How do I find the age of a star?

[ageorge95]

I'm a yr 12 student doing a full year research assignment and i have decided to find the age of the star, Sirius. I have access to a pretty good telescope and equipment but I am not sure where to start. Suggestions anyone?

 

[Drakkith]

This is generally not possible with individual stars. See here for more.
http://www.scientificamerican.com/article.cfm?id=how-do-scientists-determi

 

[Cosmo Novice]

I'm a yr 12 student doing a full year research assignment and i have decided to find the age of the star, Sirius. I have access to a pretty good telescope and equipment but I am not sure where to start. Suggestions anyone?

As Drakkith has advised this is generally not possible with individual stars, what you could do however is start your assignment on the pretence of finding the age of the star. Then outline the reasons this is not going to be particularly accurate as your main body of work - would still be a good assignment.

Cosmo

 

[e^(i Pi)+1=0]

Couldn't you get a good approximation by its spectra? The more heavy elements, the older the star.

 

[ageorge95]

Couldn't you get a good approximation by its spectra? The more heavy elements, the older the star.

I was hoping to do just that and use the Hertzsprung-Russell diagram which requires the luminosity and colour of a star to determine the age of the star. How would I do get this information using a telescope?

 

[ageorge95]

Thanks for the advice Cosmo Novice and Drakkith the link was very useful thank you

 

[phyzguy]

Couldn't you get a good approximation by its spectra? The more heavy elements, the older the star.

This isn't correct. Stars create more heavy elements through fusion as they age, but these heavy elements remain in the core of the star and don't migrate to the surface. The spectrum only sees the surface of the star, and hence just tells you what the initial composition of the star was when it was born. So stars with more heavy elements were formed more recently, and the amount of heavy elements you see in the spectrum doesn't change as the star ages.

 

[Chronos]

Using stellar evolutionary models, we have a fairly good guess as to the age of Sirius. The presence of its white dwarf companion star was an obvious plus given an accurate mass estimate is vitally important in such modelling. See http://www.astronomy.com/en/sitecor...s/2005/07/The life and times of Sirius B.aspx
The original paper can be found at: http://arxiv.org/pdf/astro-ph/0507523v2.pdf
Note that the authors had access to some pretty sophisticated data, and the proximity of Sirius to Earth certainly didn't hurt.

 

[Drakkith]

I was hoping to do just that and use the Hertzsprung-Russell diagram which requires the luminosity and colour of a star to determine the age of the star. How would I do get this information using a telescope?

The Hertzspurng-Russel diagram does not let you determine the age of the star. It merely shows "the relationship between the stars' absolute magnitudes or luminosities versus their spectral types or classifications and effective temperatures." -Quoted from wikipedia.

This means that if you have a star that is 10 times the Suns luminosity and and was white in color it would be a Main Sequence star. If the star had 100 times the luminosity of the Sun and was very Red in color, it's surface temperature is very cool, meaning it's grown to a large size and is on Branch III, the "Giant" branch.
http://upload.wikimedia.org/wikipedia/commons/6/6b/HRDiagram.png

 

[Radrook]

This method [a new one presently limited to certain types of stars] is based on how fast the star is spinning.

Gyrochronology
http://www.google.com/search?source...ox&ie=UTF-8&oe=UTF-8&rlz=1I7ACAW_enUS378US378

A new method is helping scientists assess the ages of isolated stars, including all stars known to have planets...A star's rotation slows with time, research shows, giving scientists a clock to understand its age.


The research is published in May 20 issue of The Astrophysical Journal Letters.

http://news.discovery.com/space/star-age-exoplanet-110523.html

 

[Drakkith]

Nice! Never heard of that before, thanks Radrook.

 

[ageorge95]

This method [a new one presently limited to certain types of stars] is based on how fast the star is spinning.

Gyrochronology
http://www.google.com/search?source...ox&ie=UTF-8&oe=UTF-8&rlz=1I7ACAW_enUS378US378

Thanks for the suggestion Radrook. Do you think that I can measure stellar rotation with a 10" LX200 SCHMIDT CASSEGRAIN TELESCOPE. It looks like this:
http://www.google.com.au/imgres?q=10%22+LX200+SCHMIDT+CASSEGRAIN+TELESCOPE&um=1&hl=en&sa=N&biw=1366&bih=705&tbm=isch&tbnid=3W30xEqYlfT3xM:&imgrefurl=http://www.skiesunlimited.net/index.php%3FProductID%3D845&docid=gJdFDfre6zLVdM&imgurl=http://www.skiesunlimited.net/images/products/845_main.jpg&w=300&h=474&ei=4_o9T4OoGKTLmAWkzvXOBw&zoom=1&iact=hc&vpx=341&vpy=312&dur=117&hovh=282&hovw=179&tx=116&ty=259&sig=112911186707980595689&page=1&tbnh=152&tbnw=96&start=0&ndsp=20&ved=0CIEBEK0DMA8

 

[Radrook]

Thanks for the suggestion Radrook. Do you think that I can measure stellar rotation with a 10" LX200 SCHMIDT CASSEGRAIN TELESCOPE. It looks like this:
http://www.google.com.au/imgres?q=10%22+LX200+SCHMIDT+CASSEGRAIN+TELESCOPE&um=1&hl=en&sa=N&biw=1366&bih=705&tbm=isch&tbnid=3W30xEqYlfT3xM:&imgrefurl=http://www.skiesunlimited.net/index.php%3FProductID%3D845&docid=gJdFDfre6zLVdM&imgurl=http://www.skiesunlimited.net/images/products/845_main.jpg&w=300&h=474&ei=4_o9T4OoGKTLmAWkzvXOBw&zoom=1&iact=hc&vpx=341&vpy=312&dur=117&hovh=282&hovw=179&tx=116&ty=259&sig=112911186707980595689&page=1&tbnh=152&tbnw=96&start=0&ndsp=20&ved=0CIEBEK0DMA8

This is what they use to make these observations possible:

In a four year preparatory study conducted with specially designed instrument (Hectochelle) mounted on the MMT telescope on Mt. Hopkins in southern Arizona, Meibom and his colleagues sorted out information in nearly 7000 individual stars and used Kepler data to determine how fast those stars were spinning.

http://www.universetoday.com/85901/a-new-spin-on-stellar-age/

So we have:

1. Hectospec & Hectochelle
2. Telescope on Mt. Hopkins
3. Keppler Mission Data

Hectospec & Hectochelle
A Brief Description:
http://mmto.org/node/55

MMT Obervatory
http://en.wikipedia.org/wiki/MMT_Observatory

Keppler Data Archive
The data from the Kepler Mission are processed and archived in the Multimission Archive at Space Telescope Science Institute (STScI). The public Kepler Planet Candidates are there as well.
http://kepler.nasa.gov/Science/ForScientists/dataarchive/

Links for the SCHMIDT CASSEGRAIN TELESCOPE that delineate its capabilities.

"
SCHMIDT CASSEGRAIN TELESCOPE
http://www.opticsplanet.net/meade-10-lx200gps-telescopes.html

Instruction Manual
8", 10", 12", 14", 16" LX200GPS Schmidt-Cassegrain Telescopes
7" LX200GPS Maksutov-Cassegrain Telescope
with Autostar II Hand Controller

http://www.cgtp.duke.edu/~plesser/observatory/LX200GPS_manual.pdf

BTW
Observation from the ground without using Keppler will significantly limit the range of stars that can be assessed

...the rotation periods of stars older than about half a billion years can't be measured from the ground where Earth's atmosphere interferes. Fortunately, this is not a problem for the Kepler spacecraft .
http://www.sciencenewsline.com/space/2011052512580000.html

 

[Radrook]

Nice! Never heard of that before, thanks Radrook.

Welcomed.

 

[ageorge95]

Since I cannot find the age of a star individually how would I find the age of a star cluster?

 

[cepheid]

Since I cannot find the age of a star individually how would I find the age of a star cluster?

This is something you would use a Hertzsprung-Russell Diagram for. The idea is that for stars on the main sequence, the ones that are bluer, hotter, and more luminous don't "live" for as long as the stars that are redder, cooler, and dimmer. The reason for this is that the hotter and more luminous stars have a larger mass. More mass means a higher central core temperature. A higher core temperature means a higher rate of nuclear fusion. Now, the "lifetime" of a star is defined as the amount of time it spends on the main sequence. The main sequence is defined as the portion of the stellar life cycle during which stars produce energy by nuclear fusion of hydrogen into helium in their cores. If the hotter and more luminous stars have a higher fusion rate, then they will run out of their nuclear fuel (hydrogen) in their cores sooner than the dimmer stars. Therefore, the hotter and brighter stars will spend less time on the main sequence. Once they run out of core hydrogen and fusion ceases, the stellar radii and surface temperatures change. This causes those stars to move off the main sequence on the H-R diagram. They move up and to the right onto the red giant branch (corresponding to becoming brighter and having cooler surface temperatures).

The net effect of this is that if you assume that all the stars in the cluster were roughly born at the same time, then there will be certain point on the main sequence to the left of which stars simply don't exist (i.e. that portion of the main sequence is missing). The reason is because the lifetimes of stars bluer than this are shorter than the age of the cluster. So stars of those spectral types have already "veered" off the main sequence and onto the giant branch. We call this point on the H-R diagram at which the main sequence cuts off the "main sequence turn-off point." The older a cluster is, the farther to the right the main sequence turn-off point will be (because in an older cluster even the cooler, dimmer, and more longer-lived stars have "died" i.e. evolved off the main sequence).

So, you can age a cluster simply by looking at where the main sequence turn-off point occurs. The age of the cluster is equal to the main sequence lifetime of the stars at the turn-off point.

 

[ageorge95]

This is something you would use a Hertzsprung-Russell Diagram for. The idea is that for stars on the main sequence, the ones that are bluer, hotter, and more luminous don't "live" for as long as the stars that are redder, cooler, and dimmer. The reason for this is that the hotter and more luminous stars have a larger mass. More mass means a higher central core temperature. A higher core temperature means a higher rate of nuclear fusion. Now, the "lifetime" of a star is defined as the amount of time it spends on the main sequence. The main sequence is defined as the portion of the stellar life cycle during which stars produce energy by nuclear fusion of hydrogen into helium in their cores. If the hotter and more luminous stars have a higher fusion rate, then they will run out of their nuclear fuel (hydrogen) in their cores sooner than the dimmer stars. Therefore, the hotter and brighter stars will spend less time on the main sequence. Once they run out of core hydrogen and fusion ceases, the stellar radii and surface temperatures change. This causes those stars to move off the main sequence on the H-R diagram. They move up and to the right onto the red giant branch (corresponding to becoming brighter and having cooler surface temperatures).

The net effect of this is that if you assume that all the stars in the cluster were roughly born at the same time, then there will be certain point on the main sequence to the left of which stars simply don't exist (i.e. that portion of the main sequence is missing). The reason is because the lifetimes of stars bluer than this are shorter than the age of the cluster. So stars of those spectral types have already "veered" off the main sequence and onto the giant branch. We call this point on the H-R diagram at which the main sequence cuts off the "main sequence turn-off point." The older a cluster is, the farther to the right the main sequence turn-off point will be (because in an older cluster even the cooler, dimmer, and more longer-lived stars have "died" i.e. evolved off the main sequence).

So, you can age a cluster simply by looking at where the main sequence turn-off point occurs. The age of the cluster is equal to the main sequence lifetime of the stars at the turn-off point.

Thanks Cepheid. So you're saying all I need to do is find the luminosity and colour and apply this to the HR diagram. I only have two questions.
1. How do I measure luminosity and colour using a telescope?
2. How do I convert the point on the HR diagram to the age of the cluster?
Sorry for asking basic questions but there is little information on the internet on how to do this.

 

[Chronos]

Direct measurement of color and luminosity requires expertise and equipment generally more sophisticated than accessible to most amateurs. I would suggest using published values from databases such as Vizier. Padova might be a good source for modelling cluster age, although I'm sure there are others.

 

[Drakkith]

Thanks Cepheid. So you're saying all I need to do is find the luminosity and colour and apply this to the HR diagram. I only have two questions.
1. How do I measure luminosity and colour using a telescope?
2. How do I convert the point on the HR diagram to the age of the cluster?
Sorry for asking basic questions but there is little information on the internet on how to do this.

What you are asking about is pretty much astrophotography. Head over to cloudynights.com and hit up the forums there, as that site is dedicated to the hobby. If you can't find the information on their forum, just post a thread asking about it and I'm sure someone can give you some links. The basics of astrophotography are required for your project, so even if it seems like some of it doesn't apply to you, it probably does. But be warned, this is probably not something you can learn to do in just a few weeks or even months. Getting used to using a telescope and the associated equipment, along with the night sky, is probably going to take upwards of a year or so. (Based on my personal experience in the hobby) If you have someone who can be there to show you everything would make things go much faster, but if you don't, then it's going to take a while probably.

As Chronos suggested, getting the values directly from a listing would probably be the quickest and easiest way.

 

[ageorge95]

What you are asking about is pretty much astrophotography. Head over to cloudynights.com and hit up the forums there, as that site is dedicated to the hobby. If you can't find the information on their forum, just post a thread asking about it and I'm sure someone can give you some links. The basics of astrophotography are required for your project, so even if it seems like some of it doesn't apply to you, it probably does. But be warned, this is probably not something you can learn to do in just a few weeks or even months. Getting used to using a telescope and the associated equipment, along with the night sky, is probably going to take upwards of a year or so. (Based on my personal experience in the hobby) If you have someone who can be there to show you everything would make things go much faster, but if you don't, then it's going to take a while probably.

As Chronos suggested, getting the values directly from a listing would probably be the quickest and easiest way.

Thanks Drakkith. I attended a session for astrophotography last year and there is an expert at the school. So I don't think I will have a problem taking photos. I'm just not sure how to extract this information from the photo. Also can anyone answer my second question from my last post. How do you convert the turn off point on the HR diagram to the age of the cluster?

 

[cepheid]

I'm with Chronos on this one. I think that obtaining the actual data for this project might be somewhat beyond the means of an amateur, and I don't really don't see how it is merely "astrophotography."

Also can anyone answer my second question from my last post. How do you convert the turn off point on the HR diagram to the age of the cluster?

If you have to ask this question, then you didn't understand my explanation of the main-sequence turn-off point. Give it another read and let me know what parts of it aren't making sense. In the mean time, I would re-iterate this point in particular:

So, you can age a cluster simply by looking at where the main sequence turn-off point occurs. The age of the cluster is equal to the main sequence lifetime of the stars at the turn-off point.

 

[ageorge95]

If I have understood this correctly. (The length from start to turnoff/ the length from start to finish) * lifespan of star class = age of cluster.
Assuming this is right, why can't i do the same with an individual star?


Also this is a website that showed how to determine colour;
http://www.astronomynotes.com/starprop/s5.htm
This requires measuring the flux which this website says can be easily done with a CCD camera;
http://curious.astro.cornell.edu/question.php?number=37

 

[SHISHKABOB]

If I have understood this correctly. (The length from start to turnoff/ the length from start to finish) * lifespan of star class = age of cluster.
Assuming this is right, why can't i do the same with an individual star?Also this is a website that showed how to determine colour;
http://www.astronomynotes.com/starprop/s5.htm
This requires measuring the flux which this website says can be easily done with a CCD camera;
http://curious.astro.cornell.edu/question.php?number=37

see, the way you figure out how old a cluster is by just saying, for example:

There are no stars to the left of F in temperature in the given cluster. How long do stars *right at the point where there are no more stars* remain on the main sequence? That is how old the cluster is.

Like, let's say you look at a cluster and you see the image I attached to this post just pretend you're only looking at the main sequence stars. You can see that there are no stars past a certain point on the main sequence. What we can then say is that the age of the cluster is similar to the time that it takes for a star at that point to leave the main sequence.

So like in this one it turns out I ended up with stars like our sun as the turn-off point. We now say that the age of the cluster is about as old as the time it takes a sun-like star to leave the main sequence.

age of cluster = length of time that the stars at the turn-off point take to turn off.

if you just look at any given star, all you see is the luminosity and the spectra and you can also tell how fast it *looks like* it's heading towards you.

To figure out the age of a star you'd need to know how much fuel it started with and how much fuel it has right now and also the rate at which its using up that fuel. If you could know those things then you could figure out the age of the star. However, all the fuel of a star is in the center of a star, and the fuel that it used to have is in the past and impossible to measure. I think you can figure out the rate at which it uses up its fuel based on its temperature, but that's it.
I THINK I got that right.

 

[ageorge95]

Thank you SHISHKABOB. I think i understand what you're trying to say but I don't think I will be able to do it within 6 months. On th other hand look at this HR diagram with Sirius plotted on it. If I take the length of the main sequence to be 1 billion years the life span of Sirius the length from the start of the main sequence to the point where Sirius is the age of Sirius is 340 million years. This is reasonably close to what has been listed in this website;
http://www.exoplaneten.de/sirius/english.html

I'm sure there must be something wrong with what I have done.
http://outreach.atnf.csiro.au/education/senior/astrophysics/images/stellarevolution/hrgenericsml.jpg

 

[vociferous]

The mass of the star puts an upper limit on its main sequence life.

The metalicity puts an approximate age on the material it formed from (although this method leaves much to be desired in terms of accuracy).

However, accurately measuring the spectra and inferring the metalicity of one specific star is no trivial task for an amateur astronomer. It might be more doable if you were say, comparing an entire cluster to stars in the disk.

 

[SHISHKABOB]

I think you've got a slight misunderstanding of what the Main Sequence is. Stars don't start out at the bottom right and move up along it as they age.

What happens is once a star begins burning hydrogen, it appears on the main sequence. The mass of the star is what determines where it appears on the sequence.

Low mass stars appear in the bottom right. This is because they are not very hot and they do not have very much luminosity.

Medium in the middle, and then high mass in the top left.

All three of these things, mass, luminosity and temperature, are directly related to one another. The amount of mass a star has is determined by how much mass was in the gas cloud that it was originally formed in.

The life of a star can be split up into a few ways if we say it starts its life on the main sequence. First it's on the main sequence, after a while it runs out of hydrogen to burn and starts burning other stuff. Once it does this it turns into a giant star, which are the stars over on the top right. After a while it sort of putters out and loses a lot of mass and turns into a white dwarf. This is a massive simplification of how it works, but you can follow the evolution on the H-R diagram.

You start on the MS, move up to the top right, and then you swing over to the left and down into the white dwarf stage.


This is why we can use the method that we've talked about with globular clusters. The higher your mass, the further to left you are on the MS, and the shorter your life span.

But if we just look at a star and know its mass and position on the MS, we can't say how long its already been on the MS because we can't look at how much fuel it has left.

 

[ageorge95]

Okay can someone give me a clear step by step procedure as to what to do because I am very confused.

 

[vociferous]

Okay can someone give me a clear step by step procedure as to what to do because I am very confused.

Okay, if you want to measure the age of Sirius you first have to determine what kind of star it is. If you want to do this observationally, you need to take a photograph of the star in three filters, usually the U, V, and B filter. By using its color values, you can infer approximately what color it is and therefore what the effective temperature is (using Plank's law). You could also attempt to measure the parallax by determining how far it has moved in relation to background stars in 6 months, thus determining its distance and measuring its absolute magnitude. You could also measure the magnitude of one of its companion stars whose absolute magnitude is "known" and use that to compute the magnitude of Sirius and thus estimate the temperature.

Now, if you do not want or cannot do any of this, all this information is available and you can look it up. You will find that Sirius is an A type star, specifically an A1, which will put an upper limit on its lifetime sometime in the hundreds of millions of years.

That is the easy part. The only way we can infer the age of stars (besides them moving off the main sequence) is based upon their metalicity. The big bang created a Universe that was almost entirely hydrogen and helium. There were a lot of stars created early in the formation of the Milky Way. Some of the less massive ones are probably still around. The more massive ones went supernovae and scattered all kinds of heavy elements, which astronomers call metals, around the galaxy. New stars formed from these enriched dust clouds and started the process all over again.

Astronomers realized that by determining the metalicity of stars they could estimate their age. The found the most of the stars in the disk seem to have high metalicity while most of those in the halo had low metalicity, thus determining that stars in the disk tended to form later than stars in the halo.

Stars emit radiation at different intensities at different frequencies (colors). This is called Black Body radiation, and by hooking up a ccd and a spectrograph to your telescope, you can take a picture of this spectra. STars' atmospheres have all kinds of elements which tend to absorb radiation at certain frequencies, and these will show up in the spectrograph once you have normalized it to remove the black body curve. By looking at this spectra, you can use various techniques to compute the metalicity and thus infer the metalicity of the gas which the star formed from which can be used to approximate the age of the star, since the metalicity of gas in the galaxy has been increasing at a "known" rate.

Unfortunately, using photometry or spectroscopy to infer the metalicity of a single star is no easy task.

 

[ageorge95]

Thanks a lot Vociferous. I have two questions.
1. How do you derive the colour values from the photos taken using the filters?

2. Do you know of any websites that clearly explain these processes? My teacher has informed that I cannot rely entirely on a forum. I need other sources.

 

[vociferous]

While technically there are a number of algorithms that are possible when dealing with color filters, when Astronomers are looking for quick and basic data, they can usually get what they need by taking CCD images in only three filters, typically U, B, and V. Good CCD cameras will often have five filters built in.

While there is typically a lot of massaging of the data, what it ultimately breaks down to is coming up with three normalized images, computing the photon count of the star in each filter, using that to compute the magnitude, then subtracting two filter magnitudes to get a color magnitude.

A typical example would be to take a photo of a star in B, V, and U, convert it to a Johnson color system, then compute the B-V and U-B color magnitudes. This is a whole lot easier than trying to compute the "true" color by spectroscopy and using the right equations/software, it will give you a pretty accurate idea of what frequency the star peaks at.

I do not know of any websites that clearly explain the process. The three books I have that were used in my observational astronomy classes that explain these techniques to a certain extent are:

https://www.amazon.com/dp/0521747686/?tag=pfamazon01-20

https://www.amazon.com/dp/0521617626/?tag=pfamazon01-20

https://www.amazon.com/dp/3540198989/?tag=pfamazon01-20

Keep in mind that not all of the material will be fully comprehensible without a sufficient background in Calculus, Linear Algebra, and Computer Science. However, most of the material should still be understandable.

Proper color photometry is no simple matter, especially if you are just going to pick up a book and try to do it yourself. It is best learned under the guidance of someone who knows what they are doing. My suggestion would be to contact your local astronomy club and see if there is anyone familiar with color photometry who may be willing to assist you in your endeavor.

Also remember that determining the color of a star allows you to compute its temperature, and therefore its maximum age, not its current age.

 

[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.