<p>@ProfRob has already given a good answer to the question, but I wanted to add just a little more detail addressing the observational data side.  As Rob already stated, the fundamental data often come (these days) from satellites like Kepler or TESS, which can measure a star's brightness with very high precision, over an uninterrupted period of many days.  So these timeseries brightness measurements are the key observational data.</p>
<p>Because the star is pulsating slightly, its brightness changes slightly.  By analyzing the brightness timeseries (e.g. with Fourier techniques), it is possible to find the frequencies at which the star is pulsating.  It is this set of frequencies (their absolute values and their relative strength and spacing) that allows calculation of the sound speed.  An example of this &quot;power spectrum&quot; (the relative strength of different pulsational frequencies) looks like this:</p>
<p><a href="https://i.sstatic.net/NQUxh.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NQUxh.png" alt="pulsation frequency spectrum" /></a></p>
<p>(linked from <a href="https://astrobites.org/2014/12/04/asteroseismic-spin-drs/" rel="nofollow noreferrer">this Astrobites post</a>)</p>
<p>And the different pulsational modes (with parts of the star moving outward while others moving in) are often shown in diagrams like this:</p>
<p><a href="https://i.sstatic.net/RmzbG.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RmzbG.jpg" alt="image of pulsating star" /></a></p>
<p>linked from <a href="https://astrobites.org/2011/08/17/investigating-stars-like-our-sun-using-asteroseismology/" rel="nofollow noreferrer">this Astrobites post</a>.</p>
<p>Those modes come about because the variation of pressure with depth changes the speed at which sound waves (pressure waves) can propagate, which bends their paths via refraction.  So you get paths like this:</p>
<p><a href="https://i.sstatic.net/jZzmA.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/jZzmA.png" alt="waves propagating inside a star" /></a></p>
<p>(Tosaka, CC BY-SA 3.0 <a href="http://creativecommons.org/licenses/by-sa/3.0/" rel="nofollow noreferrer">http://creativecommons.org/licenses/by-sa/3.0/</a>, via Wikimedia Commons)</p>
<p>Only paths that close back on themselves are reinforced, leading to a discrete set of oscillation frequencies.  Since the bending angle of a given wave depends on the pressure structure with depth, this is what links the surface behavior (pulsation modes) to the interior structure of the star.</p>

CC BY-SA 4.0
2021-05-09T12:56:44.133Z
The question asked about determining the age, and also specifically about going from observations to an age.  ProfRob answered by saying that you need “the characteristic oscillation frequencies”.  B--rian asked in a followup comment about how those are measured. My goal, as stated in the first sentence of my answer, was not to give a complete answer, but to explain the observational side, i.e. how does one actually determine those frequencies from observable quantities.  I also added a bit to explain how those frequencies are related to stellar pulsation, and thus the sound speed.
Eric Jensen
CC BY-SA 4.0
2021-05-09T16:57:33.810Z
Ah, Okay I see now, yes this is very helpful. *Sorry about that!*
uhoh
CC BY-SA 4.0
2021-04-14T13:51:23.373Z
2021-04-14T13:51:23.373Z
Eric Jensen
<p>Asteroseismology effectively measures the sound speed inside a star by finding the characteristic oscillation frequencies of a star.</p>
<p>The sound speed depends on the composition because the pressure at a given temperature depends on the average mass of a particle in a gas.</p>
<p>As the star gets older, it turns its hydrogen into helium, changing the composition, the average mass per particle in the gas, and hence the average sound speed.</p>
<p>Asteroseismology tells you the age of the star.</p>
<p>The answer is somewhat model-dependent, so ideally you would have an effective temperature and surface gravity in order to constrain matters. Precisions of 10% of the main sequence lifetime are possible for stars of around a solar mass. Accuracy is hard to assess since we have an accurate age for only one star - the Sun.</p>

CC BY-SA 4.0
2021-04-14T09:30:04.233Z
Thanks for your answer. How exactly is the sound speed measured, I.e. which with kind of satellites or telescopes?
B--rian
CC BY-SA 4.0
2021-04-14T09:31:10.903Z
Also: Do I understand it correctly that the results depend on the star models used in numerical simulations?
B--rian
CC BY-SA 4.0
2021-04-14T10:17:23.837Z
@B-rian the asteroseismological frequency spectrum is used to estimate a sound speed profile inside the star. The data are most often taken by satellites like Kepler and TESS. There is some model dependence yes. If you like you can think of the raw measurements as giving you something that scales with what you are interested in and you can set some sort of zeropoint using the Sun, but other stars are not exactly like the Sun so some model-dependence remains.
ProfRob
CC BY-SA 4.0
2021-04-14T10:19:25.527Z
Perfect, thanks! Maybe you could edit that in to your answer, or should I?
B--rian
CC BY-SA 4.0
2021-04-14T11:18:55.410Z
@B--rian you asked for an answer "in simple terms for a primary school kid."  I'm not sure that is actually possible, but the details of the process are obviously much more complex than I have given in my answer.
ProfRob
CC BY-SA 4.0
2021-04-14T12:06:32.427Z
The kid asking already knows about Hubble Space Telescope etc, so your answer plus the comment is exactly what I was after.
B--rian
CC BY-SA 4.0
2021-04-13T22:33:45.790Z
2021-04-14T08:07:22.473Z
2021-04-14T08:07:22.473Z
ProfRob
<p>I keep reading that a standard way to determine the age of a star is asteroseismology, and I tried to learn more about it. I am wondering if somebody could help me to describe the method in simple terms for a primary school kid. That should be easier for experts of that field.</p>
<p>I found a review article <a href="https://www.frontiersin.org/articles/10.3389/fspas.2020.578584/full" rel="nofollow noreferrer">Asteroseismology of High-Mass Stars: New Insights of Stellar Interiors With Space Telescopes</a> a good starting point for myself, but that is not yet at the layperson level I am aiming for:</p>
<blockquote>
<p>The study of stellar structure and evolution using stellar oscillations—asteroseismology—has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2, and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modeling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars.</p>
</blockquote>
<p>My question in other words: What observation variables does one need from a star in order to calculate the age using asteroseismology? Following what recipe will bring me from the observations to a number for the age? What accuracies are possible?</p>
<h3>Related</h3>
<ul>
<li>Wikipedia on <a href="https://en.wikipedia.org/wiki/Stellar_age_estimation" rel="nofollow noreferrer">Stellar Age Estimation</a></li>
<li><a href="https://astronomy.stackexchange.com/q/33556/37191">Can someone calculate the age of the KOI-4878 star?</a></li>
</ul>

<star><astrophysics><age><definition><asteroseismology>
How to determine the age of a star using asteroseismology?
B--rian
# How to determine the age of a star using asteroseismology?

(Asked by: username_0 on 2021-04-13)

I keep reading that a standard way to determine the age of a star is asteroseismology, and I tried to learn more about it. I am wondering if somebody could help me to describe the method in simple terms for a primary school kid. That should be easier for experts of that field.

I found a review article [Asteroseismology of High-Mass Stars: New Insights of Stellar Interiors With Space Telescopes](https://www.frontiersin.org/articles/10.3389/fspas.2020.578584/full) a good starting point for myself, but that is not yet at the layperson level I am aiming for:

> The study of stellar structure and evolution using stellar oscillations—asteroseismology—has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2, and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modeling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars.

My question in other words: What observation variables does one need from a star in order to calculate the age using asteroseismology? Following what recipe will bring me from the observations to a number for the age? What accuracies are possible?

### Related

* Wikipedia on [Stellar Age Estimation](https://en.wikipedia.org/wiki/Stellar_age_estimation)
* [Can someone calculate the age of the KOI-4878 star?](https://astronomy.stackexchange.com/q/33556/37191)

**Tags:** star, astrophysics, age, definition, asteroseismology

---

## 2 answers

### Answer by username_3 on 2021-04-13. Score: 6 | Accepted answer

Asteroseismology effectively measures the sound speed inside a star by finding the characteristic oscillation frequencies of a star.

The sound speed depends on the composition because the pressure at a given temperature depends on the average mass of a particle in a gas.

As the star gets older, it turns its hydrogen into helium, changing the composition, the average mass per particle in the gas, and hence the average sound speed.

Asteroseismology tells you the age of the star.

The answer is somewhat model-dependent, so ideally you would have an effective temperature and surface gravity in order to constrain matters. Precisions of 10% of the main sequence lifetime are possible for stars of around a solar mass. Accuracy is hard to assess since we have an accurate age for only one star - the Sun.

> **Comments:**
> **username_0**: Thanks for your answer. How exactly is the sound speed measured, I.e. which with kind of satellites or telescopes?  
> **username_0**: Also: Do I understand it correctly that the results depend on the star models used in numerical simulations?  
> **username_3**: @B-rian the asteroseismological frequency spectrum is used to estimate a sound speed profile inside the star. The data are most often taken by satellites like Kepler and TESS. There is some model dependence yes. If you like you can think of the raw measurements as giving you something that scales with what you are interested in and you can set some sort of zeropoint using the Sun, but other stars are not exactly like the Sun so some model-dependence remains.  
> **username_0**: Perfect, thanks! Maybe you could edit that in to your answer, or should I?  
> **username_3**: @B--rian you asked for an answer "in simple terms for a primary school kid."  I'm not sure that is actually possible, but the details of the process are obviously much more complex than I have given in my answer.  
> **username_0**: The kid asking already knows about Hubble Space Telescope etc, so your answer plus the comment is exactly what I was after.  

---

### Answer by username_1 on 2021-04-14. Score: 3

@ProfRob has already given a good answer to the question, but I wanted to add just a little more detail addressing the observational data side. As Rob already stated, the fundamental data often come (these days) from satellites like Kepler or TESS, which can measure a star's brightness with very high precision, over an uninterrupted period of many days. So these timeseries brightness measurements are the key observational data.

Because the star is pulsating slightly, its brightness changes slightly. By analyzing the brightness timeseries (e.g. with Fourier techniques), it is possible to find the frequencies at which the star is pulsating. It is this set of frequencies (their absolute values and their relative strength and spacing) that allows calculation of the sound speed. An example of this "power spectrum" (the relative strength of different pulsational frequencies) looks like this:

[![pulsation frequency spectrum](https://i.sstatic.net/NQUxh.png)](https://i.sstatic.net/NQUxh.png)

(linked from [this Astrobites post](https://astrobites.org/2014/12/04/asteroseismic-spin-drs/))

And the different pulsational modes (with parts of the star moving outward while others moving in) are often shown in diagrams like this:

[![image of pulsating star](https://i.sstatic.net/RmzbG.jpg)](https://i.sstatic.net/RmzbG.jpg)

linked from [this Astrobites post](https://astrobites.org/2011/08/17/investigating-stars-like-our-sun-using-asteroseismology/).

Those modes come about because the variation of pressure with depth changes the speed at which sound waves (pressure waves) can propagate, which bends their paths via refraction. So you get paths like this:

[![waves propagating inside a star](https://i.sstatic.net/jZzmA.png)](https://i.sstatic.net/jZzmA.png)

(Tosaka, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons)

Only paths that close back on themselves are reinforced, leading to a discrete set of oscillation frequencies. Since the bending angle of a given wave depends on the pressure structure with depth, this is what links the surface behavior (pulsation modes) to the interior structure of the star.

> **Comments:**
> **username_1**: The question asked about determining the age, and also specifically about going from observations to an age.  ProfRob answered by saying that you need “the characteristic oscillation frequencies”.  B--rian asked in a followup comment about how those are measured. My goal, as stated in the first sentence of my answer, was not to give a complete answer, but to explain the observational side, i.e. how does one actually determine those frequencies from observable quantities.  I also added a bit to explain how those frequencies are related to stellar pulsation, and thus the sound speed.  
> **username_2**: Ah, Okay I see now, yes this is very helpful. *Sorry about that!*  

---

