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4.5.4 Analytic Partial Derivatives

For some of the parameters, partial derivatives, dlcal/9xi, involved in the least-squares problem can be calculated analytically, or can be derived from other quantities available when computing a light curve. This is true for the third light (3.4.2), the parallax as in (3.9.3), and in the Wilson-Devinney program for 91 j/9L1. As has been shown in Chap. 3, the monochromatic flux from component j is

I j (0) =f Xs (0) I (r, cos y; g, T,X)cos yda, (4.5.15)

where xs is the characteristic function defined in (3.3.2) ensuring that we only integrate over the visible surface. In spherical polar coordinates, (3.2.48) takes the form

rn r2n cos y 2

I j(0) =/ Xs(0)I(rs, cos y; g, T,k)-Lr2 sin 0d<pd(9. (4.5.16)

Jo Jo cosp

Adding all contributions of the binary system, the total emitted flux 1(0) is (3.2.50)

with constant third light l3. Therefore, we have

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