Understanding Disk Structure and Spectral Energy Distributions for Planet Formation

1. Disk Structure and Spectral Energy Distributions (SEDs) Ge/Ay133

2. How are stars and planets made? B68 B68 HH30 outflow outflow x1000 in scale infall BVI JHK Cloud collapse Rotating disk HD 141569 Mature solar system Planet formation Adapted from McCaughrean

3. Disks are thus critical, how can we study them? #1 – Silhouette Disks Only works for H II regions on the ‘front side’ of a cloud!

4. #2 – Edge-on Disks Highly informative, but also rare! Age →

5. While edge-on disks provide a natural coronograph, … AU Mic, Keck HD 141569A, HST more generally, need special circumstances for detection.

6. Remember, disks are small: Angular momentum budget: For a MMSN mass profile Keplerian disk of radius R, J~(3x1020 cm2/s)(R/100 AU)1/2 1 A.U. = 7 milli-arcseconds for D=140 pc (Taurus, Ophichus)

7. Imaging surveys/unresolved photometry rather easier. What do such surveys tell us? R=MIPS1 G=IRAC2 B=IRAC1 in Serpens Spitzer Blue=main sequence star Red =protostar/AGB star VV Ser

8. IR disk surface within several 0.1 – several tens of AU (sub)mm disk surface at large radii, disk interior. What determines disk properties (radius, flaring, T)? Characterizing large disk samples? SED Models: HH 30 G.J. van Zadelhoff 2002 Chiang & Goldreich 1997

9. Two different limits: Accretion-dominated vs. Passive How hot do accretion disks get? At the very least, infalling material must dissipate an energy of order (GM*/Rdisk) per unit mass. Balance this against thermal radiation: (GM*/Rdisk)(Mdisk)~2pRdisk2sT4·t where t=accretion timescale. Numerically, T~(500 K)(1 AU/Rdisk)3/4 for t=105 yr and a solar mass star. Thus, more massive and/or faster evolving disks are hotter. Notice the different vertical temperature structure for more realistic models.

10. Passive Disks: The SHAPE is critical If the central stellar mass dominates, the “vertical” acceleration at a distance R and height above the midplane z is g=geff≈ (GM*/R3)·z = W2·z where W=(vK/R)=the Keplerian angular vel. For an ideal gas, the sound speed c is simply c=(RT)1/2 (R=ideal gas constant). From the equation of hydrostatic equilibrium dP/dz=-rgeff=-rW2z=-(P/RT)W2z=-P(W/c)2z For a vertically isothermal disk this gives P = P0exp(-z2/H2) , Where the scale height H=c/W. For a sound speed of 1 km/s and WR~10 km/s, H/R=(sound speed)/(Keplerian vel.)~0.1. More quantitative models give (a=R):

11. The simplest model: Blackbody disks The first disk SED models assumed a flat disk geometry and that the disk radiated as a perfect blackbody. In this limit, the long wavelength tail has lFl l-4/3 Only a few disks obeyed this relationship, most showed much larger fluxes at longer wavelengths. The solution, as first recognized by Kenyon & Hartmann (1987, ApJ, 323, 714), was that actual disks are flared as derived in the slides above. The increased flaring with distance permits the disk to intercept more light from the star and re-radiate it in the far-IR.

12. Somewhat more realistic: Two layer disk models While still not fully self-consistent, a rather better two-layer disk model was developed by Eugene Chiang for his thesis. The basic idea is that the stellar light is absorbed by the surface layers of the disk that are optically thin to re-radiated infrared energy from grains. This approach w/flared disks provides a good fit to most observed SEDs. Chiang & Goldreich 1997, ApJ, 490, 368

13. Next step: Include grain model opacities The grains in disk surfaces are not perfect black- or greybodies, but instead have wavelength dependent emissivities. Predicts silicate emission bands for the SiO stretching and bending modes at 10/18 mm.

14. Grain Emission/Growth in Disk Surface Layers 10 mm band 20 mm band Data Models Kessler-Silacci et al. 2006, ApJ

15. Warning: Recent data suggest complex disk atmospheres Many disks display intense molecular emission even at R=600 (Spitzer IRS)! See water, organics. How do such species survive near the disk surface? Transport?

16. How unique are these models? Nearly all are degenerate for l<30 mm.

17. How bad are these model degeneracies? Bad! Note that for these two limiting cases the disk size differs by a factor of two, and the masses by a factor of nearly six! Can be broken with resolved images at longer wavelengths, as we’ll see next time.

18. How do we know how old pre-main sequence stars are? ← Mass ← Time Young stars contract to main sequence, need accurate data on M, L, T along with * models. Old clusters `dated’ with turn-off stars.