A Balance of Forces

Stars live out their lives in an exquisitely detailed equilibrium, or balance, between two powerful forces -- outward pressure and the inward pull of gravity.  The gravity force is a property of the mass of the star, and in order to support itself against gravity the star generates energy in its core. The amount of energy the star generates is exactly that needed to maintain the thermal pressure to support the star against gravity -- not too much, and not too little.  So the energy generation is regulated by the star's mass.  The ultimate life and death of a star depends on its initial mass.  Today we will look at the life of low-mass stars, which are those with mass less than about 2 times the mass of the Sun (less than 2 solar masses).  So the Sun is a low-mass star.  All such stars follow the same basic pattern.  The next higher category, intermediate-mass stars, have masses from 2 to 8 solar masses.  The lives of these stars really is not so different from low-mass stars, so we will discuss both low- and intermediate-mass stars together.  These stars typically end up as white dwarf stars.

However, the third category are high-mass stars, with masses greater than 8 solar masses, and these end up quite different than the stars of lower mass.  They can explode into Supernovae, become exotic objects like neutron stars and black holes, and so on.  We will discuss these high-mass stars next time.

We have already talked a great deal about the formation of the solar system from a collapsing cloud of gas.  All stars form in the same basic way, but we really did not talk much about the cloud itself.  Where do such clouds come from?  What are they like?  Why do parts of the cloud collapse to form stars?  These are questions we will discuss now.

The Origin of the Clouds
When we look out into the galaxy, we see many places were there are gas and dust clouds, but only in certain places.  In this picture of the Andromeda Galaxy (the nearest spiral galaxy) you can see the gas and dust concentrated in the spiral arms.

Our galaxy is similar.  Here is a photo of part of the Milky Way, in the direction of the center of our galaxy.  Here again you can see lots of dust (the dark parts, where the dust is covering up the stars), and gas (generally brighter parts, where the light from stars is reflected).

When we look at one of these clouds up close, we see lots of structure, as in this photo of the gas and dust pillars in the Eagle Nebula.

So where did it all come from?  Some of it is left over from the original creation of the Universe.  It is the hydrogen and helium gas from which the galaxy itself formed.  However, a lot of it comes from previous generations of stars.  When stars, especially the more massive ones, go through their lives and die, they return most of their mass to the Interstellar Medium.  This material, enriched in heavy elements like carbon, oxygen, nitrogen, and heavy metals that we need to survive, goes into the new generation of stars.

What Are the Clouds Like?
Space is full of hot (fast moving) particles and high-energy radiation (photons) from stars that make for a high temperature.  In order for a cloud to collapse to form a star, it has to be very dense and it has to be very cold, typically only 10-30 K.  The dust in the clouds is very important in keeping the cloud cold, by shielding the inside of the cloud from the radiation, and by reradiating internal heat in the infra-red.  Inside the clouds, the gas cools down and starts to combine into molecules, like H₂, CO, CO₂, H₂O, and many even larger molecules.  For this reason, these are called molecular clouds.

What Causes the Collapse?
In the densest part of the clouds, it is also the coldest, and these two things combine to allow gravity to take hold and start the collapse.  You can imagine that the mass of the star that results from a local collapse is random, and depends only on the mass of the initial part of the cloud, by chance.  Most stars end up being of order 1 solar mass, and the more massive stars are rare.  The gas is swirling around, and any random rotational motion is highly magnified during the collapse due to conservation of angular momentum.

From Cloud to Protostar
As the initial collapse begins, the particles of gas and dust begin to fall toward the concentration of mass in the center.  This is the same gravitational contraction that we discussed earlier, and it converts potential energy into kinetic energy, i.e. heat.  But the initial collapse is slow enough that the heat can be radiated away in the infra-red, keeping the cloud cool.  During this time, the temperature remains below 100 K, and the cloud glows in long wavelength IR.

Eventually, the central parts become so dense that they become opaque to IR, and the heat can no longer escape.  At this point, the internal pressure and temperature rise dramatically, and the central object becomes what is known as a protostar, the seed from which a star will grow.  During this time, a protostellar disk forms due to conservation of angular momentum.  Magnetic fields generated inside the central, rapidly spinning object sweep through the disk, transferring momentum from the protostar to the disk.  The magnetic fields also generate a protostellar wind that is directed mostly out from the poles of the protostar, creating polar jets.  Here is a photo of a protostar called HH30, which clearly shows the dark disk and the polar jets.  The HH stands for Herbig-Haro objects, named after their discoverers.

Of course, planets can form from the dense protostellar disk, as we have learned earlier.  Eventually, the strong protostar winds will sweep away all of the gas of the disk, and leave the planetesimals behind to coalesce into a few larger bodies of planets.

A Star Is Born
Eventually, the internal pressure and temperature grow high enough (more than 10 million K) to start fusing hydrogen (protons) into helium.  At the onset of nuclear fusion, the object officially becomes a star.  Once fusion gets going and the star adjusts to its new equilibrium, the gravitational collapse halts and the star becomes a Main Sequence star.  Where it falls on the Main Sequence is entirely dependent only on the initial mass of the star.  All stars of the same mass will have the same surface temperature, and the same size, and so will have the same luminosity and will be in the same place on an H-R diagram.

Prior to arriving at the Main Sequence, however, the protostar would have a different surface temperature and luminosity, and so would be in a different place on the H-R diagram -- and this location would change with time.  It is interesting to plot the location of protostars in the H-R diagram as they evolve (called an evolutionary track).  Each point merely represents its surface temperature and luminosity at each some moment during its life as a protostar.  The next figure shows these evolutionary tracks for different mass stars.

We can easily describe the stages of life of a low-mass star.  We will see that as a star ages, its external characteristics -- size and surface temperature -- change.  Remember that what causes the changes is the star's fuel supply, coupled with the interplay between the inward force of gravity and the outward pressure.   When the star first arrives on the Main Sequence, it is burning hydrogen fuel into helium in its core.  All stars on the Main Sequence are doing this.  This is the most efficient way of producing enough energy to support the star, so the fuel burns relatively slowly.  Most of the lifetime of the star is spent on the Main Sequence.  In the case of the Sun, this is 10 billion years.

After 10 billion years, the Sun begins to run out of hydrogen fuel in its core.  All this time it was converting hydrogen into helium, so near the end of this period the core is entirely helium.  The helium is inert, and in fact is an interesting state of matter called degenerate matter.  The pressure and density are so high that the pressure no longer depends on temperature at all.  When the core runs out of hydrogen, something has to happen to keep the star from collapsing.  What happens is that the core shrinks into this degenerate state, and the hydrogen in higher layers reaches a high-enough temperature to allow it to start fusion reactions.  This is called hydrogen shell burning, and it occurs at an even higher rate than the core burning.  Because of the higher rate of energy production, the overall luminosity of the star increases.  During this stage, the star begins to expand, and becomes a Red Giant.  The star "turns off" of the Main Sequence and grows more luminous but at the same time the surface temperature decreases.  As hydrogen burns hotter and hotter in the star, the surface continues to expand while the core contracts.

After several hundred million years in this process, the core to reaches such a high temperature, 100 million K, that suddenly the helium ignition temperature is reached.  The once inert core suddenly (in a matter of minutes!) flashes into ignition and inflates the core rapidly.  Paradoxically, this inflation of the core causes the outer layers to shrink, and the Red Giant actually grows smaller.  The moment of ignition is called the Helium Flash.  In helium fusion (called the triple-alpha process), three helium atoms combine into a carbon atom.  This occurs at a much higher temperature than hydrogen fusion due to the fact that helium nuclei each have two + charges, whose repulsion must be overcome by crashing them into each other at high speeds.  The shrinking star gets a hotter surface temperature, but a lower luminosity, so it moves back toward the Main Sequence.  It stays here, burning helium in its core (and perhaps burning hydrogen in a shell at the same time), for about another billion years.

Eventually, the helium in the core is again going to all be used up, and the entire process happens again.  We can almost use the same words above, except replacing hydrogen with helium, and helium with carbon.  Eventually the core contains only inert carbon, and a shell around the core starts burning helium.  In this helium shell burning stage, the core again shrinks and the outer layers of the star expand due to the increase in rate of energy production (luminosity).  This time the star may become a Red Supergiant, but its days are numbered.  It already ran out of hydrogen fuel in the previous Red Giant stage, and now it is running out of helium fuel.

For stars like the Sun, the core never can reach the temperature (600 million K!) needed to fuse carbon into heavier elements.  Instead, during a process that is not at all understood, the outer layers of the star are ejected into space in a planetary nebula.  Such planetary nebulae are seen throughout the galaxy, and in other galaxies, in quite large numbers considering that they only last for a few thousand years before they dissipate and disappear into the interstellar medium. 

What is happening in the star to cause this?  The problem is that the helium shell burning phase is very unstable.  We said that the temperature has to be at least 100 million degrees.  But it is hard to regulate such a high temperature when the amount of mass in the outer layers (the pressure cooker lid) is so small.  The temperature gets a bit too high, and the star expands too much.  The temperature drops and the pressure goes down, so the outer layers shrink again, but then they shrink too much, the temperature rises, and the whole thing starts again.  These are called thermal pulses.  The outer star layers oscillate, losing mass in each oscillation until most of the outer layers are gone.

What is left, then, is just the inert carbon core, which is VERY hot (100,000 K at first), and small (only about the size of Earth), even though it has a mass of nearly one solar mass.  This is a White Dwarf star.  It no longer generates any energy (no fusion takes place any longer), so it slowly cools down and follows the sloping line for constant radius in the H-R diagram that we mentioned last time.

To see the process graphically, let's work through Lesson 2 of the Stellar Evolution Tutorial.