The envelope model inputs are the

• Dust Parameters
• 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

  n(a)da   =   Cia-3.5da

  where a is the grain radius and C_i is a constant which gives the abundance of grain type i. Limiting grain sizes for both graphite and silicates are a_min=0.005 µm and a_max=0.25 µm. Optical constants and grain abundances are from Draine & Lee 1984, ApJ, 285, 89 ,   Draine & Lee 1987, ApJ, 318, 485 ,  and Laor & Draine 1993, ApJ, 402, 441, where C_C = 10^-15.16 H^-1 µm^2.5 and C_Si = 10^-15.11 H^-1 µm^2.5.
• 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.
• Shell Parameters
• Inner radius - R_i, 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 R_i. 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/R_i must be greater than 10 (iii) The graphite grain temperature at R_i must be less than 3000 K when exposed to the radiation from the central source alone.
• Radiation Parameters
• 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:

• Spectral Energy Distribution
• Emitted spectrum - The frequency-dependent flux at the outer radius R₀,  F_nu(R₀). The frequency-dependent luminosity is given by

  Lnu = 4 R02 Fnu(R0)

  and the observed flux is

  Fnu(D) =  (R0/D)2Fnu(R0)

  where D is the distance to the source.
• Intensity profile
- The frequency dependent intensity as a function of impact parameter, I_nu(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.
• Temperatures
• 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.