Temperature, size and luminosity

• Hotter things are brighter.
  • Energy radiated per unit time per unit area is proportional to T⁴,
  • so bigger T means more energy radiated
• Bigger things are brighter.
  • Energy radiated per unit time per unit area is proportional to T⁴,
  • so bigger surface area means more energy radiated.

This suggests a possibility to try. Maybe all stars are the size of the Sun, but the hotter ones are more luminous just because they are hotter. We can test this with the HR diagram:

Our hypothesis would be that all main sequence stars fall on the blue line.

Here is the comparison:

Our idea was wrong. But we learned something. The coolest main sequence stars are a lot smaller than the sun. The hottest main sequence stars are a lot bigger than the sun.