How do we know the age of stars

We can find out the age of a star cluster by plotting the stars on a graph called a Hertzsprung-Russell diagram.

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One of the most common questions we get at our stargazing sessions is how do we know the age of stars. It is a complex question and the answer lies in a bunch of assumptions that have proven themselves over many decades. We know quite a lot about stars basically through watching them since people first looked in telescopes around 400 years ago. It wasn’t long before early astronomers noticed that stars seemed to be arranged in groups called open clusters and other tighter groups called globular clusters – and a whole bunch in between. It is really difficult to determine the age of a star but it is quite easy to determine the age of a star cluster and we do it by using graphs.

Life Cycle of Stars

The life of stars follows a pattern that is very consistent and is driven by the laws of physics and is manifested through the tussle between the force of gravity and radiative pressure caused by nuclear fusion. This means that the life cycle of a star goes through some fairly well defined phases. Take a huge area of space, many light years across, that has a good amount of gas and is cold and then disturb it a bit. What will happen is a bunch of points in that gas cloud will be slightly denser than other areas and if the conditions are right then the gas around these points will slowly collapse due to the force of gravity into sphere that gets hotter and hotter. These balls of gas, mainly hydrogen, get denser and denser until the temperature in their core reaches around 15 million degrees kelvin. Up until that point we call them protostars. The length of time it takes for a star to get to the end of the protostar phase is inversely proportional to its mass. The more mass the shorter the length of time and the less mass the longer it takes. A star the size of the Sun could take about 50 million years to reach the end of the protostar phase of its evolution.

Hitting the Main Sequence

Once the magic 15 million degrees Kelvin is reached in the core of the star, nuclear fusion begins. Basically the hydrogen in the core slowly gets squashed together and makes helium. This phase is called the Main Sequence and is the longest phase of the life of a star and it is when a star ends its time on the Main Sequence is how we know the age of stars. After the hydrogen runs out in the core of the star it gets unstable and the star expands an enormous amount, beginning the red giant phase of its life. If the mass of the star is enough then gravity will crush the core to where it is about 80 million degrees and then helium can fuse to make carbon. The helium burning phase is called the horizontal branch. For stars like our Sun that’s where the fun ends as it doesn’t have the mass to fuse carbon so once the helium runs out in the core the nuclear fusion engine shuts down and the outer layers of the Sun are expelled leaving a stellar remnant called a white dwarf. This is essentially the core of the star slowly cooling down. For our Sun that whole process takes about 10 billion years. For more massive stars it can be just a few tens of millions of years.

Measuring Stars

There are some things which are quite easy to measure about stars. One is the mass, one is the luminosity and one is the temperature. If you know the distance to the star the luminosity is quite easy to calculate as the energy reaching the earth diminishes based on a relationship dependent on the distance. Working out the mass is a bit trickier and requires some accurate measurements and observations of the star’s movements over time. The final measurement is the temperature, this is very easy to measure as it relates to the colour. For example a red star is much colder on the surface than a blue star. Over the years astronomers have measured the luminosity, mass and temperature of thousands and thousands of stars and plotted these on a graph that has luminosity on the y axis (the up and down one) and temperature on the x axis (the horizontal one). This graph was developed by Mr Hertzsprung and Mr Russell at about the same time, so is called the Hertzsprung-Russell diagram. It has been found to depict a very consistent relationship between temperature and luminosity.

The Hertzsprung-Russell Diagram
The plot of Temperature vs Luminosity, known as the Hertzsprung-Russell diagram, this version made by the author.

The Hertzsprung-Russell Diagram

Mass comes into it through the stars with the least mass being in the lower right corner and the stars with the highest mass being in the the upper left corner. Any given star will have a journey on the Hertzsprung-Russell diagram that will track it’s evolution through the different life cycle phases. Astronomers have plotted so many stars on the Hertzsprung-Russell diapgram that it is possible to read the mass of the star just by plotting the luminosity and temperature.

You can also plot the life of one star on a Hertzsprung-Russell diagram to show the different phases it goes through that I described above.

The evolution of a star
This is the life cycle of a Sun like star – just follow the numbers (by the author)

The Age of a Star Cluster

The tricky bit with all of this is that we don’t know where in a particular phase a star is, very easily, in fact sometimes it is quite tricky to know if a star is in the main sequence or in another phase. Fortunately for the majority of stars we observe we can tell if they are main sequence. The problem is we don’t know how far through the main sequence they are, we don’t know how much of the hydrogen is left in the core. What we do know is how long a star of a given mass will be in the main sequence for. So if we plot all of the stars in a cluster on the Hertzsprung-Russell diagram then we will get a graph that will show the current position of all of the stars and from that is how we know the age of stars. We will see all of the stars on the Main Sequence and there will be a sudden right turn off the Main Sequence, we call this sharp turn the Main Sequence Turn Off and based on the position where this occurs on the Hertzsprung-Russell diagram we can estimate the age of the cluster. Basically the younger the cluster the higher (towards the upper left) of the Main Sequence the turn off will be. The older the cluster then the lower in the Main Sequence the turnoff will be.

A star cluster plotted on a Hertzsprung-Russell diagram for how we know the age of stars.
Here’s a diagram of what a plot of how a cluster might look like – maybe 100 million years old.

How we know the age of stars

A star about 6 times the solar mass of the Sun will burn hydrogen (be in the Main Sequence) for about 100 million years. So in the above diagram if we don’t see any stars on the Main Sequence that have a higher mass that’s bigger than 6 times the mass of the Sun when we can estimate the age of the cluster to be 100 million years and that’s how we can know the age of stars!