Analysis of the Light Changes in the Time Domain

Abstract

After the preliminary remarks contained in the foregoing paragraphs, let us turn now to the actual task of an analysis of the observations of instantaneous brightness of an eclipsing variable in the course of time, with the aim of deducing from them the elements of the system enumerated in the introduction. Photometric observations of such systems performed by different methods (visual, photographic, photoelectric) furnish, in general, a series of discrete values of instantaneous brightness of the system prevalent at different time or phase of the orbital cycle. If both components are spherical, the light of the system should remain constant between eclipses*, and will hereafter be adopted as a unit in terms of which the instantaneous luminosity l observed at a time t, or phase angle

$$ \theta = (2\pi /P)(t - {t_0}) $$

((0.1))

can be expressed. If, moreover, the orbital plane of our binary is inclined by an angle of 90° ± i to the line of sight and R stands for the separation of both components hereafter regarded as constant,† the apparent separation δ of the centres of the two stars projected on the celestial sphere will be given by the equation

$$ {\delta^2} = {\sin^2}\theta {\sin^2}i + {\cos^2}i = 1 - {\cos^2}\theta {\sin^2}i $$

((0.2))

.