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## Homework Statement

Show that the Hubble profile of surface brightness

[tex]I(r) = I_0 \left(1+\frac{r}{R}\right)^{-2}[/tex]

leads to an infinite total luminosity, while the law

[tex]I = I_0 exp[-(r/a)^{1/4}][/tex],

with a a constant, does not.

Here [tex]I_0[/tex] and R are constants and r is the distance from the centre. The scale length R is typically around 1 kpc.

**2. The attempt at a solution**

I have no clue. How can I relate total luminosity with surface brightness?

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