For example, if a source is observed to vary its light output substantially over a period of a week, this implies that the spatial extent of the energy producing region can be no larger than the distance light can travel in a week (a "light-week"). On the other hand, if a source varies its intensity on a scale of a day or less, the size of the energy source must be less than the distance light can travel in a few hours. This is comparable to the size of the Solar System.
Thus, the observation that some quasars vary their light output substantially on a timescale of a day or less argues that their prodigious energy source is contained within a volume the size of the Solar System or smaller, which is incredibly small for an object outputting energies larger than that from large galaxies. There is relatively uniform agreement that rotating black holes containing of order a billion solar masses (which would be smaller in size than the Solar System) are the most plausible candidates for such energy mechanisms.
These general arguments only place an upper limit on the sizes of variable sources. It is quite possible that the signals causing the variation travel at less than light speed in particular cases, so that the size of the energy producing region is actually considerably less than the upper limit imposed by these arguments. Nevertheless, this is a very powerful argument, because it depends only on a general principle (finite speed of light) and not on the internal details of the source in question.
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