Stellar Evolution

This is a brief series of articles on stellar evolution, neutron stars, and black holes. This series consists of 3 parts:

  1. Stellar Evolution - Part I of the article - this page
  2. White Dwarfs and Neutron Stars - Part II of the article
  3. Black Holes - Part III of the article

The series begins with a brief introduction to star formation, covering the birth, lifetime and death of a star. The second part describes neutron stars, including special types of neutron stars, such as pulsars and magnetars. The third part describes black holes.

The Life and Death of Stars

This is a brief account of the formation, life and death of stars. A star can last anywhere from a few million, to hundreds of billions of years (more than the universe's lifetime!), depending on its mass.

Stars form in primordial gas/dust clouds which are as cold as space. Spiral galaxies, like our Milky Way, contain a diffuse interstellar medium of gas (mostly hydrogen, some helium, a few trace elements) at very low densities (around 0.1 - particle per cubic centimeter). In some places, the gas forms denser clouds, reaching densities of 100-1000 particles per cubic centimeter. These denser regions are called diffuse nebulae or giant molecular clouds, and this is where new stars are formed. Large diffuse nebulae can be up to 100 light years across, and contain as much mass as 6 million Suns. The closest one to us is the Orion Molecular Cloud Complex, a huge complex of nebulae hundreds of light years in size, located in the constellation of Orion, about 1500-1600 light years from Earth. The complex spans the region roughly between Orion's belt and his sword, and includes well known nebulae such as M42 and M43, the Horsehead Nebula, M78, etc. There are many active regions of star formation here, with a great number of protostars and very young stars.

Artist's Impression of Gliese 570 D, a brown dwarf discovered in 2000. Image © Dr. R. Hurt

Diffuse nebulae can remain in equilibrium for long periods. The gas is in equilibrium, with gravity being countered by the gas pressure (the kinetic energy of the gas molecules). However, if the nebula grows very massive, gravity can overwhelm the gas pressure, and initiate collapse. The precise size at which collapse starts depends upon density and temperature of the cloud, and is called the Jeans Mass. External factors can also initiate the collapse of smaller clouds, such as shock waves from nearby supernova explosions, tidal forces produced by collisions between gas clouds, etc.

As collapse starts, gravity causes the gas to clump together. As the clump grows in mass, its gravitational pull increases, and it pulls in more and more gas from its surroundings, until the clumped gas is massive enough to form a proto-star. As the gas falls in towards the center of the proto-star, gravitational potential energy is released, and the proto-star shines. However, it's hard to see proto-stars, because they shine in the far infra-red, and they are usually shrouded by gas and dust clouds.

As the material of the proto-star continues to fall inwards, the density at its core increases. The higher density at the core starts to trap the energy constantly being released by the infalling of mass towards the center (the gravitational potential energy). This causes the core temperature to rise sharply.

The infalling matter has some angular velocity relative to the clump in the center, so the protostar begins to rotate. This rotation continues through the life of the star. As a result of the rotation, the gas cloud takes the shape of a disc, which is important in planet formation.

What happens next depends on the mass of the proto-star. Before we proceed, let's define a couple of standard masses, to make this easier to understand. The first is the mass of the Sun (1.9891 x 1030 kg) which we'll call S. The other is the mass of the planet Jupiter (1.8986 x 1027 kg), which we'll call J. The ratio between them is 1 S = 1047.7 J, which we'll simplify by approximating, so 1 S = 1000 J.

Protostars with Mass <13 J

Protostars which mass less than 13 J will end up as gas giant planet-type objects. As their material continues to fall inward and the core density increases, they continue to shine. However, the core never reaches a temperature sufficient to start a nuclear reaction, and eventually the proto-star reaches equilibrium. As no more mass is falling in, heat is no longer generated, and the proto-star cools down, forming a large planet sized mass, much like Jupiter. The largest extrasolar planet found so far (TrES-4) is about 70% bigger than Jupiter, though less massive, since it has a very low density.

Hertzsprung-Russell diagram, showing a plot of luminosity against color for 22000 stars from the Hipparcos Catalog, plus 1000 stars from the Gliese Catalog. © Richard Powell

Protostars with Mass between 13 J and 90 J

These protostars have the potential to become brown dwarfs. Brown dwarfs are a relatively recent category, and the definitions are still in flux. However, as a general rule these are objects large enough to produce deuterium fusion at the core. This is not hydrogen fusion, as seen in Sun-like stars, but rather the fusion of the hydrogen isotope deuterium, which fuses at lower temperatures. Larger brown dwarfs also fuse Lithium, which is one of the markers of brown dwarfs. Stars such as our Sun show no lithium (or perhaps only a little lithium in their outer atmosphere), since their temperature is hot enough to break down any lithium into helium. However, brown dwarfs usually show the presence of lithium in their spectra, which helps distinguish them from ordinary stars. Brown dwarfs also have a characteristic size: about the same as Jupiter. So while a brown dwarf may mass anywhere from 13 J to 65+ J, it's size will still be about the same as Jupiter (they are much denser). The deuterium and/or lithium in a brown dwarf soon runs out, usually within a few million years. After that they continue to cool, during which period they still give off light.

Protostars with Mass above 70-90 J

Proto-stars with masses above 70 J (for population I objects) or 90 J (for population II objects) have enough mass to become regular stars (Population I and II refer to the metallicity, or metal content of the star. Population I stars, such as our Sun, contain more metals than population II stars, because they are younger, and contain metals produced by previous generations of stars). These stars are large enough to create core temperatures at which hydrogen fusion ignites. When hydrogen fusion starts at the core of a star, it is said to have entered the main sequence. The majority of stars we can see in the sky are main sequence stars.

Once hydrogen fusion starts, the star blows away much of the dust cloud surrounding it, and shines brightly in the visible range of the spectrum. It soon reaches equilibrium, where the pressure of the hot core balances the force of gravity, enabling the star to maintain a more-or-less steady size and luminosity. Stars typically spend most of their lives in the main sequence, billions of years for average size stars such as our Sun. Larger stars burn through their fuel faster, so their main sequence may be much shorter, sometimes as short as a few million years.

Hertzsprung - Russell Diagram

Because of the extremely long lifetime of stars, and our very short observation period on Earth in historic times, our knowledge of stellar evolution does not come from actually watching stars evolve. Instead, it comes from studying millions of stars, viewing each as a snapshot in it's history. We can see stars of different ages, in different stages of their evolution. Such observations, combined with computer modeling, are the main source of our knowledge.

Observationally, the easily observed characteristics of a star are its apparent magnitude (how bright it appears to us from Earth) and its color (spectral class). The apparent magnitude can be converted to an absolute magnitude, if the distance to the star is known.

In 1910, Ejnar Hertzsprung and Henry Russell plotted the absolute magnitude against the spectral class of several stars. This plot is known as the Hertzsprung - Russell diagram, which is commonly used today to classify stars.

[CLICK FOR LARGE VIEW] The evolution and fate of stars.

The H-R diagram on this page is one of several forms of the H-R diagram in current use. It shows absolute magnitude on the y-axis, and spectral class on the x-axis. Since absolute magnitude correlates with luminosity, the luminosity is also shown along a y-axis in the diagram. Note that the luminosity scale is logarithmic, since absolute magnitude follows a logarithmic scale. The spectral class (O, B, A, F, G, K, M) correlates with the temperature, with the hotter stars on the left and the cooler stars on the right. The scale at the bottom (B-V scale) is another way of measuring the temperature of a star. Photographs of the star are taken through Blue and Violet filters, Subtracting the V image from the B image (B-V) gives the B-V index. The smaller this index, the hotter the star. Note that the color of a star (as shown by the spectral class) represents the surface temperature, not the core temperature. We see stars from the light that leaves their surface.

When plotted on the H-R diagram, stars naturally fall into clusters, indicating the processes going on inside them. The large majority of stars fall along a curve called the Main Sequence. The left side of this curve shows larger, hotter, bluer stars. The right side shows smaller, cooler, redder stars. But they all share the key feature that they are fusing hydrogen to helium in their cores. The very large proportion of stars on the main sequence is a reflection of the fact that stars spend by far the longest part of their life in the main sequence. So it is natural that in any statistical snapshot, such as an H-R diagram of the visible sky, these stars will predominate.

Several horizontal clusters can be seen to the right. These represent giant stars, which are burning helium at the core, and hydrogen in a shell around the core. This is explained in more detail in other sections below. Giant stars fall into several subclusters, with the largest being ordinary giant stars, and much smaller clusters of supergiants.

At the bottom of the graph is a cluster representing white dwarfs. This is a very late stage in the evolution of a star, after it has burned through its fuel. White dwarfs do not burn fuel, they shine due to the heat remaining after fusion has stopped. Note that most white dwarfs are towards the left of the graph, indicating that they have very high temperatures. The reasons for such high temperatures are described below.

The Fate of Main Sequence Stars

The material forming a star exists under a balance of forces. Nuclear fusion at the core generates tremendous heat, which (according to the ideal gas law) increases pressure and consequently the volume, pushing to increase the size of the star. Conversely, gravity pulls everything in towards the core, thus shrinking the volume. A star is in a state of balance between these two forces. As fuel is used up, imbalances between the pressure of nuclear fusion and gravity occur, which forces the star to find a new energy source. Eventually, the star runs out of all available fuel, and dies. The dead hulk of the star continues to produce light for a long time, as it gradually cools.

Like protostars, the fate of main sequence stars is also determined by their size. All stars which are large enough to ignite hydrogen fusion at their cores enter the main sequence. But from that point on, their fates diverge, depending on mass.

[CLICK FOR LARGE IMAGE] Fusion in Main Sequence Stars

Stars with Mass < 0.5 S

The cores of stars have convection currents, much like Earth's oceans. These stars are small enough to have convection currents that reach almost to the surface of the star. Larger stars have convection currents that only reach part way to the surface. The importance of these currents is that they bring in fresh hydrogen from the outer layers of the star, as the hydrogen in the core is depleted by being fused to helium.

Small stars like these burn through their hydrogen very slowly. Their fate is not known from direct observation, since these stars have an extremely long lifetime, and the universe is not yet old enough for them to have burned through their fuel and go past the main sequence. It's been calculated that a star with a mass of about 0.1 S would have a main sequence life of about 6 trillion years. This is hundreds of times longer than the universe has been in existence.

Because of their small size and slow fusion, such stars are reddish in color, and are known as red dwarfs. Red dwarfs are the commonest type of star in the Solar neighborhood. The star closest to Earth, Proxima Centauri, is a red dwarf of about 0.123 S mass. Several planets have been observed circling red dwarf type stars. The smallest extrasolar planet so far discovered orbiting a normal star (as opposed to a neutron star) is Gliese 581 c, which orbits the red dwarf Gliese 581, about 20 light years from Earth. This planet is about 5 times the mass of Earth, and about 1.5 times Earth diameter. It's very close to the habitable zone around the parent star, and might be a likely candidate for the search for extraterrestrial life. Recent computer simulations, however, show that it probably has a runaway greenhouse effect going, which would make it too hot. The star also has another planet in the habitable zone, Gliese 581 d, which is about 7 times Earth mass, and is farther away from the star than Gliese 581 c. Current research shows that liquid water might exist on this planet.

The habitability of planets orbiting red dwarfs is under debate. Because of the low energy output of these stars, the habitable zone lies very close to the star. At such close ranges, the planets would likely be tidally locked, always presenting the same face to the parent star. However, some computer models show that a thick atmosphere or large ocean could transfer enough heat even in tidally locked planets for conditions to be suitable for life. Red dwarfs are often also quite variable, changing their energy output as much as 40%. However, they are still interesting candidates, if only because their very long lives allow plenty of time for life to develop.

In time, all the hydrogen in the core and the range of the convection currents is exhausted. At this stage, fusion moves out from the core into a shell around the core. This produces two effects: the outer layers of the star expand greatly in size, as the fusion heat source moves closer to the surface, and the star overall cools down a bit, since the expansion outpaces the fusion rate. At this stage, the star becomes a red giant. Stars that become red giants produce a lot more energy, at rates 1000 to 10,000 times higher than they were originally. But since fusion has moved closer to the surface, the outer layers are blown out much farther away from the core, and they become cooler. This is what makes red giants "red", since their surface temperature has cooled. Of course, the much larger surface area means that they are still able to emit much more energy than did they before, when they were smaller.

Not all small stars will become red giants. If the convection currents reach to the surface, and if they continue for the life of the star, it will stay in the main sequence until the end of its energy-producing life, and never be a red dwarf. However, if the currents "stagnate", and the core runs out of hydrogen, fusion may move to a shell surrounding the core, and the star will become a red giant.

These stars will never be hot enough to fuse helium. There may still be plenty of hydrogen left in the outer layers, but there is not sufficient temperature and pressure in the outer layers to sustain fusion. The fusion engine shuts down, and the star rapidly collapses. Stellar collapse is a violent process. The outer layers are thrown off (a star may lose 80% of its mass this way), forming a planetary nebula. The remaining material collapses into a white dwarf.

White dwarfs produce no heat, since fusion has shut down. They will, however, continue to emit heat and light as they slowly cool. The stellar collapse that produces white dwarfs generates massive amounts of energy, due to the release of gravitational potential energy. As a consequence, white dwarfs are born very hot (150,000 °K), and can continue to shine for a long time.

Stars with Mass > 0.5 S

Larger stars also go through the same phases, initially fusing hydrogen at the core, and then later expanding into red dwarfs as fusion moves outwards into a shell around the core.

However, the larger mass means that when the hydrogen eventually runs out and they collapse, enough heat is generated at the core to initiate helium fusion. As the star runs out of hydrogen, the core starts to collapse. The collapsing core generates enormous amounts of heat. The temperature rises far above what it was during the main sequence, when it was burning hydrogen (15-25 million °K). This extremely high temperature makes the outer layers expand, turning the star into a red giant. As the core continues to collapse, its temperature reaches up to 100 million °K, at which point helium fusion begins.

In larger stars (> 2.25 S), the temperature rises fairly fast as the core collapses, and quickly reaches the point where helium fusion can begin. At this point, helium fusion starts generating heat which prevent further collapse. But for smaller stars (< 2.25 S), the collapse can proceed pretty far before the core is hot enough to initiate helium fusion. In fact, the core can collapse far enough that matter at in the core becomes degenerate, and it's degeneracy pressure preventing further collapse. If this happens before helium ignition, we see a helium flash. A helium flash is simply helium ignition starting in degenerate matter instead of normal matter. Degenerate matter is a good conductor of heat, so the helium ignition spreads very quickly, and heat is easily transferred away from the core, preventing the core from heating up rapidly. This allows a lot of helium to fuse very rapidly, before the core temperature rises far enough to slow it down - resulting in a "flash". The star can produce 100 billion times its normal output for a few seconds.

Class
Temperature °K
Color
Mass
Radius
O
>30,000
blue
>16 S
>6.6 R
B
10,000 - 30,000
blue-white
2.1 - 16 S
1.8 - 6.6 R
A
7.500 - 10,000
white
1.4 - 2.1 S
1.4 - 1.8 R
F
6,000 - 7,500
yellow-white
1.04 - 1.4 S
1.15 - 1.4 R
G
5,200 - 6,000
yellow
0.8 - 1.04 S
0.96 - 1.14 R
K
3,700 - 5,200
orange
0.45 - 0.8 S
0.7 - 0.96 R
M
<3,700
red
<0.45 S
<0.7 R
Spectral Classes of Stars. The mass is a multiple of "S" which represents 1 solar mass. The radius is a multiple of "R", which represents 1 solar radius.

The star again reaches an equilibrium, based on helium fusion, and shines brightly. In time, the helium at the core is exhausted, and helium fusion moves to a shell around the core. The star again expands into a red giant, burning helium. After some time, the helium is also exhausted, the star collapses, and may form a planetary nebula and a white dwarf.

Even larger stars can repeat this cycle, fusing progressively heavier elements. The cycle remains the same - the fusion starts at the core, moves to a shell surrounding the core when the core is exhausted (again swelling the star into a red giant), and then collapses when the fuel runs out. Stars that are larger than the Sun can go through these cycles several times, moving in and out of the red giant phase. Successive fusion stages last for shorter periods. For example, a star might be fusing hydrogen for billions of years, but when it gets to silicon, it uses up all the available silicon in only a few days.

Large stars (~10 S) can acquire an onion-like layered structure as a result of these processes. As each element fuses, the resulting products rain down towards the center, while convection currents bring in fresh material from outside the fusing shell. The heaviest elements are towards the center, so towards the end of the stars fusion life, it will have an iron-rich core, with concentric rings rich in silicon, oxygen, neon, carbon, helium, and finally hydrogen. This is important in the final collapse, in which the iron at the center plays an important role, as will be discussed later.

Note that very massive stars (~40 S) may never become red giants. They burn much hotter and produce powerful stellar winds which blow off the outer layers before they could burn through their hydrogen and reach the red giant stage. Red supergiants, therefore, are formed from massive stars that are still less than about 40 S in mass. The theoretical limit for a star's size is about 120 S, after which it would simply disintegrate from the radiation pressure of its own stellar winds.

As the fusion moves up the periodic table, it reaches iron. There is no lighter element than iron available in the core that can fuse, everything else has been used up. At this point, no matter how massive the star, fusion has to stop, since the binding energy per nucleon peaks at iron. Fusing iron, or elements heavier than iron, does not produce net energy - it absorbs energy.

This is when the fusion engine finally starts to shut down for good. If a star reached the iron stage, it would have been fairly massive to begin with. As it collapses, the core shrinks rapidly, and the core temperature rises. It reaches the point that the iron in the core fuses. However, the fusion of iron absorbs energy instead of generating energy. This sudden and massive absorption of energy chills the core, and stops all fusion abruptly. The star implodes under its own gravity.

The rebound from the implosion can create a supernova - one of the brightest objects in the sky. For a few days, the supernova can be brighter than a whole galaxy of stars. The core then becomes a white dwarf, or a neutron star, or black hole, depending on its mass.

Fusion in Main Sequence Stars

The fusion process in main sequence stars is often termed the p-p chain (the proton-proton chain), but this may be misleading, since it involves a lot more than protons. The chain is described below. Please note that this only describes main sequence stars. While several other elements appear in the chain (Beryllium, Lithium, Carbon, Nitrogen, Oxygen, etc.), these are simply intermediaries, and there is no net production of these elements. These elements are not being used up, as would happen later, when the star completes the main sequence and starts fusing other elements for fuel (except for lithium, see lithium burning).

The p-p process is represented below using the same notation used to describe chemical reactions. Note that e represents an electron, ν represents a neutrino, and γ represents gamma radiation (photon).

COMMON 1H + 1H ⇒ 2H + e+ The P-P chain consists of a common portion, and a number of sub-branches. All of them result in the production of He-4. Which branch is more active depends on the temperature of the star's core.
2H + 1H ⇒ 3He + γ
e+ + e- ⇒ 2 γ
P-P I BRANCH 3He + 3He ⇒ 4He + 2 1H Dominant at core temperature of 10-14 million °K. Not active at temperature below 10 million °K.
P-P II BRANCH 3He + 4He ⇒ 7Be + γ This branch is dominant at temperatures of 14-23 million °K. This branch is the reason why the core of main sequence stars contains no lithium, which is one way to distinguish them from brown dwarfs.
7Be + e- ⇒ 7Li + ν
7Li + 1H ⇒ 2 4He
P-P III BRANCH 3He + 4He ⇒ 7Be + γ Dominant at temperatures >23 million °K. Only produces 0.11% of the Sun's energy, but does produce some very high energy neutrinos.
7Be + 1H ⇒ 8B + γ
8B ⇒ 8Be + e+ + ν + γ
8Be ⇒ 2 4He
P-P IV BRANCH 3He + 1H ⇒ 4He + e+ + ν Predicted, but never observed. Probably because it's very rare.

 

Since most stars are contaminated with other elements besides hydrogen and helium, another fusion chain can also occur. This is the CNO chain (carbon, nitrogen, oxygen process), which also results in the production of He-4 from H-1, although it uses other elements as intermediaries.

FIRST BRANCH 12C + 1H ⇒ 13N + γ This cycle starts and ends with C-12. A proton is used in 4 different steps to create different isotopes of C, N and O, and a He-4 is produced at the end.
13N ⇒ 13C + e+ + ν
13C + 1H ⇒ 14N + γ
14N + 1H ⇒ 15O + γ
15O ⇒ 15N + e+ + ν
15N + 1H ⇒ 12C + 4He
SECOND BRANCH 15N + 1H ⇒ 16O + γ This process starts with N-15 to produce N-14 plus a He-4 at the end. During the process, 3 protons are used. The N-14 produced at the end is a common point with step 3 of the first branch.
16O + 1H ⇒ 17F + γ
17F ⇒ 17O + e+ + ν
17O + 1H ⇒ 14N + 4He

 

The CNO process only occurs in stars which already have a presence of carbon, and only above core temperatures of 15 million °K. At temperatures above 25 °K, the CNO process is the main source for converting hydrogen to helium. Since core temperature largely depends on the star's mass, the CNO process only occurs in larger stars. Our Sun's core temperature is around 13.6 million °K, which is insufficient for the CNO chain. The Sun produces its energy through the P-P chain only.

Stars that are larger than about 1.2 S, with cores hotter than 15 million K have fusion through the CNO chain. At 2 S, about half the fusion energy is produced by the CNO chain and the other half by the P-P chain. At 3 S and higher, pretty much all the helium production happens through the CNO chain. These numbers are for stars which have the same relative abundance of elements as the Sun.

Stars of masses up to 3 S can burn hydrogen only. The larger of these will go through the red giant phase, as the hydrogen fusion moves from the core to a shell around the core. Stars >3 S are hot enough to fuse helium after the collapse. Stars larger than 8 S can fuse heavier elements. Fusion of heavier elements follows different processes:

As mentioned earlier, the binding energy per nucleon peaks at around iron in the periodic table. Some nickel forms, which decays into cobalt (half life about 6 days), which in turn decays into iron (half life about 77 days). However, at this point the star doesn't have any time left. The silicon burning process took about a day, and at the end of this there is no more fuel that can be fused to produce energy.

The star starts to collapse rapidly. The collapse raises the core temperature to about 5 billion K. However, with nothing left to burn, there is no way to oppose this collapse with pressure generated by a fusion reaction. At this high temperature, the iron in the core fuses. However, the fusion of iron is an endothermic reaction, which absorbs massive quantities of heat, cooling the core. This further accelerates the collapse, and within a few seconds, the star implodes.

The implosion of massive stars is one of the most powerful events in the universe. The outer layers are stripped away, and the star can lose 20% to 80% of its mass in this fashion. Small stars lose their outer skins and collapse into white dwarfs. Massive stars collapse much more violently. The implosion is so powerful that the rebound spews matter outwards at speeds in excess of the escape velocity. This is a Type II supernova. The remainder of the core (about 2-3 S from a star that was originally 8-11 S) collapses into a neutron star. Even more massive stars can collapse into black holes.

Continue to read about White Dwarfs and Neutron Stars.