Debris disc modelling
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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

Philippe Thébault

Paris Observatory/Stockholm Observatory

Disc modelling: going from there….

…to there…

…and there


  • 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)

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

relative timescales:

collisions are the dominant process!

Example: β-Pic (Artymowicz, 1997)

protoplanetary discs around YSOs

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

« protoplanetary » discs

Debris discs

Greaves (2005)

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.

Imaging of debris discs: visible/near IR

b-Pictoris (1984)






β-Pictoris: multi wavelength imaging

the debris disc zoo

and some more…

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)

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

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

what we see

  • Dust ~ [µm,mm]

  • Gas (sometimes)

what we’d like to know about

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

  • Planets

Numerical Modelling, why?

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


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

SB profile

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?

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….

Size Distributions derived from observations are model dependent…

(Li & Greenberg 1998)

what we see

...and restricted to a narrow size range

collisional cascade

~radiation pressure cutoff

unseen parent bodies

size distribution ???

~observational limit


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

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

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

statistical collisional evolution code

  • « Particle in a box » Principle

  • divide the population in size bins

  • evolution Equ.:

  • Collision Outcome prescription (lab.experiments)







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 (!)

evolution of an extended debris disc

size distribution evolution (Thebault&Augerau, 2007)

(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

collision rates

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

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”

Main Conclusions (2)

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

III. Collisional avalanches

Grigorieva, Thebault&Artymowicz 2007

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

collisional avalanches: combined statistical and dynamical code

Collisionnal cascade after large planetesimal/cometary breakup

collisional avalanches: face-on spiral structures

collisional avalanches: two-side asymetries

IV. Outer edges of debris discs:

how sharp is sharp?

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

a-3.5 slope

(Thébault & Wu, 2008)

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

the ”universal” a-3.5profile

low mass disc

high mass disc

”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

fitting a ”razor-sharp” edge: HR4796

in short

”natural” outer edge profile

”natural” if highly anisotropic scattering

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

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!

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)

thickening of an initially thin disc

equilibrium profile

Disc thickness

Future work?

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