1. Planet and Gaps in the disk
Hwihyun Kim
Feb

2. PAPERS Forrest, W. J., et al., 2004, ApJS, 154, 443
“Mid-IR spectroscopy of disks around classical T Tauri stars”
Quillen, A. C., et al., 2004, ApJL, 612, L137
“On the planet and the disk of CoKu Tauri/4”
Varnière, P., et al., 2006, ApJL, 637, L125
“Observational properties of protoplanetary disk gaps”

3. INTRODUCTION Debate Recent discovery of CoKu Tau/4
About the nature and time-scales
Recent discovery of CoKu Tau/4
Young star containing a 10 AU hole (Forrest et al., 2004)
Link between the inner hole in the disk and the presence of planet
Outer disk is still accreting
Inner hole is left after the formation of a planet
Associated with planet formation in the disks surrounding young stars
2. suggests that planet formation can take place quite early stage of evolution
3. Ability to open a gap that block the mass flow to smaller radii
4. Because massive planet can not be formed at small radii from the star

4. PARAMETERS Disk viscosity (ν) : Reynolds number (Re) :
Timescale for the inward accretion (τν) :
α : viscosity parameter
cs : sound speed
h : scale height
Ω : angular rotation rate
r : radius of orbit
1.Viscosity : resistance of a fluid, or resistance to pouring
2. Reynolds number : dimensionless number, smoothness of the flow of fluid, ratio of inertial force to viscous force
Laminar flow : low Re, high viscosity / Turbulent flow : high Re, low viscous (Saturn ring picture)
3. Viscous timescale : high viscous material (low Re) can fall inward quickly

5. Wavemaker moon
Low viscous material-----high Reynolds number (turbulent flow)

6. CLEARING THE INNER DISK
Planet in the stellar disk forms a hole
Outer disk material is prevented from the accretion
Presence of the hole
Implies that the inner disk material has time to accrete onto the star
For low α and low h
Low viscosity, so high Re : higher τν
Inner disk has no time to accrete onto the star
Should be τp < τν < τage
1. Outer disk material cannot be accreted across the planet’s orbital radius because there is the transfer of orbital angular momentum from the planet to the disk.

7. GAP OPENING
Inner disk will begin accreting after a newly formed planet opens a gap
To open a gap...
Sufficiently massive : q > 40 Re-1
q = Mp/ M*
Mp of CoKu Tau/4 > 0.1 Mj
To open a gap, a planet must be massive because the spiral density waves(dissipated in the disk) should overcome the inward flow(due to viscosity).

8. PLANET MIGRATION Interaction between the planet and surrounding disk
To maintain the gap,
Balance of the torque density from spiral waves and inward torque from viscous accretion
Mp < Md : outward migration
CoKu Tau/4 : lack of significant migration
Migration is caused by the interaction. Interaction leads a transfer of ang. Mom.
Migration may occur after opening a gap
Spiral waves from the different resonances
No migration : still resides a large distance from the star. Sufficient mass has not accumulated in the disk edge.

9. CoKu Tauri/4 Location : Taurus-Auriga cloud
Spectral Type : M1.5 / Mass : 0.5 M⊙
Luminosity : 0.6 L ⊙ / Distance : 140 pc
Very special young star
Gap with radius 10 AU
Inner wall with half-height 2 AU
Gas planet with age < 1 Myr
Suggests that the planet formation can take place quite early in the evolution of protostellar systems

10. SPECTRUM Excess of emission
5-8 μm : characteristic of accretion disks around young stars
Beyond 8 μm : emission from small silicate grains
Spectrum from Spitzer observation shows the excess of emission

11. FM Tau vs. CoKu Tau 4 FM Tau CoKu Tau 4 Has accretion disk
Actively accreting
CoKu Tau 4
Decrease in emission in short-wave IR
Dusty disk with a gap at 10 AU
CoKu Tau is unique. No excess emission from the accretion disk in 5-8 micron.
Below the extrapolated stellar continuum
Broad peak and small dip 12.5 then rapid rise. This emission is from the heated dust surrounding the star
Low excess means that there are very few small grains closer to the star gap!!

12. HOW THE GAP CAN EXIT Interactions with the outer disk
Lindblad Resonances → Angular momentum
Constraints on the mass
Angular momentum → inward migration
MP > M disk edge → no migration
MP ≤ M disk edge → migration
Before we see the CoKu Tau 4 ‘s disk structure, more about the gap.

13. DISK MORPHOLOGY Lindblad resonances
This is the predicted disk morphology with a planet mass 0.1Mj. Because of the proximity of the planet and disk, high-order spiral density waves are driven by the planet at Linblad resonances. If these waves are constructive interference, the result is a spiral pattern rotating with the planet.

14. DISK MORPHOLOGY Proximity of the planet to the disk edge
More than one resonance
Multiple spiral density waves can be driven
at these resonances
Spiral pattern depends on
Scale height and disk temperature
(i.e. Smaller height and cooler disk : tightly wound)
High Reynolds number or large planet mass
Disk edge would be far from the planet
high Re : viscous time scale is long
Large planet mass : no migration to the outer disk

15. INNER HOLES IN DISKS Observation Simulation
Detected through the study of SEDs
Confirmed by direct images (scattered light image)
CO line emission in T Tauri stars
Simulation
Combination of 2D hydrodynamics simulation and 3D Monte Carlo radiative transfer code
3D simulation : because the gap is vertically extended
They can make the planetary gap with vertically extended density.

16. SCATTERED LIGHT IMAGE
The top panels : log of the disk surface brightness viewed at an inclination of i = 5
The bottom panels : disks viewed at i = 70
On the left : no gap in the disk
On the right : a gap created by a 2MJ planet at 1 AU
Created using 10^8 photons
The gap width (FWHM) is about 1 AU
The images show a 7 AU × 7 AU region.
Edge of the disk to the inner hole is brighter than outer disk on both with a gap and w/o a gap.

17. SURFACE BRIGHTNESS PROFILE
Bright bump : 4 times larger than the emission from the smooth disk
This is caused by the direct illumination of the outer wall of the gap because the stellar photon can not be absorbed anymore by the disk material.
The photon from the star hit the wall of outer gap.
Comparison between the two disks
* : no planet : 2Mj planet at 1AU
Decrease near the planet and bright bump at the outer edge of the gap

18. SPECTRAL ENERGY DISTRIBUTION
Current instruments
Insufficient spatial resolution
only detect gaps in the outer regions
SEDs
Indirect detection of planetary gaps
BUT, no unique features

19. SEDs IR SEDs Left : small-hole (r=0.07 AU) Right : large-hole (r=1 AU)
Small-hole : shallow bump(emission deficit) large-hole : deep bump & excess of emission
Gap doesn’t change the bolometric IR flux
Focus on the right-bottom
IR SEDs
Left : small-hole (r=0.07 AU)
Right : large-hole (r=1 AU)
Top : ISM dust
Bottom : HH 30 dust (high portion of big grains)
Solid line : with a gap
Dotted line : no gap

20. Planets sweep up the material around them and clean up the gaps.
When the accretion stops, the disk is dissipated and creates a large central hole!

21. SUMMARY Recent discovery by Forrest et al.(2004)
Young stellar system with a planet (CoKu Tau 4)
Inner disk has accreted within a time equivalent to the age of the star(1 Myr)
Planet could be accreting material and interact with the disk by driving waves into the disk from resonances
Simulation of the inner hole in the disk
Direct back illumination by stellar photons of the vertical disk wall
Back illumination heats the outer gap wall (emission excess and deficit in SED)