# What is the average lifespan of a star?

Jan 29, 2016

Between less than a million years and tens of billions of years!

#### Explanation:

Stars are big. Because they're big, they're also very massive. That mass is important to the star, it creates intense pressure in the centre which gets hot enough to fuse hydrogen to helium (And also Helium into heavier elements but that phase is always less than 5-10% of the star's age). Finally we know that the bigger the star is, the hotter the centre is (more pressure=higher temperature).

However stars can't fight gravity forever: they may be big but they don't have infinite Hydrogen (let's ignore He, C, N, etc) to burn. This means that their age is basically determined by:

1) The amount of fuel they have
2) The rate at which they burn their fuel.

1) is simple, it's just the mass of the star times the fraction of hydrogen (~0.75). So as the mass increases, the amount of fuel increases linearly. Simple!

2) is much more complex. The simplest plot to convince you is the mass-luminosity relationship. Basically it shows how bright a star is(how fast it burns fuel) vs its mass. . This is a log-log plot meaning for an increase of mass by 10, the luminosity increases by 4 (!!) orders of magnitudes!

So (from 2), a star 10x the sun's mass will burn its fuel 10,000 times faster. From 1, it will roughly have 10x the fuel meaning it will live about 10 million years instead of 10 billion. From personal experience, this is a pretty good approximation, I did a simulation of a 8 solar mass star for a project and got 50 Myr lifespan.

It's amazing how good a first order approximation is!

So now that you have the model you can figure out how long the biggest (100 solar mass) and the smallest stars (~0.05 solar mass) stars will live!