4.2 Stellar lifetime as a function of mass
At the end of last week, you calculated the lifetime of the Sun based on the mass of hydrogen available and the rate at which it is being used up to sustain its luminosity and stability. This resulted in a lifetime of about 10 billion years. We are now in a position to see how the lifetimes of stars of other masses compare to this figure.
Although stars more massive than the Sun have more hydrogen available to use as fuel they also have much higher luminosities, meaning that the hydrogen is used up at a greater rate. As you have seen in Figure 4, the luminosity increases much more rapidly than the mass, meaning that heavier stars will actually have shorter lifetimes.
This is illustrated in the following table, which calculates the lifetimes of stars compared to that of the Sun:
| Mass (solar masses) | Luminosity (Sun = 1) | Lifetime in years |
|---|---|---|
| 0.5 | 0.03 | 180 billion |
| 0.75 | 0.3 | 30 billion |
| 1.0 | 1 | 10 billion |
| 1.5 | 5 | 3.3 billion |
| 3 | 60 | 550 million |
| 15 | 17 000 | 10 million |
| 25 | 80 000 | 3.4 million |
The life of a star depends on the amount of hydrogen fuel available and the rate at which it is used up. As shown in the table, the luminosity increases much more rapidly than the mass. A star of just three solar masses has 60 times the luminosity. It has three times as much fuel available, but at 60 times the rate of consumption it will all be used up in one-twentieth the time – just 550 million years. Even heavier stars with luminosities many thousands of times more than the Sun have lifetimes of just a few million years. The smaller K and M stars however – those with less mass than the Sun – use up their fuel at a very slow rate, giving them projected lifetimes of many tens or even hundreds of billions of years – longer than the current age of the universe.
From this table you can also see that it is very fortunate for life on Earth that our Sun is a relatively small, average star, fairly low down on the main sequence and the scale of luminosity. Given that the Earth is 4.6 billion years old, a star just a bit larger than our own Sun at 1.5 solar masses would have expired by now, but luckily our own Sun is only about halfway through its main sequence life.
This naturally leads us to think about what happens to a star when the hydrogen in its core does run out, and you will conclude this week by considering this.