How do I find the age of a star?

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

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

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."

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:

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 cant 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

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.

Attached Thumbnails

 

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.

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, 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:

http://www.amazon.com/Measure-Sky-In...0384900&sr=8-1

http://www.amazon.com/Astronomy-Camb...0384874&sr=8-1

http://www.amazon.com/Telescopes-Tec.../dp/3540198989

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.