ExploraTour: A Peek into the Lives of the Stars
You can Predict a Star's Lifespan
A star's mass and luminosity are closely related. The heavier the outer layers of a star, the hotter the core becomes. Nuclear reactions proceed more efficiently when the core is hotter. The hotter the core, the brighter the star becomes. The star's mass and luminosity are approximately related by:
L ~ M**3.5
where L is given in units of solar luminosity and M is given in units of solar mass.
The lifetime of a star depends on the energy supply and the rate the energy is used. The energy supply is proportional to the mass of the star since mass converted to energy is the star's fuel. The rate, at which the energy is consumed, is proportional to the star's luminosity. We can summarize this as:
Lifetime is proportional to M / L ~ M / M **3.5 ~ 1 / M** 2.5
In this case, the lifetime is in units of the sun's lifetime. Let's give it a try.... Vega has a mass that is 2.5 times the sun's. It will last approximately :
1 / (2.5)**2.5 = 1 /10 solar lifetime
Try it yourself ....
A star that is 10 solar masses will last 1 / 300 solar lifetimes and one that is 1 / 10 of the solar mass will last 300 times as long as the sun. In reality it is a little more complicated than this simple formula because the relationship between mass and luminosity varies a bit with the mass of the star.