1 Xr

The structure of the software is as follows. At first, based on (6.3.2 ), a discrete representation of the stellar surface is computed. For both stars, for a given distribution of grid points (0;, pj), the corresponding radial vectors r\j = ^(0,, pj; q , F,Q,d) are determined, and a system of surface points rs is established. Note that both Q1 and are measured in the coordinate system of component 1. To generate the surface of component 2, it is necessary to transform to the coordinate system of component 2.

The inverse transformation to (6.3.3) is

The Wilson-Devinney program uses the following geometrical conventions: The normal vectors point into the interior of the stars, and the line-of-sight vector originates at the binary and points to the observer. This implies that only points satisfying the condition cos y < 0 contribute to the flux seen by the observer.

In the WD program, the local flux function contribution dli(cos y; gi, T\, X) in the integrand of (3.2.49) is computed for each component j according to dll(rs, cos y; gl, Tl, X) = GjDjRjlj cos yda, (6.3.5)

where the dimensionless ratios Gj = Gj (rs), Dj = Dj (rs), and Rj = Rj (rs) account for gravity darkening, limb darkening, and reflection effect, and Ij is a reference intensity. The computation of these factors is performed according to the formulas (6.3.8), (3.2.23) or one of the other limb-darkening laws in Sect. 3.2.4, (3.2.46), and (6.3.7). Some further details are discussed below.

Because an analysis of photometric data allows the derivation of only relative dimensions of the components (such as the ratio of radii, masses, or luminosities), many quantities and parameters in the model are dimensionless. This has the following consequences for intensities and luminosities. Since the flux at the poles is unknown, a scaling factor Ij, j = 1, 2, is introduced. Ij is the normal surface intensity at the pole of component j, which is computed to reproduce the luminosity Lj:

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