Accuracy and efficiency in the binary star reflection effect

The geometric and irradiation heating problems for the binary star reflection effect theory are developed in terms of equipotential level surfaces and are sufficiently general so as to include eccentric orbits and nonsynchronous (even centrifugally limited) rotation and to treat multiple reflection. The requisite physics, mathematics, and logic are then presented and the computations are organized so that a given quantity is computed only as often as necessary, emphasizing the distinction between local surface quantities and aspect-related quantities. The local geometric, bolometric, and wavelength-specific quantities are grouped for storage according to how often they need to be recomputed. Some tests of a computer program based on this reflection model are given in the form of graphs in which program results are compared to a special exact case, and with results from an earlier program. The new program gives intuitively reasonable output for all tests, and the tests give an idea of how accurate the old program is, adopting the detailed reflection computations of the new program as a standard for comparison. A table is given which shows the convergence of the multiple reflection computations to a constant distribution of surface effective temperature.