Monday, April 8, 2013

The Sun Part 4: Helium Eventually Seals The Sun's Fate

The Sun Approaches The End of The Main Sequence Phase

The Sun's core consists of protons (hydrogen nuclei) and alpha particles swarming with very fast moving electrons. Alpha particles (helium nuclei) are the heaviest particles in the plasma. They tend to condense toward the center of the core, forming a helium-rich inner core zone where no fusion takes place (yet). This inner core of helium gradually forces the nuclear fusion reaction outward. This means fusion is forced into a slightly cooler less dense zone, where it is not as easily sustained. As fusion slows, outward pressure decreases and gravity causes the core to condense. As long as the Sun remains in the main sequence phase, with enough fusable hydrogen available, the core condenses and heats up and the fusion rate increases once again. This process maintains a finely tuned equilibrium that operates over most of the Sun's lifespan, but eventually overall fusion pressure falls as the pool of available hydrogen, under sufficient pressure and heat to fuse, grows smaller, and what's left is continually forced outward. Inward gravitational force begins to win out over outward fusion pressure and the density of the core begins to increase rapidly, adding pressure to the already intensely pressurized helium-rich zone in the center.

Hydrogen now fuses only in a thin shell around the core. The Sun, at this point is becoming a red giant. The density of the core has been increasing sharply, heating it so intensely that it rapidly heats a layer surrounding it. Despite its distance from the core, the hydrogen in this layer is heated enough to begin to fuse at a rapid pace. This new phase of intense fusion activity increases the Sun's luminosity by a factor of thousands. This rapid rate of fusion, however, can only last so long, perhaps as briefly as a few hundred million years. On the Sun's scale that's a very short period of time.

The Sun Evolves Into A Red Giant

Meanwhile, the outer layers of hydrogen plasma expand greatly as they are heated. The Sun's radius balloons outward hundreds of times larger than it is now. The outer envelope of gases cools at it expands because its thermal energy is spread out over an increasing area. Its lower surface temperature now gives it a red appearance as the Sun's blackbody radiation shifts from white (around 5500°C) toward the red end of the visible spectrum (around 3500°C).


The diagram left shows how drastically the Sun will change as it evolves into a red giant.

Meanwhile, the helium center has been compressed into a new state of matter called degenerate matter.

This kind of matter operates under a new set of behavioural rules, and it brings the Sun, along with most other stars, to various kinds of violent endings.

Helium In The Core Becomes Degenerate

At this point, the helium no longer follows ordinary gas laws. Before this point, the pressure of the completely ionized helium plasma followed the ideal gas law where pressure = density x temperature x the Boltzmann constant. Now, the plasma no longer exerts an outward pressure dependent on temperature. Its pressure instead comes only from degenerate pressure. The intense pressure in the helium core tries to force all the electrons into lowest possible quantum energy states. It's a bit like forcing them back into an atom-like state but going much further. In this case, it tries to force countless electrons into the same 1s orbital, regardless of the spin-determined two-electron orbital maximum that stems from the quantum mechanical nature of electrons. The electrons, being fermions, resist because they follow the Pauli exclusion principle. In atoms, electrons tend to fill the lowest energy levels first, but in normal gases, there are actually many empty energy levels and the electrons in each atom are free to move up and down them, depending on their energy. In degenerate plasma, electrons (with tremendous kinetic energy) are forced to fill up the lowest energy levels and they are locked in as a group there. An electron in this state of matter, being stuck in a minimum energy quantum state, can't give up any extra energy by moving into a lower energy level and emitting a photon. It can't absorb an electron and move into a higher energy state either. However, it is still "laterally" mobile because the matter is still in a plasma state. The difference between an ordinary gas atom and a degenerate state atom is shown below right.

On the right hand side above, electrons resist being forced into the same quantum state because they are following the Pauli exclusion principle. This resistance manifests as outward pressure on the system, called degenerate pressure. Unlike an ideal gas that experiences outward pressure as the kinetic motion of its atoms increases, degenerate plasma experiences only degenerate pressure, which does not depend on temperature at all. This means there is no longer any stabilizing and cooling expansion possible in the core. Even though the outer layers of the Sun as a red giant expand greatly, an inner layer of plasma around the helium center continues to contract under gravitational pressure, and the temperature continues to rise. Suddenly, the temperature spikes at over 100,000,000°C and at this point helium nuclei are hot enough to fuse, using the triple alpha process, shown below left.


This is a runaway reaction called helium flash. In a matter of seconds, three quarters of the Sun's helium fuses and the temperature soars, creating so much energy that the luminosity would equal that of the entire Milky Way, if it could be observed. This energy burst, however, takes place deep inside the core, where the energy goes into a soaring helium fusion rate rather than blowing up the star.

The Sun Enters The Horizontal Branch

After the helium flash, the Sun shrinks back down to about ten times its current size. It is now on what is called the horizontal branch of star evolution. Over the following 100 million years it will be about 50 times more luminous than it is today and it will expand once again, but this time very gradually. However, as helium runs out, the Sun will once again go through an intensified expansion phase where it will once again become a red giant. The sudden expansion into a red giant happens much faster this time and the Sun will become even larger and more luminous than it did before. The Sun will last only about 20 million years in this second red giant phase, called the asymptotic branch, because it is growing increasingly unstable all the while.

The Sun's core now has a new composition. Most of the helium has fused into carbon as well as oxygen. If you look at the diagram above of the triple alpha process, you'll notice that three helium nuclei (4He) don't fuse directly into one carbon nucleus (12C). When the core is hot enough it begins to fuse helium into beryllium (8Be). However, no new stable nuclei form yet because beryllium-8 is very unstable. As the core continues to grow even hotter, helium nuclei begin to fuse faster than the beryllium can decay. Now that both beryllium and helium are available, it is energetically favourable for them to fuse together to create a stable carbon nucleus, and carbon builds up. Some carbon nuclei will then fuse with additional helium nuclei to create stable oxygen (12O) nuclei as well. The oxygen-creation reaction is not shown in the diagram above. Each of the three fusions releases gamma radiation and a tremendous amount of energy.

The Sun Expands Into An Unstable  Red Giant

Meanwhile, in a thin shell around the core, helium is soon hot enough to fuse. Outside this fusion layer, the Sun's plasma rapidly expands even further outward than it did during its first red giant phase, this time probably far enough to engulf Earth. In a thin shell around the helium, hydrogen is also hot enough to fuse. This reaction restricts the very thin layer of helium fusing underneath it, preventing it from fusing stably. Helium in the hydrogen shell builds up until the helium shell beneath it ignites in a massive nuclear explosion. The Sun expands and cools, shutting off hydrogen shell fusion. Then, the Sun contracts gravitationally and the whole cycle begins again. Each of these thermal pulses, as they are called, lasts a mere 100,000 years or so, becoming more intense each time, and each time the Sun loses a significant amount of mass as material blasts outward in the explosion. Most researchers expect the Sun to experience four pulses before it loses its outer envelope of plasma altogether, leaving the Sun with about half of its current mass.

The graph below follows changes in luminosity and surface temperature as the Sun leaves the main sequence phase (the black line), expands into a red giant, enters the horizontal phase, and then expands once again into a red giant, before it moves on to a much more quiescent phase as a white dwarf star (top line). The second, and final, red giant phase is simplified in the graph. It will likely include four "mini-phases" as described above, where luminosity and surface temperature swing up and down following the Sun's expansion and contraction. This eventful solar "last stand" will begin about 4.5 billion years from now, when the Sun is about 10 billion years old.
When the Sun reaches its final red giant phase, Earth will probably be incinerated but distant stars and moons, such as Titan, may be offered a brief window of opportunity for life to evolve from the energy boost to the rich compliment of organic compounds there.

Star cores generally experience three kinds of outward pressure: 1) radiation pressure, 2) kinetic pressure according to the ideal gas law, and 3) degenerate pressure. Degenerate pressure is technically always present in matter but its effects are overshadowed when matter is not in a degenerate state.

The helium burst creates tremendous radiation pressure. The sudden flash of intense gamma radiation exerts outward pressure because each photon created carries momentum. A solar sail could someday utilize the (much lower) radiation pressure from the current Sun for interplanetary travel, although the pressure in this case more accurately comes from fast-moving particles as well as from electromagnetic radiation.

The Sun Enters Its Final Phase As A White Dwarf

Once the Sun ejects its outer plasma layers, forming a planetary nebula, which will surround it at a distance, much of what's left is carbon-oxygen core material. Ultimately the Sun becomes a white dwarf, a dense stellar remnant in a degenerate matter state. It is very hot, emitting blue-white light. We can see from a distance what our Sun as a white dwarf might look like in the photograph below. The star itself is a very tiny white dot slightly off center to the left. It is surrounded by a planetary nebula called NGC 2440 (photograph taken by the Hubble space telescope).

Ultraviolet radiation from the white dwarf makes the gases glow. This is one of the hottest white dwarfs known, with a surface temperature of 200,000°C.

All fusion has been exhausted so it will eventually cool, but the rate of cooling is astoundingly slow. Our current Sun would take about 20 million years to cool off if nuclear fusion suddenly stopped in the core. The entire current Sun is composed of ordinary matter so all of it can lose heat through thermal radiation. The degenerate matter in a white dwarf has no mechanism to release energy. Only the thin outer shell of ordinary matter surrounding it can release energy as thermal radiation. When a white dwarf starts out, it is very luminous. The one above is emitting as much light as 500 current Suns. This radiation comes from the thin outer shell of ordinary matter. The degenerate matter underneath is in a locked state, where no photons can be absorbed or emitted because the electrons are locked in low energy orbitals.

This means that the inside of a white dwarf stays very hot for a very long time. Even the oldest white dwarfs in the universe maintain an almost constant internal temperature of about 10,000,000°C, and a surface temperature of just under 2800°C.

The outer shell of non-degenerate matter in a white dwarf releases some energy, so it will eventually cool from 10,000,000°C to about 9000°C, and then maintain this temperature, radiating blackbody radiation that will make it appear bluish white for tens of billions of years. It should very gradually dim to red and then, theoretically, eventually, to black, but our universe may not exist long enough to house such objects. It is difficult to say with certainty how long it would take the Sun as a white dwarf to cool completely. Researchers believe a white dwarf, like all objects, should contain dark matter, which might decay very slowly, releasing heat as it does so. Protons in the degenerate matter may also eventually decay and they too could contribute some heat to the star.

White Dwarf Degenerate Matter is a Fermi Gas

Thermal radiation isn't possible from degenerate matter, but this matter is highly electrically conductive because the electrons are "laterally" mobile, much like they are inside metals. Although neither degenerate matter nor metals are what we'd think of as gas states, physicists can describe this kind of group electron behaviour as a Fermi gas.

As a white dwarf, about half the Sun's current mass will be compressed into a sphere the size of Earth. That represents a density similar to a car crushed down to a sugar cube. It will stay this way forever, even as it cools. The degenerate matter in a white dwarf will never spring back into a normal atomic state, because there is no mechanism available to unlock the electrons within it. The pressure in degenerate matter comes only from the kinetic energy of the degenerate electrons in it. Adding heat doesn't increase this energy and losing heat doesn't decrease it, so the pressure squeezing the matter into its degenerate state remains in place even as the star cools. Nothing will decrease the degeneracy pressure but additional mass will increase it, and instead of making it larger as you would expect with ordinary matter, it would make it smaller still.

White Dwarfs, Neutron Stars and Black Holes

So far I have been describing electron degenerate matter. Neutron degenerate matter is also possible inside stars, but it all depends on mass. A white dwarf remnant is always left with fairly low mass. About half the Sun's mass, for example, will be blown off in the planetary nebula, so the Sun as a white dwarf will be about 0.5 solar mass. No white dwarf can exceed a maximum of 1.4 solar masses. Only stars of low to medium mass, like the Sun, end as white dwarfs (electron degenerate matter). Almost all stars in the Milky Way, most of which are red dwarfs, fall into this category. They will all eventually end as white dwarfs. More massive stars end much more spectacularly. Stars with between 8 and 20 solar mass explode as supernovae, leaving behind remnant cores called neutron stars. These stars are made of neutron degenerate matter.

A white dwarf can pull off a supernova, but only if it attracts enough mass. If a white dwarf were to receive mass from a companion star or if it gradually accreted enough nearby gas and dust, it could eventually exceed the mass limit of 1.4 solar masses. It would explode as a Type 1a supernova, thanks to a process called carbon detonation. This is a runaway carbon fusion reaction that, unlike the runaway helium fusion reaction described earlier, releases enough energy to unbind the star altogether. Type 1a supernovae are fairly common and they always explode with identical brightness, making them perfect standard candles for astronomers.

Very massive stars, more than about 20 times the Sun's mass, explode and leave behind black holes, in which matter entirely collapses, shown to the right in the diagram below.

Comparing White Dwarf Electron Degenerate Plasma With Metals

Does the white dwarf cartoon, above left, remind you a bit of a metallic lattice? For a refresher, scroll down to Metallic Bonding in this Scientific Explorer article. In a metal, the outermost electrons are so loosely bound to their atoms that they move about freely. Some researchers call this an "electron sea." All the electrons exist in one shared molecular orbital, and this shared (same energy) quantum state, while obeying the Pauli exclusion principle, allows electrons to flow, making the metal electrically conductive and allowing some metals to have magnetic properties as well. Both metals and white dwarf plasma are considered by some researchers to be examples of electron degenerate matter. They both behave like Fermi gases, as mentioned earlier. Both examples also exhibit a crystalline structure. The electron degenerate plasma in a white dwarf is thought to resemble a diamond-like crystalline solid. There are important differences though. Degenerate pressure may be one reason why metals resist compression but it is not the most important source of internal outward pressure, whereas in white dwarf plasma it is. Only the outermost conducting electrons in metals are degenerate. The inner electrons remain in ordinary electron orbitals. An exception here is metallic hydrogen because it has only one electron per atom to free up. Metallic hydrogen, like white dwarf matter, is degenerate matter. It relies only on degeneracy pressure. Like white dwarf matter, it is expected to have a crystalline structure composed of positive nuclei (protons here) surrounded by an electron sea. I should note too that Wikipedia limits electron degenerate matter to matter that is compressed into degeneracy, technically excluding metals then, but other sources do not.

Electron degeneracy is a fascinating concept to ponder on. It reveals some of the oddness of the quantum mechanical nature of electrons, and it ties in with a puzzle I explored recently in the article Electrons, Strings and Spooky Action, if you are curious.

To sum up this article, try this Naked Science 45-minute video, describing the Sun and its ultimate fate:

Our Sun has another 5 billion years to go before it ends its life as a white dwarf. Before then, it will continue to experience a mysterious regular cyclic pattern of activity that peaks every 11 years. During these peaks, we enjoy more colourful auroras around the poles and, sometimes, we endure intense and destructive geomagnetic solar storms as well.

This 11-year cycle of activity is the focus of intense current solar research in an effort to learn how to predict damaging and dangerous solar storms. Scientists know that each cycle ends with a dramatic magnetic flip-flop, like a bar magnet suddenly reversing its poles. We will start by peering deep into the Sun to see how its magnetism works, next, in The Sun Part 5.


  1. You ask - "Are you curious?" To which my answer is a resounding "Yes!"
    In an article in the Guardian newspaper on his 70th birthday, Stephen Hawking was quoted as saying
    "Remember to look up at the stars and not down at your feet ... Try to make sense of what you see and about what makes the universe exist. Be curious."

    I'm 65 next birthday - and grow increasingly fascinated by the joy of finding things out (another quote, I realise! Feynman of course).

  2. What awesome quotes, Margarita! I must admit I'm a huge Feynmann fan myself :-). I'm always excited to meet fellow curious explorers. Have a great 65th when it comes and thank you!