We cannot watch a star age for billions of years, but we can read ages from star clusters. A cluster is a family of stars born together from one cloud: open clusters such as the Pleiades hold hundreds to thousands of stars, and globular clusters hold hundreds of thousands, packed into a ball. Plotting a cluster on the H–R diagram works like a clock, using what you know about how stars leave the main sequence.
Why it works
All the stars in a cluster formed at nearly the same time, but with a wide range of masses. Massive stars burn out first. So as a cluster ages, its main sequence is eaten away from the top: the hottest, brightest stars peel off to become giants, then the next ones, and so on. The point where the main sequence ends, the turnoff, marks the stars that are just now running out of core hydrogen. Their main-sequence lifetime equals the cluster's age: $t \approx 10\ \text{billion years} \times M_{\text{turnoff}}^{-2.5}$.
Key idea
A cluster's age equals the main-sequence lifetime of the stars at its turnoff. The lower the turnoff on the main sequence, the older the cluster.
Worked examples
Worked example: Reading a turnoff
A cluster's main sequence ends at stars of $2.25$ solar masses. How old is it?
- $2.25^{2.5} = 2.25^2 \times \sqrt{2.25} = 5.06 \times 1.5 = 7.59$.
- $t \approx \frac{10}{7.59} = 1.3$ billion years.
Answer: About $1.3$ billion years.
Worked example: Old clusters
Globular clusters have turnoffs near $0.85$ solar masses. Estimate their age.
- $0.85^{2.5} = 0.85^2 \times \sqrt{0.85} = 0.7225 \times 0.922 = 0.666$.
- $t \approx \frac{10}{0.666} = 15$ billion years by this rough rule; detailed models give about 12 to 13 billion years, among the oldest objects known.
Answer: Roughly 12 to 15 billion years (detailed models: about 12 to 13).
Common mistake
A natural guess is that a cluster's brighter, bluer stars are younger and its dimmer ones older. In fact they were all born together; they just have different masses, so they age at different rates. Check: in a young cluster like the Pleiades, about 100 million years old, the hot blue stars are still on the main sequence; in an old globular cluster, every star hotter than about the Sun's temperature has already left it.