How do I find the age of a star?

[ageorge95]

I know its been a while but does anyone know of a model which shows how a star like sirius changes over time ie. luminosity ?

 

[lpetrich]

Stars do increase in brightness during their Main-Sequence phase, but one needs to have good mass and chemical-composition numbers and good modeling to get an age out of that. A valuable input for such modeling is asteroseismology, detection of starquakes. As a star's interior's chemical composition changes, the star's resonant frequencies also change.

That's been done for the Sun: The age of the Sun and the relativistic corrections in the EOS | A&A The authors come with an age of 4.57 +- 0.11 Gyr, in close agreement with the ages of meteorites.

It's also been done for other stars: [1108.6153] Ages of Exoplanet Host-Stars from Asteroseismology : HD 17156, a Case Study, [1003.5796] Age determination of the HR8799 planetary system using asteroseismology, etc.

I couldn't find if anyone had done that for Sirius, however, though I haven't done much searching.

 

[ageorge95]

Can I use the luminosity and spectra of a star to determine its age?

So Sirius A has a luminosity of 25.4.

From this I can work out the amount of energy it produces every second.

Luminosity of Sirius -> 25.4 x 3.826 x 10^26
= 9.718 x 10^26 W
= 9.718 x 10^26 Joules/sec

The reaction in stars combine 4 hydrogen ions to form helium. The excess mass is converted to energy. Using E=mc^2 the amount of energy produced in a reaction can be determined to be:

Energy in one reaction -> 4.3 x 10^(-12) Joules

From this the number of reactions every second can be determined.

No. of Reactions in one second -> 2.26 x 10^38

In one reaction 6.69 x 10^(-27) kg of hydrogen is consumed. Therefore:

Amount of hydrogen consumed in one second -> 2.26 x 10^38 x 6.69 x 10^(-27)
= 1.512 x 10^12 kg

The mass of Sirius is 4.0176 x 10^30 kg. Therefore:

Lifespan of Sirius -> (4.0176 x 10^30)/(1.512 x 10^12)
= 2.657 x 10^18 s
= 8.42 x 10^10 years

Using a spectral analysis can I determine the amount of hydrogen left in the star and thereby determine its age?

Is there anything wrong with this process? If there is, how do I work around it?

 

[vociferous]

That is a pretty impressive order of magnitude calculation and comes pretty close to the "true" lifespan. Sirius will fuse hydrogen for about 10^9 years.

Large stars do not have very good convection (the ability to transport materials from outside the core) so they actually start fusing Helium long before they come close to exhausting their supply of hydrogen, so the lifespan of the star is less than you calculate.

Because of poor convection, these massive stars cannot transport things such as helium (which forms a shell around the core) to the surface of the sun where the change might be observed by spectroscopy. The plasmas we observe are more or less in the same ratio as when the star first formed.

However, as I mentioned before, we can estimate a star's age from the ratio of hydrogen and helium to metals (everything heavier). The more metals, the younger the gas the star formed from, because stars release metals into the galaxy when they form white dwarfs or explode in a supernova, so they have slowly been building up in the Milky Way.

 

[ageorge95]

That is a pretty impressive order of magnitude calculation and comes pretty close to the "true" lifespan. Sirius will fuse hydrogen for about 10^9 years.

Large stars do not have very good convection (the ability to transport materials from outside the core) so they actually start fusing Helium long before they come close to exhausting their supply of hydrogen, so the lifespan of the star is less than you calculate.

Because of poor convection, these massive stars cannot transport things such as helium (which forms a shell around the core) to the surface of the sun where the change might be observed by spectroscopy. The plasmas we observe are more or less in the same ratio as when the star first formed.

However, as I mentioned before, we can estimate a star's age from the ratio of hydrogen and helium to metals (everything heavier). The more metals, the younger the gas the star formed from, because stars release metals into the galaxy when they form white dwarfs or explode in a supernova, so they have slowly been building up in the Milky Way.

Thanks Vociferous for the quick reply.

I had seen a website about convection but hadn't really understood it. Thanks for clarifying on this. How would I take this into account when calculating the lifespan?

You also mentioned that the ratio of hydrogen and helium to the metals can be used to determine the age. How exactly would I do this?

 

[vociferous]

That is another excellent question. For a simple order of magnitude calculation like you are doing, you can probably ignore convection, especially in massive stars. For very low mass stars, your calculation would probably predict the main sequence lifespan of the star pretty accurately. Try it for the lowest mass stars. You might be surprised how long they will live.

Your calculation was actually pretty good, it just made the faulty assumption that a star will undergo normal proton-proton fusion until it has used up 100% of its hydrogen. This is a good assumption in very low-mass stars, which are fully convective. It is a faulty assumption in stars that are as massive as Sirius or our sun.

What actually happens is that helium builds up inside the core of the star and at a certain point the pressure and heat are great enough to start the fusion of helium into heavier elements. Seeing as fusion happens in the core, the core contains less than 50% of the mass of the star, and the star will not fuse all of its hydrogen during its main sequence life, you can see why you over-estimated the main sequence age of the star.

By the way, when we talk about the lifespan of a star, we refer to its main sequence life. Once it starts burning helium, it is no longer on the main sequence. Even when stars "die", they leave a corpse, either a white dwarf, black hole, or neutron star.

 

[Chronos]

Calculating stellar ages is an inexact science and is heavily dependent on our stellar evolution models. A star like Sirius, for example, can be aged to a fairly narrow range due to its spectral class [A] and it has a companion. Spectral classes O, B and A are characteristic of fairly massive stars [~2 solar in the case of Sirius] that are relatively young. Spectroscopy is not terribly helpful in narrowing its age because sun sized and larger stars have very little convection, meaning its surface chemistry is not representative of its core composition, as vociferous noted. The fact it has a companion, Sirius B, is helpful. Sirius B is a relatively young white dwarf with an estimated progenitor mass of about 5 solar. Stellar evolution models suggest the system is between 200 and 300 million years old. Generally speaking, higher mass stars tend to be easier to date because they have relatively short lifespans and stars with companions are also easier to date. Sun size and smaller mass stars are much more difficult to date with any particular accuracy.

 

[twofish-quant]

Using a spectral analysis can I determine the amount of hydrogen left in the star and thereby determine its age?

No, for most stars you can't.

The problem is that fusion happens at the center of the star, and so the extra helium that is formed is not directly visible on the surface. When you are looking at the spectra, that gives you an estimate of the age of the universe when the star was formed, but until something dramatic happens, the surface composition doesn't change much.

What ends up happening is that as you have more helium in the core, this changes the brightness, although the effect is subtle.

I do think that as we understand more about the evolution of star systems that we'll probably soon be able to figure out how old a star is by the characteristics of the planets around it. The other thing is that we see how a star vibrates and that's allowed us to fix the age of Alpha centauri.

 

[twofish-quant]

However it turns out that lithium does seem to change with age for stars like the sun.

http://adsabs.harvard.edu/abs/1984A&A...140..427S

And there is also a subtle effect that changes the strength of Calcium lines.

 

[twofish-quant]

Also if you want some projects which are doable with a ground telescope, start with

http://www.aavso.org/

 

[ageorge95]

Calculating stellar ages is an inexact science and is heavily dependent on our stellar evolution models. A star like Sirius, for example, can be aged to a fairly narrow range due to its spectral class [A] and it has a companion. Spectral classes O, B and A are characteristic of fairly massive stars [~2 solar in the case of Sirius] that are relatively young. Spectroscopy is not terribly helpful in narrowing its age because sun sized and larger stars have very little convection, meaning its surface chemistry is not representative of its core composition, as vociferous noted. The fact it has a companion, Sirius B, is helpful. Sirius B is a relatively young white dwarf with an estimated progenitor mass of about 5 solar. Stellar evolution models suggest the system is between 200 and 300 million years old. Generally speaking, higher mass stars tend to be easier to date because they have relatively short lifespans and stars with companions are also easier to date. Sun size and smaller mass stars are much more difficult to date with any particular accuracy.

Chronos, could you please link me to some stellar evolution models? I'm having trouble finding them.

 

[phyzguy]

Here is a nice site with stellar evolution models. Try reviewing the movie 'Evolution of a 1 MSun Star'. You can see the He build-up in the core and the onset of He burning, as twofish discussed.

 

[ageorge95]

Could someone please explain how to actually use a stellar evolution model?
Also to the phyzguy, thanks for the link but the link to 1MSun Star did not work. Are there any other links?

 

[ageorge95]

I was searching about the age metallicity relation that was mentioned when I came across this science journal. A group of scientists investigated this relationship.

http://www.aanda.org/index.php?opti...es/aa/full/2001/39/aah2739/aah2739.right.html

Please have a look at figure 13. It contains 5 graphs showing the relationship between age and [Me,H]. The five graphs depict different temperature range. Sirius falls in the highest temperature range which is the graph with the best correlation.

Can this be used to determine the age of Sirius? Also does anyone know the value of [Me,H] in Sirius?

 

[phyzguy]

Also to the phyzguy, thanks for the link but the link to 1MSun Star did not work. Are there any other links?

It's an MPEG4 file. You need to download the file and then play it on your machine, so you need an MPEG4 player. If you don't have one, you should be able to download one.

 

[ageorge95]

It's an MPEG4 file. You need to download the file and then play it on your machine, so you need an MPEG4 player. If you don't have one, you should be able to download one.

Thanks Phyzguy. I use a school laptop so that's probably why it didn't work.

 

[ageorge95]

Okay so I have decided to conduct a spectroscopy of a star. Does anyone know of a clear step by step procedure to do this?

 

[lpetrich]

I've found some pages on amateur-astronomer spectroscopy:
Amateur Spectroscopy
CAOS: Club of Aficionados in Optical Spectroscopy
http://www.bathastronomers.co.uk/?p=72 - has lots of nice pictures of what you can get

 

[seinfelddvds]

If we can date an old star we will know that the minimum possible age of the entire universe must be equal or more than that. Sun is a relatively young star, near the half-life of uranium at 4.5 gy.

 

[Drakkith]

If we can date an old star we will know that the minimum possible age of the entire universe must be equal or more than that. Sun is a relatively young star, near the half-life of uranium at 4.5 gy.

Yep. We just found 2 white dwarfs less than 100 light years from Earth that are about 12 billion years old! They were 2-3 solar masses during their main sequence lives and have been cooling for around 11 billion years now. They are believed to be some of the oldest white dwarfs in the galaxy.