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Planet Formation

Planet Formation. Topic: Disk thermal structure Lecture by: C.P. Dullemond. This is because energy is: . Spectral Energy Distributions (SEDs). Plotting normal flux makes it look as if the source emits much more infrared radiation than optical radiation:.

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Planet Formation

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  1. Planet Formation Topic: Disk thermal structure Lecture by: C.P. Dullemond

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

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

  4. 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: 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.

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

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

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

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

  9. Viscous heating or irradiation? T Tauri star

  10. Viscous heating or irradiation? Herbig Ae star

  11. Irradiation flux: Cooling flux: Flat irradiated disks 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. flaring vertical structure irradiation heating vs cooling Flared disks • 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. The flaring angle: Irradiation flux: Cooling flux: Express surface height in terms of pressure scale height: Flared disks: Chiang & Goldreich model

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

  15. We therefore have: with Flaring geometry: Flared disks: Chiang & Goldreich model 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. Heating: a = radius of grain = absorption efficiency(=1 for perfect black sphere) Cooling: Thermal balance: Intermezzo: temperature of a dust grain 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 • Model has two components: • Surface layer • Interior Chiang & Goldreich (1997) ApJ 490, 368

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

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