What is a star cluster?
A star cluster is a group of stars that are close together and held by their own gravity. The stars in it were born from the same cloud of gas and dust, at almost the same time.
That gives two big facts: all the stars have the same age and the same starting chemicals. The only thing that is different is their mass. This makes a cluster a perfect test lab for how stars live and die.
A nebula is the cloud itself. Young clusters can still be wrapped in the glowing gas they were born from.
Open clusters and globular clusters
There are two main kinds.
- Open cluster: a loose group of tens to a few thousand stars, a few light-years across. Mostly young (millions to a few billion years), blue-white, and found in the disc of the galaxy. Gravity is weak, so over time the stars drift apart.
- Globular cluster: a tight ball of 100,000 to millions of stars. Very old (around 10 to 13 billion years), mostly red and yellow stars, and found in the halo around the galaxy. Strong gravity keeps the ball together for ever.
Old stars in globular clusters have very few 'heavy elements' (anything heavier than helium) because they formed early, before many stars had made those elements. Young disc stars, like the Sun, have more. These two groups are called populations of stars.
The colour-brightness graph (colour-magnitude diagram)
Astronomers plot every star of a cluster on a graph. Across: colour (hot blue on the left, cool red on the right). Up: brightness. This is a colour-magnitude diagram, a close cousin of the H-R diagram.
All stars in a cluster are at nearly the same distance, so how bright they look compares fairly with how bright they really are. Stars fall on a clean curve: the main sequence, where stars fuse hydrogen into helium. Heavy stars are hot, blue and bright (top left). Light stars are cool, red and dim (bottom right).
Stars that have used up the hydrogen in their cores leave the curve and move to the upper right as giants, cool but very bright.
Finding the age from the turn-off
A star's life depends on its mass. Heavy stars live short lives: they burn fuel very fast. A rough rule is
life on main sequence ≈ 10 billion years × (mass in Suns)−2.5
At any time the heaviest stars are gone from the main sequence, so the top of the curve is cut off. The place where the curve ends and bends toward the giants is the main-sequence turn-off. The stars right at the turn-off have a life equal to the cluster's age.
So: find the turn-off, read its mass or brightness, use the rule, and you get the age. A turn-off near the top means a young cluster; a turn-off low down means an old one.
Key formulas and definitions
- Main-sequence life ≈ 10 × M^(−2.5) billion years (M in Suns)
- Cluster age ≈ life of the stars at the turn-off
- Turn-off mass ≈ (10 ÷ age in billion years)^0.4
Worked examples
1. How long does a star of 4 Suns stay on the main sequence?
Life ≈ 10 × 4^(−2.5). 4^2.5 = 4² × √4 = 16 × 2 = 32. So life ≈ 10 ÷ 32 ≈ 0.31 billion years (about 310 million years).
2. The stars at a cluster's turn-off have mass 2 Suns. What is the cluster's age?
Age ≈ 10 × 2^(−2.5). 2^2.5 ≈ 5.66. Age ≈ 10 ÷ 5.66 ≈ 1.8 billion years.
3. Cluster A has a turn-off at 6 Suns. Cluster B has one at 1 Sun. Which is older, and by how much roughly?
B is older. Life at 6 Suns ≈ 10 ÷ 6^2.5 ≈ 10 ÷ 88 ≈ 0.11 billion years. Life at 1 Sun = 10 billion years. B is about 90 times older.
Common mistakes
- Thinking stars in a cluster have different ages. They are born together; only their masses differ.
- Thinking the bright blue stars live longest. Brighter and heavier means a faster burn and a shorter life.
- Mixing up the two types: open clusters are young, loose and in the disc; globular clusters are old, dense and in the halo.
- Reading the age from the top of the curve. The age is read at the turn-off (the bend), not at the brightest star.