Last month you learned how stars are born and join the Main Sequence. This month you'll learn how a star ages, leaves the Main Sequence and eventually dies. So this month's lessons take us off the Main Sequence but first I want to review what you have learned so you will understand where we are going.
Recall that all stars on the Main Sequence have a core of hydrogen that is undergoing nuclear fusion to create helium. The energy given off by this nuclear reaction makes its way through the layers, which consists of the radiative and convection zones, to the surface where it is released as light. The total amount of light given off is the star's luminosity. Its surface temperature determines its color. These two factors, luminosity and color or temperature, are determine by the star's mass and together they determine where the star is plotted on the Hertzsprung-Russell Diagram. | ![]() |
Therefore, all stars "burning" hydrogen in their core are part of the Main Sequence and their position on the Main Sequence is determined by their mass.
Yeah, I know that. So what?
So pay attention.
Stars of greater mass "burn" their hydrogen at a faster rate than stars of lower mass, so the more massive stars give off more light and heat from their surface. That's because a big star has more hydrogen to begin with and because a big star has a stronger gravitational force to squeeze the hydrogens together (thus producing more heat required for nuclear fusion). Therefore large mass stars are very luminous and very hot so they are found in the upper left of the H-R Diagram.
Bellatrix is a fine example
of a big star. Rigel is too, but note that it is an exceptionally
massive member of the Main Sequence "club". Some might
argue that it is off the Main Sequence, but you should remember
that no position in the Main Sequence
club is easy to define. Rigel "burns" hydrogen in its core, so
it is a Main Sequence star. Rigel is often called a "blue
giant" because of its color (temperature) and luminosity.
Conversely, small stars are small because they have less mass
and less hydrogen. Small stars "burn" their hydrogen
more slowly producing a cool, dim surface, so they are in the
lower right of the H-R Diagram.
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The Main Sequence runs from blue giants (like Rigel) in the upper left to red dwarfs (like Wolf 339) in the lower right. All of them are powered by the hydrogen that is undergoing nuclear fusion in their cores. About 90% of stars are on the Main Sequence and the majority of them are red dwarfs.
Why is the Main Sequence so wide and poorly defined?
That has to do with the way stars age.
When a star first enters the Main sequence its core is relatively "pure". What I mean is that a new star has plenty of hydrogen (fusion fuel) and very little helium (fusion leftovers). Such new stars are often called Zero Age Main Sequence stars (or ZAMS stars) and they will sit in a very exact position on the Main Sequence, near the ZAMS line. That position is determined by the star's mass.
As time goes by helium accumulates in the core and this affects the star's energy output. That affects the star's luminosity and surface temperature so it slightly changes its position on the H-R Diagram, causing it to drift from the ZAMS line. (We are talking about movement of the star on the H-R Diagram. It's true movement in space is another matter and is not connected to this discussion or the H-R diagram.) | ![]() |
The length of time a star is on the Main Sequence depends upon its
mass.
Big stars "burn" hot and bright so they
run out of hydrogen more quickly than small stars. True - big stars have more hydrogen anyway, but they squander it. They are "show-offs"!
A star as big
as Rigel may use up all its core hydrogen in a billion
years. Big stars follow the example of the movie star James Dean,
"live fast and die young". They may be brilliant for
a time but their time is short because bright stars age quickly.
On the other hand, a small star like Wolf 339 slowly "smolders"
its fuel so it lasts a long time. Some astronomers estimate that
the smallest red dwarfs could last a hundred billion years!
Our Sun is a star of intermediate mass - not too big or too small. It started with enough hydrogen to last about 10 billion years and it joined the Main Sequence about 4 or 5 billion years ago, so our Sun is middle age. Notice, in the diagram above, that the Sun has drifted about halfway from its position on the ZAMS line - where it once stood when it first formed.
How can you estimate the age and life span of a star?
Well, we can make rough estimates. It can be very complicated, in the details, but I'll walk you through the general idea.
First the astronomer estimates the mass of the star. There are several ways to do this - some better than others. The best way is to measure how rapidly something is orbiting that star. Usually that "something" is another star. From that data an astronomer can estimate the mass of the star s/he is interested in. ["Simple" Newtonian mechanics are used to do that calculation. It isn't very difficult, really, but I don't want to go any deeper in this course.] Another way is to use the Eddington limit (which you learned about last month) to get at least an upper estimate to a star's mass (based upon its luminosity). Regardless, the first step is to estimate the star's mass. That information is feed into further calculations to estimate the length of time the star will be on the Main Sequence.
Assuming the star starts out as a ball of pure hydrogen, its time on the Main Sequence will be
This (rough version of the proper) equation is derived from a pretty good understanding about the physics of fusion. It may have to be "tweaked" slightly to take into account the star's initial composition but most stars start out with over 99% hydrogen, so it isn't something to get too worked up about.
Notice that if you plug the Sun into that equation, the two masses cancel each other out and, you find that the Sun has a Main Sequence life span of 10 billion (1010) years.
I don't know the mass of Rigel but last month I used Eddington's limit to figure out that Rigel must be at least 2.4 times as massive as the Sun. So, Rigel's maximum time on the Main Sequence =
1 / (2.4)2.5 X 1010 years = 1/8.9 X 1010 years = 0.11 X 1010 years = slightly more than a billion years.
(You need a calculator that allows you to do xy functions in order to do that calculation.)
That's not very long at all. (The Sun will live about 10 times longer.) And remember, because we used Eddington's limit to estimate Rigel's mass, we were working with Rigel's minimal mass. Rigel could be (probably is) much more massive than 2.4 solar masses so its life span is probably much shorter than a billion years. So, quick, get out there and have a look at Rigel before it runs out of fuel!
On the other hand, a small star will last a long time. You'll recall from last month's lessons that a star can be smaller than our Sun. It's possible that there are red dwarfs out there with only 1/10th the mass of the Sun. Those small, dim stars will continue to slowly burn their hydrogen and remain on the Main Sequence for
1 / (0.1)2.5 X 1010 years = 1/0.00316 X 1010 = years 316 X 1010 years = over 30 billion years!
So, I hope I have convinced you that small red dwarfs last a long time while big blue giants don't.
OK, that's the star's life span. How do we know its (current) age?
Ah, yes - part two of your question.
Most stars start out as nothing but hydrogen, and those that start out with other elements are still made mostly of hydrogen.
Spectroscopic analysis, which you learned about last month when I told you about spectroscopy, can tell us what the star is currently made of.
Using computer models, astronomers then figure out how long that star has been undergoing nuclear fusion in order to have accumulated the extra elements. As you might imagine, the devil is in the details, and these models are constantly being refined. Based upon these techniques, astronomers estimate that our Sun has been burning hydrogen for about 5 billion years (so we have 5 billion years left).
The population of stars on the Main Sequence are like the population of people in a city - it's made up of individuals of different ages. New stars, ZAMS stars, are constantly joining the Main Sequence. Other stars have spent plenty of time on the Main Sequence and drifted away from the point at which they started. The biggest stars drift away from the ZAMS line more quickly than other stars because big stars age faster.
But what happens as a star ages (runs out of hydrogen)?
As time goes by a star becomes burdened by its helium products. Helium is denser than hydrogen so it sinks to the center of the core where it accumulates and interferes with hydrogen fusion. This forces the hydrogen fusion region to move outward from the center, away from the core. However, the outer core is not as hot and dense as the center so there is a reduction in the efficiency of hydrogen fusion, causing the star to dim. Due to this decrease in energy output the star collapses inward, drawn by its own gravitational force. You might think this is the end of the star but it's not. Instead, this is a transition stage for the star, kind of like a second childhood!
Around the core of the star is a shell of hydrogen that never took part in the hydrogen fusion down below. Due to the contraction of huge amounts of the star's materials, this shell is exposed to the same intense heat
and pressures that occurred in the core of the star when it was young. The hydrogen in the shell begins to fuse! This produces a very unusual star, powered by hydrogen fusion occurring in its shell surrounding an inert core of helium.
Fusion of hydrogen in the shell of a star is not as efficient as the fusion of hydrogen that once occurred in the core but the contraction causes the core to heat up (due to the pressure) and this provides heat that moves to the star's outer layers. This heat causes the outermost layers, called the envelope, to expand!
I know this is confusing but as the core is crushed smaller and gets hotter it causes the outer layers to heat up and expand. This expansion is the same effect you get whenever you heat up a gas. Hot gasses expand and as they do, they cool. As the star's envelope expands it cools. This produces a lower surface temperature and the final light released is red in color. However, the amount of light released is increased so this star will have an increase in luminosity. | ![]() |
At this point the star has left the Main Sequence and becomes
a "red giant". Red giants fuse hydrogen in their
shells not in their cores, so they are no longer members of the
Main Sequence. They are cool because their energy output from hydrogen fusion in the shell is very poor. They are big (giants) because their outer layers have expanded. Indeed, this expansion is so great that the outer surface of a red giant is composed of gas that is barely held by the star's gravity. I like to think of red giants as having a fluffy surface like cotton candy.
All stars eventually age and leave the Main Sequence by becoming red giants.
Bigger stars "age" quicker because
they use up their hydrogen faster, so a big star like Bellatrix
will spend less time on the Main Sequence than our Sun.
Very big stars become very big red giants called red supergiants.
Betelgeuse is a perfect example of a red supergiant. Betelgeuse
probably evolved from a giant star similar to Rigel.
Red giants and red supergiants make up about 1% of the stars on the H-R Diagram. They have a cool surface, so they are placed on the right side. They are also very bright because they have increased their size, so they are placed in the upper part of the H-R Diagram. This confuses some students. | ![]() |
Yeah! If a red giant is brighter, why is it cooler?
Because it is now bigger.
As a star becomes a red giant, its size increases more than its energy output and that is
why it has a cooler surface temperature.
Let's use our Sun as an example.
Currently our Sun has
a radius of about 700,000 kilometers. That's
pretty big. The sizes of stars are difficult to comprehend, so
let's use these numbers for comparisons only. In about 5 billion
years our Sun's core will run out of hydrogen and our Sun
will become a red giant. Its hot, inert core surrounded by a shell of fusing hydrogen will cause
the Sun's envelope to swell. This expanded envelope will
increase the Sun's radius by 430 fold, so it will
grow to a radius of around 300 million kilometers! That means the surface of the Sun will extend beyond the orbit of Mars! Of course, our little blue world will also be destroyed when the Sun expands into a red giant. (But the view from Jupiter's moons will be spectacular, so book your trip early. )
The Sun's luminosity will increase to 20,000 times its current luminosity but its surface temperature will be only 3500oC (or oK). Take a look at the H-R Diagram and see where that places our future Sun. It will move to the red giant corner.
If you are comfortable calculating the surface area of a sphere
(4 r2) you can determine the surface area of our Sun as a red giant,
and compare it to the surface area of our current Main Sequence
Sun. You will discover that the increase in the Sun's
radius by 430 fold increases its surface area by 185,000 fold. That's one heck of a big surface and every bit of that surface will be emitting light! However, that energy output will only be 20,000 times greater so when distributed over a surface 185,000 times bigger you end up with a star that emits only about 10% as much energy per square kilometer. Therefore, our red giant Sun will have less energy output per square kilometer than when it was a Main Sequence star. So it will be cooler. (And if the math is too much for you, don't worry about it.)
While the surface of a red giant is cool and fluffy (low density) its core is the exact opposite. The core is constantly being compressed by the powerful gravity so it gets hotter and denser. Recall that the energy is so high in the core that all the atoms are stripped of their electrons but the electrons are not gone. They are just free to wander around in the core. (They are not associated with any nuclei.) Eventually the core's electrons are crushed to the point at which its electrons can no longer be compressed and the material is said to be electron degenerate. The details of electron degeneracy are complicated and have to do with the amazing branch of physics called quantum mechanics. Once material is electron degenerate it can be made hotter but not denser. (More on this later.)
So, is that the end of the story? Is that the end of stellar evolution?
No, not at all.
As the red giant's shell of hydrogen undergoes fusion two products are formed - energy and helium. Most of the energy is radiated into space but some of it is retained and heats the helium in the core. Remember the core of the red giant is surrounded by a shell of hydrogen fusion so it must get pretty hot in the core. Also, the helium made by hydrogen fusion in the shell falls into the core. This goes on for millions of years making the red giant's core hotter and filling it with more helium.
Eventually, about 100 million years for an average red giant, the core temperature reaches 100 million oC (or oK)
and the helium in the core begins to undergo nuclear fusion! Two helium nuclei fuse to form a new element called beryllium. Three helium nuclei fuse to form carbon atoms. Four helium nuclei fuse to make oxygen. It turns out, for reasons that have to do with nuclear synthesis, that most of the helium is fused into carbon and some of it into oxygen in a process called the triple alpha process.
Due to the electron degeneracy of the core, the start of helium fusion in the core causes a catastrophic event called the helium flash. | ![]() |
During the helium flash incredible amounts of energy well up from the star's core and work towards the surface. This greatly increases the star's brightness and causes its surface to expand even more, so it becomes more luminous and cooler. This rapid change in the star's luminosity and temperature during this initial helium flash causes the star to rapidly move far into the upper right corner of the H-R diagram. The red giant eventually settles down, contracts a little and in the process it decreases its luminosity while increasing its temperature (slightly). This "post flash" behavior moves the red giant down and to the right of its "flash point" on the H-R diagram, but still in the red giant corner.
Once settled, this star has a core
powered by the fusion of helium and a shell that is powered by fusion of hydrogen.
It's still a red giant but it has two sources of energy!
Helium fusion is not as efficient as hydrogen fusion so the star "burns" its helium rapidly into carbon and oxygen. Eventually a red giant's core becomes full of carbon and oxygen and the core starts to run out of helium. This causes the helium fusion reactions to move to the outer parts of the core, just like the hydrogen fusion did when the core became too inefficient for fusion due to the contaminating products. The movement of the helium fusion reactions to outer parts of the core does not go smoothly. It is as if tiny helium flashes occur rapidly and repeatedly. These helium shell flashes causes the star's surface to pulse and the star's luminosity to fluctuate. | ![]() |
Smaller helium shell flashes can continue to occur, apparently at random, for a long time.
Perhaps you will remember that I had been evasive about the magnitude of my favorite red giant, Betelgeuse. That's because she is an old red giant experiencing hot flashes. I mean helium flashes! Her magnitude can be as low as 0.9 or as high as 0.4 (and probably as high as 0.1 according to some observers).
These flashes of energy can be so powerful that they actually blow off some of the outer layers of the star. Recall that the outer surface of a red giant is so far from its core (which is its center of gravity) that its surface is barely held by the star's gravity.
With each helium shell flash a superwind is created that blows bits of the star's surface away. This is followed by contractions and heating of the core. At this point the star is really on its death bed and convulsing as it gasps for its last breath. (Metaphorically speaking, of course.) All this energy and movement of mass is very unstable and eventually an extremely powerful superwind, an explosion of wind, pushes the star's envelope cleanly away from the core. The loss of the star's envelope is also the loss of any chance of reviving nuclear fusion. She's now dead.
So, the red giant dies in a massive explosion and when it does it leaves behind a very strange "corpse".
You can continue on and learn about the strange object left behind by the exploding red giant. Otherwise, take a break and come back after you're refreshed.