Father Sun’s Fusion Factory

Why is the Sun so hot?

Why is it getting hotter?

©Bob Field 2004

Sea Otters and Stellar Opacity

Thermoregulation and Energy Transfer

How does a sea otter resemble the Sun? Both trap internally generated heat in order to survive. The sea otter’s thick fur traps the energy released by oxidizing food. The Sun’s interior traps the energy released by thermonuclear fusion. Extremely high or low temperatures can kill a sea otter or a star. Thermoregulation is the key to survival.

The sea otter is a voracious predator that consumes about 25% of its body weight each day in sea food. Does this enable it to grow rapidly, to put on a heavy layer of fat, or to swim rapidly to chase its prey? No. No. No. The sea otter is a small, lean, warm-blooded mammal whose prey is usually slow moving at best and most of the energy released from its food is used to generate heat. Warm-blooded mammals evolved on land in order to maintain metabolic activity at night when reptiles are dormant. Many biochemical processes benefit from elevated body temperatures.

Air is a poor thermal conductor but can be very efficient at heat transfer through thermal convection. Mammals evolved fur to reduce convection heat losses. Since water is a good thermal conductor, fur is not very helpful unless it is thick enough to trap air efficiently. Many humans want the same things that sea otters need: lots of sea food and a thick fur coat to keep warm.

Throughout its ten billion year life, the energy that the Sun radiates at its surface will be equal to the energy it generates in its core from thermonuclear fusion. Yet the temperature of the Sun never reaches equilibrium. The average temperature of the Sun is a thousand times hotter than its surface temperature. This is very important because thermonuclear fusion requires highly elevated temperatures, but a hotter surface would radiate energy away faster. If the surface were millions of degrees, it would radiate a trillion times more energy than it does. Most of the energy would be deadly X-rays instead of benign sunlight. Within hours, the interior would be too cold to sustain thermonuclear fusion. Of course at these temperatures, the Sun’s gravity could not keep hot gases from escaping as well.

SO how does the Sun trap heat in the interior? SO! SO could stand for Sea Otter. Or it could stand for Stellar Opacity. Opacity is the inverse of transparency. Opaque objects are not transparent. Why is the Sun opaque? Electromagnetic energy – whether it is sunlight or X-rays or gamma rays - cannot travel very far in the Sun before being scattered or absorbed by ionized gas. Photons interact with the gas because their electromagnetic fields accelerate charged particles. Since the particles move faster, the gas is hotter.

The short wavelength gamma rays produced by thermonuclear fusion lose most of their energy the first time they encounter an electron. The electrons emit photons at lower energies because they are in local thermal equilibrium. Scattering delays the escape of a photon by sending it off in a random direction. Absorption is much more common than scattering and typically occurs in a picosecond or a trillionth of a second. The photon may travel 0.3 mm. When a photon is re-emitted, its direction has been randomized. So it may not be traveling toward the Sun’s surface any more.

The electron carries this energy for a relatively long time, perhaps a nanosecond or a billionth of a second. Even a very hot electron is not as fast as a photon, but if its velocity is a few percent of the speed of light, it may travel a much greater distance than the photon it absorbed before it radiates the energy away by emitting a new photon. The electron may travel a few centimeters, but it may scatter off other electrons billions of times, so its long path is a zigzag that advances less than a micron from its starting point.

Scientists have a name for this kind of motion, whether it is a photon, an electron, or an atom in a gas. It is a random walk because the particle direction changes randomly after each encounter. It is also called a drunkard’s walk. There is a whole branch of physics called statistical mechanics that studies these processes in three dimensions.

The Sun is continuously radiating energy into space, but the path to the surface is marked by a billion trillion absorption and scattering events during which photons are absorbed and re-emitted for ten million years before the energy of fusion escapes. Most of the delay is in the deep interior where the temperature and density are extremely high. This is also the location of the greatest density of photons and the most energetic photons. Radiant energy density in the interior can be a trillion times greater than near the surface and can include a billion times more photons per cubic centimeter, each with a thousand times more energy. They are mostly X-rays rather than visible light.

So most of the energy of the Sun is contained as heat in the gas rather than as radiant energy, but almost all of the advancement of energy toward the surface occurs through the motion of photons rather than electrons. Thus the bulk of the Sun’s interior is called the radiative zone rather than the conduction zone.

The radiative zone ends about 0.3 of the radius below the surface of the Sun. At this point, the opacity begins to rise sharply because the lower temperature allows for electrons to be bound to atoms and to absorb the less energetic photons found in this region. The photons cannot travel very far before dumping their energy into the gas. The increased temperature gradient favors energy transfer by convection, the physical movement of gas from the depths to the surface. Ironically, this is a very efficient process and the energy is transported very quickly through the convective zone despite the high opacity.

The sea otter conducts heat to its surface where its fur regulates its convection heat loss in trapped air to reduce its conduction losses in water. The opacity of the Sun regulates its radiative losses until convection takes over near its surface. Thermal conduction losses are very low in the sea otter’s fur and throughout the Sun.

An interesting contrast to the opacity of the Sun to photons is its transparency to neutrinos. Fusion also produces energy in the form of electrically neutral neutrinos that cannot interact electromagnetically with matter and rarely interacts at all. Neutrinos escape from the Sun in seconds without transferring significant energy to the gas. The loss of energy through neutrinos does not contribute to the thermal life of the Sun or to its luminosity. Fortunately for us, only a few percent of the fusion energy is in neutrinos. Otherwise the Sun would not retain as much heat as it does and it would function in a way that is less favorable for life on Earth.

Hot & Heavy - Thermonuclear Fusion

Nucleosynthesis and Energy Generation

Thermonuclear fusion fuses small nuclei into larger ones with more protons and neutrons. If nucleosynthesis is the “goal” of fusion, then energy generation is a by-product. You could consider sunlight to be a waste product, the elimination of extraneous heat. Like evolution, Einstein’s famous E=mc² is just a theory, but it predicts that matter can be converted into energy. When four hydrogen nuclei fuse to form a helium nucleus, the two protons and two neutrons are tightly bound and have slightly less mass than the original four protons. Most of the missing mass is transformed into highly energetic gamma rays.

Many processes require energy to get started. Atoms and molecules need to be in close contact in order to react. Chemical, biological, and nuclear reaction rates often depend on particle velocity and concentration. Fast moving particles interact more often and have more energy to overcome other forces. Greater concentrations also increase the frequency of interactions. Particle velocity is the microscopic property that determines temperature. The concentration of microscopic particles determines density. Therefore thermonuclear fusion occurs in gases that are “hot and heavy”.

The “hot” is maintained by the opacity of the interior to the photons produced by fusion itself. While the surface is only 6000 degrees, the core is 15 million degrees. The “heavy” is the great pressure and density of gas produced by the sheer weight of the enormous mass of the Sun under its own gravitational influence. The Sun’s mass is 300,000 times that of the Earth. Although the average density is only slightly greater than water and much less than rocks, the density of the core of the Sun is 160 times that of water and 16 times the density of the iron core of the Earth.

Ironically, the high temperatures maintain a high pressure that limits the need for high density. Even the pressure of the photons scattering off the electrons helps keep the Sun’s gases from contracting to greater densities. This is all very fortunate for us because higher densities accelerate the fusion process and shorten the lifetime of the Sun. Since it has taken half of the Sun’s ten billion year lifetime for humans to evolve on Earth, a short-lived star would not be very hospitable to advanced life forms on its orbiting planets.

What are the forces that influence thermonuclear fusion? What does the high temperature actually do for fusion at the microscopic level? Protons are positively charged particles that repel each other with electrical fields; at close range, the strength of their repulsion grows quadratically. Nuclear forces are extremely short-ranged; they don’t act at great distances. Imagine a meteor crater with a high rim and a deep hole in the center. If you fall into the hole, you gain a lot of kinetic energy due to gravitational acceleration. But you can’t get to the rim unless you have enough energy to overcome gravity and climb up the rim. Protons need a lot of energy to climb the rim before they can gain the energy release of thermonuclear fusion. That is what temperature does – it gives protons enough velocity to overcome the repulsive electric field of other protons.

If 15 million degrees provides protons with enough energy to climb the rim, why don’t all the protons fuse simultaneously causing a massive hydrogen bomb-type explosion instead of a steady “burning”? The answer is 15 million degrees is nowhere near enough energy to climb the hill. In fact 15 million degrees is pathetic – a thousand times too cold. Most protons don’t have enough energy to fuse. But not all particles in a gas have the same velocity or energy. There is a distribution of faster and slower particles.

How many of the 10⁵⁷ protons in the Sun have enough energy to climb the hill and fuse at any moment? Probably none! If the entire universe with its 10⁸⁰ protons were as hot and dense as the Sun, then it would be unlikely that any single proton would have enough energy to overcome the electrostatic repulsion. So according to classical physics, thermonuclear fusion cannot occur in this universe! Fortunately for us, classical physics is “just a theory” and quantum physics is a better theory. It says that there is a slight chance that a proton can tunnel through the rim and drop into the crater without climbing over the top. So it turns out that 15 million degrees is just right for a slow but steady rate of thermonuclear fusion that can maintain stellar stability and equilibrium for billions of years for our Sun. Similar temperatures maintain conditions for thermonuclear fusion for 100 billion stars in each of the 100 billion galaxies.

The Father of the Sun – a Star is Born

Gravity, Heat, and Light

In my Sunlight and Sea Life mind walk, I compared the struggle between sunlight and gravity to the Star Wars movie battle between Luke Skywalker (sunlight – the good side of the force) and Darth Vader (gravity – the dark side of the force). Sunlight is necessary for life, but gravity pulls things below the photic zone of the ocean, where photosynthesis is possible. Water is not transparent. This is good because the absorption of sunlight by water keeps oceans from freezing solid as they radiate their heat into space. One episode of Star Wars reveals that Darth Vader is the father of Luke Skywalker. So is gravity the father of sunlight? We shall see.

There is a chicken and egg problem with thermonuclear fusion: stellar opacity produces high temperatures by trapping the energy released by thermonuclear fusion but thermonuclear fusion requires great temperatures to occur. Which came first: fusion or high temperatures? Obviously high temperatures, but how did a mass of cold gas heat up as it condensed? Gravity of course.

The gravitational attraction of massive numbers of gas particles accelerates them - they gain speed. Their kinetic energy turns into heat because their motions have been randomized by many collisions. The moving particles never stop moving; they just scatter. Why don’t they scatter completely and disperse into space? What holds them together? Gravity cannot hold them if they have enough energy to escape back to space. The particles can’t escape because the gas radiates half of its kinetic energy into space as it condenses. This binds the particles together as a self-gravitating mass of gas and produces a stable star. So an enormous amount of radiant energy is released and the particles come together to form a very hot energetic gas before fusion begins. So gravity is the father of sunlight!

We are fortunate that the gravitational attraction of the Sun confined matter long enough for the Earth to form from atoms whose nuclei fused in other stars. That is why I call it Father Sun. Also the Sun’s gravity continues to confine the Earth to a nearly circular orbit that exposes it to a steady supply of solar energy whose absorption is essential to sustain the web of life and to sustain liquid oceans and a gaseous atmosphere. The importance of galaxies to us is that other stars are the source of the larger nuclei that form us and our planet and the gravitational attraction of the entire galaxy is necessary to confine gases long enough to condense to form our Sun and its solar system with rocky planets made from so-called metallic atoms. All of the chemical elements in the periodic table other than hydrogen and some helium originated through nucleosynthesis inside distant stars.

Older but Brighter

Stellar Size, Composition, Structure, & Evolution

How large is the Sun compared to the Earth and its orbiting Moon? If the Earth were at the center of the Sun, the Moon would orbit a little over half way to the surface.

What is the Sun made out of? It is a highly ionized gas, called a plasma, mostly hydrogen and helium. The atoms are almost entirely ionized because the electrical attraction of a positively-charged nucleus is not sufficient to confine a highly energetic negatively-charged electron to an orbit about a nucleus. Since the Sun has been fusing protons for five billion years, it has much more helium now than when it started. The mobility of nuclei in the dense core is so poor that the helium is still there. The core is about 2/3 helium while the rest of the Sun is 72% hydrogen. The Sun, being much younger than the 13.7 billion year old universe, also includes a percent or so of larger nuclei that it acquired from exploding Supernova that lived and died before the Sun formed. These nuclei are mostly oxygen, carbon, and nitrogen, all of which are essential for life. There is also a little iron and silicon and many other elements essential for the formation of a rocky planet.

Because the composition of the Sun is changing, the Sun is constantly evolving. It has less hydrogen “fuel” to “burn” than in its youth but this composition change has actually caused it to “burn” hotter. The radius and surface temperature of the Sun have both increased over time. The total power produced in the core and radiated into space from the surface has increased 40% over time. When cyanobacteria ruled the world two billion years ago, the Sun did not radiate enough solar energy to keep the oceans from freezing solid. Luckily for us, the Earth’s atmosphere was full of carbon dioxide, a greenhouse gas, which produced enormous global warming by trapping infrared energy from escaping from the surface of the oceans and land. As the Sun heated up, the cyanobacteria were able to fix enough carbon dioxide dissolved in the oceans from the atmosphere to reduce the greenhouse effect and keep the oceans from evaporating and producing a hell like Venus.

So how do composition changes increase the rate of thermonuclear fusion and the luminosity of the Sun? The kinetic energy of a gas depends on the number of particles and their temperature. Since the total kinetic energy of the gas does not change when nuclei fuse, but the number of particles decreases, the average kinetic energy per particle increases. Therefore the temperature of the gas increases slowly but steadily for billions of years as fusion reduces the number of particles but the Sun’s opacity traps the kinetic energy.

The decrease in hydrogen in the core reduces the rate of fusion because fewer nuclei are participating and their probability of encountering another hydrogen nucleus decreases. On the other hand, the temperature increase accelerates the fusion process, generating more energy which maintains the temperature increase even as more energy escapes from the Sun’s surface. The net decrease in fusion results in a gravitational contraction which increases temperature and fusion cross-sections while increasing the number of nuclei participating in fusion. As the energy diffuses toward the surface, the outer gases expand increasing both the surface area of the Sun and its surface temperature. The higher luminosity is due to both higher temperatures and a larger surface area.

The Natural History of the Sun

Why is the Sun so hot? Why is it getting hotter? The first question leads to three more questions: How did the Sun get hot? What keeps the interior hot? Why is the surface so cold? The answers involve the formation of the Sun, the generation of energy in the core, energy transport in the interior, heat loss at the surface, and changes in composition over time. Subjects include thermonuclear fusion, thermoregulation, conduction, convection, radiation, absorption, scattering, emission, nucleosynthesis, gravitational attraction, and electric repulsion.

The Sun formed from cold gases that condensed under their own gravitational attraction. As they condensed they simultaneously radiated energy into space and heated up. The high temperature and high density ignited a slow and steady thermonuclear fusion because of the quantum mechanical effect called tunneling that occurs even though no protons actually have enough energy to overcome the electrical repulsion of the other protons. Fusion in the Sun converts hydrogen into helium in the core. Most of the excess mass is converted to electromagnetic energy in the form of gamma rays.

The energy is trapped by the opacity of the Sun and maintains the elevated temperature of the interior of the gas as its electrons scatter, absorb, and re-emit photons for millions of years while the energy diffuses through the radiative zone. Most of the radiant energy is absorbed by free or bound electrons before it can scatter from an electron. The energy stored in the gas is about one thousand times greater than the energy stored in the radiant energy, but the electrons scatter far too often to transport the energy any significant distance. This energy is necessary for thermonuclear fusion to proceed and to provide high pressure that keeps the Sun from collapsing due to gravitational attraction. Some of the pressure is also due to the outward diffusion of radiant energy.

When the energy diffuses to the convective zone, a region of lower temperature, the rising opacity due to bound electrons halts the outward diffusion of photons. The energy of the absorbed photons is transported by highly mobile low density hot gases that rapidly rise by convection to the Sun’s surface. At the surface, the gases radiate electromagnetic energy into space as sunlight.

In non-convective regions of the Sun, hot gas particles are moving very rapidly, but they do not travel very far because they scatter so frequently off of each other. Since particles are trapped in the same neighborhood for billions of years, the composition of the core changes slowly as nucleosynthesis reduces the abundance of hydrogen. Decreases in pressure differences allow gravity to increase the density, temperature, and radius of the thermonuclear core. Because the resulting increase in density and temperature offsets the reduction in hydrogen, the fusion process accelerates and the Sun’s surface warms and expands, becoming more luminous as it radiates more sunlight into space. Core contraction also converts some gravitational potential energy into thermal energy. When the hydrogen in the core is consumed in five billion years, the fusion process will change in dramatic ways that will transform the Sun into a red giant that expands to envelope the Earth.

The web of life depends on photosynthesis to store sunlight in molecules. Since thermonuclear fusion in the core of the Sun generates deadly gamma rays, sunlight is the by-product of stellar opacity, the scattering and absorption of photons by electrons. Since the Big Bang produced hydrogen and helium, carbon, oxygen, and nitrogen, the atoms of life, were synthesized in the core of long dead massive stars whose remains were dispersed into space and incorporated into our own solar system. Gravity, the weakest force in nature, triggers the most violent nuclear reactions by condensing and heating massive gas clouds through its long range influence. Photons generated in thermonuclear fusion prevent the Sun from collapsing by heating and pressurizing the gaseous interior of the Sun.