(TI-59) Analysis of the Light Curves of Eclipsing Variable Stars

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An excerpt from Analysis of the Light Curves of Eclipsing Variable Stars, Master of Science In Astrophysics Thesis, Physics Dept., University of Alberta, Spring 1984, 212 pages

                                 ABSTRACT
       Four methods for determining the geometric elements
of an eclipsing binary from its light curve are explored
in detail. The methods discussed are those of Russell
(specifically, the version due to Tabachnik), Kitamura,
Kopal (frequency domain approach), and Wood. In each case,
the underlying model of an eclipsing binary system is dis-
cussed. The various methods of light analysis are then
applied to the eclipsing binaries HS Herculis, W Delphini,
and HD 219634. The results of each analysis are discussed,
and the various methods of analysis are compared with one
another. Finally, the relative merits of each model of an
eclipsing binary system are considered. Computer programs
for the various methods of light curve analysis, along with
explanations of their use, are presented in the appendices.

                   REFERENCES
Appendix 1   Russell Model Programs and Rectification
                   A1.1 Computer Programs
                   A1.2 An Example, of Rectification
Appendix 2   Program for Kitamura's Method
Appendix 3   Programs for Kopal's Method
Appendix 4   The WINK8 Program
Appendix 5   HD219634-observations

 … The present author has written a program for the TI-59 pro-
grammable calculator to use equation (2:17) in the analysis
of eclipsing binary light curves. The values of sin²θ and
P are used as input. The TI-59 calculator is particularly
convenient since it has a built-in least-squares linear fit
routine, which can be easily incorporated into a larger
program. This program will be used in later sections when
particular stars are considered. A listing of the program
is presented in Appendix 1.
 …
 … Equation (7.1) is solved using a simple iterative
procedure.. A program for the TI-59 programmnabie
calculator, which performs this calculation, may be found
in Appendix 1.
 …
 … A program using Tabachnik's method is also Given for the
TI-59 calculator. The instructions are self-explanatory.
 …
Appendix 1 Russell Model Programs and Rectification
 …
Russel Model
Program solves for the elements of an eclipsing binary (r_i,r₂,i)
in the case of complete eclipses (ie., total or annular).
Method used is a variation of Kopal's method due to V.M. Tabachnik,
which fits a line of the form y=ax+b, where y=(1+kp)², x=sin²,
a=sin²i/r², and b=cos²i/r², (k=r₂/r_i). p is the geometrical depth,
and is used as input data {use Russell-Merrill tables of α(k,p)}.
Elements are given by: tan i=a/b, r=(a+b)^-½ r₂=kr_i (k used as input)
 …
TI PROGRAMMABLE
PROGRAM RECORD
Depth Equation Solution
Solves the depth equation using an iterative procedure. Input
data is the limb darkening x (larger star), 1-λ{sub}b[/sub](λ=ℓ(θ) at internal
tangency of annular eclipse), ℓ_α=depth of total eclipse (or value of ℓ(θ)
at internal tangency of total eclipse), and an initial estimate of k.
 …

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