1. Sculpting Circumstellar Disks Netherlands April 2007 Alice Quillen University of Rochester

2. Motivations Planet detection via disk/planet interactions – Complimentary to radial velocity and transit detection methods Rosy future – ground and space platforms Testable models – via predictions for forthcoming observations. New dynamical regimes and scenarios compared to old Solar system Evolution of planets, planetesimals and disks Collaborators: Peter Faber, Richard Edgar, Peggy Varniere, Jaehong Park, Allesandro Morbidelli, also Eric Blackman, Adam Frank, Pasha Hosseinbor, Amanda LaPage

3. Observational Background Submillimeter imaging Optical scattered light Beta Pictorus HD 100546 HD 141569A Credits, ESO,Schneider Wilner, Grady, Clampin, HST, Kalas HR4796A Fomalhau t Young Clusters: 5--20% of stars surveyed in young clusters are T- Tauri stars hosting disks with large clearings – Dozen or so now with IRS/Spitzer spectra, more identified with Spitzer/IRAC photometry Older Disks and Debris Disks: Fraction detected with disks with IR excess depends on age, wavelength surveyed and detection limit. 50—100 now known from Spitzer/MIPS surveys Unexplained structure: edges, clearings, spiral arms, warps, clumps

4. Dynamical Regimes for Circumstellar Disks with central clearings 1. Young gas rich accretion disks – “transitional disks” e.g., CoKuTau/4. Planet is massive enough to open a gap (spiral density waves). Hydrodynamics is appropriate for modeling.

5. Dynamical Regimes– continued 2. Old dusty diffuse debris disks – dust collision timescale is very long; e.g., Zodiacal cloud. Collisionless dynamics with radiation pressure, drag forces, resonant trapping, removal of orbit crossing particles 3. Intermediate opacity dusty disks – dust collision timescale is in regime 10 3 -10 4 orbital periods; e.g., Fomalhaut, AU Mic debris disks

6. This Talk i.Planets in accretion disks with clearings -- CoKuTau/4 ii.Planets in Debris disks with clearings -- Fomalhaut iii.Embryos in Debris disks without clearings -- AU Mic iv.Total mass in planets in older systems -- Clearing by planetary systems What mass objects are required to account for the observed clearings, What masses are ruled out?

7. Transition Disks Estimate of minimum planet mass to open a gap requires an estimate of disk viscosity. Disk viscosity estimate either based on clearing timescale or using study of accretion disks. Mp > 0.1MJ 4 AU 10 AU CoKuTau/4 D’Alessio et al. 05 Wavelength μm

8. Models for Disks with Clearings 2. Planet formation, gap opening followed by clearing (Quillen, Varniere) -- more versatile than photo-ionization models but also more complex Problems: Failure to predict dust density contrast, 3D structure Predictions:Planet masses required to hold up disk edges, and clearing timescales, detectable edge structure 1. Photo-ionization models (Clarke, Alexander) Problems: -- clearings around brown dwarfs, e.g., L316, Muzerolle et al. -- accreting systems such as DM Tau, D’Alessio et al. -- wide gaps such as GM Aur; Calvet et al. -- single temperature edges Predictions: Hole size with time and stellar UV luminosity

9. Minimum Gap Opening Planet In an Accretion Disk heat from accretion heat from stellar radiation Park et al. 07 in preparation Gapless disks lack planets

10. Minimum Gap Opening Planet Mass in an Accretion Disk Planet trap? Smaller planets can open gaps in self- shadowed disks Hole radii scale with stellar mass (Kim et al. in prep) Retired A stars lack Hot Jupiters? (Johnson et al. 07)

11. Fomalhaut ’s eccentric ring steep edge profile h z /r ~ 0.013 eccentric e=0.11 semi-major axis a=133AU collision timescale =1000 orbits based on measured opacity at 24 microns age 200 Myr orbital period 1000yr

12. Free and forced eccentricity radii give you eccentricity If free eccentricity is zero then the object has the same eccentricity as the forced one e forced e free

13. Pericenter glow model Collisions cause orbits to be near closed ones. Small free eccentricities. The eccentricity of the ring is the same as the forced eccentricity We require the edge of the disk to be truncated by the planet  We consider models where eccentricity of ring and ring edge are both caused by the planet. Contrast with precessing ring models.

14. Disk dynamical boundaries For spiral density waves to be driven into a disk (work by Espresate and Lissauer) Collision time must be shorter than libration time  Spiral density waves are not efficiently driven by a planet into Fomalhaut’s disk A different dynamical boundary is required We consider accounting for the disk edge with the chaotic zone near corotation where there is a large change in dynamics We require the removal timescale in the zone to exceed the collisional timescale.

15. Chaotic zone boundary and removal within What mass planet will clear out objects inside the chaos zone fast enough that collisions will not fill it in? M p > Neptune Saturn size Neptun e size collisionless lifetime

16. Chaotic zone boundaries for particles with zero free eccentricity Hamiltonian at a first order mean motion resonance corotation regular resonance secular terms

17. Dynamics at low free eccentricity Expand about the fixed point (the zero free eccentricity orbit) For particle eccentricity equal to the forced eccentricity and low free eccentricity, the corotation resonance cancels  recover the 2/7 law, chaotic zone same width goes to zero near the planet same as for zero eccentricity planet

18. Dynamics at low free eccentricity is similar to that at low eccentricity near a planet in a circular orbit No difference in chaotic zone width, particle lifetimes, disk edge velocity dispersion low e compared to low e free planet mass width of chaotic zone different eccentricity points

19. Velocity dispersion in the disk edge and an upper limit on Planet mass Distance to disk edge set by width of chaos zone Last resonance that doesn’t overlap the corotation zone affects velocity dispersion in the disk edge M p < Saturn

20. cleared out by perturbations from the planet M p > Neptune nearly closed orbits due to collisions eccentricity of ring equal to that of the planet Assume that the edge of the ring is the boundary of the chaotic zone. Planet can’t be too massive otherwise the edge of the ring would thicken  M p < Saturn

21. First Predictions for a planet just interior to Fomalhaut’s eccentric ring Neptune < M p < Saturn Semi-major axis 120 AU (16’’ from star) Eccentricity e p =0.1, same as ring Longitude of periastron same as the ring

22. The Role of Collisions Dominik & Decin 03 and Wyatt 05 emphasized that for most debris disks the collision timescale is shorter than the PR drag timescale Collision timescale related to observables

23. The numerical problem Between collisions particle is only under the force of gravity (and possibly radiation pressure, PR force, etc) Collision timescale is many orbits for the regime of debris disks: 100-10000 orbits.

24. Numerical approaches Particles receive velocity perturbations at random times and with random sizes independent of particle distribution (Espresante & Lissauer) Particles receive velocity perturbations but dependent on particle distribution (Melita & Woolfson 98) Collisions are computed when two particles approach each other (Charnoz et al. 01) Collisions are computed when two particles are in the same grid cell – only elastic collisions considered (Lithwick & Chiang 06)

25. Our Numerical Approach Perturbations independent of particle distribution: Espresate set the v r to zero during collisions. Energy damped to circular orbits, angular momentum conservation. However diffusion is not possible. We adopt Diffusion allowed but angular momentum is not conserved! Particles approaching the planet and are too far away are removed and regenerated Most computation time spent resolving disk edge

26. Parameters of 2D simulations

27. Morphology of collisional disks near planets Featureless for low mass planets, high collision rates and velocity dispersions Particles removed at resonances in cold, diffuse disks near massive planets angle radius

28. Profile shapes chaotic zone boundary 1.5 μ 2/7

29. Rescaled by distance to chaotic zone boundary Chaotic zone probably has a role in setting a length scale but does not completely determine the profile shape

30. Density decrement Log of ratio of density near planet to that outside chaotic zone edge Scales with powers of simulation parameters as expected from exponential model Unfortunately this does not predict a nice form for t remove

31. Using the numerical measured fit To truncate a disk a planet must have mass above (here related to observables) Observables can lead to planet mass estimates, motivation for better imaging leading to better estimates for the disk opacity and thickness N c =10 -3 α=0.001 Log Planet mass Log Velocity dispersion N c =10 -2

32. Application to Fomalhaut Upper mass limit confirmed by lack of resonant structure Lower mass limit ~ lower than previous estimate unless the velocity dispersion at the disk edge set by planet Log Velocity dispersion Log Planet mass Quillen 2006, MNRAS, 372, L14 Quillen & Faber 2006, MNRAS, 373, 1245 Quillen 2007, astro-ph/0701304

33. Constraints on Planetary Embryos in Debris Disks AU Mic JHKL Fitzgerald, Kalas, & Graham Thickness tells us the velocity dispersion in dust This effects efficiency of collisional cascade resulting in dust production Thickness from gravitational stirring by massive bodies in the disk h/r<0.02

34. The size distribution and collision cascade Figure from Wyatt & Dent 2002 set by age of system scaling from dust opacity constrained by gravitational stirring observed

35. The top of the cascade

36. Gravitational stirring

37. Comparing size distribution at top of collision cascade to that required by gravitational stirring >10objects gravitation stirring top of cascade Hill sphere limit size distribution might be flatter than 3.5 – more mass in high end  runaway growth? > 10objects Earth

38. Comparison between 3 disks with resolved vertical structure 10 7 yr 10 8 yr

39. Clearing by Planetary Systems Assume planet formation leaves behind a population of planetesimals which produce dust via collisions Central clearings lacking dust imply that all planetesimals have been removed Planets are close enough that interplanetary space is unstable across the lifetime of the system ~ 50 known debris disks well fit by single temperature SEDs implying truncated edges (Chen et al. 06)

40. Clearing by Planetary Systems Log10 time(yr) Chambers et al. 96 μ=10 -9 μ=10 -5 Faber et al. in preparation Separation

41. Clearing by planetary systems r min set by ice line r max set by observed disk temperature Result is we solve for N and find 3-8 planets required of Neptune size for most debris disks. This implies a total minimum mass in planets of about a Saturn mass

42. Summary Quantitative ties between disk structure and planets residing in disks Better understanding of collisional regime and its relation to observables In gapless disks, planets can be ruled out – but we find preliminary evidence for embryos and runaway growth The total mass in planets in most systems is likely to be high, at least a Saturn mass More numerical and theoretical work inspired by these preliminary crude numerical studies Exciting future in theory, numerics and observations

46. Prospects with ALMA PV plot 5km/s for a planet at 10AU Edgar’s simulations

47. Diffusive approximations