1. Sculpting Circumstellar Disks with Planets Mar 2008 Alice Quillen University of Rochester

2. All extrasolar planets discovered by radial velocity (blue dots), transit (red) and microlensing (yellow) to 31 August 2004. Also shows detection limits of forthcoming space- and ground-based instruments. Discovery space for planets based on disk/planet interactions Discovery Space

3. Outline Regimes + mechanisms for planet+disk interactions When can planets be ruled out? Gapless gaseous disks Gapless dusty disks Predicting planets or embryo properties Collaborators: Peter Faber, Richard Edgar, Peggy Varniere, Jaehong Park, Allesandro Morbidelli, Alex Moore, Adam Frank, Eric Blackman, Pasha Hosseinbor

4. Physical Regimes Gaseous disks. Large dust opacity. Spiral density waves, accretion, migration, depletion. Gas depleted dusty disks. Intermediate opacity. Planestimals growing or/and eroding. Collisions and gravitational scattering. –Orbits between collisions ~ 1/ τ ~ 10 3 a regime not well studied dynamically as most of the Solar System either well above or below this

5. Minimum Gap Opening Planet in an Accretion Disk Edgar et al. 07 Gapless disks lack planets gap opening criterion: viscosity vs min gap opening planet mass Gap opening is independent of density but does depend on alpha and temperature Temperature scaling depends on opacity, energy source radiation accretion, optically thick ~

6. Minimum Gap Opening Planet Mass in an Accretion Disk Smaller planets can open gaps in self- shadowed disks Dead zones: lower mass objects can open gaps in the dead zone (Matsumura, Oishi). Active layer could continue to accrete through gap or could be shielded and so disappear.

7. Gap opening in debris disks If spiral density waves are driven effectively then viscous condition for gap opening can be used If collision timescale is longer than resonance libration timescale then spiral density waves are not driven Transition opacity but dependent on planet mass as libration frequency depends on q 2/3 Disk truncation via gravitational scattering – possible role of chaotic zone boundary associated with corotation

8. Based on diffusive numerical models for collisions To truncate a disk a planet must have mass above here related to observables; Quillen 2007 Observables can lead to planet mass estimates τ~10 -4 α=0.001 Log Planet mass Log Velocity dispersion τ~10 -3

9. Planet mass estimates for “transition” disks Mass estimate for CoKuTau4 was based on a gap opening criterion – this requires an estimate for the disk viscosity –1: Viscosity estimated via comparison to other disks with same SED but no clearing –2: Viscosity estimated via a clearing timescale and age of system Both constraints give a similar minimum planet mass estimate for a planet interior to the disk edge ~ Saturn Larger planet masses required to keep steep edge and gap empty. Hydro alone insufficient to account for density decrement. Accretion in edge could cause gas inflow (e.g. Chiang & Murray 07), while photoionization might help with clearing.

10. Disk clearing following gap opening Why gap did not migrate? Planet fails to migrate much until density is sufficiently high in disk edge – migration rates can be time dependent and depend on disk density Inner disk clearing happens on an accretion timescale unless perhaps planet drives high disk eccentricity at the 3:1 resonance interior to the planet If planet causes disk to self shield then accretion timescale exterior to edge could be longer Disk clearing takes longer than the age of the system for large clearings. Either another clearing mechanism is required or multiple planets are required to clear material. (Spitzer does not detect small gaps, only large clearings) e.g., Varniere et al. 06; Edgar et al. 2007

11. Edge structure Fraction of light emitted related to edge height, so far as I can tell height consistent with thermal structure expected for disk edge. If the edge density is higher then more light remitted at longer wavelengths This effect is irrelevant compared to role of dust size distribution which for CoKuTau4 seems to be dominated by small particles Low mm fluxes for this object imply low density outer disk, opposite true for DM Tau Imaging likely required to break degeneracy in SED fitting. 4 AU 10 AU CoKuTau/4 D’Alessio et al. 05 Wavelength μm

12. Vertical motions in the disk edge v z in units of Mach number (radius) azimuthal angle density slice Spiral structure driven by planets difficult to detect directly however may have indirect effects (e.g. mascarades as turbulence or causes shadowing, or kicks dust up) Edgar et al. 08

13. Edge structure time dependent structure, one armed when planet close to edge, higher density leads to thicker tau=1 surface, planet itself may be bright, accreting or have an outflow, asymmetries would lead to scale height variations

14. Edge structure For disks with denser outer disks, clearings have been confirmed at mm wavelengths (LkHa330 subm Brown et al. 08, TWHy 7mm Hughes et al. 07) Accreting systems tend to also have evidence for hot dust. However the accretion rate is set by gas density at small radii. The radial extent and total dust + gas mass of these inner disks is not constrained from accretion rate alone. If these inner accreting disks extend to clearing edge then they must be highly depleted of dust. Mechanisms proposed keep larger dust grains in disk edge, stronger coupling of small dust with gas flows (e.g., Rice et al 06, Fouchet et al. 07) Existence of at least 2 systems with clearings lacking accretion imply that inner disk clearing can be faster than disk depletion OR multiple planet formation occurs OR they are binaries.

15. Debris Disk Clearing Spitzer spectroscopic observations show that many dusty disks are ~ consistent with one temperature, hence nearly empty within a particular radius Assume that dust and planetesimals must be removed via orbital instability caused by planets and gravitational scattering

16. Planetesimal Clearing by Planets Log10 time(yr) Faber & Quillen 07 μ=10 -7 μ=10 -3 Simple relationship between spacing, clearing time and planet mass Invert this to find the spacing, using age of star to set the stability time. Stable planetary system and unstable planetesimal ones.

17. How many planets? Between dust radius and ice line ~ 4 Neptune’s required ~a Jupiter mass in planets is required to explain clearings in all debris disk systems Spacing and number is not very sensitive to the assumed planet mass It is possible to have a lot more stable mass in planets in the system if they are more massive Eccentric planets are more efficient at clearing (Jiang, Duncan and Lin 06) perhaps less mass required, though eccentricity causing mechanism is then required. Velocity dispersion in dust disk relevant toward telling these two possibilities apart!

18. Planet spacing when there are dust belts Moro-Martin et al. 07, located dust belt based on stability requirements, 2RV planet system. Epsilon Eridani (any moment now) will become an interesting system to reconstruct in terms of planets + dust belts Some other object that Mark Wyatt mentioned

19. 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

20. 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

21. Pericenter glow model Collisions cause orbits to be near closed ones. This implies the free eccentricities in the ring are small. The eccentricity of the ring is then 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.

22. 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 Neptune size collisionless lifetime

23. 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

24. 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

25. Caveats and predictions Do mechanisms exist to cause eccentric clearings that don’t require planets? Ring is not thick, no evidence for highly scattered planetesimal population Yet eccentric planet possibly present Collisions are destructive so how did the ring damp to the low free eccentricity orbit? Small amounts of gas (Aki)? Or did debris heat post planet? Planet predicted. So far no morphology variations predicted @higher angular resolution or with wavelength.

26. 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 increased by gravitational stirring by massive bodies in the disk h/r<0.02

27. 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

28. The top of the cascade related to observables, however exponents not precisely known

29. Gravitational stirring

30. 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

31. Caveats No formation timescale and self-stirring Other possible sources of vertical heating not yet considered (spiral density waves?) Extrapolating over 10 orders of magnitude is not likely to be very predictive I can’t yet think of any way to test this model

32. Summary Largish planets can be ruled out for gapless disks both for accretion disks (but then viscosity must be known) and for collisional disks (related to dispersion and opacity but based on diffusive approximation) If a planet is present then the same criterion can be used to place a limit on planet mass If planet is responsible for truncating the disk then it is likely located near the clearing edge Large empty clearings likely require multiple planets. Stability criteria can be used to estimate how many. Done for circular orbits. Not yet explored for eccentric systems. Systems with both planets and dust belts just starting to be explored. Some hints of large debris in gapless disks, alternative models yet to be explored. Alternate explanations for eccentric holes yet to be explored.