Free Access
Volume 547, November 2012
Article Number A58
Number of page(s) 15
Section Planets and planetary systems
Published online 29 October 2012

Online material

Appendix A: Dust density sampling in the MCFOST grid

thumbnail Fig. A.1

Map of the logarithm of the number of SPH particles per MCFOST grid cell in the meridian (R,z/R) plane for the 1 MJ planet.

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thumbnail Fig. A.2

Same as Fig. A.1 in the horizontal (R,φ) plane.

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In order for MCFOST to produce accurate synthetic images from the output of SPH simulations, the dust density distribution must be sufficiently sampled with SPH particles in each cell of the radiative transfer grid. Figures A.1 and A.2 show 2D maps of the logarithm of the number of SPH particles per grid cell in the (R,z/R) and (R,φ) planes respectively. In most of the disk, the number of SPH particles contributing to the density in any grid cell varies from a few hundred to a few thousand (as a reference, SPH codes typically use a few tens of neighbouring particles to compute physical quantities). Only in the upper layers at large distances from the star does this number fall to values of a few, because there is very little material in these regions. Indeed, as can be seen in Fig. 1, dust grains 100 μm in size and larger settle efficiently to the midplane and smaller grains follow the distribution of the gas phase, which has a curved outer-rim and therefore a very low density in these regions. Both maps show smooth variations in the radial and vertical directions, whereas azimuthal variations are negligible (note the different colorscale in Figs. A.1 and A.2), and demonstrate the adequate sampling of the dust distribution for the radiative transfer calculations.

Appendix B: Impact of the disk inner radius on the temperature structure

The inner radius of the disk models is set to 4 AU in the SPH calculations, much larger than the characteristic inner radius of most T Tauri disks (usually located at the dust sublimation radius  ≈0.05 AU). The resulting temperature structure is therefore incorrect in the central parts of the model, where the dust is directly heated by the star. Our disk models remain optically thick in the radial direction however. As a consequence the temperature in the outer parts is computed correctly in these regions, as the heating of the disk midplane (where most of the millimeter emission is coming from) is due to reprocessing of the stellar light absorbed and scattered by the disk surface. In these regions, the transfer of radiation is mostly vertical and the temperature structure does not depend on the details of the inner disk. Figure B.1 shows the radial profile of the surface and midplane temperatures. In the inner region, the dust is heated directly by the stellar radiation and both temperatures are equal. They start to decouple at r ≈ 10 AU, when the disk midplane no longer sees the star directly. The temperature structure and corresponding millimeter images can therefore be considered accurate from r > 15 AU, corresponding to 0.1′′ in most of our simulations.

thumbnail Fig. B.1

Radial temperature profile at the disk surface (solid red line) and in the disk midplane (black dashed line).

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Appendix C: Additional figures

We present here figures similar to Fig. 4 for other wavelengths: λ = 350  μm in Fig. C.1, λ = 1.3 mm in Fig. C.2, and λ = 2.7 mm in Fig. C.3.

thumbnail Fig. C.1

Same as Fig. 4 at λ = 350  μm.

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thumbnail Fig. C.2

Same as Fig. 4 at λ = 1.3 mm.

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thumbnail Fig. C.3

Same as Fig. 4 at λ = 2.7 mm.

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© ESO, 2012

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