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Jérémy Lebreton EXOZODI Kick-off Meeting

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Different and complementary approaches to model debris disks Collisional Dynamical Radiative 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 disks Fitting SEDs, resolved images and interferometric observations Allows statistical analysis on a large parameter space. Modeling debris disks with GRaTeR J. Lebreton 2

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Star properties Spectral type, magnitude, distance Geometrical properties Surface density profile Inclination Dust grains properties Size distribution Composition Modeling debris disks with GRaTeR J. Lebreton 3

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NextGen synthetic stellar spectrum (log g, T eff ) Scaled to V magnitude or Spitzer IRS spectrum NextGen stellar Spectrum Excess emission Modeling debris disks with GRaTeR J. Lebreton 4

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Parametrical profiles 1-power law (r 0, α out ) 2-power law (r 0, α in, α out ): Ring-like disks Anything you want Profiles derived from inversion of resolved images Profiles derived from dynamical models Modeling debris disks with GRaTeR J. Lebreton 5

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Optical indexes available for various materials Amorphous silicates, olivine,... Carbon, organic refractories,... Amorphous, crystalline ices,... Multi-component grains Use of an effective medium theory (Maxwell-Garnett / Bruggeman EMT) Porous aggregates The spheres are partly filled with vacuum Modeling debris disks with GRaTeR J. Lebreton 6

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Classical power-law dn/da a -κ, from a min to a max idealized collisional equilibrium: 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 J. Lebreton 7

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Mie theory - Valid for hard, spherical grains Absorption efficiency : Q abs (a, λ, composition) Scattering efficiency : Q sca (a, λ, composition) Radiation pressure efficiency Q RP (a, λ, composition) Possibly anisotropic scattering : g HG ( Q PR = Q abs + (1-g HG )Q sca ) Modeling debris disks with GRaTeR J. Lebreton 8

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Central stars gravity Drag forces Radiation pressure β PR = |F RP / F G | Blowout size : a blow = a(β PR =0.5) Eccentricity: e(β PR ) = β PR /(1-β PR ) Poynting-Robertson drag Beta ratios (F8 star) Krivov et al Modeling debris disks with GRaTeR J. Lebreton 9

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Sublimation Each material sublimation temperature Each grain equilibrium temperature vs. distance sublimation distance D sub When D < D sub : material is removed A more sophisticated treatment of the grain sublimation physics (cf. next previous talk) Modeling debris disks with GRaTeR J. Lebreton 10 - Solid line : 50% silicates + 50% carbons - Dashed line: 100% carbons

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Collisions Collision time scale To date: ~ t orb /8Σ 0 (r) (Backman & Paresce 93) Π : mean scattering cross section Σ 0 (r): Midplane surface density Independent of the grain size Valid for circular orbits Modeling debris disks with GRaTeR J. Lebreton 11

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Need for a more sophisticated calculation of the collisional lifetime Method from Hahn et al Considers all possible orbits and grain sizes Calculate collision probability densities between streamlines Tc(s i ) α T0 Modeling debris disks with GRaTeR J. Lebreton 12

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Fitting strategy: Chi-square minimization Bayesian analysis Independent assessment of each parameter + uncertainties Provides the best parameters: Disk mass Grain properties (size distribution, composition) Dust location And additional ouput: Blowout size Optical depths Time scales Modeling debris disks with GRaTeR J. Lebreton 13

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Interferometric observations : Need to take the transfer function into account (spatial filtering) Sublimation process are very important Transient events, … Other specificities ? Blue: near-IR CHARA Red : mid-IR MMT nulling Modeling debris disks with GRaTeR J. Lebreton 14

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Examples of GRaTeR achievements Modeling debris disks with GRaTeR J. Lebreton 15

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Absil et al Submicronic grains (a min 0.3 μm) Highly refractive: graphite/ amorphous carbon + Olivine (~50-50) Concentrated close to the star: r0 = 0.17–0.30 AU r0 < r sub ~0.6AU) M disk = 8x10 -8 M Earth Submicronic grains (a min 0.3 μm) Highly refractive: graphite/ amorphous carbon + Olivine (~50-50) Concentrated close to the star: r0 = 0.17–0.30 AU r0 < r sub ~0.6AU) M disk = 8x10 -8 M Earth Modeling debris disks with GRaTeR J. Lebreton 16

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Sublimation temperatures were re-evaluated: T sub (astrosi) = 1200 K T sub (Acar) = 2000 K Spatial distribution could be less steep (r -3.0) Modeling debris disks with GRaTeR J. Lebreton 17

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Augereau et al (in prep.) Modeling debris disks with GRaTeR J. Lebreton 18

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Modeling debris disks with GRaTeR J. Lebreton 19

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D UST R ING : Mass : 0.04 M Earth Mass : 0.04 M Earth Surface density: r -2 Surface density: r -2 Belt peak position: 75-80AU Belt peak position: 75-80AU Fit to the SED Fit to the PACS Radial Profiles G RAIN PROPERTIES : Minimum grain size ~ 1.5 m Size distribution: power law index Close to silicate-ice mixture Modeling debris disks with GRaTeR J. Lebreton 20

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Lebreton et al (in prep.) Modeling debris disks with GRaTeR J. Lebreton 21

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Composition Astrosilicates: 20% Organic refractory: 10% Amorphous ice: 70% Vacuum: porosity = 65% Size distribution dn a -κ.da κ = a min =0.70 μm < a blowout =5.46 μm Mass = 0.05 M Earth (up to 1mm) Temperature : K Composition Astrosilicates: 20% Organic refractory: 10% Amorphous ice: 70% Vacuum: porosity = 65% Size distribution dn a -κ.da κ = a min =0.70 μm < a blowout =5.46 μm Mass = 0.05 M Earth (up to 1mm) Temperature : K Best model Up to 8 mm here! Modeling debris disks with GRaTeR J. Lebreton 22

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GRaTeR is a flexible toolbox to model dusty disks Will be used to model systematically the SED of the near-IR excess detected through interferometry Will be coupled to the dynamical codes to derive synthetic observations Future improvements Better description for the dust sublimation Better estimates of the time scales Modeling debris disks with GRaTeR J. Lebreton 23

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