Star Figure 7.4: Light from a star in the LMC is deflected by a MACHO on...

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Star Figure 7.4: Light from a star in the LMC is deflected by a MACHO on its way to an observer in the disk of our galaxy (seen edge-on in this figure). (07_macho_star.pdf) If the MACHO is exactly along the line of sight between the observer and the lensed star, the image produced is a perfect ring, with the angular radius OE Source plane MACHO = (² 4GM 1 - I (7.45) where M is the mass of the lensing MACHO, d is the dis- tance from the observer to the lensed star, and xd (where 0 < x < 1) is the distance from the observer to the lensing MACHO. The angle is known as the Einstein radius. Star c²d x MACHO Observer 1/2 a xd Observer Question: Derive Eq. (7.45). Hint: start from Fig. 7.5 and let 0 → 0. Star Figure 7.4: Light from a star in the LMC is deflected by a MACHO on its way to an observer in the disk of our galaxy (seen edge-on in this figure). (07_macho_star.pdf) If the MACHO is exactly along the line of sight between the observer and the lensed star, the image produced is a perfect ring, with the angular radius OE Source plane MACHO = (² 4GM 1 - I (7.45) where M is the mass of the lensing MACHO, d is the dis- tance from the observer to the lensed star, and xd (where 0 < x < 1) is the distance from the observer to the lensing MACHO. The angle is known as the Einstein radius. Star c²d x MACHO Observer 1/2 a xd Observer Question: Derive Eq. (7.45). Hint: start from Fig. 7.5 and let 0 → 0.

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