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Modeling debris disks with GRaTeR (Grenoble Radiative TransfeR )

Jérémy Lebreton EXOZODI Kick-off Meeting 10-02-2011. Modeling debris disks with GRaTeR (Grenoble Radiative TransfeR ). Introduction. Different and complementary approaches to model debris disks Collisional Dynamical Radiative transfer GRaTeR :

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Modeling debris disks with GRaTeR (Grenoble Radiative TransfeR )

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  1. Jérémy Lebreton EXOZODI Kick-off Meeting 10-02-2011 ModelingdebrisdiskswithGRaTeR(Grenoble Radiative TransfeR)

  2. Introduction • Different and complementaryapproaches to model debrisdisks • Collisional • Dynamical • Radiative transfer • GRaTeR: • Originallydesigned to model cold dustdisksaroundKuiper-Belt analogues like HR4796A (Augereau et al. 1999) • Efficient radiative transfermodeling of opticallythindisks • FittingSEDs, resolvedimages and interferometricobservations • Allowsstatisticalanalysis on a large parameterspace. Modeling debris disks with GRaTeR

  3. General description of a debrisdisk • Star properties • Spectral type, magnitude, distance • Geometricalproperties • Surface density profile • Inclination • Dust grains properties • Size distribution • Composition Modeling debris disks with GRaTeR

  4. Stellarphotosphere • NextGensyntheticstellarspectrum (log g, Teff) • Scaled to V magnitude or Spitzer IRS spectrum Excessemission NextGenstellar Spectrum Modeling debris disks with GRaTeR

  5. Surface density profiles • Parametrical profiles • 1-power law (r0,αout) • 2-power law(r0, αin, αout): Ring-likedisks • Anythingyouwant • Profiles derivedfrom inversion of resolved images • Profiles derivedfromdynamicalmodels Modeling debris disks with GRaTeR

  6. Grain composition • Optical indexes available for variousmaterials • Amorphous silicates, olivine, ... • Carbon, organicrefractories, ... • Amorphous, crystallineices, ... • Multi-component grains • Use of an effective medium theory (Maxwell-Garnett / Bruggeman EMT) • Porousaggregates • The spheres are partlyfilledwith vacuum Modeling debris disks with GRaTeR

  7. Grain size distribution • Classicalpower-law • dn/da ∝a-κ,fromaminto amax • idealizedcollisionalequilibrium: κ = -3.5 • Independent of the distance from the star • « Wavy » size distribution (Thébault & Augereau 2007) • Possibly a distance-dependent distribution • ... Modeling debris disks with GRaTeR

  8. Grain response to stellar irradiation • Mie theory- Valid for hard, spherical grains • Absorption efficiency : Qabs(a, λ, composition) • Scatteringefficiency : Qsca(a, λ, composition) • Radiation pressure efficiency QRP(a, λ, composition) • Possiblyanisotropicscattering : gHG ( QPR = Qabs + (1-gHG)Qsca ) Modeling debris disks with GRaTeR

  9. Physicalprocess Beta ratios (F8 star) • Central star’sgravity • Drag forces • Radiation pressure • βPR= |FRP / FG| • Blowoutsize :ablow = a(βPR =0.5) • Eccentricity: e(βPR) = βPR/(1-βPR) • Poynting-Robertsondrag Krivov et al. 2006 Modeling debris disks with GRaTeR

  10. Physicalprocess • Sublimation • Eachmaterial → sublimation temperature • Each grain → equilibriumtemperature vs. distance ⇒ sublimation distance Dsub • When D < Dsub : materialisremoved • A more sophisticatedtreatment of the grainsublimation physics(cf. nextprevious talk) - Solid line : 50% silicates + 50% carbons- Dashed line: 100% carbons Modeling debris disks with GRaTeR

  11. Physicalprocess • Collisions • Collision time scale • To date: ~ torb/8Σ0(r) (Backman & Paresce 93) Π<s2> : meanscattering cross section Σ0(r) : Midplane surface density • Independent of the grain size • Valid for circularorbits Modeling debris disks with GRaTeR

  12. Collision time scale • Need for a more sophisticatedcalculation of the collisionallifetime • MethodfromHahn et al. 2010 • Considers all possible orbits and grain sizes • Calculate collision probabilitydensitiesbetween streamlines • Tc(si) α T0 Modeling debris disks with GRaTeR

  13. Output of the model • Fittingstrategy: • Chi-squareminimization • Bayesiananalysis • Independent assessment of eachparameter + uncertainties • Provides the best parameters: • Disk mass • Grain properties (size distribution, composition) • Dust location • And additionalouput: • Blowoutsize • Optical depths • Time scales Modeling debris disks with GRaTeR

  14. Notes on Exozodimodels • Interferometric observations : • Need to take the transfer function into account (spatial filtering) • Sublimation process are very important • Transient events, … • Other specificities ? Blue: near-IR CHARARed : mid-IR MMTnulling Modeling debris disks with GRaTeR

  15. Examples of GRaTeRachievements Modeling debris disks with GRaTeR

  16. The Vega inner systemDetection of the exozodiwith CHARA/FLUORShort baselinevisibilitydeficit → K-bandexcess 1.29±0.19% Absil et al. 2006 • Submicronic grains • (amin ≤ 0.3 μm) • Highlyrefractive: graphite/ amorphouscarbon + Olivine (~50-50) • Concentrated close to the star: • r0 = 0.17–0.30 AU • (@0.1μm: r0 < rsub ~0.6AU) • Mdisk = 8x10-8MEarth Modeling debris disks with GRaTeR

  17. The Vega inner systemNew IOTA/IONIC H-bandmeasurements and models Sublimation temperatureswerere-evaluated: Tsub (astrosi) = 1200 K Tsub (Acar) = 2000 K Spatial distribution couldbe lesssteep (r ≤ -3.0) Modeling debris disks with GRaTeR

  18. q1 EridaniA planethost-starharboring a cold debrisdisk(2 Gyr, F8V star, 17 pc) Augereau et al. 2011 (in prep.) Modeling debris disks with GRaTeR

  19. q1 EridaniDetailed simultaneous modeling of the SED and PACS images Modeling debris disks with GRaTeR

  20. q1 EridaniDetailed simultaneous modeling of the SED and PACS images • Grain properties: • Minimum grain size~1.5 mm • Size distribution: - 3.5 power law index • Close to 50-50 silicate-ice mixture • 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 Modeling debris disks with GRaTeR

  21. HD 181327 Lebreton et al. 2011 (in prep.) Modeling debris disks with GRaTeR

  22. HD 181327 Best model • Composition • Astrosilicates: 20% • Organicrefractory: 10% • Amorphousice: 70% • Vacuum: porosity = 65% • Size distribution • dn ∝ a-κ.da • κ = - 3.43 • amin=0.70 μm < ablowout=5.46 μm • Mass = 0.05 MEarth (up to 1mm) • Temperature : 40-88 K Up to 8 mm here! Modeling debris disks with GRaTeR

  23. Conclusions • GRaTeRis a flexible toolbox to model dustydisks • Will beused to model systematically the SED of the near-IRexcessdetectedthrough interferometry • Will becoupled to the dynamical codes to derivesynthetic observations • Future improvements • Better description for the dust sublimation • Betterestimates of the time scales Modeling debris disks with GRaTeR

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