with CB, which is constant for a given binary star system and surface grid

1A AbA0a


and Ka, which (as well as GA) does not change in the course of iterations

2 sin 0A^9A

A cos pA

and, finally, QAB, cos YA cos yb

The iterative procedure (note that rA) really represents a vector of reflection factors R® over the whole surface) is then defined by r£+" = 1 + Fa (RA ) , TAk+1) = /Rf TAk). (E.25.8)

The formulas for the other components are just achieved by interchanging the subscripts A and B. For further details and the logic of the implementation the reader is referred to Wilson (1990).

E.26 MLRG - Computing Absolute Dimensions

MLRG stands for mass, luminosity, radius, and gravity. This subroutine computes absolute dimensions and other quantities for the stars of a binary star system. This includes the masses, radii, and absolute bolometric luminosities of the stars in solar units as well as the logarithm to base 10 of the mean surface acceleration (effective gravity) of both components.

E.27 MODLOG - Handling Constraints Efficiently

This subroutine controls some of the geometrical constraints. If, for instance, a contact binary should be modeled, then this subroutine enforces the equations A2 = A1, g2 = g1, and = ^1.

E.28 NEKMIN - Connecting Surface of Over-Contact Binaries

This subroutine is only called for contact binaries (modes 1 and 3). A plane through the connecting neck defines the star boundaries. The ("vertical") plane is essentially at the neck minimum, so not exactly at the Lp point. Subroutine NEKMIN computes the x-coordinate of that plane as described by Wilson & Biermann (1976).

E.29 OLUMP - Modeling the Reflection Effect

In order to understand the meaning of the bolometric albedos used in the WilsonDevinney model to describe the reflection effect, it is useful to have a detailed knowledge of how the reflection effect is modeled. We first describe subroutine OLUMP, which means "old LUMP." OLUMP is used for eccentric orbit calculations. It is a bit less accurate but much faster than subroutine LUMP.

As shown in Fig. E.5, d denotes the distance between the star centers in unit a. For a circular orbit d = 1. The index 2 refers to the secondary component. Let

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