thermal emission:mid-IR,far-IR,mm

4. Is there a M(t) evolution? « protoplanetary » discs Debris discs

5.  -Pictoris: the crowned queen of debris discs 0.5µm 1-2µm 10-20µm 850µm

6. « debris discs » around MSS

7. Numerical Simulations, why? What are discs made of? Size Distribution Total mass “hidden” bigger parent bodies (>1cm) What is going on? Explain the Observed Spatial Structures Presence of Planets? AND OR

8. Numerical simulations are about making the right approximations

9. Size Distribution/Evolution: the basic problem ~radiation pressure cutoff ~observational limit collisional cascade unseen parent bodies size distribution ???

10. Size Distributions derived from observations are model dependent (Li & Greenberg 1998)

11. ? What we see What we don’t see Theoretical collisional- equilibrium law dN  R -3.5 dR

12. (4) Overdensity due to lack of (3), etc… cutoff size R PR (2) overabundance due to the lack of smaller potential impacotrs (1) Lack of grains< R PR (3) Depletion due to the overabundance in (2)

13. Size Distribution/Evolution: Statistical “Particle in a box” Models Approximations/Simplifications No (or poor) dynamical Evolution No (or poor) spatial resolution Principle Dust grains distributed in Size Bins (and possibly spatial/velocity bins) “Collision” rates between all size-bins Each bin i -bin j interaction produces a distribution of bin l<max(i,j) fragments

14. « Particle in a box » Principle Collision Outcome prescription (lab.experiments) How to do it

15. EXAMPLE: Collisional dust production in debris discs Thébault Thébault & Augereau (2006) High e orbits of grains close to the R PR limit a  (1), e  (1) a1a1 a2a2 a3a3 a4a4 a5a5 da Numerical model Extended Disc: 0-120AU Size range: 1μm – 50km Cratering, fragmentation, etc... strong departure from the ”equilibrium” distribution in dN  R -3.5 dR 10 3 yrs 10 4 yrs 10 5 yrs 10 6 yrs 10 7 yrs

16. Warps Spirals Offsets Brightness asymmetries Rings & Clumps Dynamical Evolution Models GOAL: explain the observed structures

17. 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 …

18. Dynamical Evolution: Deterministic “N-Body” models Approximations/Simplifications N numerical ~10 4 -10 5 <<<< N real No Size Distribution Principle Dust grains represented by “test particles” Forces: F G-Star(s), F G-planet(s), F Rad-Pres, F Gas-Drag,… Step-by-Step Equation of motion integatror:Runge-Kutta, Swift,…

19. Integrator Example: Runge-Kutta Equation of motion

20. An Example: HD141569 observations 0.2M Jup planet at 250AU simulations Wyatt (2005) Augereau & Papaloizou (2004) Passing star 350AU

21. Another one: Fomalhaut observations simulations 133AU 15AU

22. warps: This causes disc near planet to become aligned with the planet, but that far away keeping the initial symmetry plane Augereau et al. (2001) A way to get a warp, is to introduce a planet into the disk on an orbit inclined to the disc midplane Heap et al. (2000) HST image of  Pic Model

23. Indirect detection of planets through debris disc structures (?) Theory tells us: debris discs and (proto)-planets should co-exist…

25. Wyatt (2006)

26. An attempt at coupling both approach: “Super-Particles” ( Grigorieva, Artymowicz&Thebault,2006 ) Collisionnal cascade after planetesimal/cometary breakup