It may seem obvious that the most powerful stars are the brightest. This is even truerthan it seems. Because of Stefan's Law
\[\lambda_{PEAK}= \frac{2.9 \times 10^{-3}}{T}\]
where, treating the star as a black body,
\[\lambda_{PEAK}\]
is the peak in peak in the black body spectrum
\[2.9 \times 10^{-3} m \cdot K\]
° is Stefans constant
\[T\]
is the surface temperature of the star.
Because of this relationship, the peak of the spectrum can occur at different wavelengths. If the peak for a star is in the visible region, and the peak of a hotter, more powerful star is at a shorter wavelength, the first star can appear relatively brighter than we would think just by considering its power output. The more powerful star can be brighter at all wavelengths, but relatively less bright than in the visible region.
