; Basic Debris Disk Model
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Basic Debris Disk Model


  • pg 1
									Is there evidence of planets
      in debris disks?

               Mark Wyatt

        Institute of Astronomy
       University of Cambridge

La planètmania frappe les astronomes
       Kalas, P. 1998, La Recherche 314, 38
Is there evidence for planets in debris disks?

Yes!  Eridani has both a dust disk (Greaves et al. 1998) and a planet detected by
radial velocity surveys (Hatzes et al. 2000)

But radial velocity planets and debris disks are at different locations
and it is unclear to what extent the two phenomena are related
(Greaves et al. 2004; Beichman et al. 2005)
Do debris disks contain evidence for planets?

 • What signature would a planet impose on a debris disk?

 • Have these signatures been observed?

 • Is there any other possible cause of these signatures?

 • Can we make further testable predictions?
Central cavities

Central cavities were inferred                         But it was imaging which
from the lack of mid-IR                                proved the existence of
emission in the SED:                                   the inner holes:

                                                       HR4796                  Fomalhaut
Log(F, Jy)

                                                      Telesco et al. (2000)   Kalas et al. (2005)

              1        10       100
               Wavelength, m         Walker & Wolstencroft (1998)
Central cavities: without planets P-R drag
would fill in the hole?
Without planets to scatter or trap dust                         This was the model
in resonance, P-R drag would fill in the                        proposed to explain the
inner hole in tpr = 400r2/Mstar years                          hole in the  Pictoris disk
                                                                (>5Mearth planet at 20AU)
            Kuiper Belt dust distribution

                                                    Number density
        With and                  Without Planets                          Distance, AU

               Liou & Zook (1999)                                             Roques et al. (1994)
Central cavities: no, P-R drag is insignificant

                                                            Wyatt (2005)

                                        Tenuous disks

   The balance of P-R drag and
   collisions results in a surface
   density that depends only on
   o = 5000(ro)[ro/M*]0.5/
                                                           Dense disks

Tenuous disks 0 < 1 flat density distribution          P-R drag dominated
Dense disks   0 > 1 dust confined to planetesimal belt collision dominated

    o is an observable parameter, which for the known debris disks is >10
         P-R drag is insignificant in all detectable debris disks
Origin of the inner holes?

• Lack of mid-IR emission implies few colliding planetesimals in inner regions
(Wyatt 2005)

• Few planetesimals expected in middle of planetary systems as planets clear
gaps along their orbits (Wisdom 1980)

• Growth of planetesimals into planets is faster closer to the star resulting in
the formation of inner holes (Kenyon & Bromley 2002)

• Could the early evolution of circumstellar disks also produce inner holes?
    • Radial transport of dust (Takeuchi & Artymowicz 2001)
    • Viscous draining of inner disk (Clarke et al. 2001)

     Inner holes are weak, though credible, evidence of planets
Secular perturbations: warps
A planet's gravity affects the orbits of planetesimals and dust in a debris disk.
Perturbations from a planet can be secular or resonant (Murray & Dermott 1999).

Secular perturbations are the long term effect of the planet’s gravity and
act on all disk material over >0.1 Myr timescales

A planet aligns planetsimals to its orbital plane so that a disk is warped if
    • one planet is misaligned with the disk (Augereau et al. 2001)
    • two planets with different orbital planes

                                                   Augereau et al. (2001)
Secular perturbations: spirals and offsets
Planets on eccentric orbits impose eccentricities on nearby planetesimals

           spiral structure                     offset centre of symmetry

                                                                Wyatt et al. (1999)

                              Wyatt (2005)
Resonant perturbations: clumpy rings

Resonances affect material at locations where orbital periods are a ratio of two
integers times that of planet: Pres = Pplanet*(p+q)/p

Resonances cover small regions of parameter space, but can be filled:
• Inward migration of dust
    Dust spirals in due to P-R drag and     Star          Pl
    resonances halt inward migration

• Outward migration of planet
    Planet migrates out sweeping            Star          Pl
    planetesimals into its resonances

Resonant filling causes a clumpy ring to form along the planet’s orbit
Why resonances are clumpy
Dust migration into resonance
Dust created in the asteroid belt spirals in      …causing a
toward the Sun over 50 Myr, but resonant          ring to form
forces halt the inward migration…                 along the                  Sun     Earth
                                                  Earth’s orbit
 axis, AU

                      Time                                              Dermott et al. (1994)

Models of dust
migration into
have also been
applied to
debris disks              Ozernoy et al. (2000)    Wilner et al. (2002) Quillen & Thorndike (2002)
Summarising dust migration structures
The type of structure expected when dust migrates into planetary resonances
depends on the planet’s mass and eccentricity (Kuchner & Holman 2003):

I low mass, low eccentricity
   e.g., Dermott et al. (1994),
   Ozernoy et al. (2000)  Eri

II high mass, low eccentricity
   e.g., Ozernoy et al. (2000) Vega

III low mass, high eccentricity
   e.g., Quillen & Thorndike (2002)

IV high mass, high eccentricity
    e.g., Wilner et al. (2002), Moran et al. (2004)
Resonant structures due to planet migration

Resonant structures due to planet migration

Have these signatures been observed?





Clumpy rings
Other causes of signatures? collisions

Could this be the cause of the clumps?
                                                           Telesco et al. (2005)

 No for clumps seen in                           Yes for clumps seen
 the sub-mm (e.g.,                               in the mid-IR around
 Fomalhaut):                                     young systems (e.g., 
 • the collision would                           Pictoris):
 have to involve two                             • smaller colliding
 >1400 km objects                                objects, ~100km
 • too few can coexist                           • witnessed at special
 in the disk for this to                         point in time
 be likely                 Wyatt & Dent (2002)
Other causes of signatures? ISM sandblasting

   If ISM
   sandblasting                                     Motion relative
   of a debris                                      to the ISM
   disk is
   can arise…
                      Artymowicz & Clampin (1997)

  … however, the ISM contribution is only important >400 AU from the star
Other causes of signatures? binary companions

As well as truncating disks, binary companions can also impose
spiral structure and asymmetries…

   Secular perturbations cause           Tidal perturbations cause open
   asymmetric extended structure         two armed structure

                                                 Quillen et al. (2005)
        Augereau & Papaloizou (2003)

… but the binary companions cannot explain all the spiral structure in the
HD141569A disk (Wyatt 2005)
Other causes of signatures? stellar flybys
 Stellar flybys induce
 perturbations which excite            Such an event may explain clumps
 eccentricities which cause            seen in the NE of the  Pictoris disk
 spiral structure which
 collapses into nested
 eccentric rings

                                                             Kalas et al. (2000)

                                   However, flyby encounters of field stars at
                                   an appropriate distance to perturb the
                                   disk (<1000 AU) are extremely rare
          Larwood & Kalas (2001)
Exoplanet statistics?
Is it too early to consider the statistics of
these putative planets in debris disks?

                                                Perhaps it is, but these
                                                planets occupy a region
                                                of parameter space
                                                unexplorable with other

                                                Thus it is vital to confirm
                                                their existence
Debris disk planet predictions

• Detect planet itself directly or
indirectly: hard

• Multi-epoch imaging:

    • Resonant structures
        • orbit with planet
        • decade timescales
        • 2 detection of rotation
        in  Eri (Greaves et al. 2005)

    • Secular structures
        • >0.1Myr timescales

• Multi-wavelength imaging:
    • can be done now!
Summary of the Vega planet migration model
• Vega’s two asymmetric clumps seen in the
sub-mm can be explained by the migration of
a 17Mearth planet from 40-65AU in 56 Myr
• Most planetesimals end up in the planet’s
2:1(u) and 3:2 resonances


    Orbit Distribution         Spatial Distribution Emission Distribution
                                                                      Wyatt (2003)
 Dynamics of small bound grains
 • Radiation pressure alters the orbital periods of small dust grains and so their
 relation to the resonance
 • Libration widths increase for small grains until they fall out of resonance for

                   >0.0020.5 or D<200m (Lstar/Mstar)-0.5
                         where =Mpl/Mstar in Mearth/Msun



                                                                        Wyatt (submitted)
Dynamics of small unbound grains
• Radiation pressure puts small (>0.5) grains on hyperbolic trajectories
• The collision rate of planetesimals in resonance is higher in the clump region

                     3:2                                     2:1

                                                                     Wyatt (submitted)
Particle populations in a resonant disk
      Population   Spatial distribution
          I        Same clumpy distribution as planetesimals
          II       Axisymmetric distribution
          III        r-1 distribution
            IIIa   Spiral structure emanating from resonant clumps
            IIIb   Axisymmetric distribution



                                                                     Wyatt (submitted)
Application to Vega

SED modelling used to convert Su et al.
3 component model into continuous
size distribution to assess contribution
of different grain sizes to observations
in different wavebands

                                           For Vega:
                                           • Sub-mm observations sample
                                           population I grains
                                           • Mid- to far-IR observations sample
                                           population III grains

                                           Observations in different wavebands
                                           sample different grain sizes, thus
                                           multi-wavelength images should
                                           have different structures and can be
                                           used to test models     Wyatt (submitted)
Application to Vega
Size distribution used to derive collisional lifetimes of different grain sizes
             Size distribution                     Collisional lifetime

                                                                          Wyatt (submitted)
  • Population II reduced by collisions with
  blow-out grains (Krivov et al. 2000)
  • Population III grains removed at 2M/Myr
  • Population II destroyed at 0.02M/Myr
  • Population III is type IIIa and mid- to
  far-IR images should exhibit spiral
  structure emanating from clumps

• Planets would impose structures on debris disks ranging from clumps to
warps, offsets, brightness asymmetries and spirals

• All of these structures have been observed in debris disks and (in most
cases) there is no other explanation

• Planets also cause holes, but this is weak evidence of planets

• This is a credible and unique exoplanet detection technique

• We need to confirm planetary interpretation through
   • multi-epoch imaging
   • multi-wavelength imaging

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