An AGN is observed to double in brightness over seven days and then to grow dim again in the nex

step 1 All right, so we know that distance is equal to velocity times time. So light, which does follow

An AGN is observed to double in brightness over seven days...

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Key Concepts

Conversion of Light-Travel Distance to Astronomical Units

After establishing the light-travel time distance as the upper limit on the size of the AGN, it is necessary to convert this distance into astronomical units (AU), a common unit for measuring distances within our solar system. This conversion requires knowing the distance light travels in a given time period (in this case, the distance light travels in seven days) and then converting that distance into AU by using the fact that 1 AU is the average distance between the Earth and the Sun.

Variability Timescale and Causality in Astrophysics

This concept involves the idea that any observable change in brightness of an astronomical object, such as an AGN, must be communicated across the region at the speed of light. Therefore, the rate at which the brightness changes sets an upper limit on the size of the emitting region, because a region larger than the distance light can travel in the observed time interval would not be able to vary coherently. In this problem, the doubling and subsequent dimming in brightness over a period of seven days implies that the source’s size is limited to approximately the distance that light can travel in seven days.

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