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## PowerPoint Slideshow about 'debris disc modelling' - talli

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- 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)

- 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

protoplanetary discs around YSOs

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

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 IRAS/ISO/Spitzer

b-Pictoris (1984)

the debris disc zoo IRAS/ISO/Spitzer

and some more… IRAS/ISO/Spitzer

Circumstellar disc observations: IRAS/ISO/Spitzer

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 = 2898m/T = 10.4r0.5/L*0.25

rprobed = 0.012L*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) IRAS/ISO/Spitzer

- 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: IRAS/ISO/Spitzer

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 = Fd2/[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=850m with =1

what we see IRAS/ISO/Spitzer

- Dust ~ [µm,mm]
- Gas (sometimes)

what we’d like to know about

- pebbles, rocks, planetesimals, asteroids, comets.…
- Planets

Numerical Modelling, why? IRAS/ISO/Spitzer

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

SED

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

SB profile

Numerical Modelling, what for? IRAS/ISO/Spitzer

- What are discs made of?
- Size Distribution
- Total mass
- “hidden” bigger parent bodies (>1cm)
- Long term evolution, lifetime

AND

OR

- What is going on?
- Explain the Observed Spatial Structures
- Presence of Planets?

II. Collisional Evolution models IRAS/ISO/Spitzer

- 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 dependent…

...and restricted to a narrow size range

collisional cascade

~radiation pressure cutoff

unseen parent bodies

size distribution ???

~observational limit

? dependent…

doing it the lazy way: the drr3.5dr distribution

Theoretical collisional-equilibrium law dN r-3.5dr

What we don’t see

What we see

many reasons why the dependent…dNr3.5dr 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: dependent…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 dependent…

- « Particle in a box » Principle
- divide the population in size bins
- evolution Equ.:

- Collision Outcome prescription (lab.experiments)

a dependent…5

a4

da

a3

a2

a1

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 dependent…extended debris disc

size distribution evolution (Thebault&Augerau, 2007)

(2) dependent… 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 dependent…

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

why should we care? / Main Conclusions dependent…

- 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) dependent…

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

III. Collisional avalanches dependent…

Grigorieva, Thebault&Artymowicz 2007

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

collisional avalanches: combined statistical dependent…and dynamical code

Collisionnal cascade after large planetesimal/cometary breakup

collisional avalanches: two-side asymetries dependent…

IV. Outer edges of debris discs: dependent…

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 ring left to itself

- 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

”extreme” case with ring left to itselfSB 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 ring left to itself

in short ring left to itself

”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) ring left to itself

- 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 ring left to itself

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: dnrdr
- Size range: 0.04<β<0.4
- Inelastic collisions

Thébault & Brahic (1995)

thickening of an initially thin disc ring left to itself

equilibrium profile ring left to itself

Disc thickness ring left to itself

Future work? ring left to itself

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