A few days ago I wrote about a planetary system discovered around an ancient star. I noted that the age of this star had been determined using asteroseismology, but how exactly does that work? What do sonic vibrations in a star have to do with its age?

The density and temperature of a Sun-like star over time. Credit: Brian E. Martin

It all has to do with the way stars age. A main sequence star such as the Sun spends most of its life in a balance between its gravitational weight trying to crush the star, and the fusion driven pressure of its core opposing that weight. While the Sun and other stars are mostly composed hydrogen, the nuclear interactions in their cores gradually transform some of that hydrogen into helium and other elements. This means that the density of a star increases with age. Since a more dense star allows gravity to squeeze it more strongly, the pressure and temperature also increase over time. Given the rate at which stars give off light energy, we can determine the rate at which fusion occurs, and thus determine how the density, pressure and temperature of a star will change over billions of years.

This is where asteroseismology comes in. The behavior of sound waves in a medium depends upon things like pressure, temperature, and density. By observing the oscillations of a star due to the sonic waves moving through it, we can categorize them into different modes. One type known as p-mode depend upon the speed of sound in the star, from which we can determine pressure and density. Another known as f-mode depends upon the surface gravity of a star. Given the density and surface gravity we can calculate the star’s mass. From these different modes we can determine where a star is along its evolutionary history, and thus determine its age.

There are other ways to determine the age of a star, and it is always useful to compare different methods for better accuracy, but one can get a fairly reasonable answer from stellar sounds alone.

Paper: Yveline Lebreton, et al. Stellar ages from asteroseismology. Proceedings IAU Symposium No. 258 (2008)

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Determining the age of galaxies and globular clusters can be a bit of a challenge. There are several ways you can get a handle on galactic age. One of these is by looking at the ratio of red dwarf stars to larger stars. Red dwarf stars burn very slowly, so their lifetimes can be 100 billion years or more. Given that the universe is only about 14 billion years old, this means that red dwarfs haven’t had time to die off. Larger stars die off faster, so the higher the proportion of red dwarf stars, the older the galaxy should be.

Of course this assumes that all the stars in a galaxy formed around the same time. While this is generally true for star clusters, and to a lesser degree for globular clusters, it isn’t very accurate for galaxies. In galaxies, the largest stars will go supernova, scattering gas and dust that mix with other stellar remnants to collapse into new stellar nurseries. Thus galaxies can produce new generations of stars from old ones. You can still use the red dwarf count to estimate age, but this method isn’t as accurate with galaxies as it is with globular clusters.

Another method is to look at what is known as the metallicity of the stars in a galaxy. In astrophysics, we generally refer to any element other than hydrogen and helium as “metals”. The reason for this is that the amount hydrogen and helium in the universe dwarfs all the other elements combined, so we can put them in the “other” category. The metallicity of a star is a measure of the fraction of metal (in the astrophysics sense) a star has compared to hydrogen and helium.

Metals can only be produced in the cores of stars, so if a star has a high metallicity it must have been formed from the remnants of earlier stars. Stars with low metallicity have formed mainly from the original hydrogen and helium of the universe. So high metallicity stars are younger than low metallicity ones. In this way you can distinguish the initial stars in a galaxy from subsequent generations of stars. This gives you another handle on the age of a galaxy or globular cluster.

There is a third way to determine the age of a galaxy, known as the white dwarf luminosity function. White dwarfs are the remnants of stars like our Sun. If a star is too small to become a supernova when it dies, it will swell to a red giant, casting of some of its outer material before collapsing to a white dwarf. White dwarfs have three important properties that make them very useful in determining the age of a galaxy.

The first is that white dwarfs are generally about the mass of the Sun. There’s a limit to how massive a white dwarf can be (known as the Chandrasekhar limit), of about 1.4 solar masses. If a stellar remnant has more mass than that it will collapse to a neutron star. If it has much less mass than that of the Sun, then it is likely a red dwarf that hasn’t had time to die off yet.

The second is that white dwarfs also have the same general size (about that of Earth). Their size is determined by the pressure of free electrons pushing against each other (a quantum effect known as electron degeneracy pressure). This means their size doesn’t vary with the star’s temperature.

The third is that they form at a temperature of about a million Kelvin. Since white dwarfs have no way to generate heat within themselves, this means they cool over time by radiating light. The amount of radiant heat they emit depends on its temperature and its size.

So white dwarfs have roughly the same temperature and size when they are formed, and they cool via radiation at a rate that depends on their temperature and size. This means you can determine the age of a white dwarf by measuring its temperature. Since hotter white dwarfs are brighter than cooler ones, you can determine their temperature by observing their brightness (or luminosity). The white dwarf luminosity function of a galaxy is the distribution of the luminosities of the white dwarfs in the galaxy. By looking at this function, you can determine not only the age of the oldest white dwarfs, but also the rate at which white dwarfs have formed.

White dwarfs cool rather slowly. As a result most of them are still relatively bright, so they can be observed fairly easily despite their small size. You can see an image of these white dwarfs in a globular cluster in the figure above. Even though they are not as bright as most of the other stars, their high temperature gives them a distinctive bluish hue that makes them easy to distinguish.

White dwarfs are like cosmic cooling embers. In their dying glow is the evidence of the fires of stellar formation, and their glow tells us just how long ago those fires burned.

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Determining the age of a star poses a bit of a challenge for astronomers. After all, stars exist over a timescale of billions of years, and they are light years away.  We can’t use radiometric dating like we do for rocks and other objects on Earth.  So just how do we determine the age of a star? It turns out that there are several ways, and it’s getting easier to do.

One of the ways is to compare a star’s mass with its brightness (absolute magnitude).  We can determine the mass of a star if it is part of a binary system, and if we have a good measure of its distance (say, through its parallax) then we can observe its apparent magnitude and use its distance to determine its absolute magnitude.  The way we determine its age is by recognizing that main sequence stars grow hotter and brighter over time.  Stars produce light and heat through nuclear fusion in their core.  As more hydrogen fuses into helium, the fusion rates gradually increase, producing more heat and light.  So for stars of a particular mass, brighter stars are older than dimmer stars.  By observing stars that are newly formed and stars at the end of their life we have an idea of the rate at which stars brighten over time, so we can get a measure of a star’s age.

Another way is to measure a star’s rate of rotation.  For stars around a solar mass or less, the rate of rotation of a star gradually decreases.  So the rotation rate of a star depends upon its mass and age.  By measuring the rotation of a star and comparing it to the rotation of the Sun (for which we know its age very well), we can determine its age.

There are a few downsides with these age measurements.  For one, they only work with main sequence stars, so very young and very old stars need to be studied with different measures.  For another, they depend upon measurements that have traditionally been challenging to do well.  But a new method presented in the Astrophysical Journal could provide an easier and more effective way to determine stellar ages.

The method uses what is known as helioseismology, which is the study of sonic oscillations within a star.  Helioseismology has long been used to study the interior structure of the Sun, but more recently it can also be used with stars.  Since the frequency of sound oscillations depends upon the mass and density of a star, helioseismology can be used to determine the mass and radius of a star pretty effectively.  Knowing that, one can use observations of a star’s spectrum to determine its temperature.  The mass, radius and temperature of a star can then be used to determine its age.

What makes this new method potentially powerful is that it depends upon the type of observational data gathered by sky surveys.  This initial study looked at about a thousand stars.  A larger project known as the Stroemgren survey for Asteroseismology and Galactic Archaeology (SAGA) is analyzing data gathered by the Kepler telescope.  Future observations by telescopes such as GAIA could provide a large survey of stellar ages within our galaxy.

The reason why this is important is that knowing the age of a large number of stars allows us to study the history of our galaxy.  By analyzing stellar ages, we can determine when star production was common, and when it was rare.  We might even be able to determine past collisions with our galaxy, which tend to drive star production.  This new method is still young, so it will take time to determine if it lives up to its potential.  But if it does we may soon gain deeper understanding of the history of our galaxy.

Paper: L. Casagrande, et al. Stroemgren survey for Asteroseismology and Galactic Archaeology: let the SAGA begin.  L. Casagrande, et al. arXiv:1403.2754 (2014)

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