1. The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond

2. Spectral Energy Distributions (SEDs) Plotting normal flux makes it look as if the source emits much more infrared radiation than optical radiation: This is because energy is:

3. Spectral Energy Distributions (SEDs) Typically one can say: and one takes a constant (independent of ). In that case is the relevant quantity to denote energy per interval in log. NOTE:

4. Calculating the SED from a flat disk Assume here for simplicity that disk is vertically isothermal: the disk emits therefore locally as a black radiator. Now take an annulus of radius r and width dr. On the sky of the observer it covers: and flux is: Total flux observed is then:

5. Multi-color blackbody disk SED Wien region multi-color region Rayleigh- Jeans region F

6. F 3 (4q-2)/q Multi-color blackbody disk SED Rayleigh-Jeans region: Slope is as Planck function: Multi-color region: Suppose that temperature profile of disk is: Emitting surface: Peak energy planck: Location of peak planck:

7. (4q-2)/q F 3+ Disk with finite optical depth If disk is not very optically thick, then: Multi-color part stays roughly the same, because of energy conservation Rayleigh-Jeans part modified by slope of opacity. Suppose that this slope is: Then the observed intensity and flux become:

8. AB Aurigae SED of accretion disk Remember: According to our derived SED rule (4q-2)/q=4/3 we obtain: Does this fit SEDs of Herbig Ae/Be stars? HD104237 Bad fit Higher than observed from veiling (see later)

9. Viscous heating or irradiation? T Tauri star

10. Viscous heating or irradiation? Herbig Ae star

11. Flat irradiated disks Irradiation flux: Cooling flux: Similar to active accretion disk, but flux is fixed. Similar problem with at least a large fraction of HAe and T Tauri star SEDs.

12. Flared disks flaring irradiation heating vs cooling vertical structure Kenyon & Hartmann 1987 Calvet et al. 1991; Malbet & Bertout 1991 Bell et al. 1997; D'Alessio et al. 1998, 1999 Chiang & Goldreich 1997, 1999; Lachaume et al. 2003

13. Flared disks: Chiang & Goldreich model The flaring angle: Irradiation flux: Cooling flux: Express surface height in terms of pressure scale height:

14. Flared disks: Chiang & Goldreich model Remember formula for pressure scale height: We obtain

15. Flared disks: Chiang & Goldreich model We therefore have: with Flaring geometry: Remark: in general is not a constant (it decreases with r). The flaring is typically <9/7

16. The surface layer A dust grain in (above) the surface of the disk sees the direct stellar light. Is therefore much hotter than the interior of the disk.

17. Intermezzo: temperature of a dust grain Heating: a = radius of grain = absorption efficiency (=1 for perfect black sphere) Cooling: Thermal balance: Optically thin case:

18. Intermezzo: temperature of a dust grain Big grains, i.e. grey opacity: Small grains: high opacity at short wavelength, where they absorb radiation, low opacity at long wavelength where they cool.

19. The surface layer again... Disk therefore has a hot surface layer which absorbs all stellar radiation. Half of it is re-emitted upward (and escapes); half of it is re-emitted downward (and heats the interior of the disk).

20. Chiang & Goldreich: two layer model Chiang & Goldreich (1997) ApJ 490, 368 Model has two components: Surface layer Interior

21. Flared disks: detailed models Global disk model...... consists of vertical slices, each forming a 1D problem. All slices are independent from each other.

22. Flared disks: detailed models Malbet & Bertout, 1991, ApJ 383, 814 D'Alessio et al. 1998, ApJ 500, 411 Dullemond, van Zadelhoff & Natta 2002, A&A 389, 464 A closer look at one slice:

23. Dust evaporation and disk inner rim Natta et al. (2001) Dullemond, Dominik & Natta (2001)

24. SED of disk with inner rim

25. Covering fraction

33. Covering fraction of torus with height H and radius R Reprocessed luminosity can be expressed as: Observed reprocessed luminosity depends on inclination but roughly one can write (modulo inclination):

34. Example: HD100546 Must have weak inner rim (weak near-IR flux), but must be strongly flaring (strong far-IR flux)

35. Example: HD 144432 Must have strong inner rim (strong near-IR flux), but either small or non-flaring outer disk (weak far-IR flux)

36. Measuring grain sizes in disks van Boekel et al. 2003 The 10 micron silicate feature shape depends strongly on grain size. Observations show precisely these effects. Evidence of grain growth.

37. Grain sizes in inner disk regions R < 2 AUR > 2 AU...infrared interferometry Resolving inner disk region with... van Boekel et al. 2004

38. Probing larger grains in disks At (sub-)millimeter wavelength one can measure opacity slope (remember!). But first need to make sure that the disk is optically thin. A measured flux, if F ~ 3, can come from a blackbody disk surface. Measure size of disk with (sub-)millimeter interferometry. If disk larger than that, then disk must be optically thin. A slope of F ~ 3 then definitely point to large (cm) sized grains! Evidence for large grains found in many sources. Example: CQ Tau (Testi et al.)

39. Probinging the shape of disks We have sources with weak mid/far-IR flux, and sources with strong mid/far-IR flux. One of the ideas is that disk can be self-shadowed to obtain weak mid/far-IR flux. Disk starts as flaring disk: strong mid/far-IR flux. Few big grains produced. As disk gets older: part of dust converted into big grains. Disk loses opacity, falls into own shadow. Many big grains observable at (sub-)millimeter wavelengths.

40. Probinging the shape of disks Acke et al. 2004 looked for such a correlation, and indeed found it: Flaring disks Self-shadowed(?) disks