Light Curve Synthesis ( Binary Stars)
We have seen that the light curve of an eclipsing (or of a nearly eclipsing) binary system can be complex and difficult to interpret. The most important effects that must be taken into account are the following
DISTORTION :A single star, like the Sun, is essentially spherical. When two stars are close together, however, mutual gravitational forces distort each star. The problem of what shape such stars are has not been solved, but it is possible to get a good idea of the answer by approximate methods. If both stars are rotating at the same speed as the system as a whole, and if each star may be approximated by taking all its mass to be concentrated at its centre while the rest of it consists of a massless fluid, the stars take up the shape defined by Roche potentials.
LIMB DARKENING: A stellar atmosphere appears to be of varying brightness when viewed from different angles. At the edge of a star we are viewing the atmosphere obliquely, while at the centre we look straight down into it. The edges of a star appear less bright than its centre.
GRAVITY DARKENING. When a star is distorted those parts of the atmosphere that are furthest from the centre of the JT general cooler. The effective temperature varies over the surface of distorted star and allowance must be made not only for the relative brightness of various parts of the stars,but also for the filter through which observations are being made
REFLECTION EFFECT: When two stars are close enough, each of them can subtend an appreciable angle to the other. Each can intercept a significant fraction of the light emitted by the other. The result is that those parts of the stars in close proximity to each other are hotter than might be expected.
A computer can be used to take all these effects into account, to calculate what each star looks like from various phases of the orbit, and to determine how much of one star is obscured by the other at each moment in time. In effect, if the computer is given the size (relative to the orbital separation) and luminosity of each star, it can compute a synthetic light curve for an eclipsing system. The synthetic curve can then be compared to the real one. If there are differences between the two, some of the initial parameters must be changed. By trial and error and a judicious choice of the para¬meters of the synthetic system at each stage, it is possible to produce a good imitation of the real light curve and hence a good estimate of the actual orbital elements.