Sculpting

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Sculpting Circumstellar Disks
Alice Quillen University of Rochester
Netherlands April 2007
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Motivations

• Planet detection via disk/planet interactions
  Complimentary to radial velocity and transit
  detection methods
• Rosy future ground and space platforms
• Testable models via predictions for
  forthcoming observations.
• New dynamical regimes and scenarios compared to
  old Solar system
• Evolution of planets, planetesimals and disks
• Collaborators Peter Faber, Richard Edgar, Peggy
  Varniere, Jaehong Park, Allesandro Morbidelli ,
  also Eric Blackman, Adam Frank, Pasha Hosseinbor,
  Amanda LaPage

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Observational Background
Submillimeter imaging

• Young Clusters 5--20 of stars surveyed in young
  clusters are T-Tauri stars hosting disks with
  large clearings Dozen or so now with
  IRS/Spitzer spectra, more identified with
  Spitzer/IRAC photometry
• Older Disks and Debris Disks Fraction detected
  with disks with IR excess depends on age,
  wavelength surveyed and detection limit. 50100
  now known from Spitzer/MIPS surveys
• Unexplained structure edges, clearings, spiral
  arms, warps, clumps

Fomalhaut
HD 100546
HR4796A
Optical scattered light
Beta Pictorus
HD 141569A
Credits, ESO,Schneider Wilner, Grady, Clampin,
HST, Kalas
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Dynamical Regimes for Circumstellar Disks with
central clearings

• 1. Young gas rich accretion disks
  transitional disks e.g., CoKuTau/4.
• Planet is massive enough to open a gap (spiral
  density waves).
• Hydrodynamics is appropriate for modeling.

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Dynamical Regimes continued

• 2. Old dusty diffuse debris disks dust
  collision timescale is very long e.g., Zodiacal
  cloud.
• Collisionless dynamics with radiation pressure,
  drag forces, resonant trapping, removal of orbit
  crossing particles
• 3. Intermediate opacity dusty disks dust
  collision timescale is in regime 103-104 orbital
  periods e.g., Fomalhaut, AU Mic debris disks

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This Talk
What mass objects are required to account for the
observed clearings, What masses are ruled out?

• Planets in accretion disks with clearings
• -- CoKuTau/4
• Planets in Debris disks with clearings
• -- Fomalhaut
• Embryos in Debris disks without clearings
• -- AU Mic
• Total mass in planets in older systems
• -- Clearing by planetary systems

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Transition Disks

• Estimate of minimum planet mass to open a gap
  requires an estimate of disk viscosity.
• Disk viscosity estimate either based on clearing
  timescale or using study of accretion disks.
• Mp gt 0.1MJ

Wavelength µm
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Models for Disks with Clearings
1. Photo-ionization models (Clarke, Alexander)
Problems -- clearings around brown
dwarfs, e.g., L316, Muzerolle et al. --
accreting systems such as DM Tau, DAlessio et
al. -- wide gaps such as GM Aur Calvet et
al. -- single temperature edges Predictions
Hole size with time and stellar UV luminosity

• 2. Planet formation, gap opening followed by
  clearing (Quillen, Varniere) -- more versatile
  than photo-ionization models but also more
  complex
• Problems Failure to predict dust density
  contrast, 3D structure
• Predictions Planet masses required to hold up
  disk edges, and clearing timescales, detectable
  edge structure

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Minimum Gap Opening Planet In an Accretion Disk
Gapless disks lack planets
Park et al. 07 in preparation
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Minimum Gap Opening Planet Mass in an Accretion
Disk
Smaller planets can open gaps in self- shadowed
disks Hole radii scale with stellar mass (Kim et
al. in prep) Retired A stars lack Hot Jupiters?
(Johnson et al. 07)
Planet trap?
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Fomalhauts eccentric ring

• steep edge profile
• hz/r 0.013
• eccentric e0.11
• semi-major axis a133AU
• collision timescale 1000 orbits based on
  measured opacity at 24 microns
• age 200 Myr
• orbital period 1000yr

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Free and forced eccentricity
radii give you eccentricity If free eccentricity
is zero then the object has the same eccentricity
as the forced one
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Pericenter glow model

• Collisions cause orbits to be near closed ones.
  Small free eccentricities.
• The eccentricity of the ring is the same as
  the forced eccentricity
• We require the edge of the disk to be truncated
  by the planet ?
• We consider models where eccentricity of ring and
  ring edge are both caused by the planet.
  Contrast with precessing ring models.

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Disk dynamical boundaries

• For spiral density waves to be driven into a disk
  
• (work by Espresate and Lissauer)
• Collision time must be shorter than libration
  time
• ? Spiral density waves are not efficiently driven
  by a planet into Fomalhauts disk
• A different dynamical boundary is required
• We consider accounting for the disk edge with the
  chaotic zone near corotation where there is a
  large change in dynamics
• We require the removal timescale in the zone to
  exceed the collisional timescale.

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Chaotic zone boundary and removal within
What mass planet will clear out objects inside
the chaos zone fast enough that collisions will
not fill it in? Mp gt Neptune
Neptune size
Saturn size
collisionless lifetime
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Chaotic zone boundaries for particles with zero
free eccentricity

• Hamiltonian at a first order mean motion
  resonance

secular terms
regular resonance
corotation
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Dynamics at low free eccentricity

• Expand about the fixed point (the zero free
  eccentricity orbit)
• For particle eccentricity equal to the forced
  eccentricity and low free eccentricity, the
  corotation resonance cancels
• ? recover the 2/7 law, chaotic zone same width

goes to zero near the planet
same as for zero eccentricity planet
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Dynamics at low free eccentricity is similar to
that at low eccentricity near a planet in a
circular orbit
different eccentricity points

• No difference in chaotic zone width, particle
  lifetimes, disk edge velocity dispersion low e
  compared to low efree

width of chaotic zone
planet mass
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Velocity dispersion in the disk edgeand an upper
limit on Planet mass

• Distance to disk edge set by width of chaos zone
• Last resonance that doesnt overlap the
  corotation zone affects velocity dispersion in
  the disk edge
• Mp lt Saturn

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cleared out by perturbations from the planet Mp gt
Neptune
nearly closed orbits due to collisions eccentricit
y of ring equal to that of the planet
Assume that the edge of the ring is the boundary
of the chaotic zone. Planet cant be too massive
otherwise the edge of the ring would thicken ?
Mp lt Saturn
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First Predictions for a planet just interior to
Fomalhauts eccentric ring

• Neptune lt Mp lt Saturn
• Semi-major axis 120 AU (16 from star)
• Eccentricity ep0.1, same as ring
• Longitude of periastron same as the ring

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The Role of Collisions

• Dominik Decin 03 and Wyatt 05 emphasized that
  for most debris disks the collision timescale is
  shorter than the PR drag timescale
• Collision timescale related to observables

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The numerical problem

• Between collisions particle is only under the
  force of gravity (and possibly radiation
  pressure, PR force, etc)
• Collision timescale is many orbits for the regime
  of debris disks 100-10000 orbits.

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Numerical approaches

• Particles receive velocity perturbations at
  random times and with random sizes independent of
  particle distribution (Espresante Lissauer)
• Particles receive velocity perturbations but
  dependent on particle distribution (Melita
  Woolfson 98)
• Collisions are computed when two particles
  approach each other (Charnoz et al. 01)
• Collisions are computed when two particles are in
  the same grid cell only elastic collisions
  considered (Lithwick Chiang 06)

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Our Numerical Approach

• Perturbations independent of particle
  distribution
• Espresate set the vr to zero during collisions.
  Energy damped to circular orbits, angular
  momentum conservation. However diffusion is not
  possible.
• We adopt
• Diffusion allowed but angular momentum is not
  conserved!
• Particles approaching the planet and are too far
  away are removed and regenerated
• Most computation time spent resolving disk edge

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Parameters of 2D simulations
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Morphology of collisional disks near planets
radius

• Featureless for low mass planets, high collision
  rates and velocity dispersions
• Particles removed at resonances in cold, diffuse
  disks near massive planets

radius
angle
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Profile shapes
chaotic zone boundary 1.5 µ2/7
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Rescaled by distance to chaotic zone boundary

• Chaotic zone probably has a role in setting a
  length scale but does not completely determine
  the profile shape

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Density decrement

• Log of ratio of density near planet to that
  outside chaotic zone edge
• Scales with powers of simulation parameters as
  expected from exponential model

Unfortunately this does not predict a nice form
for tremove
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Using the numerical measured fit
Log Planet mass

• To truncate a disk a planet must have mass above
• (here related to observables)

Nc10-3
Nc10-2
a0.001
Log Velocity dispersion
Observables can lead to planet mass estimates,
motivation for better imaging leading to better
estimates for the disk opacity and thickness
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Application to Fomalhaut

• Upper mass limit confirmed by lack of resonant
  structure
• Lower mass limit lower than previous estimate
  unless the velocity dispersion at the disk edge
  set by planet

Quillen 2006, MNRAS, 372, L14 Quillen Faber
2006, MNRAS, 373, 1245 Quillen 2007,
astro-ph/0701304
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Constraints on Planetary Embryos in
Debris Disks
Thin
AU Mic JHKL Fitzgerald, Kalas, Graham
h/rlt0.02

• Thickness tells us the velocity dispersion in
  dust
• This effects efficiency of collisional cascade
  resulting in dust production
• Thickness from gravitational stirring by massive
  bodies in the disk

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The size distribution and collision cascade
observed
constrained by gravitational stirring
Figure from Wyatt Dent 2002
set by age of system scaling from dust opacity
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The top of the cascade
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Gravitational stirring
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Comparing size distribution at top of collision
cascade to thatrequired by gravitational stirring
size distribution might be flatter than 3.5
more mass in high end ? runaway growth?
gt10objects
gt 10objects
Earth
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Comparison between 3 disks with resolved vertical
structure
107yr
107yr
108yr
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Clearing by Planetary Systems

• Assume planet formation leaves behind a
  population of planetesimals which produce dust
  via collisions
• Central clearings lacking dust imply that all
  planetesimals have been removed
• Planets are close enough that interplanetary
  space is unstable across the lifetime of the
  system
• 50 known debris disks well fit by single
  temperature SEDs implying truncated edges (Chen
  et al. 06)

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Clearing by Planetary Systems
Log10 time(yr)
µ10-9
µ10-5
Separation
Faber et al. in preparation
Chambers et al. 96
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Clearing by planetary systems
rmin set by ice line rmax set by observed disk
temperature Result is we solve for N and find
3-8 planets required of Neptune size for most
debris disks. This implies a total minimum mass
in planets of about a Saturn mass
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Summary

• Quantitative ties between
• disk structure and planets
• residing in disks
• Better understanding of
• collisional regime and its relation to
  observables
• In gapless disks, planets can be ruled out but
  we find preliminary evidence for embryos and
  runaway growth
• The total mass in planets in most systems is
  likely to be high, at least a Saturn mass
• More numerical and theoretical work inspired by
  these preliminary crude numerical studies
• Exciting future in theory, numerics and
  observations

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Prospects with ALMA
5km/s for a planet at 10AU
PV plot
Edgars simulations
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Diffusive approximations