Distinction Between Models and Programs

Utile dulci (The useful with the agreeable)

In the context of light curve analysis, a model (see footnote on page 77 also) is a set of mathematical and physical relations which enables the mapping of a set of EB parameters x to a light curve Lcal for a given set of phase values. A light curve code or program is the software implementation of such a model. The output is typically in digital form suitable for graphic visualization of both light curves and a representation of the binary model itself. While a model is abstract and generic and relates a stellar system's physical attributes (gravitational potential, eclipse conditions, etc.), the program requires a choice of coordinates, integration or summation procedures, and matrix inversion routines. A light curve program's most important ingredient is the physical model. The degree of realism of the model fundamentally determines the reliability of the predicted light curve. However, the program itself constrains the accuracy of the result as well as the efficiency with which the result is reached. Therefore, it seems reasonable that those who develop light curve models maintain close contact with those who write and upgrade the program. In the past, model and program developer often have been one and the same person. This may change in the future, as we note in Sect. 7.3. The "models versus programs" topic is discussed more extensively in Wilson (1994).

A desirable feature of a light curve program is an ability to incorporate additional astrophysics. There is a continuing need to improve the model physics, as we become more aware of the observational properties of stars. This is also very important when we use the light curve program as a diagnostic tool and thereby derive astrophysical properties of both system and component stars from the modeling process itself. This requires the light curve software to be structurally well defined but especially expandable, as we describe in Chap. 7.

J. Kallrath, E.F. Milone, Eclipsing Binary Stars: Modeling and Analysis, Astronomy 265

and Astrophysics Library, DOI 10.1007/978-1-4419-0699-1-6, (9 Springer Science+Business Media, LLC 2009

Some (EBOP, LIGHT2, PGA-E,WD) of the most frequently used light curve modeling programs are reviewed by their authors in Milone (1993). Others, such as the Russell-Merrill procedure and Kopal's frequency domain method, are dealt with extensively in the literature. Thus, we only give a brief overview here. In McNally (1991, p. 485) and in Milone (1993), tables are given which list the percentage use of different light curve models. We make the distinction between basic geometric models in which orbit determination is the primary goal, and more elaborate models in which the radiative properties of the stars are explored also.

We begin with the mature treatment by Russell & Merrill (1952), an evolved version of the model that Russell began developing at the beginning of the twentieth century. We may call this work the Genesis of light curve modeling - an appropriate phrase since Russell was the first to travel the "royal road" of eclipses. It is also the model with the simplest geometry and is certainly not "state of the art." But we cover it in this chapter for historical reasons because many light curve solutions were determined with this method and because, even now, it is useful in providing basic views of the geometric properties of many binary star systems. Additional details of the method and the procedures used to find solutions and compute light curves are given in Appendix D.1.

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