The Pioneers The Age of Geometry

EBs play a special role in binary research. Henry Norris Russell (1887-1957), one of the most distinguished astronomers, spoke about the "Royal Road of Eclipses" (Russell 1948b). Traveling this road entails the decoding of the messages encrypted in the light curves of eclipsing variables. As a rule, a light curve is determined by geometric effects due to eclipses and by physical proximity effects between the components. In the past, light curves were "rectified" in order to get rid of the "ellipticity" and "reflection" effects and such other perturbations from the light curve as could be modeled by a truncated Fourier series [see Russell (1948a); Russell & Merrill (1952)]. In doing so, a triaxial ellipsoid model was transformed into a spherical model, with which the light curve solution could be obtained in a straightforward way from tables or with the aid of nomographs. Computer programs based on rectifiable models were developed by Jurkevich (1970), who investigated the suitability to machine coding of a number of existing light curve approaches, including two of Kopal's rectifiable models, and by Proctor & Linnell (1972). However, the underlying assumptions of rectifiable models rarely hold in reality. As a rule, fully accurate, reliable solutions could be expected only for well-separated, detached systems. Systematic deviations could be observed for semi-detached and especially for over-contact systems. For over-contact systems in particular, the solutions were almost always misleading if not completely wrong. This is illustrated by the case of TY Bootis, an over-contact system which several modelers have tackled. Table 1.1 summarizes the results.

The photometric data by Carr (1972) were analyzed with the Russell-Merrill method by Carr. The same data were used in an analysis (listed as WD) using the Wilson-Devinney program, today the most frequently used model and program in the EB community, hereafter abbreviated the WD model or WD program and further described in Sect. 6.3.6. A new data set was also analyzed with the Wilson-Devinney method (Milone et al. 1991). For an explanation of the parameter notations in the first column see the Symbols' List in Appendix F. The squarebracketed values for the absolute radii in column 2 were computed on the basis of Carr's values for rs = Rs/a and rg = Rg/a and the WD-determined value of a for the Carr data [rs and rg are the radii of the "smaller" and "greater" stars in

Table 1.1 Analysis of TY Bootis by several approaches

Parameter

Carr (1972)17

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