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Manuscript Title: Analysis of a variable spectroscopic double star.
Authors: D. Herbison-Evans, N.R. Lomb
Program title: BISPEC
Catalogue identifier: AACE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)368
Programming language: Algol.
Operating system: KIDSGROVE COMPILER.
RAM: 20K words
Word size: 48
Keywords: Astrophysics, Doppler shift, Variable-star, Spectroscopic Binary-star, Minimisation, Simplex method.
Classification: 1.7.

Nature of problem:
Measurements of the Doppler shifts of the spectral lines of a double star at different times can be used to derive the velocities of the stars at these times. The program 'bispec' derives the orbital parameters (mean velocities, amplitudes, longitude of periastron, epoch of periastron, eccentricity, orbital period, and period of rotation of the line apsides) of the stars from these velocities. The program will also find the best fitting sine wave (amplitude, period and epoch of zero phase) to the velocities, measured at various times, of an oscillating star. It can solve both problems simultaneously if one of the members of a double star is oscillating. This has been done for the star alpha Virginis.

Solution method:
A test set of orbital and oscillation parameters is used to produce calculated values of the velocities at the times of observation. A total residual is produced by summing the weigthed squares of the differences between corresponding calculated and observed velocities. A simplex method is used to search the parameters so as to minimise this residual.

The program can cope with a maximum of 605 sets of observations, although this is easily altered, and only one of the stars can be oscillatory. The program uses the third order Newton-Raphson solution of Kepler's equation.

Unusual features:
The program allows any subset of the parameters to be searched for a minimum residual. It enters a machine code to loop for greater speed if the line of apsides is assumed fixed and neither of the stars is oscillatory. It can be used to print out the residuals on a grid of values of any 2 parameters. The program produces the standard deviations of the final parameters. It will also print out an analysis of the stars' motions at the epochs of observation, if required.

Running time:
The time taken for a complete minimisation depends on the proximity of the initial parameters to the best fitting parameters, and the dimensionality of the search.