How do I find the age of a star?

[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.