How can we use variations in luminosity to set limits on the size of an active galactic nucleus?
If we see an object brighten in 1 hour, we know that the object cannot be longer than 1 light-hour in size. If it were, light from the far side of the object would start arriving at our telescopes more than an hour after the light from the front side and we would see the brightening take longer time than an hour to occur.
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How can we use variations in luminosity to set limits on the size of an active galactic nucleus?
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