Live Fast, Die Young

Stars living on the main sequence are converting hydrogen to helium in the core. Once they exhaust the hydrogen in their core, they begin to evolve. How does this timescale depend on mass?

Remember the mass-luminosity relationship:

Question: what causes this relationship?

This can be roughly fit by a power law: L ~ M⁴.

Main Sequence lifetimes -- a gas tank argument

The fuel in the gas tank is hydrogen. The rate at which the fuel is burned gives the luminosity. So the lifetime on the main sequence is proportional to
T_ms ~ M/L ~ M/M⁴ ~ M^-3

So massive stars live for a much shorter time!

Mass (M_sun) Main Sequence Lifetime

1 10 billion years

1.5 1.5 billion years

3 250 million years

5 70 million years

9 20 million years

15 10 million years

Mass (M_sun)	Main Sequence Lifetime
1	10 billion years
1.5	1.5 billion years
3	250 million years
5	70 million years
9	20 million years
15	10 million years