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 interaction
  Complimentary to radial velocity and transit
  detection methods
• Rosy future ground and space platforms
• Testable 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 ,
  Alex Moore

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Discovery Space

• All extrasolar planets discovered by radial
  velocity (blue dots), transit (red) and
  microlensing (yellow) to 31 August 2004. Also
  shows detection limits of forthcoming space- and
  ground-based instruments.
• Discovery space for planet detections based on
  disk/planet interactions

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Dynamical Regimes for Circumstellar Disks with
central clearings

• 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,
  PR force, resonant trapping and removal of
  particle in corotation region
• 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
• The transition disks
• Planets in Debris disks with clearings
• Fomalhaut
• Embryos in Debris disks without clearings
• AU Mic
• Number of giant planets
• in old systems

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Transition Disks

• 1-3 Myr old stars with disks with central
  clearings, silicate emission features,
• discovered in young cluster surveys
• Challenges to explain
• Accreting vs non
• Dust wall
• Clearing times
• Statistics
• Dust properties

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. 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
radiation
accretion, optically thick
Gapless disks lack planets
Edgar et al. 07
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Minimum Gap Opening Planet Mass in an Accretion
Disk
Smaller planets can open gaps in self- shadowed
disks
Planet trap?
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Prospects with ALMA
5km/s for a planet at 10AU
PV plot
Edgars simulations
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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.
  This implies the free eccentricities in the ring
  are small.
• The eccentricity of the ring is then 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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Diffusive approximations
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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 resonance
  clumps
• Lower mass extended lower unless the velocity
  dispersion at the disk edge set by planet
• Velocity dispersion close to threshold for
  collisions to be destructive

Log Planet mass
Quillen 2006, MNRAS, 372, L14 Quillen Faber
2006, MNRAS, 373, 1245 Quillen 2007,
astro-ph/0701304
Log Velocity dispersion
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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
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Comparison between 3 disks with resolved vertical
structure
107yr
107yr
108yr
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Debris Disk Clearing

• Spitzer spectroscopic observations show that
  dusty disks are consistent with one temperature,
  hence empty within a particular radius
• Assume that dust and planetesimals must be
  removed via orbital instability caused by planets

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Disk Clearing by Planets
Simple relationship between spacing, clearing
time and planet mass Invert this to find the
spacing, using age of star to set the stability
time. Stable planetary system and unstable
planetesimal ones.
Log10 time(yr)
µ10-7
µ10-3
Faber Quillen 07
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How many planets?

• Between dust radius and ice line 4 Neptunes
  required
• Spacing and number is not very sensitive to the
  assumed planet mass
• It is possible to have a lot more stable mass in
  planets in the system if they are more massive

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Summary

• Quantitative ties between observations, mass,
  eccentricity and semi-major axis of planets
  residing in disks
• 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 Jupiter mass
• Better understanding of collisional regime
• More numerical and theoretical work inspired by
  these preliminary crude numerical studies
• Exciting future in theory, numerics and
  observations