Non-symetrical Protoplanetary Disks Annibal Hetem Jr. (FAFIL/FSA) Jane Gregorio-Hetem (IAG/USP)

Protoplanetary disks Protoplanetary disks are thought to be the progenitors of planetary systems. Gravitational interactions may cause the dust and gas in the disk to condense into planetesimals. This process competes against the stellar wind, which drives the gas out of the system, and accretion, which pulls material into the central star.

Protoplanetary disk classification We chose disk models based on an evolutionary scenario for the HAeBe stars, proposed by Malfait et al. (1998), similar to what is seem in TT stars. We chose three main scenarios: 1.Single dust disk with near-IR and far-IR excess. 2.Single dust disk with far-IR excess. 3.Double disk (a disk with a radial gap)

HAeBe Evolutive Sequence (Malfait et al. 1998) 1 2 3

Examples of HAeBe candidates classified as group (1) PDS 027; (2) (a) PDS 126; (b) PDS0318; and (3) PDS 545. (Sartori, Gregorio-Hetem & Hetem 2003 BAS Meeting)

Periodic Eclipses Light curves of AA Tau ( Bouvier et al. 1999, Ménard et al 2003, Alencar et al – 1 st Brasil CoRoT Workshop )

Flared disk model

Model Geometry (Chiang & Goldreich 1997) Hole radiusDisk radius External height Internal height Grazing angle

The model: formalism Column density Volume density Emissivity Gravitational potential External layer temperature Internal layer temperature

Grazing angle Disk height Energy distribution The model: formalism

Light curves CoRoT data shall be plenty of star occultation details.

Light curve simulation needed Very difficult to achieve due to disk model complexity. Slow code due to integrations. Program is sensitive to tilt and rotation angles.

3D computer graphics Used as image sequence generator. “Builds” very realistic scenes, with perspective and overlapping. Accepts all physical light parameters. Need few parameters. Fast.

Model choice Pixel counting Parameter definition 3D code “film” generation Sequence of images Synthetic light curve Geometry + Physics Technique

Planet Transit High albedo

Planet Transit Low albedo

Flared disk HAeBe Model 1:

Flared disk T Tauri Model 1:

Flared disk Binary Model 1:

Flared disk Large inner hole Model 2:

Flared disk Radial gap Model 3:

Protoplanetary gap The presence of a gap is indicative of protoplanetary activity. “God! A protoplanet!”

Theory: Lindblad Resonances Occurs when the natural epicyclic frequency of the disk is an exact multiple of the forcing frequency. This interaction has the effect of pushing material away from the resonance point, and is opposed by viscous torques. Nelson et al 2000

Theory: The gap If tidal torques dominate, a large annular gap in the disk opens up around the point, and the disk becomes highly non-linear at that location. Masset & Snellgrove 2001

Gap + Tidal forces = protoplanet See Nelson et al 2000 Masset & Snellgrove 2001 Papaloizou et al

Presence of a radial gap A gap in disk generates slightily differences in the light curve (when compared to star+disk case). CoRoT sensitivity can detect missing rings due to proto-planets. The detection need to be confirmed by modeling techniques. (or: The presence of a missing ring)

Modeling techniques: CoRoT data + parameter fitting!

Too many parameters From disk model itself: radii (hole, disk); grazing angle law; height (internal+external); density law; temperature law. From tilt and rotation geometry. Gap geometry.

Solution: Genetic Algorithm fitting Admits large number of parameters. Complexity model independent. Robust. Formal. (for an exemple see discussion in Fiege et al. 2004)

Executor Judge Avaliator (model) Implementation Statistics Solutions set Generator

Non-symetrical Protoplanetary Disks Thank You!