Expert: Tom Whiting - 6/17/2008

Question
I am a grade 7 student and need to know all about measuring age of a star.

Answer
Hi Empark,
We don't really measure the age or length of life of a star, but we can "estimate" it by various means....using the Hertzsprung Russell (HR)diagram, See
http://en.wikipedia.org/wiki/Hertzsprung-Russell_diagram

Plus the additional knowledge that we already know:
1. The bigger (more massive) the star, the shorter it's lifespan.

2. Hot, large, massive, blue white giants in the upper left hand corner of the HR diagram have a very short lifespan measured in a few 10's of millions of years (Yes, that's very short). But these constitute only one in a thousand stars. (Spectral class O and B)
These end their lives as supernovae, creating all the heavy elements
you see around us. (In astronomy, a heavy element is ANY element
beyond hydrogen and helium).

3.  The little low-mass red dwarfs in the lower right hand side of the HR Diagram have very long lifespans, measured in several trillion years and they constitute about 80% of all stars. (Spectral class M).
4. The average type stars, -the solar type stars-- have 'average'
lifespans of 6-12 billion years, depending on their initial starting
mass. They constitute about 20% of all stars.
(Spectral classes F,G, and K)...the slightly more massive and hotter F stars on the shorter lifespan end, the cooler, smaller K type stars on the longer end. (Our sun is in the middle, a G2 type star).

5. The bigger and hotter...read that, more massive, the star, the
faster it uses up it's fuel supply, hydrogen, and it's an exponential increase, so that's why the very big stars use up their fuel, even though they have a lot more of it, in a few millions of
years, whereas the miserly little red dwarfs live for several trillions of years. In fact, we've never seen a red dwarf move to it's next evolutionary stage (Whatever it is) because not near enough time has passed since the beginning Big Bang 'only' 13.7 billion years ago!!  (Our Universe has only just begun, with a
total lifespan measured in the hundreds of trillions of years!)

So we only estimate an age.  First you have to determine what spectral type of star you have, then you plot it's position on
the HR diagram. There is a special line at the bottom of the Main
Sequence, the diagonal band of 90% of all stars on the HR diagram, called the ZAMS line, or Zero Age- Main Sequence line.  If the star in question is on the Main Sequence, then it's age can be inferred by
how far above the ZAMS line it has proceeded over the course of
it's life. For instance the sun has progressed about halfway up,
up off the ZAMS line, through the Main Sequence Region, so we can infer that the sun has used up about half of its fuel (life). Since the spectral class G stars have a total lifespan of about 10 billion years, we can infer therefore, that the sun is about 5 billion years old, and has about 5 billion more years left in it's TOTAL life.
(This is in good agreement with the known age of the Solar System,
namely 4.6 to 5 billion years old).
Since stars spend about 95% of their life fusing hydrogen to helium on the main sequence of the HR diagram, we can estimate that the sun has about, or at least,  4 billion years of useable hydrogen fuel left.

This is in very good agreement with nuclear physics methods of
calculation, which we can do for the sun. We know (roughly) from
nuclear physics that the sun uses up about 4 million tons of mass
per second fusing hydrogen to helium, so if you want to go through
the exercise, you can (and it's probably easier to convert every
number to the metric system) look up the total mass of the sun.
The useable hydrogen constitutes about 8-10% of the core region,
so you can divide this mass value by the mass loss per second to arrive at the total lifespan number of seconds, and it will be in the range of 10 to the 17th power seconds total life span, then divide by 31.5 million seconds per year, it will give you about 10 to the 10th power years, or about 10 billion years total lifespan. Subtracting the age of the Solar System of about 4.6 to 5 billion years, gives about another 5 billion years to go, for our star.

These methods only work for the 90% of all stars on the Main
Sequence...but not for the "special stars" that have already evolved
off the Main Sequence and are done fusing hydrogen to helium. These
include the Red Giants and Red Supergiants up in the upper right
hand corner of the HR diagram, and the lowly White Dwarf stars in
the lower left hand corner. These stars have already lived out 95%
of their life, and are in the very final stages of their life, so we have to use a different method for the age of these special stars.
In effect, we have to determine roughly what their starting mass
was (not easily)...or, must have been when they WERE on the Main
Sequence.  Astronomers do this by comparing the amounts of 'heavy'
elements (with an instrument called a spectroscope) and determine whether they have a Population II (low, or non-existent in heavy elements) or Population I star (higher in heavies)...since we roughly know how fast heavy element production has been throughout the age of the Universe, since it's the supernovae explosions in the
past that create the heavy elements (Lithium #3 up to Uranium #92).
If it's a Population II star, then it has to be very very old, but
if it's a population I star, then it's a member of a younger Population I catagory, like the sun. Astronomers can determine a rough initial starting age by the elements contained in the star itself. But that's beyond me, and your 7th grade project.
But that's roughly the way it's done, in a nutshell.

That's what the professional astronomers do for a living, and why
you and I are just 'amateurs'...but we don't have access to the
very large telescopes and the attached equipment like spectroscopes
and ultra-highspeed computers to do that stuff.
Hope all this helps,
Clear Skies,
Tom Whiting
Erie, PA USA

FOLLOW UP:
Oh, one other trick that astronomers use to determine age, but
it has to be with a whole cluster of stars...they can plot the
entire cluster on the HR diagram by luminosity and Spectral
classification.  At some point on the Main Sequence band, the plots of the cluster stars will cut off, or turn off upwards toward the upper right Red Giant region.  This is called the Main Sequence Turn-Off point (but it only works for clusters of stars which we assume  all formed up at about the same time).
Knowing the total lifespan of the various spectral groups, we can
then estimate the age of the cluster, by noting the cluster turn-off
point, departing from the Main Sequence band.  For instance, if we observe and plot that there are no longer any O,B,A,F, or G-type stars still on the Main Sequence (because they have all evolved to the Giant region) then we know that the entire cluster has to be at least 10 billion years old, the total lifespan of the sun. But if G-spectral types are still seen on the Main Sequence band, then the cluster HAS to be younger than 10 billion years, otherwise G-types would have evolved to the Red Giant region. If massive B-type stars
are still hanging around in the cluster, then it has to be a very
young cluster for that type of star to still be on the Main Sequence
because we already know that B-type stars don't live very long,
relatively speaking.  So that's how it's done, and can be done,  with star clusters, only.
Clear Skies,
Tom