Active galactic nuclei $($AGN$)$ are the most luminous persistent sources of electromagnetic radiation in the universe, emitting across the whole electromagnetic spectrum.

They are associated with very distant galaxies $($and hence we are seeing them as they

were early on in the Universe$$s history$).$ Their luminosity is observed to vary on

timescales of hours or days.

What does this tell us about the lengthscale on which the physical process responsible

for the variation occurs? Estimate this lengthscale in AU for a variation timescale of

$1$ day