Radiation Pressure and Gas Drag on Dust around Beta Pictoris

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• Radiation Pressure and Gas Drag on Dust around
  Beta Pictoris

Daniel Jontof-Hutter, Second Year Project Oral
Presentation, April 30th 2007 Supervised by Dr.
D. Hamilton, Dr. M. Kuchner
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Debris Disks

• Post Jovian Planet Formation
• Primordial Gas removed
• Dust generated by collisions

ISAS/JAXA
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• Telesco et al. (2005) IR images of ??Pictoris
• Clumps of dust attributed to planets

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UV spectral data reveal carbon rich gaseous
disk (Roberge et al 2005)
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Central Star
Dust grain
Orbiting gas
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Radiation pressure factor
Gas pressure support
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Tailwind ??????
Radiation Pressure
Dust grain
Gravity
Central Star
Headwind ??????
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Trajectory of a 500 ?m size grain with a headwind
Y(AU)
Initially at 10 AU, spirals in.
X (AU)
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Trajectory of a 250 ?m grain with a tailwind
Y (AU)
Initially at 10 AU, spirals out
X AU
X (AU)
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Gas support factor around ??Pictoris
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• Power Law depends on temperature profile
• Timescale to reach equilibrium depends on gas
  density
• Only grains larger than 100 ?m remain in inner
  100 AU

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Model Gas Disk
Density profile
Temperature profile
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1 ?m grain in dense gas ?c 10-14 g
cm-3 stopping time shorter than an orbit
Face on view Spirals out due to
tailwind ????????
Edge-on view Increases height above midplane
?????
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10 ?m grain in dense gas ???????
Face-on view Spirals out due to tailwind ??????
Edge-on view Settles down to midplane over many
orbits (??????

• In dense gas dust trajectories
• never cross the midplane

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Sparser gas ?c 10-16 g cm-3 10 ?m grain
trajectory
Spirals out due to tailwind
Crosses midplane every orbit. Loses inclination
over time.
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Sparse gas ?c 10-18 g cm-3 10 ?m grain
trajectory
Face-on view Orbit circularizes and spirals out
Edge-on view Inclination damped over time
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• Time for grains to be expelled beyond 200 AU
• All grains launched at 10 AU

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• What sort of gas and dust causes this appearance
  for ??Pictoris?
• Two planes inclined at 5o
• Inner 30 AU cannot be seen, unknown where gas or
  dust originates
• Secondary disk appears limited to 100 AU from
  the central star
• Dust orbits all appear to have the same ascending
  node,
• close to the line of sight.

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• Hypothesis
• Planetesimals may have inclinations with forced
  components due to perturbing planets, analogous
  to Hirayama families of asteroids.
• The forced inclination dominates the free
  inclination of orbits.
• Collisions generate dust which experiences
  radiation pressure and gas drag.
• Small, unbound grains are expelled in an orbital
  time.
• Large grains spiral out due to gas drag and
  slowly settle to the midplane.

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Model

• Sparse gas ?c 10-18 g cm-3 .
• Assumed Dohnanyi collisional size distribution
  for grains.
• Assumed scattering coefficient QPR 1.0.
• Grains 6 ?m to 30 ?m.
• All initial orbits at 10 AU, and 5o inclination.

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Z (AU)
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10
0
-10
-20
200
-200
-100
0
100
Projected horizontal distance (AU)
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Conclusions

• Disk can be modeled with dust generated on
  inclined orbit
• Gas drag is needed to reproduce the observations
• Grains settle to mid-plane or leave the system on
  inclined orbits
• Not enough time for grain orbits to have
  randomized ascending nodes
• More initial dust orbital parameters are worth
  testing.