Sculpting

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Sculpting Circumstellar Disks with Planets
Alice Quillen University of Rochester
Mar 2008
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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 planets based on disk/planet
  interactions

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Outline

• Regimes mechanisms for planetdisk interactions
• When can planets be ruled out?
• Gapless gaseous disks
• Gapless dusty disks
• Predicting planets or embryo properties

Collaborators Peter Faber, Richard Edgar, Peggy
Varniere, Jaehong Park, Allesandro Morbidelli,
Alex Moore, Adam Frank, Eric Blackman, Pasha
Hosseinbor
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Physical Regimes

• Gaseous disks. Large dust opacity. Spiral density
  waves, accretion, migration, depletion.
• Gas depleted dusty disks. Intermediate opacity.
  Planestimals growing or/and eroding. Collisions
  and gravitational scattering.
• Orbits between collisions 1/t 103 a regime
  not well studied dynamically as most of the Solar
  System either well above or below this

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Minimum Gap Opening Planet in an Accretion Disk
Gapless disks lack planets gap opening criterion
viscosity vs min gap opening planet mass Gap
opening is independent of density but does depend
on alpha and temperature Temperature scaling
depends on opacity, energy source
radiation
accretion, optically thick

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 Dead zones lower mass objects can open
gaps in the dead zone (Matsumura, Oishi). Active
layer could continue to accrete through gap or
could be shielded and so disappear.
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Gap opening in debris disks

• If spiral density waves are driven effectively
  then viscous condition for gap opening can be
  used
• If collision timescale is longer than resonance
  libration timescale then spiral density waves are
  not driven
• Transition opacity but
  dependent on planet mass as libration frequency
  depends on q2/3
• Disk truncation via gravitational scattering
  possible role of chaotic zone boundary associated
  with corotation

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Based on diffusive numerical models for
collisions
Log Planet mass

• To truncate a disk a planet must have mass above
• here related to observables Quillen 2007

t10-4
t10-3
a0.001
Log Velocity dispersion
Observables can lead to planet mass estimates
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Planet mass estimates for transition disks

• Mass estimate for CoKuTau4 was based on a gap
  opening criterion this requires an estimate
  for the disk viscosity
• 1 Viscosity estimated via comparison to other
  disks with same SED but no clearing
• 2 Viscosity estimated via a clearing timescale
  and age of system
• Both constraints give a similar minimum planet
  mass estimate for a planet interior to the disk
  edge Saturn
• Larger planet masses required to keep steep edge
  and gap empty. Hydro alone insufficient to
  account for density decrement. Accretion in edge
  could cause gas inflow (e.g. Chiang Murray 07),
  while photoionization might help with clearing.

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Disk clearing following gap opening

• Why gap did not migrate?
• Planet fails to migrate much until density is
  sufficiently high in disk edge migration rates
  can be time dependent and depend on disk density
• Inner disk clearing happens on an accretion
  timescale unless perhaps planet drives high disk
  eccentricity at the 31 resonance interior to the
  planet
• If planet causes disk to self shield then
  accretion timescale exterior to edge could be
  longer
• Disk clearing takes longer than the age of the
  system for large clearings. Either another
  clearing mechanism is required or multiple
  planets are required to clear material. (Spitzer
  does not detect small gaps, only large clearings)

e.g., Varniere et al. 06 Edgar et al. 2007
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Edge structure

• Fraction of light emitted related to edge height,
  so far as I can tell height consistent with
  thermal structure expected for disk edge.
• If the edge density is higher then more light
  remitted at longer wavelengths
• This effect is irrelevant compared to role of
  dust size distribution which for CoKuTau4 seems
  to be dominated by small particles
• Low mm fluxes for this object imply low density
  outer disk, opposite true for DM Tau
• Imaging likely required to break degeneracy in
  SED fitting.

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Vertical motions in the disk edge
density slice
azimuthal angle
vz in units of Mach number
Spiral structure driven by planets difficult to
detect directly however may have indirect effects
(e.g. mascarades as turbulence or causes
shadowing, or kicks dust up)
Edgar et al. 08
(radius)
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Edge structure
time dependent structure, one armed when planet
close to edge, higher density leads to thicker
tau1 surface, planet itself may be bright,
accreting or have an outflow, asymmetries would
lead to scale height variations
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Edge structure

• For disks with denser outer disks, clearings have
  been confirmed at mm wavelengths (LkHa330 subm
  Brown et al. 08, TWHy 7mm Hughes et al. 07)
• Accreting systems tend to also have evidence for
  hot dust. However the accretion rate is set by
  gas density at small radii. The radial extent
  and total dust gas mass of these inner disks is
  not constrained from accretion rate alone.
• If these inner accreting disks extend to clearing
  edge then they must be highly depleted of dust.
• Mechanisms proposed keep larger dust grains in
  disk edge, stronger coupling of small dust with
  gas flows (e.g., Rice et al 06, Fouchet et al.
  07)
• Existence of at least 2 systems with clearings
  lacking accretion imply that inner disk clearing
  can be faster than disk depletion OR multiple
  planet formation occurs OR they are binaries.

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Debris Disk Clearing

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

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Planetesimal 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
• a Jupiter mass in planets is required to explain
  clearings in all debris disk systems
• 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
• Eccentric planets are more efficient at clearing
  (Jiang, Duncan and Lin 06) perhaps less mass
  required, though eccentricity causing mechanism
  is then required.
• Velocity dispersion in dust disk relevant toward
  telling these two possibilities apart!

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Planet spacing when there are dust belts

• Moro-Martin et al. 07, located dust belt based on
  stability requirements, 2RV planet system.
• Epsilon Eridani (any moment now) will become an
  interesting system to reconstruct in terms of
  planets dust belts
• Some other object that Mark Wyatt mentioned

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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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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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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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Caveats and predictions

• Do mechanisms exist to cause eccentric clearings
  that dont require planets?
• Ring is not thick, no evidence for highly
  scattered planetesimal population
• Yet eccentric planet possibly present
• Collisions are destructive so how did the ring
  damp to the low free eccentricity orbit? Small
  amounts of gas (Aki)? Or did debris heat post
  planet?
• Planet predicted. So far no morphology variations
  predicted _at_higher angular resolution or with
  wavelength.

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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 increased by 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
related to observables, however exponents not
precisely known
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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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Caveats

• No formation timescale and self-stirring
• Other possible sources of vertical heating not
  yet considered (spiral density waves?)
• Extrapolating over 10 orders of magnitude is not
  likely to be very predictive
• I cant yet think of any way to test this model

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Summary

• Largish planets can be ruled out for gapless
  disks both for accretion disks (but then
  viscosity must be known) and for collisional
  disks (related to dispersion and opacity but
  based on diffusive approximation)
• If a planet is present then the same criterion
  can be used to place a limit on planet mass
• If planet is responsible for truncating the disk
  then it is likely located near the clearing edge
• Large empty clearings likely require multiple
  planets. Stability criteria can be used to
  estimate how many. Done for circular orbits.
  Not yet explored for eccentric systems. Systems
  with both planets and dust belts just starting to
  be explored.
• Some hints of large debris in gapless disks,
  alternative models yet to be explored.
• Alternate explanations for eccentric holes yet to
  be explored.