If an X-ray source varies significantly in brightness over a few days, what can we infer about its size?

When an X-ray source varies significantly in brightness over a short period, such as a few days, we can infer that the source is relatively small in size. This is rooted in the principle of light travel time, which indicates that the light from an object takes time to reach us. Therefore, any changes in brightness must occur within a distance where light can travel in that time frame.

If the X-ray source were larger than a few light-days in diameter, the variability in brightness would not be observable within just a few days. The changes would be smoothed out over such a large surface, as different regions would take different amounts of time for the light to reach us. Hence, the fact that we observe significant brightness fluctuations over a few days suggests that the source cannot be larger than a few light-days across, leading us to conclude that the X-ray source is no more than a few light-days in diameter.

This understanding allows astronomers to make accurate assessments about the nature of such sources, linking their size directly to their observed variability.