How do we know how old a star is?

When we move through the universe, due to the great distances we travel and the speed limit of the propagation of light, we often state that to look into the distance is to look back in time. The recent discovery by the Hubble telescope of the most distant star ever observed, Earendel, could lead us to believe that because of the issue of space-time in astrophysics, Earendel is also the oldest star we have found. Nothing could be further from the truth. Earendel is far away and its light takes a long time to reach us, but it is not an old star.

If we want to talk about old stars we could, for example, look at one of the oldest stars we are aware of with a determinate age: HD 140283, nicknamed Methuselah. HD 140283 is quite close to us, at a distance of 190 light years, and it is almost as old as the universe itself, at 13.7 billion years. Methuselah has been well-known for over 100 years because it has a very large proper motion – the change of its position in the night sky over a period of time. This means that while it is in our neighborhood, it is only visiting. It comes from the area of our galaxy known as the stellar halo and moves at a speed of over 620,000 miles an hour. By tracking its movement in the past, we have been able to determine that it was born in a primitive dwarf galaxy that was ripped apart by the gravitational field of our galaxy at least 12 billion years ago. By measuring its chemical composition, we know that it does not come from our own environment because it has a deficiency of heavy elements. That is to say it was formed in an environment consisting of ancient material in which chemical elements had not yet processed by different generations of stars.

And that brings us to the problem raised at the beginning of efforts to determine the age of celestial objects. In astrophysics there are things that we can and things that we can’t measure is a relatively simple way, taking into account of course that we are talking about the cosmos and objects that in the best of cases are so far away that we have to employ special units of measurement. The mass of an astronomical object, for example, falls into the first category and is easy to determine, as is what it is made of and its chemical composition. It is also not too taxing, if we ignore the hours of sleep we lose while looking through the telescope, to calculate the speed at which a star is traveling, the presence of accompanying stars and magnetic fields. However, determining the age of a star is considerably more complicated.

It is perhaps surprising that the only star whose age we know precisely is the Sun. We are able to calculate its exact age with some certainty only because we have access to the material it is made of. The process involves taking a sample of the Solar System in as pristine a state as possible, usually in the form of a meteorite, and measuring the amount of long-lived radioactive isotopes they contain. The problem is we do not have material from another star to study in the laboratory, so how can we determine the age of the rest of them?

It depends. When a star is from an ancient population it has few metals because it was born without them. The universe did not have time to form them in those stars and disperse them in to the void in the form of stellar winds. By decomposing the light that reaches us in the form of spectra, if we are able to measure the chemical fingerprints of uranium, and particularly that of another element on the periodic table called thorium, we can determine its age. But this measurement is very difficult to make because little thorium light reaches us and it is mixed with the marks of other chemical elements.

Another way we calculate the age of stars is by studying how they move and judging their orbits in the past, something which is made possible when they belong to young groups of stars that move together. We can also study how the speed at which they rotate decreases, because they are like spinning tops that slow down with the passage of time. We also sometimes calculate their lithium content, which gives us information about their age. Another technique that I have personally always found fascinating is asteroseismology, which measures the oscillation modes in stars and is similar to what scientists do through earthquake measurements to infer the structure of the Earth’s interior. Asteroseismology is very useful when dealing with old stars because their vibrational modes, which we call low order, pass through the center of the star and give us an idea of its density, which translates reasonably directly into a measure of its age.

However, generally speaking, we cannot determine the age of lone, isolated stars with precision. We have techniques we can work with, but we cannot measure the age of these stars as such. We can guess, infer, but we cannot determine it absolutely in isolated stars, except in the case of the Sun. If we think about it, it is the same with humans. Purely by sight it is difficult to guess the age of a child, if we do not have several other children nearby as a reference point. For this reason, one of the most-used methods consists of observing how they age together in star clusters, because these are born in a group and time does not pass in the same way for all them.

Furthermore, the age of a star is uncertain among other reasons because the moment in which it is born is badly defined. In the same way it is very clear for a mammal, if we extrapolate our day-to-day experience to the world of the heavens, we encounter vicissitudes that are difficult to resolve from an operational point of view. From a theoretical angle, the problem is simple: a star is born at the moment that its structure reaches what we call hydrostatic equilibrium. This occurs when the tensions even up and the structure neither enlarges nor contracts because the pressure exerted by the energy generated inside the star is counteracted by the inward pressure exerted by gravitational force. This exact moment is off-limits to us, we cannot see it, we only have access to see the structure in equilibrium thousands of years later, when the star has freed itself from an envelope that forms as the result of its own collapse. We have attempted to work with other definitions: when we start to see the photosphere, a luminous surface that delimits a star, of the moment in which a star reaches what is known as zero age in the principal sequence, which is when it burns hydrogen in its core, in thermonuclear terms, but from there the star already has an age and we would have to employ negative times.

The fact is that no definition of the moment of a star’s birth is perfect and no one technique works for all stars, although they provide us with complementary information. Time, by definition, has an elusive quality.