1. Models of Disk Structure, Spectra and Evaporation Kees Dullemond, David Hollenbach, Inga Kamp, Paola DAlessio Disk accretion and surface density profiles Vertical structure models and SEDs Gas models and disk surface layers Evaporation by the central star

2. Why study the structure of protoplanetary disks? Disk structure models are the backbone of planet formation models Core accretion versus gravitational instability ? What is the fraction of disks that can form planets ? dust settling, growth and planetesimal formation depend on gas-dust dynamics

3. Overview Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10 -8 M /yr ~ R -1

4. Accretion and radial disk structure Formation of the disk...

5. Accretion and radial disk structure Mass accretion

6. Accretion and radial disk structure Angular Momentum transport

7. Accretion and radial disk structure Viscous spreading of the disk...... while disk loses mass by accretion

8. Accretion and radial disk structure Viscous spreading of the disk...... while disk loses mass by accretion

9. Accretion and radial disk structure Viscous spreading of the disk...... while disk loses mass by accretion onto star Mass reservoir of the disk, which feeds the inner disk regions

10. Accretion and radial disk structure Viscous spreading of the disk...... while disk loses mass by accretion Semi-stationary region, with mass supply from outer reservoir

11. Brief history of a star and a disk After: Hueso & Guillot 2005 (Lynden-Bell & Pringle; Hartmann et al. ; Nakamoto & Nakagawa)

12. Actively accreting irradiated disks Solid line: Hueso & Guillot (2005) Dashed line: DAlessio et al. (2001) -profile clearly shallower than Minimum mass solar nebula Very young disk (accretion-heating dominated): ~R -0.5. T Tauri disk (irradiative heating dominates outer disk): ~R -1 ~ R -1 ~ R -1.5 (MMSS)

13. Overview Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10 -8 M /yr ~ R -1 Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius)

14. SEDs of intermediate-mass stars Classification of Meeus et al. 2001 Group IGroup II (Note: not to be confused with class 0,I,II,III of the Lada et al classification!) AB Aurigae (Group I)HD104237 (Group II) SEDs of intermediate-mass stars Group IGroup II

15. Fitting pure accretion disk models... AB Aurigae (Group I)HD104237 (Group II) Group I: Bad fit at >10 micron. Group II: Reasonable fit (though need high accretion rate). (Hillenbrand 1992; Rucinski 1985; Adams et al. 1988; Bertout et al. 1988; Bell et al. 1997; Lynden-Bell 1969; Lynden-Bell & Pringle 1974)

16. Fitting irradiated disks... AB Aurigae (Group I)HD104237 (Group II) Group I: Reasonable fit for overall flat SED. Group II: SED tends to be too flat (Kenyon & Hartmann 1987; Chiang & Goldreich 1997; DAlessio et al. 1998, 1999; Lachaume et al. 2004)

17. Dust evaporation: (puffed-up) inner rim... AB Aurigae (Group I)HD104237 (Group II) All sources: Dust inner rim might solve the NIR problem Group II: Still not well fitted at >10 micron (Natta et al. 2001; Tuthill et al. 2001; Dullemond et al. 2001; Muzerolle et al. 2003; Isella & Natta 2005; Akeson et al.; Monnier et al. ; Eisner et al.; Millan-Gabet et al.)

18. Reducing somehow the far-IR flux... Group II: Outer disk height can be reduced by e.g. dust settling (DAlessio et al. 1999; Chiang et al. 2001). Disk might be shadowed ( Dullemond & Dominik 2004b), but this is still under debate (Walker et al. 2006) AB Aurigae (Group I)HD104237 (Group II)

19. Irradiated surface & visc. heated midplane Vertical structure of disk at 1AU: Viscous accretion heating dominates the disk midplane, while the surface layer temperatures are set by irradiation only z [AU] 0.10.2 DAlessio et al. model

20. SED of disk with hot surface layer After: Chiang & Goldreich 1997 Calvet et al. 1991; Malbet & Bertout 1991; Many 2D/3D RT papers

21. Overview Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10 -8 M /yr ~ R -1 Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius) T gas > T dust in disk surface layers ( ross <~ 1.0): gas and dust are not well coupled molecules can form

22. Disk surface layers ross =1 no PAHswith PAHs ross =1 (Kamp & Dullemond 2004; Jonkheid et al. 2004; Nomura & Millar 2005; Kamp et al. 2005) CTTS HAe T gas = T dust

23. Gas temperature is higher than dust temperature in the surface layers (Jonkheid et al. 2004, Kamp et al. 2004, Nomura & Millar 2005) T evap := GM * m p /kr Vertical cut at R = 9 AU T gas T dust T evap

24. Molecules like H 2, CO, OH etc. exist in these hot surface layers. Vertical cut at R = 9 AU T gas T dust T evaporation H 2 /H

25. Vertical cut at R = 9 AU T gas T dust T evaporation H 2 /HCO/C/C + Molecules like H 2, CO, OH etc. exist in these hot surface layers.

26. Gas temperature is set by the balance of photoelectric heating, H 2 formation heating and OI, H 2 line cooling. Below ross ~1, gas-grain collisions thermalize the gas and dust. Vertical cut at R = 9 AU T gas T dust T evaporation PE heating H 2 formation gas-grain collisions CO/C/C + H 2 /H

27. Vertical cut at R = 9 AU T gas T dust T evaporation PE heating H 2 formation gas-grain collisions OI cooling Ly cooling H 2 lines gas-grain collisions Gas temperature is set by the balance of photoelectric heating, H 2 formation heating and OI, H 2 line cooling. Below ross ~1, gas-grain collisions thermalize the gas and dust. CO/C/C + H 2 /H

28. Vertical cut at R = 9 AU T gas T dust T evaporation CO/C/C + H 2 /H

29. Vertical cut at R = 9 AU T gas T dust T evaporation Photoevaporation flow starts well below T gas =T evaporation (Adams et al. 2004) CO/C/C + H 2 /H origin of the flow

30. Overview Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10 -8 M /yr ~ R -1 Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius) T gas > T dust in disk surface layers ( ross <~ 1.0): gas and dust are not well coupled molecules can form Disk dispersal can proceed via photoevaporation by the FUV/EUV of the central star: FUV evaporation proceeds from outside in

31. Stellar EUV and FUV EUVFUV

32. Photoevaporation by the central star r crit = 12 (M * /1M ) (10 3 K/T gas ) AU Need to self-consistently calculate the chemistry, heating and cooling, radiative transfer, vertical and radial structure, and dynamics of flow. Approximations are made ! (Adams et al. 2004; Gorti & Hollenbach 2005) r crit viscous accretion

33. Disk evaporation by FUV photons T Tauri star: M gas = 0.03 M *, ~ R -1, R out = 200 AU Disk evaporates outside in Evaporation for various central stars: Disk survival times peak at ~ 1 M (Gorti & Hollenbach) Poster 291 timescale

34. Additional Applications of Evaporation Rapid transition from classical T Tauri to weak-line T Tauri stars: EUV photoevaporation opens a gap at r crit at a timescale of ~ 1 Myr mass supply from outer disk gets cutoff inner disk accretes onto the star on a timescale ~10 5 yr (Clarke et al. 2001), (Alexander et al. 2005) poster 292

35. Additional Applications of Evaporation Formation of planetesimals: dust settling lowers the dust:gas ratio (M dust /M gas ) in disk surfaces dust-depleted evaporation flows and dust settling leave the midplane behind with high M dust /M gas (Throop & Bally 2005) midplane can become gravitational instable (Youdin & Shu 2002) spontaneous formation of km-sized planetesimals

36. Summary Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10 -8 M /yr ~ R -1 Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius) T gas > T dust in disk surface layers ( ross <~ 1.0): gas and dust are not well coupled molecules can form Disk dispersal can proceed via photoevaporation by the FUV/EUV of the central star: FUV evaporation proceeds from outside in

37. Schematic view of protoplanetary disks Dust

38. Schematic view of protoplanetary disks Gas