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Back in my younger days when I was studying astronomy at university I wrote some simple software for the emulation of the light curve from eclipsing binary stars. You plugged in the size and luminosity of the two stars, the diameter of the orbit and the angle of the plane of the orbit to Earth and it produced a light curve.
As others have said you with eclipsing binaries you get a characteristic light curve for the system that shows two dips, a deeper one when the less bright star passes in front of the brighter, a shallower one when the less bright is eclipsed by the brighter.
However, software like mine only touched the surface of the complexity of modelling eclipsing binaries, there is far more sophisticated professional software that takes into account things like:
- the brightness per unit surface area of a star is not uniform across its disk, the center is brighter than the limb, so the loss of light as the star is eclipsed is not a simple matter of calculating the area eclipsed, it also depends on where that area is
- the secondary does not simply orbit the primary, both orbit the center of gravity, which means the primary may wobble or move in place, complicating the eclipse calculations
- if the two stars are close enough the gravity of the other may pull the other star out of shape - instead of being a sphere it will become more like an ovoid which again complicates the light curve - so that more surface area and light will be shown when the stars are square on than when the pointy end points to Earth - this becomes an extremely complex mutual interaction between the two stars as each's gravity distorts the other
- if the stars are really close the gravity of one may pull material out of the atmosphere of the other and you will get a stream of bright material between the two - that material contributes to the overall light curve and it can itself be eclipsed
- if either star is rotating fast it will not be a sphere, it will be an ovoid and there will be a change in the distribution of the brightness across the disk
- the light from one star can heat up the atmosphere of the other, so that the limb closest to the partner star is brighter than the far limb
etc etc
the aim of that very complex software is that you plug in the observed light curves over many orbits and the software then calculates the parameters of the system by trying to match the light curve to ones it generates. For systems where the two stars are widely separated and the interactions between the two are thus comparatively simple its quite straightforward to match observed to calculated light curves and establish the system parameters. But for closely orbiting stars where there are many complex interactions going on it can be very difficult to get reliable system parameters.
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