Modeling - PowerPoint Presentation

Slide1

Modeling debris diskswith GRaTeR (Grenoble Radiative TransfeR)

Jérémy Lebreton

EXOZODI

Kick-off

Meeting

10-02-2011Slide2

Different and complementary approaches to model debris disksCollisionalDynamicalRadiative

transfer

GRaTeR: Originally designed to model cold dust disks around Kuiper-Belt analogues like HR4796A (Augereau et al. 1999)Efficient radiative transfer modeling of optically thin disksFitting SEDs, resolved images and interferometric observationsAllows statistical analysis on a large parameter space.

Introduction

Modeling debris disks with GRaTeR

J. Lebreton

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Star propertiesSpectral type, magnitude, distanceGeometrical propertiesSurface density profileInclinationDust

grains

propertiesSize distributionCompositionGeneral description of a debris diskModeling debris disks with GRaTeR J. Lebreton3Slide4

NextGen synthetic stellar spectrum (log g, Teff)Scaled to V magnitude or Spitzer

IRS

spectrumStellar photosphereNextGen stellar SpectrumExcess emissionModeling debris disks with GRaTeR J. Lebreton4Slide5

Parametrical profiles1-power law (r0, αout)2-power law

(r

0, αin, αout): Ring-like disksAnything you wantProfiles derived from inversion of resolved imagesProfiles derived from dynamical modelsSurface density profilesModeling debris disks with GRaTeR J. Lebreton5Slide6

Optical indexes available for various materialsAmorphous silicates, olivine, ...Carbon, organic

refractories

, ...Amorphous, crystalline ices, ...Multi-component grainsUse of an effective medium theory (Maxwell-Garnett / Bruggeman EMT)Porous aggregatesThe spheres are partly filled with vacuumGrain compositionModeling debris disks with GRaTeR

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Classical power-lawdn/da ∝a-κ, from amin

to amaxidealized collisional equilibrium: κ = -3.5Independent of the distance from the star « Wavy » size distribution (Thébault & Augereau 2007)Possibly a distance-dependent distribution...Grain size distributionModeling debris disks with GRaTeR J. Lebreton7Slide8

Mie theory - Valid for hard, spherical grains Absorption efficiency : Qabs(a,

λ

, composition)Scattering efficiency : Qsca(a, λ, composition)Radiation pressure efficiency QRP(a, λ, composition)Possibly anisotropic scattering : gHG ( QPR = Qabs + (1-gHG)Qsca ) Grain response to stellar irradiationModeling debris disks with GRaTeR J. Lebreton

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Central star’s gravityDrag forces Radiation pressureβPR = |F

RP

/ FG|Blowout size : ablow = a(βPR =0.5)Eccentricity: e(βPR) = βPR/(1-βPR) Poynting-Robertson dragPhysical processBeta ratios (F8 star)Krivov et al. 2006

Modeling debris disks with GRaTeR

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SublimationEach material → sublimation temperatureEach grain → equilibrium temperature vs. distance

⇒ sublimation distance

DsubWhen D < Dsub : material is removedA more sophisticated treatment of the grainsublimation physics(cf. next previous talk)Physical processModeling debris disks with GRaTeR J. Lebreton10

- Solid line : 50% silicates + 50% carbons

- Dashed line: 100% carbonsSlide11

CollisionsCollision time scaleTo date: ~ torb/8Σ0(r) (Backman & Paresce

93)

Π<s2> : mean scattering cross section Σ0(r) : Midplane surface densityIndependent of the grain sizeValid for circular orbitsPhysical processModeling debris disks with GRaTeR J. Lebreton11Slide12

Need for a more sophisticated calculation of the collisional lifetime

Method

from Hahn et al. 2010Considers all possible orbits and grain sizes Calculate collision probability densities between streamlinesTc(si) α T0 Collision time scale

Modeling debris disks with GRaTeR

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Fitting strategy:Chi-square minimizationBayesian analysisIndependent assessment

of

each parameter + uncertaintiesProvides the best parameters:Disk massGrain properties (size distribution, composition)Dust locationAnd additional ouput:Blowout sizeOptical depthsTime scales Output of the modelModeling debris disks with GRaTeR J. Lebreton13Slide14

Interferometric observations : Need to take the transfer function into account (spatial filtering)

Sublimation process are very important

Transient events, …Other specificities ?Notes on Exozodi modelsBlue: near-IR CHARARed : mid-IR MMT nullingModeling debris disks with GRaTeR J. Lebreton14Slide15

Examples of GRaTeR achievementsModeling debris disks with GRaTeR

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The Vega inner systemDetection of the exozodi

with CHARA/FLUORShort baseline visibility deficit → K-band excess 1.29±0.19% Absil et al. 2006Submicronic grains (amin ≤ 0.3 μm) Highly refractive: graphite/ amorphous carbon + Olivine (~50-50) Concentrated close to the star: r0 = 0.17–0.30 AU(@0.1μm: r0 < r

sub ~0.6AU)

Mdisk = 8x10-8

MEarth

Modeling debris disks with GRaTeR

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The Vega inner systemNew IOTA/IONIC H-band measurements and models

Sublimation

temperatures were re-evaluated: Tsub (astrosi) = 1200 K Tsub (Acar) = 2000 KSpatial distribution could be less steep (r ≤ -3.0)Modeling debris disks with GRaTeR J. Lebreton17Slide18

q1 Eridani A planet host-star

harboring

a cold debris disk (2 Gyr, F8V star, 17 pc)

Augereau et al. 2011 (in

prep

.)

Modeling debris disks with GRaTeR

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q1

Eridani Detailed simultaneous modeling of the SED and PACS images Modeling debris disks with GRaTeR

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q1 Eridani Detailed simultaneous modeling of the SED and PACS images

Dust Ring:Mass : 0.04 MEarth

Surface density:

r

-2

Belt peak position: 75-80AU

Fit to the SED

Fit to the PACS Radial Profiles

Grain

properties

:

Minimum grain size

~

1.5

m

m

Size distribution: - 3.5 power law

index

Close to 50-50 silicate-ice mixture

Modeling debris disks with GRaTeR

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HD 181327Lebreton et al. 2011 (in prep.)

Modeling debris disks with GRaTeR

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HD 181327

CompositionAstrosilicates: 20%Organic refractory: 10%Amorphous ice: 70%Vacuum: porosity = 65%Size distribution

dn

∝ a

-κ

.da

κ

= - 3.43

a

min

=0.70

μm

<

a

blowout

=5.46

μm

Mass = 0.05

M

Earth

(up to 1mm)

Temperature

: 40-88 K

Best model

Up to 8 mm

here

!

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GRaTeR is a flexible toolbox to model dusty disksWill be used to model systematically

the SED of the

near-IR excess detected through interferometryWill be coupled to the dynamical codes to derive synthetic observationsFuture improvementsBetter description for the dust sublimationBetter estimates of the time scalesConclusionsModeling debris disks with GRaTeR J. Lebreton23