Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effects of scattering and dust grain size on the temperature structure
  of protoplanetary discs: A three-layer approach   The temperature in the optically thick interior of protoplanetary discs is
essential for the interpretation of millimeter observations of the discs, for
the vertical structure of the discs, for models of the disc evolution and the
planet formation, and for the chemistry in the discs. Since large icy grains
have a large albedo even in the infrared, the effect of scattering of the
diffuse radiation in the discs on the interior temperature should be examined.
We have performed a series of numerical radiation transfer simulations
including isotropic scattering by grains with various typical sizes for the
diffuse radiation as well as for the incident stellar radiation. We also have
developed an analytic model including isotropic scattering to understand the
physics concealed in the numerical results. With the analytic model, we have
shown that the standard two-layer approach is valid only for grey opacity (i.e.
grain size $\ga10$ \micron) even without scattering. A three-layer
interpretation is required for grain size $\la10$ \micron. When the grain size
is 0.1--10 \micron, the numerical simulations show that isotropic scattering
reduces the temperature of the disc interior. This reduction is nicely
explained by the analytic three-layer model as a result of the energy loss by
scatterings of the incident stellar radiation and of the warm diffuse radiation
in the disc atmosphere. For grain size $\ga10$ \micron (i.e. grey scattering),
the numerical simulations show that isotropic scattering does not affect the
interior temperature. This is nicely explained by the analytic two-layer model;
the energy loss by scattering in the disc atmosphere is exactly offset by the
"green-house effect" due to scattering of the cold diffuse radiation in the
interior.

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The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th