- #1
Logarythmic
- 281
- 0
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. 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
[tex]I(r) \propto r^{-2}[/tex]
but how is the surface brightness related to the total luminosity?