1. Some considerations on disk models
Antonella Natta
Osservatorio di Arcetri
Schloss Ringberg, April 13-17, 2004

2. What is a protoplanetary disk ?
A star
A disk of gas (dominant in mass ) and dust (dominates the opacity)
Mdisk << Mstar (but..)
Material moves radially toward the star: accretion disk
Schloss Ringberg, April 13-17, 2004

3. Schloss Ringberg, April 13-17, 2004
What is a disk model ?
Which are the dominant physical processes (angular momentum transfer, ionization, heating, etc.)
T, r, chemical composition, ionization fraction, etc. etc. in each point for gas and dust
 a large range of (very high) density and temperature
 very optically thick (RT)
 dust is highly processed
How all of this changes with time
The environment is important (binaries, clusters, etc.)
Everything is coupled
Schloss Ringberg, April 13-17, 2004

4. Schloss Ringberg, April 13-17, 2004
Outline:
A little history
One (or two) examples
Some comments
Schloss Ringberg, April 13-17, 2004

5. Lyndell-Bell and Pringle 1974
The viscous a-disk
Shakura and Sunyaev 1973
Lyndell-Bell and Pringle 1974
(Pringle ARAA 1981)
Viscosity n = a Cs H
Temperature TMacc1/4 R-3/4
Surface density S  R-3/4 a-1
r(R,z) = r(R,0) exp(-z2/2H2)
There is a relation between Macc and n
Question: what is the physical mechanism behind viscosity?
Challenge: to account for the observed accretion rates
Schloss Ringberg, April 13-17, 2004

6. Observed Macc in PMS Objects
Macc decreases with Mstar
Macc decreases
with age
r-Oph
Taurus
Cha
Calvet et al. 2000
Muzerolle et al. 2003
Natta et al. 2004
Schloss Ringberg, April 13-17, 2004

7. Irradiated disks: the stellar radiation heats the disk
Geometrically thin, optically thick (blackbody) disks:
T~ 0.67 Tstar (R/Rstar) -3/4
Same SED (but different LD) for active and passive BB
disks (most TTS have passive disks)
Do models reproduce
the observations? No
parametric power-law disks:
T  R-q, S  R-p
Form Beckwith et al. 1990
Schloss Ringberg, April 13-17, 2004

8. Irradiated Flared Disks
Kenyon & Hartmann 1987:
Disks in hydrostatic equilibrium (between stellar
gravity and thermal pressure along z) are flared
(i.e., the opening angle increases with R)
Calvet et al. 1994:
Irradiated disks are hotter on the surface than
in the midplane  emission features
Chiang & Goldreich 1997:
2-layer approximation
Schloss Ringberg, April 13-17, 2004

9. Irradiated Flared Disks
They intercept a larger
fraction of Lstar
The temperature profile
is flatter
Shapes
SEDs
Emission features
Nice range of temperatures for chemistry
Schloss Ringberg, April 13-17, 2004

10. The story of the HAe SEDs and the inner rim
High near-IR excess
The 3 mm bump
A ring on the sky
Hillenbrand et al. 1995
Natta et al. 2001
Millan-Gabet et al. 2001
Dullemond et al. 2001
Schloss Ringberg, April 13-17, 2004

11. When all we have are few points on the SED: BD disks
Flat or flared?
Large or small silicates?
Pascucci et al. 2003
All flavors, as TTS
Mohanty et al., submitted
Natta & Testi 2002
Schloss Ringberg, April 13-17, 2004

12. Grain growth, settling, planetesimals and planets
All these processes occurr in PMS disks and change them (opacity, decoupling gas and dust, dynamical interactions, etc.)
Observational tests are in their infancy
very large grains (sand and pebbles) in the outer disks of many PMS stars (Calvet et al. 2002; Natta et al. 2004)
gaps
We may have underestimated significantly disk masses in PMS stars
Schloss Ringberg, April 13-17, 2004

13. A never-ending discussion: disks or envelopes?
What is an envelope? matter with a more spherically-symmetric geometry
infalling envelopes (early phases)
wind (if dusty) ?
Important effects (due to scattering and emission) on the heating of the outer disk
If the emission in the far-IR is very extended, it is likely to be due to an envelope
One needs to worry on a case-by-case basis
Schloss Ringberg, April 13-17, 2004

14. From BB disks to radiation transfer codes (DUST)
2-layers: features from the optically thin surface,
approximate SEDs
1D: vertical temperature profile, scattering
2D: axially-symmetric structures (disk+envelopes,rims)
3D : spirals, vortices
See Pascucci et al. 2004a,b
for a banchmark study of several
2D and 3D RT codes
Schloss Ringberg, April 13-17, 2004

15. What do we want to do with the RT codes?
Predict observable quantities:
SED
Features
Intensity maps
Everything else
How?
Integrating radiation transfer into physical models
(D’Alessio et al., Bell et al.)
Using disk structure from “physical” models
(e.g., S, grain properties, etc.) as an input for RT
Schloss Ringberg, April 13-17, 2004

16. Grain growth, settling, planetesimals and planets
Schloss Ringberg, April 13-17, 2004

17. Schloss Ringberg, April 13-17, 2004
The rho-Oph sample
[Natta et al. 2002] ]
[see also Pascucci et al. 2003]
Schloss Ringberg, April 13-17, 2004

18. Schloss Ringberg, April 13-17, 2004
GY11 : a ~8-15 MJ object
with a flared disk
Schloss Ringberg, April 13-17, 2004
[Testi et al. 2002]

19. BDs are actively accreting: Broad Ha
Macc from veiling (TTS) or by fitting
Ha profiles with magnetospheric
accretion models
r-Oph CAM 032
[Muzerolle et al. 2003, Natta et al. 2004]
Schloss Ringberg, April 13-17, 2004

20. Disks and accretion in TTS:
A. Dutrey, 2001
Schloss Ringberg, April 13-17, 2004

21. First detections at mm wavelengths of two BDs in Taurus
[Klein et al, ApJ submitted; SCUBA at JCMT]
Disks models:
Flat disk
If flared, large inner hole and high rim
[Pascucci et al, ApJ in press]
Schloss Ringberg, April 13-17, 2004