Table 1
Major parameters.
Av | Visual extinction |
![]() |
See Eqs. (6) and (7) |
Bλ,T | Blackbody function |
d | Distance to the target |
Fobs;λ | Observed flux for the central illuminating source at the wavelength λ |
Fλ(x, y) | Flux that the extended disk or envelope receives from the central source at the wavelength λ |
fλ | A factor to correct foreground extinction for the wavelength λ (see Eq. (30)) |
Ia;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (via single scattering) |
Ib;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (via double scattering) |
Ic;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (thermal emission from the surface layer) |
Id;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (thermal emission from the disk interior) |
Ia′;λ(x, y) | Intensity distribution for the extended envelope at the wavelength λ (via single scattering) |
Ic′;λ(x, y) | Intensity distribution for the extended envelope at the wavelength λ (thermal emission) |
i | Viewing angle of the extended disk or envelope |
P1(λ,θsca) | Scattering phase function for the scattering angle θsca at the wavelength λ |
P2(λ,θsca) | Product of the scattering phase function and polarization for the scattering angle θsca at the wavelength λ |
P2(H) | Representative constant for P2(λ; θsca) for the H band (λ = 1.65 μm) |
(PI)obs;H (x, y) | Observed PI distribution for the H band |
r | Distance to the central source projected to the midplane ![]() |
Td(x, y) | Temperature at the disk interior |
Te(x, y) | Temperature in the envelope |
Ts(x, y) | Temperature at the surface layer of the disk |
x, y | Coordinate in the midplane |
z | Coordinate perpendicular to the midplane |
zdisk(x, y) | Location of the disk surface |
zenv(x, y) | Typical height of the envelope |
α(x,y) | Sine of the radial gazing angle of the disk surface β(x,y) |
β(x,y) | Radial grazing angle of the disk surface with respect to the incident light (see Fig. 2) |
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Typical grazing angle of the flat compact disk from the disk surface or the envelope |
δ(x, y) | Radial inclination of the disk surface with respect to the midplane (see Fig. 2) |
θsca(x, y, i) | Scattering angle of the light from the central illuminating source (see Fig. 2) |
κext;λ | Dust opacity for the wavelength λ |
λ | Wavelength |
∑env(x, y) | Surface density for the extended envelope |
τl,λ(x, y) | Optical thickness of the extended envelope at line of sight of the observations |
τr,λ(x, y) | Optical thickness of the extended envelope from the central source in the radial direction |
ωλ | Scattering albedo for the wavelength λ |
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