Astronomers have a new trick for calculating the age of stars

Shine, shine little star, I wonder how old you are.

Not an easy question to answer. Stars are notoriously difficult to age. We know the age of the Sun because we happen to live on one of its orbiting rocks, and we know very well how old the rock is. Without this information, things get a little more confusing. But that could change thanks to a new study.

We know some general rules about determining the age of a star. For example, generally the higher the metallicity of a star, the younger it is. And main-sequence stars like the Sun tend to get hotter as they get older, so if two stars have the same mass and composition, the hotter of the two is probably the older. But by themselves, these general rules are not sufficient to obtain an accurate age determination. For this, we typically look at star clusters.

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Star clusters such as open clusters and globular clusters generally form within a single molecular cloud and do so at roughly the same time. When you look at the stars in a cluster, you know they are all the same age. Astronomers can exploit this fact to get good ages for star clusters. Individually there will be variations in things like metallicity and temperature, but statistically, determining the mean age is a good measure of cluster age.

But one thing that has been noticed is that among star clusters, older clusters have stars that rotate more slowly than stars in young clusters. This suggests that a star’s rotational speed slows as it ages. This would be a great way to determine stellar age because many stars have star spots, which we can use to measure rotation quite easily. There are only two problems. The first is that within a cluster, stars can be gravitationally bound and this interaction could be the basis of the slowdown. In that case, individual stars would not experience the same rotational decay. The second is that a star’s metallicity affects its density and temperature, so metallicity could have a significant effect on how fast it slows down.

Age of star clusters (lines) vs. age of binary stars (circles/diamonds). Credit: Gruner, et al

However, the technique would have been so useful that a team wanted to explore it further. They examined 300 broad binary stars. These are binary stars with orbital distances large enough that their rotations are independent of each other. And since binary systems all form at once, the team could be sure that the binary pairs were the same age.

The team then applied the cluster method using temperature and rotational speed to determine the age of each star in a pair. They found that the ages of the binary pairs matched using this method. And with 300 samples to work with, they’re confident the method works. The team also found that the approach worked regardless of the stars’ metallicity. So while metallicity might have a small effect on stellar age, the rotation approach works just the same.

From this work, astronomers can feel confident using rotation as a measure of age whether a star is single, binary, or part of a cluster. This is great news. Telescope satellites like Gaia and the upcoming PLATO mission have exoplanet searches as part of their mission. The same method used to find the dip in stellar brightness during the transit of an exoplanet can also be used to measure the rate of rotation of a star through starspots. In time it could know the age of billions of stars, as well as their movement and whether they have planets.

Reference: Gruner, D., S.A. Barnes and K.A. Janes. “Broad binaries demonstrate coherence of rotational evolution between open clusters and field stars”. Astronomy and astrophysics 675 (2023): A180.

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