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debris disc modelling. Philippe Thébault Paris Observatory/Stockholm Observatory. Disc modelling: going from there…. …to there…. …and there. Outline. I . Observational data: the need for modelling II . Size and spatial distributions of debris discs III . Collisional avalanches

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Debris disc modelling

debris disc modelling

Philippe Thébault

Paris Observatory/Stockholm Observatory

Debris disc modelling

Disc modelling: going from there….

Debris disc modelling

…to there…

Debris disc modelling

…and there

Debris disc modelling


  • I. Observational data: the need for modelling

  • II. Size and spatial distributions of debris discs

  • III. Collisional avalanches

  • IV. Outer edges of debris discs

  • V. Vertical structure of debris discs (work in progress)

Debris disc modelling

what is a debris disc?

  • it is not a protoplanetary disc

  • Lagrange et al.(2000):

    • Mdisc<<0.01 M*

    • Ldisc/L*<<1

    • Dust and gas dynamics decoupled (Mgas<10Mdust)

    • Dust lifetime < System’s age (« debris »)

  • debris discs are made from collisionally eroding leftovers from the planet-formation process

Debris disc modelling

relative timescales:

collisions are the dominant process!

Example: β-Pic (Artymowicz, 1997)

Debris disc modelling

protoplanetary discs around YSOs

Young (<107yrs) and massive (~100M) discs, with Mgas/Mdust~100

Debris disc modelling

« protoplanetary » discs

Debris discs

Greaves (2005)

Debris disc modelling

Discoveries of debris discs, the IR trilogy: IRAS/ISO/Spitzer

IRAS (ESA, 1983): all sky survey.

Resolution~0.5’-2’. First IR-excess detection: Vega (“vega-type” stars). ~170 IR-excess detections => ~15% of stars with debris discs

ISO (ESA, 1996): pointed telescope.

Resolution~1.5”-90”. 22 new detections. ~17% of stars with discs. Spectral type dependancy: A:40%, F:9%, G:19%, K:8%.

Spitzer (NASA, 2003): pointed telescope, currently operating.

Resolution~1”-10”. Truckload of new results

coming out.

Debris disc modelling

Imaging of debris discs: visible/near IR

b-Pictoris (1984)

Debris disc modelling






β-Pictoris: multi wavelength imaging

Debris disc modelling

the debris disc zoo

Debris disc modelling

and some more…

Debris disc modelling

Circumstellar disc observations:

wavelength vs radius probed

Circumstellar discs have been studied at all wavelengths from optical to cm

Different wavelengths probe different locations in the disc; e.g., thermal emission from an optically thin disc, assuming black body grains:

Tdust = 278.3 L*0.25/r0.5

peak = 2898m/T = 10.4r0.5/L*0.25

rprobed = 0.012L*0.5 AU

NIR=0.1AU, MIR=1AU, FIR=30AU, SUB=1000AU (though smaller as not observed at peak)

Debris disc modelling

What do we se? DUST (<1cm)

  • Total flux = photometry

    • One wavelength shows disk is there

    • Two wavelengths determines dust temperature

    • Model fitting with multiple wavelengths (Spectral Energy Distribution)

  • Composition = spectroscopy

    • Can be used like multiple photometry

    • Also detects gas and compositional features

  • Structure = imaging

    • Give radial structure directly and detects asymmetries

    • But rare as high resolution and stellar suppression required

Scattered light: UV, visible,near-IR

Thermal emission:mid-IR,far-IR,mm

Debris disc modelling

Deriving dust masses:

sub-mm/mm photometry

  • Sub-mm/mm observations are the best way of deriving dust mass:

  • unaffected by uncertainties in Tdust

  • discs are optically thin so most of the mass is seen

  • larger grains contain most of the mass

  • little contribution to flux from stellar photosphere

  • The basic equation is:

  • Mdust = Fd2/[B(T)]

  • where d is distance,  = 1.5Q/(D)  0(0/) is the mass opacity and a value of 0=0.17m2/kg is often used for 0=850m with =1

Debris disc modelling

what we see

  • Dust ~ [µm,mm]

  • Gas (sometimes)

what we’d like to know about

  • pebbles, rocks, planetesimals, asteroids, comets.…

  • Planets

Debris disc modelling

Numerical Modelling, why?

  • Observations only give partial (size, radial location) and model dependent information


  • Most of the mass (r>1cm) remains undetectable

SB profile

Debris disc modelling

Numerical Modelling, what for?

  • What are discs made of?

    • Size Distribution

    • Total mass

    • “hidden” bigger parent bodies (>1cm)

    • Long term evolution, lifetime



  • What is going on?

    • Explain the Observed Spatial Structures

    • Presence of Planets?

Debris disc modelling

II. Collisional Evolution models

  • Derive accurate size & spatial distributions for the whole visible grain populations

  • Characterize the invisible population of eroding parent bodies

  • Understand what is going on: dynamical state, mass loss rate, presence of transitory events, etc….

Debris disc modelling

Size Distributions derived from observations are model dependent…

(Li & Greenberg 1998)

Debris disc modelling

what we see

...and restricted to a narrow size range

collisional cascade

~radiation pressure cutoff

unseen parent bodies

size distribution ???

~observational limit

Debris disc modelling


doing it the lazy way: the drr3.5dr distribution

Theoretical collisional-equilibrium law dN r-3.5dr

What we don’t see

What we see

Debris disc modelling

many reasons why the dNr3.5dr distribution just doesn’t work

  • assumes infinite size distribution

  • wrong: rmin due to radiation pressure

    rmaxbecause finite mass

  • assumes scale-independent collisional processes

  • wrong: response to impacts varies with size (strength regime for small targets, grav.regime for big ones)

  • neglects the specific dynamics of small grains

  • wrong: radiation places high-β on eccentric orbits

Debris disc modelling

Size Distribution/Evolution:Statistical “Particle in a box” Models

  • Principle

    • Dust grains distributed in Size Bins (and possibly spatial/velocity bins)

    • “Collision” rates between all size-bins

    • Each bini-binj interaction produces a distribution of binl<max(i,j) fragments

  • Approximations/Simplifications

    • No (or poor) dynamical Evolution

    • Poor spatial resolution

Debris disc modelling

statistical collisional evolution code

  • « Particle in a box » Principle

  • divide the population in size bins

  • evolution Equ.:

  • Collision Outcome prescription (lab.experiments)

Debris disc modelling







a(1), e(1)

High e orbits of grains close to the RPR limit

multi-annulus collisional code (Thebault&Augereau, 2007)

  • takes into account

  • Collisions (fragmentation, cratering, re-accretion)

  • simplified dynamics

  • Radiation pressure effects

  • Extended Disc: 10-120AU

  • Size range: 1μm – 50km (!)

Debris disc modelling

evolution of an extended debris disc

size distribution evolution (Thebault&Augerau, 2007)

Debris disc modelling

(2) overabundance due to the lack of smaller potential impacotrs

(1) Lack of grains< RPR

(3) Depletion due to the overabundance in (2)

(4) Overdensity due to lack of (3), etc…

cutoff size RPR

the ”wavy” size distribution

Debris disc modelling

collision rates

the ”magical” tcol=(Ωτ)-1formula can also be *very* wrong

Debris disc modelling

why should we care? / Main Conclusions

  • Wavyness is a robust feature

  • Overdensity of ~2rcutoff grains

  • Depletion of 10rcut<r<50rcut grains

  • Optical depth dominated by a narrow range rcut<r<2rcut

  • visible dust radial distribution ≠ parent bodies distribution

  • (flatter) (steeper by a factor ~a)

Be careful when reconstructing ”asteroid belts”

Debris disc modelling

Main Conclusions (2)

  • this has consequences on data anlysis from Spitzer/Herschel...

Debris disc modelling

III. Collisional avalanches

Grigorieva, Thebault&Artymowicz 2007

Could clumpy or spiral structures be explained by transient violent collisional events?

Debris disc modelling

collisional avalanches: combined statistical and dynamical code

Collisionnal cascade after large planetesimal/cometary breakup

Debris disc modelling

collisional avalanches: face-on spiral structures

Debris disc modelling

collisional avalanches: two-side asymetries

Debris disc modelling

IV. Outer edges of debris discs:

how sharp is sharp?

Debris disc modelling

Outer edges: ”natural” collisional evolution of a narrow ring left to itself

a-3.5 slope

(Thébault & Wu, 2008)

Debris disc modelling

processes at play

  • Collisions in the ”birth ring” produce high-β grains on high-e orbits

  • Steady state: 0.2<β<0.4 grains dominate in the aring<a<4rring region

Debris disc modelling

the ”universal” a-3.5profile

low mass disc

high mass disc

Debris disc modelling

”extreme” case with SB profile steeper than a-3.5

dynamically ”cold” system: e=2i < 0.01

main problem:

how likely is it?

high-β grains production is unefficient (low v among parent bodies) while high-β grains destruction is still very efficient (high v among small grains) => Depletion of β>0.1 grains

Debris disc modelling

fitting a ”razor-sharp” edge: HR4796

Debris disc modelling

in short

”natural” outer edge profile

”natural” if highly anisotropic scattering

”natural” only if e<0.01...otherwise, need for ”something” else to act

Debris disc modelling

V. Vertical structure of debris discs (work in progress)

  • Very few discs are resolved in z

  • the H/a ratio is our only reliable information on the disc’s dynamical state...

if equipartition: H/a ~ 2<i>~<e> ~ <dV>/VKep

ex: H/a=0.1 => <dV>~ 450m/s

=> Vesc(RBIG) ~ 450m/s => RBIG~500km

  • ...or is it? => Radiation Pressure on small grains!

Debris disc modelling

a numerical experiment

Q: how do mutual collisions redistribute orbital elements for a population of grains affected by Radiation Pressure?

  • ”bouncing balls” code

  • ~20000 test particles

  • Size distribution: dnrdr

  • Size range: 0.04<β<0.4

  • Inelastic collisions

Thébault & Brahic (1995)

Debris disc modelling

thickening of an initially thin disc

Debris disc modelling

equilibrium profile

Debris disc modelling

Disc thickness

Debris disc modelling

Future work?

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