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This article has an erratum: [https://doi.org/10.1051/0004-6361/202452059e]


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)
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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