Table 2
Limb darkening (LD) models used to interpret the interferometric observations of Canopus.
LD model | Intensity profile | Hankel → transform | Complex visibility function |
---|---|---|---|
name | Iλ(μ)∕Iλ(1) | V (z), where z = π⊘Bp∕λ | |
Uniform disk (UD) | 1 | → | ![]() |
Linear | 1 − uλ(1 − μ) | → | ![]() |
Power law | μαλ | → | ![]() ![]() |
Notes. Equations for the intensity profiles, I(μ), and the corresponding complex visibilities, V, are given. In these equations, μ(= cos(θ)) is the cosine of the angle θ between thedirection perpendicular to the stellar surface and the direction toward a distant observer. For a line-of-sight starting at the center and moving toward the limb of the stellar disk, μ varies between 1 and 0. Also, Γ is the gamma function and is the Bessel function of first kind and of order νλ. The dimensionless variable z is given by π⊘Bp∕λ, where Bp (= |Bp|) is the interferometric baseline length projected onto the target, λ is the effective wavelength of the observation, and ⊘ is the stellarangular diameter for the considered LD model. In an interferometric study of a given star, as is the case here, one generally seeks to observe at several spatial frequencies for a good uv coverage, with observations performed on many different realizations of the vector Bp∕λ = (u, v), as in Fig. 1.
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