# Luminosity physics question

## Homework Statement

Show that the Hubble profile of surface brightness

$$I(r) = I_0 \left(1+\frac{r}{R}\right)^{-2}$$

leads to an infinite total luminosity. r is the distance from the center and R is a constant.

2. The attempt at a solution
For large r this is related as

$$I(r) \propto r^{-2}$$

but how is the surface brightness related to the total luminosity?

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