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In eclipsing binary, the eclipsed object becomes dimmer. But why microlensing, which essentially is an object being occulted, causes the occulted object to brighten?

- Jared (01.05.2003)

If you see a photo of gravitational lens (as below) , you will find the image of the occulted object becomes a ring. (Assuming the occulted object, gravitational lens and observer are in a perfect straight line.) Such ring is called Einstein Ring.

Photo credit: NASA

Most Einstein Rings are too small to be seen directly. We can only detect the brightening of the occulted object by the "focusing" action of the gravitation lens. This effect is called microlensing.

Theoretically, Einstein Ring is formed whenever occultation happens. However, if the ring formed is smaller than the occulting object, the whole ring will be covered and we can only observe the dimming of the occulted object. This is exactly the case for eclipsing binary.


The formula of angular radius of Einstein Ring is as follows:

where cE is the angular radius of Einstein Ring; dL is the distant to the gravitational lens; dS the distant to the occulted object; dLS is the distant between them; G is the gravitation constant; M is the mass of the gravitational lens; c is the speed of light. 

As you may see, the smaller the mass of gravitational lens, the smaller the Einstein Ring is. On the other hand, if the two objects are close to each other, dLS/ dLdS0. Both conditions are satisfied in eclipsing binary. That is why we cannot observe the brightening of the occulted star.

LAU Kai-Ip
Asst. Curator, Hong Kong Space Museum