Microstructures and Macrostructures

Thomas D. Le

Sometime ago, Dr. Tran Manh Ngo asked why the smallest structure (microstructure) such as an atom resembles the structure of the large (macrostructure) such as the solar system or the galaxies.

If by resemblance is meant the composition of chemical elements in  the structure of matter, then all matter (from microstructures to macrostructures) is made up of atoms, whose nuclei consist of a number of protons and neutrons with their electrons hovering in a surrounding cloud at various energy levels. Protons have a positive charge, electrons a negative charge, and neutrons a neutral (0) charge.  The number of protons (called atomic number, Z) in the nucleus determines the element. The number of neutrons in the nucleus is called the neutron number, N.  Together protons and neutrons are called nucleons. And the number of nucleons in a nucleus is the mass number, A. Thus, the mass number is the sum of the atomic number and the neutron number, A = Z + N. Different isotopes of the same element have the same number of protons but different numbers of neutrons. For example, hydrogen (H) has 1 proton and no neutrons. Because the hydrogen isotopes are important, they receive their own names.  Thus, deuterium (Hydrogen-2) has 1 proton and 1 neutron, making its mass number equal to 2. Tritium (Hydrogen-3) with 1 proton and 2 neutrons has its mass number equal to 3. Carbon-14 with the atomic number 6 has the mass number 14. The force that binds the particles together in the nucleus is the strongest of the  four fundamental forces of nature.  Hence, it is called the strong force.  The remaining three forces in order of strength are the electromagnetic force, the weak force, which is responsible for nuclear decay, and gravitation. Though the most powerful, the strong nuclear force operates within a very short range of 1 femtometer (one thousand trillionth of a meter) whereas the weakest force, gravitation, equal to 10-34 newtons (1 over 1 followed by 34 zeros), or 10-43 that of the strong force, can operate to infinity. All matter, the sun, the planets, the stars, the galaxies and everything else in the universe including all living organisms, is subject to these forces and is made up of atoms.

An atom at rest is in its lowest energy level called the ground state. Consider the simplest model of the hydrogen atom with one proton in its nucleus and one electron in its orbit. When excited from its ground state by collision with a particle, the atom absorbs part of its energy to bump its electron to a higher energy level and the particle leaves the atom with less kinetic energy.  The harder the collision, the more energy the atom absorbs and the higher the energy level of its electron.  If the atom collides with a photon, it becomes excited and increases its energy by absorbing the photon. Since the excitation does not last longer than about ten millionth of a second, its electron loses energy and reverts to its ground state. In the process the atom spontaneously emits a photon in any direction. If a particle strikes an excited atom in a collisional deexcitation, the electron loses energy and drops to the ground state.  The outgoing particle gains an equal amount of kinetic energy.  No photon is emitted.  If an atom gains enough energy, the electron escapes from its nucleus and the atom is ionized.  The process is called ionization. The loss of an electron requires an energy called ionization energy and entails a rearrangement of the atom's energy levels and a change in its spectrum.

Now that we have seen what is similar in all matter, I take the question posed simply to be about how the universe evolves from the small to the large.

If my hunch about the question is right, the answer takes us through the current, widely accepted cosmological model known as the Big Bang.   I shall be brief for an attempt at a detailed examination of the model will take us into book-length treatments.

Scientists believe that the universe, and that encompasses space and time, began as a primeval fireball in the distant past when all the matter in the universe (galaxies and all) was condensed into one point of infinite density (i.e., a singularity).  Along with Einstein, they believe that on the largest scale the universe is homogeneous (every region is the same as any other region) and isotropic (the universe looks the same in any direction).  No one could tell any part of the universe from any other part of it.  This is known as the cosmological principle.  The universe has no boundary, no center.  It is a mistake to think of the Big Bang as occurring from a center and expanding from there into the surrounding space. The Big Bang involved the entire universe as it marked the beginning of space and time.  The Big Bang is an extrapolation from a network of interlocking theories, observations, assumptions and evidence that is successful in describing the evolution back to a time when the separation between particles was about ten orders of magnitude smaller than what it is now.

No one knows exactly when the initial event occurred.  Estimates using Hubble's law and the Hubble constant vary depending on the value of the latter.  Some believe the Hubble constant to be 50 km/s/Mpc (50 km per second per megaparsec; a megaparsec = 3.26 million light years) while others think it as high as 90 km/s/Mpc, giving a range of between 20 and 10 billion years as the age of the universe.  If we take the Hubble constant to be in the mid range of  75 km/s/Mpc, the universe is about 13 billion years old.  Another method of estimating the age of the universe is to date the oldest objects found.  This of course provides the lower limit on the age.  White dwarf stars, which have gone through their life cycle without reaching the supernova stage, are very old and tend to dim with age.  The dimmest of them, if found, would provide this lower limit.

Evidence of the Big Bang resides in the presence of cosmic microwave background radiation (CBR), which persists at 2.7 K (degrees Kelvin) until today and is uniform across the sky.  This radiation, remnant of the initial expansion, bears the attributes expected of a cosmic hot origin.

Many of the important events of the early Big Bang occurred very rapidly, in tiny fractions of seconds.  Of events from the Big Bang expansion until Planck time, which is 1.35 x 10-43 s (1.35 over 1 followed by 43 zeros), we know nothing because no known laws of physics exist in that time frame; even general relativity breaks down at that time. But we can estimate the energy that exists in the universe today.  Each cubic meter contains 4 x 10-14 J or, equivalently via E = mc2, 4 x 10-31 kg of matter. All the visible matter, if spread uniformly, would have a density of 4 x 10-28 kg per cubic meter.  Thus, each kilogram of matter corresponds to a cosmic radiation of 1014 J (100 trillion J), enough energy to heat up the universe to more than 1012 K (1 trillion degrees kelvin).  That is the temperature of the primeval fireball, at which no one knows how matter would behave. The temperature  1012 K would correspond to a time 10-24 s after time zero.

The entire thermal history of the universe comprises four eras: (1) a heavy-particle era, (2) a light-particle era, (3) a radiation era, and(4) a matter era, in which we live. Protons and neutrons would be considered “heavy” particles, and electrons would be “light” particles in this terminology.

In the beginning, when the temperature is greater than 1012 K, and the time is less than 10-6 s (one millionth of a second), the universe is a sea of photons consisting of high-energy gamma rays and X-rays energetic enough to produce massive particles such as protons.  Each collision of two photons produces a pair of particle-antiparticle, such as proton-antiproton,  which quickly annihilate each other.  Neutrons/antineutrons, neutrinos/antineutrinos, and electrons/positrons are also created and annihilated.  This pair production does not last long because the universe cools off very fast, leading to the end of the heavy-particle era.

Between the time 10-6s and about 6 s, the temperature has cooled to between 1012 K and 6 x 109 K (6 billion K), not hot enough to produce heavy particles, but sufficiently hot to generate electrons/positrons.  This is the light-particle era.  Protons and electrons combine to form neutrons.  At the lower temperature range, photons can no longer create electrons and positrons.  And neutrons are no longer produced by the interactions of protons with electrons or electrons with positrons.  This marks the end of the light-particle era.

From 6 to 300 s the universe has cooled to about 109 K (1 billion K) and enters the radiation era, which lasts almost a million years. Even after the first few years, the universe is still too hot, at about 1 million K. At that temperature photons, protons and electrons violently collide, and atoms are not stable. Whenever a proton and an electron combine to form an atom, it is torn asunder by the energetic photons or by collision with another particle. The gas at that time, called plasma, is opaque because photons are quickly absorbed or scattered by the electrons.  The protons and neutrons that remain react to form nuclei of simple elements. Deuterium is created by a combination of one proton and one neutron. If they do not decay, neutrons end up as part of the nuclei of deuterium. Continuing reactions between deuterium and neutrons create helium and tritium.  From the combinations of deuterium and tritium, small amounts of beryllium and lithium are generated.

About a million years after the Big Bang, the universe enters the matter-dominated era.  The temperature has plunged to 3000 K.  The radiation shifted from gamma rays and X rays to ultraviolet and visible light.  The universe becomes transparent because the temperature is low enough for atoms to survive. Neutral atoms that form, such as hydrogen and helium, become more stable.  Light can now travel unimpeded across the sky.  The universe sees a decoupling of radiation from matter, or a recombination of nuclei and free electrons to form stable atoms.  For this reason, this era is also known as the era of recombination.

We are now living in this same era. After the first million years, the universe still has no heavier elements beyond hydrogen and helium and a little beryllium and lithium. Where did heavy elements such as iron, lead, cobalt, and so on come from? A short answer is they all come from nuclear processes that take place in the interior of stars.  And stars are formed from interstellar gas and dust. Now for a bit more detail.

After the Big Bang, space is superheated and filled with gas and dust. The most common element is hydrogen. Interstellar gas tends to clump in clouds, and in different locations contains neutral atoms, ionized atoms, free electrons and molecules. We call these clouds nebulas. Between clouds there is intercloud gas, again consisting mainly of neutral or ionized hydrogen.  Colder material consists of interstellar molecules, primarily of hydrogen.  Opaque cosmic dust is called dark cloud because it conceals the light of stars in the background. The effects of interstellar dust manifest themselves in dimming starlight or reddening of vast areas of space because dust scatters blue wavelengths more efficiently than red ones. Elements in dust include hydrogen, oxygen, carbon, nitrogen, and silicon in that order.

Stars form by gravitational contraction of interstellar gas clouds. In gravitational contraction cold clouds of interstellar gas and dust condense under their own weight to form clumps called protostars. A protostar is just a huge blob of gas several times larger than the sun. The interior of the blob is too cool to support the outer layers and the protostar keeps contracting.  As it contracts temperature begins to rise, and over a few thousand years, gravitational energy is converted into thermal energy, heating up the gas and producing substantial luminosity. As the protostar continues to shrink, the temperature in its core rises to millions of degrees, triggering the process of hydrogen burning (fusion, not combustion).  This thermonuclear reaction generates enormous amounts of energy that are sufficient to counter gravity.  The protostar becomes a stable star to begin about 80% of its life in a stage in its evolutionary track called main sequence. Our sun is now halfway through its lifetime of about 10 billion years.  Depending on its size, a star may last a mere few million years (massive stars) to tens of billions of years for a star of one solar mass (like our sun).  Stars that are too small and too cold never reach the thermonuclear process and end up as brown dwarfs.

The star generates energy and transforms hydrogen to helium through the proton-proton (PP) process and the CNO (carbon-nitrogen-oxygen) process.  The proton-proton chain takes as input six protons and two electrons to form through stages a helium nucleus, two protons, two neutrinos, and gamma rays (photons). The CNO cycle has the same output as the PP process.  Both processes can occur simultaneously. In massive stars of 1.5 solar masses and above, the CNO process predominates.

As the star's core contracts further, its temperature reaches 100 million K, when another process, called the triple-alpha reaction (alpha particles are helium nuclei), fuses three helium nuclei to form a carbon nucleus with the release of energy.   Reaction between carbon nuclei and helium nuclei produces oxygen. This process is called helium burning. In massive stars core temperatures are elevated enough to use carbon and oxygen as fuels to produce silicon, sulfur, and magnesium. The radiation emitted by mostly very energetic gamma rays reach a temperature of one billion K, fully capable of breaking up nuclei and causing them to emit protons, neutrons, and alpha particles.  These particles within seconds combine with other nuclei in a complex network of simultaneous chain reactions to produce heavy nuclei composed of 50 or 60 protons and neutrons. Thus are iron and nickel formed.

When the helium is depleted, the core contracts and heats up further until carbon is fused to produce other heavier elements.  The process is called carbon burning. Thus from one stage of fusion and energy release to another, elements are formed one after another using the output of a process as input to the following one until at last iron forms, as seen above. This steady climb from light hydrogen to heavy iron that occurs in the core of a star is one form of nucleosynthesis.  The generation of elements lighter than iron releases energy whereas iron fusion requires an input of energy. The core by this time has exhausted its fuel and the star has gone on to burn its outer shell.  The burning shell expands the star until it becomes an inflated red ball called red giant. Bursts of triple-alpha energy production engenders thermonuclear explosions in its shell called thermal pulses, which occur every few thousand years. With each explosion the bubbling gases carry heavy elements outward while the star develops a superwind that quickly blows away its heated envelope. This hot expelled material forms a shell of gas called a planetary nebula. Within a few thousand to a few hundreds of thousands of years, the nebula dissipates into the interstellar medium.

Heavier elements than iron are produced by reaction between nuclei and neutrons via the s-process and the r-process.  Because neutrons without electrical charge can be captured easily, they enter into the making of heavy elements.  Neutron capture intensifies during the red giant phase while the star is burning helium in its core.  After the capture the nuclei produced are unstable and begin to decay. Because the neutron capture is slow compared with the rate of decay, the process is called the slow or s-process.  Whereas bismuth (containing 83 protons and 126 neutrons) can be formed by neutron capture, heavier elements cannot because the more massive nuclei built from bismuth are unstable and cannot result from the  s-process.  Heavier elements thus can result only if a large number of neutrons can be captured before decay reduces their number. Enter the r-process or the rapid process, which allows large numbers of neutrons to be captured.  The r-process takes place only during the collapse of the core of a star during supernova explosion discussed below.

If a star is about one solar mass or less, its remaining core would never reach the high temperature required to trigger carbon burning owing to its being degenerate. When the core is degenerate, its gas behaves like a metal and cannot contract to create high temperatures.  The star evolves within 75000 years into a white dwarf. Without energy sources, the white dwarf becomes a black dwarf and may last billions of years as long as the degenerate core continues to support the star. That is a possible fate of our sun. In short, a low-mass star like the sun goes through a life cycle stretching from protostar, pre-main sequence, main sequence, red giant, planetary nebula, white dwarf and black dwarf.

Massive stars of 5-10 solar masses with the same chemical composition as the sun have a different history because they can reach higher temperatures. While on shorter main sequence, the star burns hydrogen by the CNO cycle, which generates more energy than the PP reaction that triggers the burning of carbon and heavier elements in the core.  Its helium-rich core does not become degenerate and burns for about 10 million years.  When helium is exhausted the core contracts and fresh helium falls into the core to form a thin, helium-burning shell around the core. The star once more becomes a red giant. By the triple-alpha process thermal pulses igniting the shell around the core result in pulsations.

Now comes the supernova stage, during which the matter from the star is thrown out into the interstellar medium.  As it ages, a massive star (about 25 solar masses) becomes increasingly hotter as it contracts to ignite successive phases of thermonuclear burning. When the star's core reaches a few million kelvin, the photons are energetic enough to trigger reactions that create neutrinos. These neutrinos escape from the core carrying part of the energy off.  To replenish this loss the star has to initiate burning of thermonuclear fuel or contract or both. Detailed computer calculations unfold the following scenario.  In succession the evolution  process takes place over millions of years.  When the temperature reaches 40 million K, hydrogen burning begins and lasts 7 million years. At 200 million K, helium begins to burn for 700,000 years.  Carbon burning occurs at 600 million K and lasts 600 years.  Neon burning lasts only 1 year at 1.2 billion K. Oxygen burning lasts 1 year at 1.5 billion K.  At 2.7 billion K silicon burns, for about one day to form iron.

During the final nuclear burning stage, the star's inert iron core is surrounded by shells of silicon, oxygen, neon, carbon, helium, and hydrogen. Supported by the pressure of degenerate electrons, the core is now just a white dwarf with a surrounding red giant. When the mass of the iron core exceeds a limit (the Chandrasekhar limit), the core begins to contract. This contraction causes the core's density to increase. Electrons react with the protons in the iron nuclei to produce neutrons.  The core is thus becoming a neutron star. With each neutronization reaction, a neutrino is produced.  As the process continues, electrons disappear leaving the core to collapse from thousands of kilometers to 50 km in radius within a second. A few seconds later, the radius shrinks to 5 km as the temperature reaches 5.4 billion K.  The collapse releases huge gravitational energy, mostly in the form of neutrinos and gamma rays. Contraction halts when the core's density equals the density of nuclei of atoms. The neutron star which the core has become at 23 billion K rebounds and starts sending shock waves outward at 1/6th the speed of light. Captured in the dense core, neutrinos violently collide with neutrons to heat the gas behind the shock front and propel it toward the surface in a huge supernova explosion emitting enormous luminosity.  As a result, the material in the supernova is ejected into the interstellar medium to be used in the formation of new stars. Supernovae have been observed in the Milky Way and other galaxies.  One of the most famous is Supernova 1987a, observed on February 24, 1987.

If a star is too massive to become a neutron star, nothing stops its collapse and it eventually becomes a black hole.

Finally, galaxies are formed from interstellar gas clouds that contract or merge, just like individual stars.

2 August 2007

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