Dust InfraRed Toolbox Radiation Transfer Models
The envelope models contained in DIRT are
based on the transfer code of Wolfire
& Cassinelli 1986, ApJ, 310, 207. The code solves for the grain
temperatures and the emitted spectral energy distribution of a spherical
dust shell under the constraints of thermal and radiative equilibrium.
The envelope model inputs are the
Grain Model - grain composition, abundance, and size distribution.
Published grain models are used. For MRN we use bare graphite and
silicate grains distributed in size as a power law as
where a is the grain
radius and Ci is a constant which gives the abundance of grain
type i. Limiting grain sizes for both graphite and silicates are
amin=0.005 µm and amax=0.25 µm.
and grain abundances are from
Draine & Lee 1984, ApJ, 285, 89
Draine & Lee 1987, ApJ, 318, 485
Laor & Draine 1993, ApJ, 402, 441, where
CC = 10-15.16 H-1 µm2.5
and CSi = 10-15.11 H-1 µm2.5.
- Grain Opacity - Absorption, scattering, and extinction
cross sections are calculated using spherical Mie theory.
See also the Dust Grain Opacities page
for further details and plots. The grain size distribution is divided into
25 grain bins in our calculations.
Silicate sublimation temperature - we assume that silicates are removed
when the average silicate temperature exceeds 1,000 K.
- Inner radius - Ri, the inner radius of the shell. We assume there is no
opacity between the central star and the inner radius.
- Outer radius - R0, the outer radius of the dust shell.
We assume there is no opacity between the outer radius and us.
- Density distribution - gas density distribution between inner and outer
radius. Stored models are for power law density distributions.
- Model pre-filtering. - We pre-filter models to ensure that they make
good physical sense, for example the radius of the central star
cannot exceed Ri. Additional filters include (i) the
gas density at the outer radius must be greater than 10-21
gm cm-3 (n > 103 cm-3), (ii) The
ratio of R0/Ri must be greater than 10
(iii) The graphite grain temperature at Ri must be less
than 3000 K when exposed to the radiation from the central source alone.
- Effective Temperature -
The flux incident at the inner shell radius is given by a
black body with the effective temperature of the central source.
We assume that all radiation at energies greater than 13.6 eV is
redistributed to lower energies (while conserving the bolometric luminosity)
so that no hydrogen ionizing radiation is incident on the shell.
The spectrum of the central source is plotted in the Plot View window
using the "Fnus" axis.
We assume there is no radiation incident on the outer radius of the shell.
- Bolometric Luminosity -
The core radius is calculated to provide the input bolometric
luminosity using the input effective temperature.
The envelope model outputs include:
The radiation transfer is carried out using a variable Eddington
factor method. Scattering at all wavelengths is included.
We use a variable radial grid of between 100 and 200
points and 73 frequencies. The models are considered converged when
the bolometric luminosity is conserved to within 3 percent at every
radial grid point.
- Spectral Energy Distribution
- Emitted spectrum - The frequency-dependent flux at the outer radius
The frequency-dependent luminosity is given by
and the observed flux is
where D is the distance to the source.
- Intensity profile - The frequency dependent intensity as a function
of impact parameter, Inu(p). This is the "pencil beam" intensity
across the source with p = 0 at the source center and p = R0 at
the outer edge.
- Flux in central beams - The frequency dependent flux as a function
of beam size centered on the source. We assume Gaussian beam profiles.
Grain temperatures are calculated for each composition and grain size
(25 grain size bins).
- Gas temperature is calculated as the area averaged grain temperature. This
is strictly correct only in the strong coupling limit.
- Radiation temperature is calculated as the single temperature which
conserves the bolometric grain emission.
Please direct comments, criticisms, corrections
and contributions to Marc Pound
Page last modified:
Tuesday, 10-Jun-2003 14:24:15 EDT.