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Planets in Debris Disks
Renu Malhotra
University of Arizona
•Planet-Debris co-evolution
•Where can debris exist? Cases: Solar system, upsilon Andromedae, 47 Ursae Majoris
•What we are learning from the Kuiper Belt
STScI May Symposium, 2005
Debris tells planets where to move;planets tell debris where to stay.
Final stages of planet formation: planet-debris co-evolution
Two possible evolutionary paths:
• Planet-planetesimal disk interactions: migration as in our solar system -- planet eccentricities remain damped while semimajor axes spread out. Evidence in the solar system: Asteroid belt, Kuiper Belt, Oort Cloud.
• Planet-planet interactions: if the debris disk mass is insufficient, planet eccentricities will not remain damped, crossing orbits will develop, leading to mergers, scattering, ejection. Evidence in upsilon Andromedae (Ford et al 2005)
STScI May Symposium, 2005 Malhotra
Planet-debris co-evolution
A simulation - Hahn & Malhotra, 1999A simulation - Hahn & Malhotra, 1999
Model predictionModel prediction
Observed orbital distributionObserved orbital distribution
STScI May Symposium, 2005 Malhotra
Dynamical constraints on debris location
Single planet perturbations:• Hill stability ∆a/ap> 2.4(mp/m*)1/3 ≈ 3RH
• Resonance overlap ∆a/ap> 1.5(mp/m*)2/7
• Eccentric planet r (q-3RH,Q+3RH)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
STScI May Symposium, 2005 Malhotra
Dynamical constraints on debris…
Two planet system• No analytic global stability criterion• Direct numerical integration of test particles
STScI May Symposium, 2005 Malhotra
• Secular stability analysis
-- Laplace-Lagrange secular theory for planets: linear modes.
E.g. g5,g6 for Sun-Jupiter-Saturn system
-- Secular resonances of debris (test) particles
E.g. 5,6 for Sun-Jupiter-Saturn
-- Eccentricity excitation depends strongly on a, weakly on m1/m2
upsilon AndromedaePossible debris locations:•0.06 - 0.3 AU•beyond 8 AU
47 Ursae Majoris47 Ursae MajorisPossible debris locations:•0.3 - 0.6 AU•beyond 7.5 AU
STScI May Symposium, 2005 Malhotra
Consistent with numerical simulations (e.g., Rivera & Lissauer)
Solar system debrisSolar system debrisPossible locations:•inward of 0.5 AU•0.8 - 1.6 AU•2.0 - 4.3 AU•beyond 18 AU
STScI May Symposium, 2005 Malhotra
Solar system debris: the Kuiper Belt
Art by Don Dixon (2000)
STScI May Symposium, 2005 Malhotra
Kuiper Belt Dynamical Structure
• Resonant KBOs (3:2, 2:1, 5:2)• Main belt (40<a<47 AU) hot
and cold components• Scattered disk
(a>50 AU & 30<q<36 AU)• Extended scattered disk
(a>>50 AU & q>36 AU)• Edge at 50 AU
… All these suggest• Resonance sweeping• 9 AU outward migration of
Neptune• Excitation of e’s and i’s
-- stellar encounter? rogue planets? long term chaos?STScI May Symposium, 2005 Malhotra
Size distribution
• Observed KBOs have diameter 10<D<1000 km.
• N(D>100 km) ~ 5x104 Total mass (<50 AU) ~ 0.03 earth-mass. classical disk mass ~ 0.01 earth-mass.
• Size-class corelations - excited KBOs have more large objects and fewer small objects compared to classical disk
• Accretion models suggest that D>100 km KBOs must have formed in a massive (10-30 EM), dynamically cold disk (e,i<0.001)
Red=“classical disk”: i<5 deg, 38<d<55 AUGreen=“excited disk”
Bernstein et al., 2004
• Some process has disturbed the Kuiper Belt, excited the KBO orbits and eroded its mass.•The origin of the short-period Jupiter-family comets is uncertain.
STScI May Symposium, 2005 Malhotra
Kuiper Belt dust• Dust density nearly constant in outer
solar system (Pioneer 10,11; Voyagers 1,2)
• KB dust production rate (1m--1mm) ~ 1015 g/y [eqv. D ~ 1 km comet ground to dust every year.]
• Small particles (r < 0.5m) are blown out by radiation pressure
• Bound dust grains spiral inward under Poynting-Robertson (PR) drag
• Temporary trapping in Neptune’s MMRs produces azimuthal structure
• Gravitational scattering by Jupiter,Saturn ejects most particles; very small fraction of KB dust enters the inner solar system
Model from Moro-Martin & Malhotra, 2003
STScI May Symposium, 2005 Malhotra
Massive planetsMassive planets will also scatter and eject will also scatter and eject dust particles, creating gaps or `inner dust particles, creating gaps or `inner holes’.holes’.
Lessons for debris disksMassive planets within debris disks will shepherd the dust Massive planets within debris disks will shepherd the dust grainsgrainsWithout
planetswith Solar System planets
Uniform density diskUniform density disk
minimum at Neptune’s position (to avoid resonant planet)
Neptune
ring-like structure along Neptune’s orbit (trapping into Mean Motion Resonances)
clearing of dust from inner 10 AU (due to gravitational scattering by Jupiter and Saturn)
STScI May Symposium, 2005 Malhotra
A planet-detection technique complementary to RV
A history of Kuiper Belt dust
A schematic history of the outer solar system dust production rate
STScI May Symposium, 2005 Malhotra
Summary and Conclusions
• Planet-debris interactions: evidence in the architecture of planetary systems (Sol Sys, ups And)
• Secular stability analysis: locates debris in a planetary system
• The solar system debris has a complex dynamical structure- Cannot be explained simply by planetary perturbations.- Planet migration explains a lot, but probably not all.
• Kuiper Belt dust and extra-solar debris disks: - spatial distribution sculpted by planetary perturbations - dust particle size distribution also perturbed - high dust densities (and dust outflows) at younger epochs - planetary architectures can be discerned by detailed study
STScI May Symposium, 2005 Malhotra