Posted 05 February 2010


In Celebration of Psalm Nineteen:
God's handiwork in Creation


CAUTION: UNDER CONSTRUCTION: The numerical values quoted here need to be thoroughly checked for errors!

Introduction. In the First Fifteen Minutes after the creation of the universe in the Big Bang, all of the stable material in the universe exists as negatively charged electrons, and positively charged hydrogen and helium nuclei[FOOTNOTE: Hydrogen H-1 (80% by mass) and H-2 (Deuterium -- 0.08%), Helium H-4 (20% by mass), and trace amounts of He-3 (0.01%) and Lithium Li-7 (10-7%) nuclei]. Anti-matter is virtually non-existent -- its remnant showing itself as about 108 photons for every baryon.

The entire universe is a completely ionized plasma because it is far too hot for neutral atoms to form.
On all but the very smallest scale the early universe is neutral because of the strong mixing effect of the plasma stew of positively and negatively charged particles. It is probably fair to picture the plasma as vast numbers of virtual helium and hydrogen atoms forming and unforming in a hot equilibrium.

Although the electrical force is much stronger than the force of gravity, the electrical forces are effecively neutral on even very moderate scales of size and so the force of gravity is at work from the very first minutes accentuating minute inhomogeneities in the (nearly) uniform density of matter and ultimately forming the material universe into what will become regions of gravitational attraction. This is a very slow process -- because gravity is itself a very weak force and because the universe is very nearly uniform[FOOTNOTE: A precisely uniform universe will remain uniform because the forces of gravity are exactly balanced. But even the smallest non-uniformities will cause centers of gravitational attraction to form, and these will become more pronounced with time. The catch is, that the gravitational centers must exist but they must not include too much mass, or else they might collapse into super-massive black holes. This amounts to yet another Goldilocks paradox: not too large, not too small; just right.] -- and it will take hundreds of millions of years before the first stars and galaxies form.

Cosmic Background Radiation. About 380,000 years after the Big Bang, the ambient temperature of the universe drops to about 4,000°, a level at which proper atoms can form. When this happens, neutral atoms gradually freeze out of the plasma stew. This is a slow process (unlike the rapid process when quarks froze out to form protons and neutrons in the first seconds) but eventually the plasma is replaced by netural atoms. At this point, the universe became transparent to light. The Cosmic Background Radiation (2.6° K) dates back to this time, red-shifted by the general expansion of space over the intervening 13.7 billion years.

Star and Galaxy Formation. Over time the effects of gravity slowly cause the universe to separate out into numerous local regions or molecular clouds. Over time gravity causes the regions to contract, the effects of gravity strengthen, and temperatures rise due to gravitational acceleration. This process is called 
gravitational collapse.

Molecular clouds are sometimes referred to as star nurseries, because they are the site of new star formation. One nearby example of a star nursery is the Orion nebula, designated M42, situated in Orion's sword (Figure 1). It is a site where many new stars are forming. This nebula is the remnant of previous stars, since it shows the presence of many elements other than hydrogen and helium.

Figure 1
Orion Nebula, M42 (distance 1300 lightyears).

Note: This image is a false color composite where light detected at wavelengths of 0.43, 0.50, and 0.53 microns is blue. Light at wavelengths of 0.6, 0.65, and 0.91 microns is green. Light at 3.6 microns is orange, and 8.0 microns is red. Image credit: NASA/JPL-Caltech/STScI (11/7/2006).

The Orion Nebula (Figure 1)
The Orion Nebula is at a distance of 1340 ± 20 lightyears. It is located in the same branch of the Milky Way galaxy as our own sun. It is part of a ring of molecular clouds (called the Gould Belt) that encircle the Sun and is estimated to have formed about 30 million years ago.

Much of the dark matter in the Orion Nebula is back-lighted by the region of active star formation (the bright region in the upper center).

Large molecular clouds form galaxies. A black hole is usually at the center of a galaxy. The surrounding mass orbits it and separates into numerous local clouds and local regions of attraction. Eventually the heat of a local cloud rises to the point at which the molecules become ionized (about 5,000 °K), and further heat to the point of star formation where nuclear fusion occurs.

The precise details of what happens upon nuclear ignition depends on the size, composition and density of the star. The first stars to form are made up of primordial hydrogen and helium. The heavier helium nuclei tend to migrate to the star centers, with the lighter hydrogen nuclei on the surface.

What happens next depends on the total mass and composition of the star. Sun-like stars (under 5 solar masses) begin with hydrogen burning (the p-p reaction). It is a relatively slow process because it depends on quantum tunneling, a process in which two colliding protons fuze by jumping over the p-p coulomb barrier.  In the star interior, other nuclear processes occur at higher (more energetic) temperatures.

All nuclear processes in the stars are exothermic nuclear fusion -- they produce excess energy. This energy results in an outward pressure that balances the gravitational forces, and so the star maintains a balance of forces as long as there is material available for nuclear fusion to occur.

All of the elements up to the iron and nickel are the products of exothermal fusion produced in the stars from the fuel of lighter elements. When a star exhausts the fuel of lighter elements, it contracts and heats further and then  continues to burn heavier elements. The result of this is that the sky displays stars at all stages of burning, which depends on the star's mass, available fuel and the stage in the star's burning. The Hertzsprung-Russell (H-R) diagram (Figure 2) depicts the various star types and stages. As a star passes through its various stages, its position in the diagram changes in a predictable way. Ejnar Hertzsprung and Henry Norris Russell first developed this diagram 1910-1912 in their work at classifying star types (a lifetime pursuit of
Ejnar Hertzsprung. The physical basis for the diagram was not understood until the 1950s.

Hertzsprung-Russell diagram
Figure 2
The Hertzsprung-Russell Diagram
Star colors are approximately as shown

The Lifecycle of Sun-like Stars.
In the 1950s scientists discovered that stars are the fiery forges of the elements. Prior to this time many scientists assumed that the elements either are eternal or that they were created in the cataclysm of the early moments after the Big Bang. Several, notably Fred Hoyle, disputed this, and with the mathematical insight of quantum mechanics, they determined that the stars are the true forges of all elements heavier than hydrogen and helium. The crowning achievement of this reasoning process came in the 1957 paper, Synthesis of the Elements in Stars which created an entire branch of science -- stellar nucleosynthesis -- in one fell swoop. This paper became so famous that it is commonly referred to by the initials of its authors, B2FH ("B-squared F H"). This paper describes the nuclear processes that create the elements, explains the physical basis for star placement in the H-R diagram, and describes how stars migrate through the H-R diagram over their lifetimes.

It was while contemplating the work that led to B2FH, that Fred Hoyle made his famous statements: "I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars," and "A common sense interpretation of the facts suggests that a super intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question." (See the box on Fred Hoyle).

In particular, the life cycle of the Sun from the first formation out of a particle cloud about 4.55 billion years ago, to its future death as a white dwarf is shown in Figure 3.

Solar Life Cycle
Figure 3
Life Cycle of the Sun (from Wikipedia)

The B2FH paper includes the following diagram (Figure 4) which gives the timescale for different stages in the star's life. I will make further remarks on the various burning processes in the following, but note one particularly significant fact: Only hydrogen burning (the process that characterizes the Main Sequence of the H-S diagram) has a duration measured in billions of years. All other stellar processes are much faster.

We will see in later chapters that natural processes required to build up a habitable environment require times on the order of billions of years. Thus only hydrogen burning is able to provide a steady source of energy and light for the length of time needed to support a habitat suitable for life. This is remarkable because hydrogen burning (as we shall see) involves an "impossible" process called quantum tunnelling. It is the difficulty (and hence rarity) of this process that accounts for the long-drawn-out burning that allows the stars to last for the necessary billions of years. See the box on  Quantum Tunnelling.

Creation of the Elements in Stars
Starburning Timescale
Figure 4
Timescale for Nucleosynthesis in stars
Source: B2FH p. 558

Note: The various processes in this diagram are discussed below.

Element Formation in Stars: Hydrogen Burning (Main Sequence Stars).

The stars in the Main Sequence of the H-R Diagram obtain their energy by burning hydrogen into helium. This is how the Sun gets its energy. Hydrogen burning - see the box - is the first stage of a star's life and is the slowest star-burning process. It provides relatively steady output for a long time.

Over the lifetime of the Earth (4.5 billion years) the Sun has been a remarkably steady source of heat and light. Over that time its lumnosity has increased about 25%, closely matched by a decline in the radioactive heating of the Earth's surface from the interior[CHECK NUMBERS!]. The Earth should be habitable for at least another billion years, and then the Sun will migrate off the main-sequence move upwards toward the red-giant region of the H-S diagram, gradually growing larger in size and luminosity.

The hydrogen burning in the Sun takes place near the Sun's core (temperature 13.6 million degrees -- around 0.01 MeV). The Sun as a whole is a hot plasma (ionized atoms) but nuclear burning occurs only near the core. At the surface of the Sun the temperature is a balmy 5,800° K, which accounts for its white color (3,500° K is considered "soft white", 4,500° is blue-white and 5,500° K is "hard-white").

Hydrogen Burning
Hydrogen Burning -- the p-p reaction -- converts hydrogen into helium and takes place at a temperature of
13.6 x 106 °K -- around 0.01 MeV. It is the nuclear reaction that occurs at the core of Sun-like stars. The curious (and at first puzzling) feature of hydrogen burning is that it takes place at temperatures that are too low for the kinetic energy of the protons (hydrogen nuclei) to overcome the coulomb barrier between them (which would require over 50 MeV).  The actual process  is quantum tunneling.

Two hydrogens fuse to form Deuterium, ejecting a neutrino and positron and 0.42 MeV. The positron of course almost immediately annihilates by meeting an electron, producing two 0.51 MeV photons. The Deuterium fuses with another hydrogen to form Helium-3 and 5.49 MeV. Two of these then form Helium-4 and release 2 protons and 12.86 MeV.

Overall, the reaction is an exothermal reaction that converts 4 protons and 2 electrons into a Helium-4 and 2 neutrinos and produces 21.23 MeV. [CHECK ALL #s]

Hydrogen Burning
Figure 5
Hydrogen Burning

 Sharp Point

Sun-Like Stars and Quantum Tunnelling

A habitable planet must have a Sun that burns steadily for billions of years. Over the nearly 4 billion years that the Earth required to build a habitable environment, the output from the Sun has slowly increased about 25%, which is a close match to the slow decrease in the Earth's heating due to radioactive decay. The result is a temperature environment that has held within narrow limits over the entire 4 billion period.

Only the hydrogen burning process (p-p burning) can maintain a steady output for such lengths of time. It is long-lived because the process is difficult to do and hence occurs at a slow rate. No other stage of stellar burning is comparable. This process depends on quantum tunneling. This occurs at temperatures that are too small to overcome the coulomb repelling force, so the wave functions of the two protons tunnel through the coulomb barrier (with a low probability) to form a mass-2 nucleus. Classically this reaction would be impossible unless the two protons were exceedingly energetic (a kinetic energy equivalent to a temperature of 60 million degrees ??CHECK?? -- wouldn't there be a lot of electron shielding to reduce the energy?). In fact, quantum tunnelling occurs at 13.6 million degrees.
Quantum tunnelling is based on the fact that all particles (such as protons) have a dual particle-wave duality (just as photons do).  The wave representation of a proton is a three-dimensional space-filling probability disribution whose amplitude at a (3-dimensional) point X is interpreted as the probability density that the proton exists at X. This wave function peaks at the nominal location of the proton and then tails off towards zero in all directions. If (the wave functions of) two protons approach, the coulomb force distorts the wave function, but nonetheless the two wavefunctions fill space, and there is a small but non-zero probability that the protons are close enough to form a di-proton pair. This is unstable and almost immediately one of the protons decomposes into a neutron, positron and neutrino (called radioactive beta-plus decay in the table below), forming a Deuteron as shown in Figure 5. A second quantum tunnelling forms tritium, and two tritiums combine to form helium-4 plus two protons and a lot of energy.

Element Formation in Stars: Helium Burning and Carbon Formation. As the slow hydrogen burning process proceeds, the waste product helium gradually accumulates at the core. Since the temperature is too low for further burning, the accumulated helium contracts under gravity, and heats up from about 14 million to over 100 million degrees. At this point, helium - helium burning occurs.

At this point a dilemma arises. As we noted in the previous chapter, the product of helium burning would normally be either Lithium (He + H with atomic weight 5,
half-life about 6.83985×10-22 s) or Berillium (He + He, atomic weight 8, half-life 2.6×10-6 seconds). Both of these are exceedingly unstable and immediately dissociate again. This is the so-called Lithium Barrier at atomic numbers 5 and 8, that prevented the formation of heavier elements in the first few minutes after the Big Bang.

The only apparent way to get past this barrier is to have a triple collision of helium nuclei forming Carbon-12. The problem is that triple collisions are very low probability events. Fred Hoyle, in 1953[FOOTNOTE:
F. Hoyle, D. N. F. Dunbar, W. A. Wenzel, and W. Whaling, Phys. Rev. 92, 1095 (1953)] saw the only possible way out of this dilemma, namely that the Carbon nucleus must have a nuclear resonance at around 7.65 MeV. Subsequent investigation by Fowler established a resonance at 7.68 MeV.

The drama of this discovery is narrated in the following account[FOOTNOTE:]:

"Perhaps his most celebrated insight occurred in 1953  Fred Hoyle recognized that Salpeter's analysis in this work was incomplete. He pounced. If Salpeter's scenario were accurate, Hoyle supposed, stars would not produce enough carbon to match known cosmic abundances. Without known carbon abundances, human life—Fred Hoyle's life in particular—could not exist. Salpeter wrote:

"I calculated the rate for this indirect conversion of helium into carbon... in the summer of 1951 and published it in the following year. I noted in that paper that my calculated rate could easily be too low by a factor of 1000, say... but I did not have the chutzpah (or guts) to do anything about it: My energy production rate for red giant stars required a central temperature that was within the rather uncertain range given by stellar evolution theory at the time; my calculation would lead to most of the helium being converted to oxygen and neon instead of carbon, but I just did not have the guts to think of resonance levels that had not been found yet! A short while later Fred Hoyle demonstrated both chutzpah and insight... to show that there JUST HAD to be an appropriate resonance level in C[arbon], and he was able to predict its energy. Willy Fowler and his colleagues soon looked for Hoyle’s predicted resonance level and found it just where it should be."

"In a flash of inspiration Hoyle tried to make Salpeter's triple-alpha process work with an enhanced level in 12C. To his amazement he found that if the newly made 12C had a resonance at 7.65 MeV the reaction would proceed at just the correct rate. Hoyle crashed into Fowler's office without so much as a "by your leave" and urged him to measure the resonance levels in carbon. [Apparently Hoyle never published this insight -- which was verified two years later. dcb]

"More than half a century later, Salpeter recognized his role but has trouble forgiving himself for not seeing the door he left open for Hoyle. Astrophysicists who worked in that era say he's too hard on himself, and earned far more credit than he gives himself. 'The burning of helium into carbon is not really one [discovery] that I’m that proud of,' Salpeter told me. 'I goofed. In some ways I’m more embarrassed about that than about having done it.' I asked him why people still refer to it as the 'Salpeter process.' 'That’s just the nickname other people give to it,' he says. 'Hoyle figured it out. Let me put it this way, I’m a more pleasant guy than Fred Hoyle. Maybe they like me better. He was a slightly difficult guy to get along with. But a real genius.' "

See the box on the Triple Alpha Process.

Sharp Point          The "Impossible" Triple Alpha Process

Without two very minor and peculiar characteristics of the elements Carbon and Oxygen, the entire program of synthesis of the elements in the stars would not have happened.

"A common sense interpretation of the facts suggests that a super intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."[FOOTNOTE: Fred Hoyle, Steady-State Cosmology Revisited, Cardiff Press, 1980, cited in Fred Hoyle, "The Universe: Past and Present Reflections", Annual Review of Astronomy and Astrophysics, 20 (1982), p4. Also quoted in Michael J. Denton, Nature’s Destiny: How the Laws of Biology Reveal Purpose in the Universe, Free Press, 1998, p12.]

 Sharp Point

Fred Hoyle on the Laws of Nuclear Physics.

   "The genesis [of about half of the elements] depends on the oddest array of apparently random quirks you could possibly imagine.

   "I will try to explain what I mean in terms of an analogy....We would scarcely expect to find Government policy depending in a really crucial way on the fact that the Prime Minister possesses a moustache while the Foreign Secretary does not. These are my random quirks. And if we should find that Government policy depended in a really vital respect on the Minister of Works possessing a mole beneath his left ear, then manifestly we should be justified in supposing that new and hitherto unsuspected connexions existed within the field of political affairs.

   "Yet this is just the case for the building of many complex atoms inside stars. The building of carbon depends on a moustache, the building of oxygen on a mole, and if you prefer a less well known case, the building of the atom dysprosium depends on a slight scar over the right eye.

   "If this were a purely scientific question and not one that touched on the religious problem, I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars. If this is so, then my apparently random quirks become part of a deep laid scheme. If not, then we are back again to a monstrous sequence of accidents." Fred Hoyle, Lecture in Mervyn Stockwood, ed. Religion and the Scientists SCM 1959, p.64.

Carbon Production. In an "ordinary" world, one would expect carbon to be created as a binary collision between a beryllium or boron atom. But both of these are rare.  This leaves a triple collision of 3 helium atoms -- but triple collisions are also quite rare.

But we are not in an ordinary world! The production of carbon depends on two successive double collisions: two helium atoms collide to form beryllium-8. This is very unstable (about 7 E-17 seconds). But before disintegrating, it collides with another helium atom forming carbon-12.

Carbon production by Triple Alpha Process -- from Wikipedia

Element Formation in Stars: Oxygen, Neon and Magnesium. Carbon production is the gateway to all of the heavier elements. So it is good that the "impossible" triple alpha process works -- otherwise a rocky planet such as Earth could never have formed, and life could not have existed. But while the carbon bottleneck has been solved, there is another problem.  Carbon is literally the backbone of life -- it is the backbone of almost every structural molecule used in a living cell. So while it is necessary for heavier elements to be created from carbon, there must be a throttle that keeps a goodly amount of carbon around.

That throttle occurs in the production of Oxygen, which is formed by the reaction of Carbon with Helium: C + He -> O. Another nuclear resonance is involved in this reaction, but this time the end result is to facilitate the reaction but slow it down somewhat. 

Basic Reactions in Carbon Burning[footnote:Bradley S. Meyer et al., Nucleosynthesis and Chemical evolution of Oxygen (2004?)]
 (T~900x106 °K; d~105 g/cc)
12C + 4He + γ -> 16O  (T~300x106 °K,   d~1000 g/cc)
12C + 12C -> 24Mg + γ
12C + 12C -> 20Ne + 4He
16O + 4He + γ <-> 20Ne (resonance)

Carbon is the "ash" of the triple-alpha process described above (which is itself fairly slow because of the "uphill" effort to achieve quantum tunnelling).  This ash sinks and accumulates to form a carbon core. At the temperatures that support the triple-alpha process, the carbon cannot react further, so it accumulates and compresses under gravitational pressure, until density reaches 105 g/cc and the temperature arises to about 900 x 106 °K.  At this temperature, the carbon reacts with helium (at the surface boundary between carbon and helium) to form neon, magnesium and oxygen. The oxygen reaction also enjoys a nuclear resonance, but this time (in contrast to the case with carbon formation), the resonance energy level is a little below the combined mass-energy of C and He. This slows the reaction down somewhat, which is good, because if the reaction were too easy, then all of the carbon would fuse into oxygen and carbon-based life would not be possible.

Sharp Point          The Slightly High Nuclear Resonance in Oxygen

The position of a nuclear resonance in Oxygen is the second "coincidence" that makes it possible to have carbon/oxygen based life. In the case of carbon, the resonance was slightly above the combined mass-energy of Berillium and Helium. In the case of Oxygen, a similar resonance is slightly above the combined mass-energy of Carbon and Helium (7.68 MeV resonance vs. 7.65 MeV mass-energy). These two "accidents" determined  that the stars would produce similar amounts of Carbon and Oxygen. If the Oxygen resonance had been slightly lower, essentially all Carbon would have fused into Oxygen; if the resonance had been slightly higher, then only small amounts of Carbon would have fused into oxygen, which would have blocked not only oxygen production, but also the production of the higher elements.  The remarks of Hoyle refer to the combined effect of these two carefully chosen resonances. [CHECK SENSE OF DIRECTION!!!]

Element Formation in Stars: Other Elements up to the Iron Group. The description to this point shows how synthesis of the lighter elements proceed in stars. See the Summary of Nucleosynthesis in Stars for further remarks.

Nucleosynthesis in Stars -- Summary
Nucleosynthesis of the elements up to the Iron Group (Iron, Cobalt, Nickel) takes place within the stars in successive stages (See Figure 6). The burning (nuclear fusion) takes place in layers at the core, the hottest (highest atomic number) reactions at the core itself, with the others surrounding the core in shells of nuclear activity. At each stage, the "ash" sinks toward the core and is the fuel for the next stage of burning.

This process ends with the Iron Group (Iron, Cobalt, Nickel). These are the most efficiently packed nuclei, and mark the end of exothermic fusion. The heat released during the fusion adds to the heat energy of the star and keeps things burning. Fusion of elements above the Iron Group absorb rather than release energy, and so their nucleosynthesis (with the minor exception of Copper) cannot be sustained within the stars.

Silicon burns to form the Iron Group in the equilibrium process. The Iron Group elements sink to the center of the star and cannot sustain further nucleosynthesis, so the core collapses under gravity. If the star is large enough, the end result is a supernova explosion as the gravitational pressure forces the innermost electron levels into the nucleus.

The most common reaction involves fusion of Helium with a heavier element. This leads to elements with even atomic humber (Helium, Carbon, Oxygen, Neon, Magnesium, and Silicon). Nitrogen, an odd-numbered element forms from hydrogen fusing at the boundary between the H and He layers. Other elements and isotopes are the products of many different types of processes.  A summary of these processes is listed in the box below.

Mature star core burning
Figure 6
Nucleosynthesis at the Core of a Mature Star
Shortly before a Supernova

This end-stage of star nucleosynthesis typically occurs in suspergiant red stars, which end their lives in supernovas. The bright red star Betelgeuse in the Orion Constellation is one such star (See Figure 7). Some sources conclude that some copper is also formed in such stars. Copper is the first endothermic element, along with all heavier elements, and cannot contribute to star burning, so such production is a parasite, so to speak, of the other exothermic star burning.

Orion with Betelgeuse
Figure 7
Constellation Orion with Super Red Giant Betelgeuse
Source of Lighter elements through Copper[FOOTNOTE: Figure from The Stellar Origin of Copper by Ken Croswell (2007)]
Note the Orion Nebula in the Sword.

Formation of the Heavier Elements in Supernovas. The last stage of burning for a red giant star produces an Iron Group core. This core cannot carry on further nucleosynthesis because all  elements with higher atomic numbers can only fuse with the input of large amounts of energy.

If the core becomes sufficiently large (Type II supernovas from Red Giants), gravity forces the core to collapse further, until the K-orbit electrons get pushed into the nucleus at which point they combine violently with protons in the nucleus by electron capture -- reverse beta decay: p + e- -> n + neutrino. This proceeds rapidly, reducing most iron group protons to neutrons and ending up with helium, lots of free neutrons, and a large flux of neutrinos. The neutrinos escape, reducing the energy that balanced the gravitational forces, raising the temperature to ~1010 °K and density ~ 3x107 g/cc. The core collapses precipitately with a speed of about 0.4 c to the point where the core is packed at about nuclear density. At this point the neutrons reach maximum packing (by the Pauli Exclusion Principle) and the collapse rebounds with a massive neutrino flux. A shock wave propels outward at speeds approaching light speed. This is the supernova explosion. As the combination of neutrino bombardment and shock wave passes through the outer shells, elements with excesses of neutrons are formed by neutron capture. The excess neutrons then beta decay: n-> p + e- + anti-neutrino to form the heavy elements. The energy required to form the endothermic heavier elements comes from the energy of the shock wave and neutrino bombardment. This is the basic physics of the r-process.

Type II Supernova Physics
Massive Red Giant stars such as Betelgeuse end life in a type II supernova. These supernovas are essential buildingblocks of the elements with atomic numbers higher than the iron group. In particular, radioactive elements such as uranium are formed in supernovas.

Such elements are essential for life to exist because radioactive decay of these long-lived heavy elements have kept the earth to a uniformly moderate temperature during the long process of preparing it for advanced life.

 Sharp Point

Importance of the Mysterious Neutrinos

Wolfgang Pauli first postulated the existence of Neutrinos in 1930 to explain apparent violations of the conservation of energy, momentum and angular momentum during beta decay: n -> p + e + [xxx]. The first experimental detection of neutrinos (actually anti-neutrinos) was not made until 1956.

Neutrinos are so elusive that direct detection takes elaborate equipment and even then they are detected only in very small numbers. The reason is that they are neutral, point particles (leptons, like electrons), have very little mass and travel close to the speed of light. For example, the massive neutrino burst associated with Supernova 1987A led to the detection of a total of 24 anti-neutrinos from 4 earth-based neutrino detectors.

Neutrinos rarely interact with matter: they will travel through large masses without interacting at all. Even neutrino-antineutrino annhilations are rare: in the rare occasions when they do join up, they generally form neutrino-antineutrino pairs rather than annhilate.

Without neutrinos and antineutrinos, supernovas would not exist and thus heavy elements would not form. Life could not exist.
An important function of neutrinos is to remove energy from the iron core of a massive red giant star, and indeed from the star itself. Very few neutrinos interact with other matter -- or indeed with anti-neutrinos. This is one reason why they are so difficult to detect.

The neutrinos simply pass through the star and escape into space. Most neutrinos and antineutrions generated in supernova explosions are still travelling through space at very high speed.

Because the neutrinos remove energy from the core, the core rapidly collapses under gravity, leading to cascading electron capture and finally neutrons arrive at maximum packing density, which results in the extreme energy bounce and shockwave of a supernova explosion.

If instead, the electron capture process released only energy instead of energy plus neutrinos, the buildup of energy in the core would tend to balance gravity and the electron capture would not become a runaway cascade. The end result would be that the iron core would slowly burn iron into lower atomic number materials, and an equilibrium would be maintained, greatly extending the life of the star. Supernovas would never occur and the heavy elements would (probably) never be made.


The Silent Speech   Element Formation and Element Abundance

One of the most powerful examples of the Silent Speech is the discovery of how the elements were formed. This discovery is based on the fact that nuclear processes follow straightforward logical rules that build up from relatively simple principles of formation.

The number of protons in the nucleus determines the element. The number of neutrons determines the isotopes of the element.  All elements heavier than hydrogen require at least one neutron in the nucleus (the so-called "di-proton" is extremely unstable and decomposes into deuterium).

Essentially all nuclear reactions are the result of binary collisions -- the high energy collision between two particles, for the geometric reason that  the simultaneous collision of three or more particles is exceedingly unlikely. Given this, only the following interactions are at all likely:


neutrinos & anti-neutrinos

These do not interact with matter or with each other to any appreciable extent except under conditions of extremely high flux in a supernova.
p + n -> deuterium + energy
Requires a free neutron. Rare interaction after the primordial synthesis since free neutrons have a half-life of about 15 minutes.
p + x -> element x+1
For an interaction to occur the kinetic energy of the proton and of x has to overcome the charge barrier posed by the nucleus of x. This barrier is increasingly formidable as the atomic number of x increases.
n + x -> isotope of x
The neutrons must come from a recent prior collision because of the neutron  half-life. Neutron interactions are relatively easy because there is no charge barrier to overcome.
x nucleus
y nucleus
x + y ->
element x+y
The charge barrier is increasingly formidable as the atomic numbers of x and y increase.
radioactive beta minus decay
n -> e + p + anti-neutrino
element x+1
occurs if the element has an excess of neutrons
radioactive beta plus decay p + energy -> n + positron + neutrino x
element x-1 occurs if the element has a deficiency of neutrons
radioactive electron capture
p + e -> n +  neutrino
element x-1
An electron is captured from the element's own shell (K-capture for the K shell). Occurs with extreme gravitational collapse.
alpha decay
x -> x-2 + He

element x-2

Black Holes?  The Schwarzschild radius for a black hole is R = 2gm/c2 where m is the mass of the black hole. The Compton wavelength is λ=h/mc where h is the Planck constant. If the Compton wavelength exceeds the Schwarzschild radius then no black hole is possible. The crossover is the Planck mass, about 2x10-11 g.  For comparison, a proton has a mass of 1.67262158 × 10-24 g -- all of the elementary particles are far too small to become black holes. According to Hawking's theory, micro black holes "evaporate away" over time so that any primordial black holes still around today would have to have masses around 1015 grams.

The intriguing question is whether black holes might have been among the "clumps" produced in the very early universe. Could these account for the missing mass in the universe? Could they have been the "seeds" for the eventual formation of the early galaxies?

There is no lower limit on the size of mass m, but of course the radius becomes very small.

Binary Interactions

Most of the nuclear reactions occur as binary interactions.

Pair Production. In pair production a high energy gamma ray produces a particle and its antiparticle. The energy of the gamma ray must exceed the combined mass-energy of the particles. Thus for electron pair production the energy must exceed 2x0.511 MeV (about 10 Billion °K).
Pair Annhilation.  Pair annhilation occurs when matter collides with the corresponding antimatter particle. The result is the production of two gamma rays of approximately equal energy corresponding to the particle mass-energy. Unlike pair production, pair annhilation can occur at any temperature.

Note that the combination of pair production and annhilation does not exactly restore the original state because one original photon becomes two photons. It is not possible for two photons to combine for form a single photon (or to engage in pair production). Thus the combination increases entropy. Of course pair production is in equilibrium with pair annhilation if the ambient temperture is sufficiently high.

Proton-Neutron Conversion #1. A proton combines with an anti-neutrino to form a neutron and positron. Q: WHEN DOES THIS OCCUR???

Proton-Neutron Conversion #2. A neutron is produced by a proton-electron collision under extremely high energy conditions, such as in K-orbit electron capture by a nuclear proton as the iron core of a dying star collapses. The ambient temperature supplies the difference in mass-energy (0.782 MeV) between the neutron and the combined proton + electron mass, and the energy equivalent of the neutrino.

Note that neutrinos and antineutrinos can be very long-lived particles. They are neutral point particles, so that there is hardly any circumstance when they would naturally collide (unlike electron-positrons which are attracted to each other by electrical forces). So when neutrinos and antineutrinos are produced in stellar nucleosynthesis, the vast majority escape into space and never interact with themselves or with other matter. The Neutron-Proton Conversion #1 occurs in the extremely high antineutrino flux conditions of a supernova explosion.

Neutron-Proton conversion. This is the standard neutron beta-decay. Free neutrons are unstable (with a half-life of 15 minutes) and decay into protons and electrons.



Spectral Analysis:
Reading The Physical and Chemical Properties of Stars

Give the story of Comte and discovery of stellar spectra.

The Silent Speech          Spectral Analysis and Stellar Processes

Until the mid-1800s scientists assumed that it would be impossible to get much scientific information about the stars, because direct experimentation is not possible. The French philosopher Augusté Comte expressed this common-sense view in 1835 as follows:

Comte Quote & Spectra

But within a generation after this remark, the use of spectral analysis to analyse the content of stars was discovered -- including the discovery of a new element, Helium from its spectral lines.

Since that discovery, the analysis of starlight has led to many deep discoveries, including the classification of stars represented in the Hertzsprung-Russell diagram.

The Silent Speech          The Spectrum of Hydrogen

Balmer series -- mathematics. Relation to speed of light. Proof that the physics of distant objects is same throughout universe. Link between constant speed of light and conservation of energy.


Stable Elements
Most stable/most abundant Isotope
    Element isotopes are formed by adding neutrons. Each isotope has its own atomic mass. The mass per nucleon indicates the binding energy of the isotope. The most stable isotope of a given element is the one with the highest binding energy per nucleon. For example, here are the results for helium:

Helium -- 2 protons
mass (amu)
Binding Energy
per nucleon (MeV)
6.8142 *Maximum* -- He-4
8.03392 3.7938

Carbon -- 6 protons
mass (amu)
Binding Energy
per nucleon (MeV)
12.00000 7.4200 *Maximum* C-12

Oxygen - 8 protons
mass (amu)
Binding Energy
per nucleon (MeV)
1.00061 6.7567
0.99968 7.7160 *Maximum* O-16
0.99995 7.5054

Neutrons cannot be added above the Neutron Drip Line. This is the point at which neutrons leak out of the nucleus because the effective binding energy of the added neutron drops below zero. Similarly the Proton Drip Line is the point at which the proton's effective separation energy is zero.

Processes involved in Stellar Nucleosynthesis
As described in
"Gravitation is a "built-in" mechanism in stars which leads to the development of high temperature in the ashes of exhausted nuclear fuel. Gravitation takes over whenever nuclear generation stops; it raises the temperature to the point where the ashes of the previous processes begin to burn." [p. 567]

T °K
Density gm/cc
H burning 13.6x106
Quantum tunnelling. The process of the main sequence stars.
He burning 100x106 to ~108 ~105 C12, O16, Ne20
density  g/cc.
a process ~109
Mg24,  SI28, S32, A36, Ca40, Ca44, Ti48
Alpha Capture. The source of the a particles is different in the a process than in helium burning. Timescale 102 to 104 years.
e process 4x109
Va, Cr, Mn, Fe, Co, Ni
Equilibrium Process. Timescale seconds to minutes.
r process
neutron density ~1024 n/cc
many isotopes
Rapid Neutron Capture. 0.01-10 s. beta-decay processes. Timescale 10-100 s.
s process

many isotopes
Slow Neutron Capture.  Time scale 100 y to 100,000 y.
p process

proton capture.
x process

D, Li, Be, Bo
unstable at star interiors. Produced in regions of low density and temperature.

Stellar Nucleosynthesis

Heinz Oberhummer, Attila Csótó and Helmut Schattl, Fine-Tuning Carbon-Based Life in the Universe by the Triple-Alpha Process in Red Giants. Published in The Future of the Universe and the Future of our Civilization: Proceedings. Edited by V. Burdyuzha and G.S. Khozin. Singapore, World Scientific, 2000. p. 197.       Abstract: Stellar model calculations for a low-mass, intermediate-mass and massive star using the different triple-alpha reaction rates obtained with different strengths of the N-N interaction have been performed. Even with a change of 0.4% in the strength of N-N force, carbon-based life appears to be impossible, since all the stars then would produce either almost solely carbon or oxygen, but could not produce both elements.

[Coyne] George V. Coyne and Michael Heller, A Comprehensible Universe: The Interplay of Science and Theology, Springer, 2008. This book might have been an extended commentary on the Silent Voice.

F. Hoyle, D. N. F. Dunbar, W. A. Wenzel, and W. Whaling, Phys. Rev. 92, 1095 (1953).

[B2FH] Geoffrey Burbidge, Margaret Burbidge, William Fowler and Fred Hoyle, Synthesis of the Elements in Stars, Reviews of Modern Physics 29 (1957) p547-650. See Wikipedia article.

An excellent presentation of the remarkable fine-tuning involved in the production of the elements is found in the  Reasonable Faith presentations:  Big Bang Theory and the Incredibly Precise Design of the Universe   and Big Bang and Beyond. The latter presentation includes notes on the "stellar mystery" of helium fusion, Hoyle's "Wild Guess" and the problem of achieving a balance between carbon and oxygen production (slides 26-33).



Posted 05 February 2010