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Manuscript Title: The light curve of a variable star subject to orbital tidal distortion.
Authors: D. Herbison-Evans
Program title: MAGBIN
Catalogue identifier: AACG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)315
Programming language: Algol.
Computer: KDF9.
Operating system: KIDSGROVE.
RAM: 20K words
Word size: 48
Keywords: Astrophysics, Light curve, Tidal distortion, Binary star, Variable star, Non-linear least squares.
Classification: 1.7.

Nature of problem:
Given a spectroscopic ephemeris of a double star system suffering tidal distortion, this program finds the inclination of the orbital plane, i, and the r1/a ratio (r1 = primary star radius, a = semi major axis of the orbit) from the variation of brightness with time (the 'light curve'). It also finds the period, P, amplitude and phase of the oscillation if one of the stars is variable. It also finds the mean brightness of the star and instrumental changes in this value if the star is observed over several years or with different instruments. This program has been used to analyse in this way some observations on alpha Virginis.

Solution method:
Trial values of the six unknown parameters (i.e. mean brightness, 2 steps in this mean, r1/a, i and P) together with the spectroscopic ephemeris are used to compute theoretical values of the brightness at the times the star was actually observed. The root square (r.m.s.) difference between calculated and observed magnitudes (the residual) is minimised by an adaptive simplex search of the parameter values. At each stage, a linear regression gives the amplitude and phase of the oscillation. Many of the procedures in the program are the same as those in the program solving a spectroscopic double star orbit.

As it stands, the program can only accept up to 1159 observations, although this can easily be altered. It only provides for 2 consecutive) instrumental jumps. The third order Newton-Raphson solution to Kepler's equation is used. The orbital light curve is assumed to be dominated by orbital variations in only the primary star. The variable star is assumed to have a sinusoidal light curve of fixed period. The program assumes that there are no eclipses and no reflection effect, and also that brightness changes are small enough to be equal to -2.5 log10**e times their magnitude changes, where e=2.718.

Unusual features:
The program allows doubtful observations to be rejected, and any subset of the parameters to be searched for a minimum residual. Periodically the program breaks off minimising and lists the best parameters so far, their standard derviations, and the values of a, r, and the stellar masses derived from these parameters. At the end of the minimisation, the data is listed with corresponding calculated values of the brightness changes due to the orbit and the oscillation, and a graphical output of the residuals is produced on the line printer. Then the calculated oscillation brightness changes are removed to give an observational orbital light curve, and finally the calculated orbital brightness changes are removed instead to give the observed oscillation light curve.

Running time:
On an English Electric KDF9 (floating multiplication 15 mu s) with 1159 observations, each residual takes 3 s to calculate. The number of residuals required by the simplex minimisation depends critically on the accuracy required and the proximity of the initial parameter values to the best ones.