How much energy do the most productive stars make?
We use the Stefan-Boltzmann law to calculate the total power output of a star. The law states the following for a black body (an idealized object in physics that absorbs all incoming light):
`Power = \sigma A T^4`
Where `sigma` is a constant, A is the surface area of the black body and T its temperature. Since luminosity is proportional to the power output of a star, all we have to do is look for the most luminous stars in the universe.
Doing a quick search, we can find a list of such stars (in the references). In the first place is the star R136a1 with a power output of around 1.73x10³³ Watts! This is around 10^7 times the power output of the Sun! In second place is M33-013406.63, with a power output of around 1.612x10³¹ Watts (this value seems to be associated with a high uncertainty, so it could be even higher than it seems)!
So the most productive stars in the universe produce around 10³² Joules per second! For comparison, humans use a total of 10^20 Joules per year! So, in less than a second, those stars would produce enough energy to power all human activities for a year!