Adam Frank, University of Rochester Department of Physics and Astronomy

1. Disk-Planet Interactions with a short Numerical Prelude Collaborators: Alice Quillen E Blackman, P. Varniere, L. Hartmann (CfA) J. Bjorkman (Toledo) Adam Frank, University of Rochester Department of Physics and Astronomy HR 4796A image G. Schneider etal. OSU Colloquium Feb, 2004

2. Table of Contents • Numerical Methods development at U of Rochester: The AstroBEAR AMR Code • Planet Searches: a brief review • Planet Disk Interactions Basic Physics • Making Gaps • Seeing Gaps • Seeing Spiral Waves • The Hole Problem: CoKuTau/4

3. AstroBEAR – MHD Adaptive Mesh Refinement • Adaptive Mesh Refinement – high resolution only where needed • “Block” AMR – Retain grids upon refinement Berger & Collella • Built on BEARCLAW formalism (Boundry Embedded AMR Conservation Law Package) • BEARCLAW developed by Sorin Mitran UNC • CLAWPACK developed by Randy LeVeque (UWash)

4. AstroBEAR features • Computations in 2D, 2.5D, and 3D • access to all features without coding or recompilation • Set of different Riemann solvers: • full non-linear hydrodynamic • linearized Roe • linearized (arithmetic average) MHD • Generic implicit 4-th order accurate source term routine • suited for arbitrary systems of source term ODEs • Modular structure for user-supplied applications • Variety of provided initial conditions • shocks and blast waves (tabulated and defined via Mach number) • arbitrary density distributions: user-specified and random • disk wind outflows with user-specified properties • jets • accretion disks

5. AstroBEAR features • Built-in physics modules: • radiative cooling via cooling curve • radiation driving via Thomson scattering • central gravity • Current AstroBEAR development: • Full ionization dynamics and photoionization • MHD • Radiation driving via Sobolev approximation (e.g. radiatively driven disk outflows) • Current BEARCLAW development: • MPI – and OpenMP – based parallelization with full load balancing • Fast Multipole Method for elliptic equations • Embedded boundaries for complicated flow geomtries BEARCLAW website: http://www.amath.unc.edu/Faculty/mitran/bearclaw.html AstroBEAR results website:http://pas.rochester.edu/~wma

6. Jets as Hypersonic Radiative Bullets: YSOs HH 47 Bowshock Patrick Hartigan (Rice University) Orion KL

7. Jets as Hypersonic Radiative Bullets: PNe Calabash Nebula: Hubble Flow! V a R CRL 618

8. Hypersonic Radiative Bullets: LBVs • “Strings” in h Carinae • High length to width ratio • Hubble flow along string

9. Mach 10 radiatively cooled bullet ambient density 103 cc-1, clump density 105 cc-1, tcool/thydro = 2.5*10-2 AMR grid generation in the system Synthetic observation (shown is the logarithm of the total projected emissivity)

10. Extremely strongly cooled systems Mach 20 radiatively cooled bullet, ambient density 102 cc-1, clump density 104 cc-1, tcool/thydro = 2.8*10-3 Mach 20 radiatively cooled bullet, ambient density 103 cc-1, clump density 105 cc-1, tcool/thydro = 2.8*10-5

11. h Carinae Strings Bullets - Correct Length Ratios and Kinematics Synthetic Image V vs Z

12. “Many Worlds” debate Millennia old question. 1600 - Bruno burnt at stake for answering yes. 100+ planets found so far. Extra-Solar Planets

13. Planets and Planet Searches Radial velocity searches

14. Planets and Planet Searches Planetary Transits • This technique measures the radius, identifying these as gas giants: “hot Jupiters” • Confusion with eclipsing binaries! HD 209458b

15. Extra-solar Solar Systems: We are the Weirdoes.

16. Diversity of Planetary Systems “Demand” for Orbital Migration • Two major classes of orbital migration models • Planet + gas disk interactions • Planet + planetesimal interactions

17. Planet-Disk interactions • Current planet search techniques biased to inner parts of solar systems. • Planet migration scenarios require planet-disk interactions. • By understanding planet disk interactions we can try to understand planet/disk formation and evolution and possibly account for the DIVERSITY of planetary systems. • We can also search for planets in the outer parts of solar systems. Complimentary to other planet search techniques.

18. Physics of Planet-Disk interactions: Gaps • Planets drive density waves into gaseous or/and planetesimal disks (Goldreich & Tremaine 1978,79, Lin & Papaloizou 1979, Ward 1997) • Because density waves carry angular momentum, which is dissipated, they govern the way planets open a gap. T = Torque Density = SmTm

19. Gaps Driven at Resonances Takeuchi et al 1996

20. Spiral Density Waves 2-armed spiral structure driven at the Inner Lindblad Resonance by an exterior planet

21. Condition to open a Gap • Angular momentum carried by the spiral density waves pushes gas away from the planet. • Viscosity resulting in accretion fills the gap • When torque from spiral density waves exceeds that from viscosity, a gap is opened.

22. Gaps Physics: Previous WorkLin, Papaloizou, Bryden, Nelson, Kley • Determine Gap Opening Condition. q = Mp/M* > 40/R • Show modifications to surface density profiles. • Link gaps and migration physics • Type I (low Mp, No Gap) • Type II (high Mp, Gap) Nelson et al 2002

23. What Was Missed.Varniere, Quillen & Frank 2004 • Condition for Gap Width Wrong. • No link between gap and planet properties. • Physics of maintaining gap edge not explicated Gap Width Reynolds Number

24. Constraints on planet masses from disk edges New Results 2d Hydro simulations of a planet opening a gap in a gaseous accretion disk. Varniere, Quillen & Frank 2004

25. Depths of gaps are strongly dependent on planet mass and viscosity • Widths are weakly dependent on both Gap Width Log Depth Planet mass Planet mass 3. Slopes of disk edges depend strongly on planet mass and viscosity

26. Model for Sharp Disk Edges Disk edges: balance inward diffusion and outward mass flux via spiral density waves driven by the planet. • Model accounts for: • The weak dependence of edge location on planet mass and viscosity • The strong dependence of slope on both quantities • The form of the dependence Mp2/ν

27. Detecting Gaps: SEDs and Direct Images Varniere et al 2004 Rice et al. 2003 proposed that the slope of the inner edge of the disk, required a 1 Jupiter mass planet to maintain it. The Models shown represent different disks with different edge slopes Spectral Energy Distribution of GM Aurigae (Rice et al. MNRAS 2003)

28. Detection of Bright Disk Edges • Use hydro models as input to Monte Carlo Rad Transfer Models (Bjrokman, Wood, Whitney) • Allow disk to flare via stellar rad heating • RESULT; Gap edge heated via stellar illumination -> Bright Annulus

29. Detection of Gap-Modified SEDs • Unlike ‘Hole’ gaps simply reprocess stellar radiation • Deficiet at one wavelength leads to excess at another • Gaps can be detected but confusion possible. Disk with Gap Disk without Gap

30. Disk Edges and Planet Formation • The location of the disk edge for Jupiter mass planets is a function of viscosity. For our simulations between 1.3 and 1.7 rp • As accretion continues … gas piles up just outside the edge. • It’s tempting to consider sequential planet formation ….. aSaturn/aJupiter= 1.8 set by viscosity and planet mass.

31. Surface Density Structure Quillen et al 2004c • Disk Morphology tells us about: • Disk properties • Evolution of the outer parts of planetary systems HST/STIS, HD 100546 Grady et al. (2001)

32. Both stellar flybys and external planets can produce spiral structure, however external perturbers truncate disks

33. HD 141569:Spiral structure driven by close passage of the binary HD 141569B,C Quillen, Varniere, Minchev, & Frank 2004

34. Case Studies Submillimeter imaging • HD 100546, probably a flyby. Flybys do not truncate the disk. Extremely unlikely in field. • HD 141569A. Binary companion. Disk strongly truncated and perturbed on each passage. • Beta Pic. Another flyby. Warp excited (Kalas et al. 2001). • Vega, Epsilon Eridani. Outer eccentric planets required to explain dust distribution. HD 100546 Optical scattered light Beta Pictorus HD 141569A Credits, ESO, Wilner, Grady, Clampin, HST

35. The Role of Birth Cluster Environment • Outer regions of large disks often show evidence of perturbations from other stars: flybys, or companion binaries. • Close or fast flybys effectively scatter a fraction of the disk. The disk is not truncated. • It is possible to excite the eccentricity of a single planet and leave most of the disk unperturbed. • “Natural” explanations for the morphologies of Epsilon Eridani’s, Beta Pic’s and Vega’s disk. • An example of a recent occurrence: HD 100546. • Flybys at 100AU or less are very unlikely in the field, however they can be important in forming stellar clusters. We might predict that the properties of young disks will depend on environment. Cluster MonR2 Guttermuth, Peterson, Pipher, Forrest, Megeath. SIRTF young cluster project

36. In Summary • We will also learn about the properties of gas and planetesimals of these systems • Disk edges are sensitive to the planets that maintain them. Disk edges are illuminated. Their shape determines the morphology of scattered light images and should affects spectral energy distributions. • We primarily probe young systems, so we learn about the evolution and formation of planetary systems. • Dynamics is RICH • Outer parts of solar systems have revealed surprises just as inner ones did! Eccentric planets, perturbations by stars. • The structure of dust, gas and planetesimals, more easily detectable than planets, let us constrain planetary properties in the outer parts of extra-solar planetary systems. • Resonances allow small perturbations by low mass planets to become important! Planets can be treated like dark matter. • Dust distributions are sensitive to planet orbit properties. Future observations will discriminate between and test models.

37. Prospects for the Future • SMA – now operating: 0.1” resolution in submillimeter. This is 10AU for an object at 100pc. • ALMA – coming on line in 2010. Ground broken this year. 0.01” in submillimeter. This is 1AU for an object at 100pc. • JWST – 0.1” resolution in mid-infrared. • Spitzer Space Telescope – detection sensitivity in IR improves by a factor ~100. “Firehose of data’’ now happening • Other miscellany – AO, interferometers, new coronagraphs and other space projects such as TPF, Kepler.

38. Condition to open a Gap • Angular momentum carried by the spiral density waves pushes gas away from the planet. • Viscosity resulting in accretion fills the gap • When torque from spiral density waves exceeds that from viscosity, a gap is opened.

39. Driving Spiral Density waves • Spiral density waves are driven at Lindblad resonances. • Torque driven depends on the strength of the mth Fourier component of the gravitational potential of the planet.