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 from the lack of mid-IR emission in the SED: Telesco et al. (2000) Kalas et al. (2005) HR4796 Fomalhaut But it was imaging which proved the existence of the inner holes: Walker & Wolstencroft (1998) Wavelength,  m Log(F, Jy)

Central cavities: without planets P-R drag would fill in the hole? Without planets to scatter or trap dust in resonance, P-R drag would fill in the inner hole in t pr = 400r 2 /M star  years Roques et al. (1994) With and Without Planets Kuiper Belt dust distribution Liou & Zook (1999) Number density Distance, AU This was the model proposed to explain the hole in the  Pictoris disk (>5M earth planet at 20AU)

Central cavities: no, P-R drag is insignificant The balance of P-R drag and collisions results in a surface density that depends only on  o = 5000  (r o )[r o /M * ] 0.5 /  Wyatt (2005) Tenuous disks Dense disks Tenuous disks  0 < 1 flat density distribution P-R drag dominated Dense disks  0 > 1 dust confined to planetesimal belt collision dominated P-R drag is insignificant in all detectable debris disks  o is an observable parameter, which for the known debris disks is >10

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 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 are the long term effect of the planet’s gravity and act on all disk material over >0.1 Myr timescales 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: spirals and offsets Planets on eccentric orbits impose eccentricities on nearby planetesimals causing: Wyatt et al. (1999) spiral structure offset centre of symmetry Wyatt (2005)

Resonant perturbations: clumpy rings Resonances cover small regions of parameter space, but can be filled: Inward migration of dust Dust spirals in due to P-R drag and resonances halt inward migration Outward migration of planet Planet migrates out sweeping planetesimals into its resonances Resonant filling causes a clumpy ring to form along the planet’s orbit Pl Resonance Star Pl Resonance Star Resonances affect material at locations where orbital periods are a ratio of two integers times that of planet: P res = P planet *(p+q)/p

Why resonances are clumpy

Dust migration into resonance Dust created in the asteroid belt spirals in toward the Sun over 50 Myr, but resonant forces halt the inward migration… Earth  Sun Ozernoy et al. (2000) Wilner et al. (2002) Quillen & Thorndike (2002) Dermott et al. (1994) …causing a ring to form along the Earth’s orbit Time Semimajor axis, AU Models of dust migration into planetary resonances have also been applied to debris disks

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 Wyatt (2003)

Resonant structures due to planet migration Wyatt (2003)

Have these signatures been observed? Warps Spirals Offsets Brightness asymmetries Clumpy rings Yes!!

Other causes of signatures? collisions Could this be the cause of the clumps? Yes for clumps seen in the mid-IR around young systems (e.g.,  Pictoris): smaller colliding objects, ~100km witnessed at special point in time No for clumps seen in the sub-mm (e.g., Fomalhaut): the collision would have to involve two >1400 km objects too few can coexist in the disk for this to be likely Wyatt & Dent (2002) Telesco et al. (2005)

Other causes of signatures? ISM sandblasting If ISM sandblasting of a debris disk is important, substantial asymmetries can arise… … however, the ISM contribution is only important >400 AU from the star Motion relative to the ISM Artymowicz & Clampin (1997)

Other causes of signatures? binary companions As well as truncating disks, binary companions can also impose spiral structure and asymmetries… Augereau & Papaloizou (2003) Quillen et al. (2005) Secular perturbations cause asymmetric extended structure Tidal perturbations cause open two armed structure … 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 eccentricities which cause spiral structure which collapses into nested eccentric rings Such an event may explain clumps seen in the NE of the  Pictoris disk Kalas et al. (2000) Larwood & Kalas (2001) However, flyby encounters of field stars at an appropriate distance to perturb the disk (<1000 AU) are extremely rare

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 techniques 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 Orbit Distribution Spatial Distribution Emission Distribution Vega’s two asymmetric clumps seen in the sub-mm can be explained by the migration of a 17M earth planet from 40-65AU in 56 Myr Most planetesimals end up in the planet’s 2:1(u) and 3:2 resonances Observed Model 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 (L star /M star )  -0.5 where  =M pl /M star in M earth /M sun Wyatt (submitted) 3:2 2:1

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 Wyatt (submitted) 3:2 2:1

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) 3:2 2:1

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 Wyatt (submitted) Observations in different wavebands sample different grain sizes, thus multi-wavelength images should have different structures and can be used to test models For Vega: Sub-mm observations sample population I grains Mid- to far-IR observations sample population III grains

Application to Vega Size distribution used to derive collisional lifetimes of different grain sizes Wyatt (submitted) Conclusions: 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 Size distribution Collisional lifetime

Conclusions 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