Your Standard Solar Model

By combining theoretical modeling of the sun’s (unobservable) interior with observations of the energy that the sun produces, astronomers have come to an agreement on what is called a standard solar model, a mathematically-based picture of the structure of the sun. The model seeks to explain the observable properties of the sun and also describe properties of its unobservable interior. With the standard solar model, we can begin to describe some of the interior regions—regions hidden, beneath the photosphere, from direct observation. Below the photosphere is the convection zone, some 124,000 miles (200,000 km) thick. Below this is the radiation zone, 186,000 miles (300,000 km) thick, which surrounds a core with a radius of 124,000 miles (200,000 km).
The sun’s core is tremendously dense (150,000 kg/m3) and tremendously hot: some 15,000,000 K. We can’t stick a thermometer in the sun’s core, so how do we know it’s that hot? If we look at the energy emerging from the sun’s surface, we can work backward to the conditions that must prevail at the sun’s core. At this density and temperature, nuclear fusion is continuous, with particles always in violent motion. The sun’s core is a giant nuclear fusion reactor.
At the very high temperatures of the core, all matter is completely ionized—stripped of its negatively charged electrons. As a result, photons (packets of electromagnetic energy) move slowly out of the core into the next layer of the sun’s interior, the radiation zone.
Here the temperature is lower, and photons emitted from the core of the sun interact continuously with the charged particles located there, being absorbed and re-emitted. While the photons remain in the radiation zone, heating it and losing energy, some of their energy escapes into the convection zone, which in effect, boils like water on a stove so that hot gases rise to the photosphere and cool gases sink back into the convection zone. Convective cells become smaller and smaller, eventually becoming visible as granules at the solar surface. Thus, by convection, huge amounts of energy reach the surface of the sun. At the sun’s surface, a variety of processes give rise to the electromagnetic radiation that we detect from the earth. Atoms and molecules in the sun’s photosphere absorb some of the photons at particular wavelengths, giving rise to the sun’s absorption-line spectrum. Most of the radiation from a star that has the surface temperature of the sun is emitted in the visible part of the spectrum.

Chain Reactions in the Sun

The sun generates energy by the converting the hydrogen in its core to helium. The details are complex, but we may content ourselves with an overview. When temperatures and pressures are sufficiently high (temperatures of about 10 million K are required) 4 hydrogen nuclei (which are protons, positively charged particles) can combine to create the nucleus of a helium atom (2 protons and 2 neutrons). Now the mass of the helium nucleus created is slightly less than that of the four protons that were needed to create it. That small difference in mass is converted into energy in the fusion process. One of the simplest fusion reactions involves the production of deuterium (a hydrogen isotope) from a proton and a neutron. When these two particles collide with enough velocity, they create a deuterium nucleus (consisting of a proton and a neutron) and the excess energy is given off as a gamma ray photon. In the sun, this process proceeds on a massive scale, liberating the energy that lights up our daytime skies. That’s a 4 ×1026 watt lightbulb up there, remember.

Fission in the Sun

On December 2, 1942, Enrico Fermi, an Italian physicist who had fled his fascistoppressed native land for the United States, withdrew a control rod from an “atomic pile” that had been set up in a squash court beneath the stands of the University of Chicago’s Stagg Field. This action initiated the world’s first self-sustaining atomic chain reaction. Fermi and his team had invented the nuclear reactor, and the world hasn’t been the same since.
Nuclear fission is a nuclear reaction in which an atomic nucleus splits into fragments, thereby releasing energy. In a fission reactor, such as the one Fermi was instrumental in creating, the process of fission is controlled and self-sustaining, so that the splitting of one atom leads to the splitting of others, each fission liberating more energy.
Nuclear fission is capable of liberating a great deal of energy, whether in the form of a controlled sustained chain reaction or in a single great explosion, like an atomic bomb. Yet even the powerful fission process cannot account for the tremendous amount of energy the sun generates so consistently. We must look to another process: nuclear fusion.
Whereas nuclear fission liberates energy by splitting atomic nuclei, nuclear fusion produces energy by joining them, combining light atomic nuclei into heavier ones. In the process, the combined mass of two nuclei in a third nucleus is less than the total mass of the original two nuclei. The mass is not simply lost, but converted into energy. A lot of energy. One of the by-products of nuclear fusion reactions is a tiny neutral particle called the neutrino. The fusion reactions themselves produce high energy gamma ray radiation, but those photons are converted into mostly visible light by the time their energy reaches the surface of the sun. Neutrinos, with no charge to slow them down, come streaming straight out of the sun’s core. The numbers that we detect give us great insight into a region of the sun that is otherwise inaccessible.

Solar flares

Most frequently at the peak of the sunspot cycle, violent eruptions of gas are ejected from the sun’s surface. The prominences and flares may rise to some 60,000 miles (100,000 km) and may be visible for weeks. Solar flares are more sudden and violent events than prominences. While they are thought to also be the result of magnetic kinks, they do not show the arcing or looping pattern characteristic of prominences. Flares are explosions of incredible power, bringing local temperatures to 100,000,000 K. Whereas prominences release their energy over days or weeks, flares explode in a flash of energy release that lasts a matter of minutes or, perhaps, hours.

Understanding Sunspot Cycles

Long before the magnetic nature of sunspots was perceived, astronomer Heinrich Schwabe, in 1843, announced his discovery of a solar cycle, in which the number of spots seen on the sun reaches a maximum about every 11 years (on average). In 1922, the British astronomer Annie Russel Maunder charted the latitude drift of sunspots during each solar cycle. She found that each cycle begins with the appearance of small spots in the middle latitudes of the sun, followed by spots appearing progressively closer to the solar equator until the cycle reaches its maximum level of activity. After this point, the number of spots begins to decline. The most recent maximum occured in early 2001.
Actually, the 11-year period is only half of a 22-year cycle that is more fundamental. Recall that the leading spots on one hemisphere exhibit the same polarity; that is, they are all either north magnetic poles or south (and the followers are the opposite of the leaders). At the end of the first 11 years of the cycle, polarities reverse. That is, if the leaders had north poles in the southern hemisphere, they become, as the second half of the cycle begins, south poles.
The cyclical nature of sunspot activity is very real, but not exact and inevitable. Studying historical data, Maunder discovered that the cycle had been apparently dormant from 1645 to 1715. At present, there is no explanation for this dormancy and other variations in the solar cycle.

Sunspots: What They Are

Sunspots are irregularly shaped dark areas on the face of the sun. They look dark because they are cooler than the surrounding material. The strong local magnetic fields push away some of the hot ionized material rising from lower in the photosphere. A sunspot is not uniformly dark. Its center, called the umbra, is darkest and is surrounded by a lighter penumbra. If you think of them as blemishes on the face of the sun, just remember that one such blemish may easily be the size of the earth or larger.
Sunspots may persist for months, and they may appear singly, although, usually, they are found in pairs or groups. Such typical groupings are related to the magnetic nature of the sunspots. Every pair of spots has a leader and a follower (with respect to the direction of the sun’s rotation), and the leader’s magnetic polarity is always the opposite of the follower. That is, if the leader is a north magnetic pole, the follower will be a south magnetic pole.
Sunspots are never seen exactly at the equator or near the solar poles, and leaders and followers in one hemisphere of the sun are almost always opposite in polarity from those across the equator. That is, if all the leaders in the northern hemisphere are south magnetic poles, all the leaders in the southern hemisphere will be north magnetic poles.
We have said that sunspots are thought to be associated with strong local magnetic fields. But why are the fields strong in certain regions of the photosphere? A meteorologist from Norway, Vilhelm Bjerknes (1862–1951) concluded in 1926 that sunspots are the erupting ends of magnetic field lines, which are distorted by the sun’s differential rotation. That is, like the gas giant jovian worlds, the sun does not rotate as a single, solid unit, but differentially, at different speeds for different latitudes. The sun spins fastest at its equator—the result being that the solar magnetic field becomes distorted. The field lines are most distorted at the equator, so that the north-south magnetic field is turned to an east-west orientation. In places where the field is sufficiently distorted, twisted like a knot, the field becomes locally very strong, powerful enough to escape the sun’s gravitational pull. Where this happens, field lines “pop” out of the photosphere, looping through the lower solar atmosphere and forming a sunspot pair at the two places where the field lines pass into the solar interior.

Sun Trivias

We have described the layers in the sun’s outer atmosphere, but have ignored some of their more interesting aspects, the storms in the atmosphere. The sun’s atmosphere is regularly disturbed by solar weather in the form of sunspots, prominences, and solar flares. With the proper equipment—or an Internet connection (http://sohowww.estec. esa.nl)—you can observe some of the signs of activity on the sun’s surface.
A Granulated Surface
If we look at the sun, its surface usually appears featureless, except, perhaps, for sunspots, which we’ll discuss in a moment. However, viewed at high-resolution, the surface of the sun actually appears highly granulated. Now, granule is a relative concept when we are talking about a body the size of the sun. Each granule is about the size of an earthly continent, appearing and disappearing as a hot gas bubble rises to the surface of the sun.
Galileo Sees Spots Before His Eyes
People must have seen sunspots before 1611, when Galileo (and, independently, other astronomers) first reported them. (As recently as March 2001, sunspots easily visible to the unaided eye have appeared.) The largest spots are visible to the naked eye (at least when the sun is seen through clouds). Yet, at the time, the world was reluctant to accept imperfections on the face of the sun.
Sunspots were not (as far as we know) studied before Galileo. Galileo drew a profound conclusion from the existence and behavior of sunspots. In 1613, he published three letters on sunspots, explaining that their movement across the face of the sun showed that the sun rotated.

What is Solar Wind

The sun does not keep its energy to itself. Its energy flows away in the form of electromagnetic radiation and particles. The particles (mostly electrons and protons) do not move nearly as fast as the radiation, which escapes the sun at the speed of light, but they move fast nevertheless—at more than 300 miles per second (500 km/s). It is this swiftly moving particle stream that is called the solar wind.
The solar wind is driven by the incredible temperatures in the solar corona. As a result, the gases are sufficiently hot to escape the tremendous gravitational pull of the sun. The surface of the earth is protected from this wind by its magnetosphere, the magnetic “cocoon” generated by the rotation of the earth’s molten core. As with many other planets, the motion of charged molten material in the earth’s core generates a magnetic field around the planet. This magnetic field either deflects or captures charged particles from the solar wind. Some of these particles are trapped in the Van Allen Belts, doughnut-shaped regions around the earth named after their discoverer. Some of the charged particles rain down on the earth’s poles and collide with its atmosphere, giving rise to displays of color and light called aurora (in the Northern Hemisphere the Aurora Borealis, or Northern Lights, and in the Southern Hemisphere, the Aurora Australis, or Southern Lights). The Auroras are especially prominent when the sun reaches its peak of activity every 11 years.

Understanding Solar Eclipse

A solar eclipse occurs when the moon moves across the disk of the sun so that the moon’s shadow falls across the face of the earth. In the heart of that shadow, called the umbra, the sun’s disk will appear completely covered by that of the moon: a total solar eclipse. The umbra, however, only falls on a small region of the earth. Thus a total eclipse can be observed only within the zone of totality, a very narrow area of the earth (where this shadow falls as the earth rotates). For this reason, total eclipses are rare events in any given geographical area. Much more common are partial eclipses, in which the moon obscures only part of the sun. Observers located in the much broader outer shadow of the moon (the penumbra) see such an eclipse.
Certainly, partial eclipses are interesting, but a total eclipse can be spectacular, not only dramatically darkening the world, but allowing sight of such solar features as feathery prominences, the chromosphere, and, most thrilling of all, the corona. These features are fleeting, since totality lasts only a few minutes at any one observing location. As mentioned elsewhere in this book, observing the sun directly is very dangerous.
Looking at the sun through an unfiltered telescope or binoculars will cause irreversible damage to your eyesight. The sun is no more or less dangerous during an eclipse than at any other time; but the point is that looking directly at the sun is always dangerous and harmful.
The sun, during an eclipse or at any time, is most safely observed by projecting its image onto a piece of paper or cardboard. You can project a telescope or binocular image onto a white card held at the correct distance from the eyepiece. But you don’t need a telescope or binoculars to project an image. Just make a pinhole in a stiff piece of cardboard and project the pinhole image onto a white card or paper. (By the way: Do not look
through the pinhole directly at the sun!)
If you want to look at the sun through your telescope during an eclipse or at another time, purchase a solar filter (glass or Mylar) from any of the major telescope manufacturers. This type of filter attaches to the front of your telescope tube, it does not screw onto the eyepiece.

A Luminous Crown

Corona is Latin for “crown,” and it describes the region beyond the transition zone consisting of elements that have been highly ionized (stripped of their electrons) by the tremendous heat in the coronal region. Like the chromosphere, the corona is normally invisible, blotted out by the intense light of the photosphere. It is only during total solar eclipses that the corona becomes visible, at times when the disk of the moon covers the photosphere and the chromosphere. During such eclipse conditions, the significance of the Latin name becomes readily apparent: The corona appears as a luminous crown surrounding the darkened disk of the sun. When the sun is active—a cycle that peaks every 11 years—its surface becomes mottled with sunspots, and great solar flares and prominences send material far above its surface.

Not That Kind of Chrome

The sun’s lower atmosphere is called the chromosphere, normally invisible because the photosphere is far brighter. However, during a total solar eclipse, which blots out the photosphere, the chromosphere is visible as a pinkish aura around the solar disk. The strongest emission line in the hydrogen spectrum is red, and the predominance of hydrogen in the chromosphere imparts the pink hue. The chromosphere is a storm-racked region, into which spicules, jets of expelled matter thousands of miles high, intrude.
Above the chromosphere is the transition zone. As mentioned earlier, the temperature at the surface of the photosphere is 5,780 K, much cooler than the temperatures in the solar interior, which get hotter the closer one approaches the core. Yet, in the chromosphere, transition zone, and into the corona, the temperature rises sharply the farther one goes from the surface of the sun! At about 6,000 miles (10,000 km) above the photosphere, where the transition zone becomes the corona, temperatures exceed 1,000,000 K. (For detailed real-time views of the solar photosphere, chromosphere, and corona, see http://sohowww.estec.esa.nl.) How do we explain this apparent paradox? It is believed that the interaction between the sun’s strong magnetic field and the charged particles in the corona heat it to these high temperatures.

The Solar Atmosphere

The sun does not have a surface as such. What we call its surface is just the layer that emits the most light. Let’s begin our journey at the outer layers of the sun (the layers that we can actually see), and work our way in. When you look up at the sun during the day, what you are really looking at is the sun’s photosphere. The layer from which the visible photons that we see arise, the photosphere has a temperature of about 6,000 K. Lower layers are hidden behind the photosphere, and higher layers are so diffuse and faint (though very hot) that we only see them during total solar eclipses or with special satellites. Above the photosphere in the solar atmosphere are the chromosphere, the transition zone, and the corona. As we move higher in the sun’s atmosphere, the temperatures rise dramatically.

Four Trillion Trillion Light Bulbs

Next time you are screwing in a light bulb, notice its wattage. A watt is a measure of power, or how much energy is produced or consumed each second. A 100 watt bulb uses 100 joules of energy every second. For comparison, the sun produces 4 1026 watts of power. That’s a lot of light bulbs—four trillion trillion of them, to be exact. This rate of energy production is called the sun’s luminosity. Many stars have luminosities much higher than that of the sun.
The source of the sun’s power—and that of all stars, during most of their lifetimes—is the fusing together of nuclei. Stars first convert hydrogen into helium, and heavier elements come later. The only fusion reactions that we have been able to produce on the earth are uncontrolled reactions known as hydrogen bombs. The destructive force of these explosions gives insight into the enormous energies released in the core of the sun. Nuclear fusion could be used as a nearly limitless supply of energy on the earth; however, we are not yet able to create the necessary conditions on Earth for controlled fusion reactions.

A Spectacular, Mediocre Star

In terms of its size, mass and energy released, the sun is by far the most spectacular body in the solar system. With a radius of 22.8 X108 feet (6.96 X108 m), it is 100 times larger than the earth. Imagine yourself standing in a room with a golf ball. If the golf ball is the earth, the sun would touch the eight-foot ceiling. With a mass of 1.99 1030 kg, the sun is 300,000 times more massive than the earth. And with a surface temperature of 5,780 K (compared to the earth’s average 290 K surface temperature), the sun would melt or vaporize any matter we know.

What’s Sun Made Of?

The sun is mostly hydrogen (about 73 percent of the total mass) and helium (25 percent). Other elements are found in much smaller amounts, adding up to just under two percent of the sun’s mass. These include carbon, nitrogen, oxygen, neon, magnesium, silicon, sulfur, and iron. Over 50 other elements are found in trace amounts. There is nothing unique about the presence of these particular elements; they are the same ones that are distributed throughout the solar system and the universe. In particular, hydrogen atoms of the sun’s core plow into one another to create helium atoms. In the process, a little mass is converted into energy. That little bit of energy for each collision means enormous amounts of energy when we count all of the collisions that occur in the core of the sun. The fact that c is a very large number means that a tiny amount of mass results in a very large amount of energy. With this energy source, the sun is expected to last not a thousand years, or even 100 million years, but about 8 to 10 billion years, typical for a star with the sun’s mass.

The Solar Furnace

Greek philosopher Anaximenes of Miletus believed the sun, like other stars, was a great ball of fire. His was an important insight, but not entirely accurate. The sun is not so simple. In terms of human experience, the sun is an unfailing source of energy. Where does all of that energy come from? In the nineteenth century, scientists knew of two possible sources: thermal heat (like a candle burning) and gravitational energy. The problem with thermal energy is that even the sun doesn’t have enough mass to produce energy the way a candle does—at least, not for billions of years. Calculations showed that the sun “burning” chemically, would last only a few thousand years.
While a sun that was a few thousand years old might have pleased some theologians at the time, there was a variety of evidence showing that the earth was much older.
So scientists turned their attention to gravitational energy, that is, the conversion of gravitational energy into heat. The theory went this way: As the sun condensed out of the solar nebula, its atoms fell inward and collided more frequently as they got more crowded. These higher velocities and collisions converted gravitational energy into heat. Gravitational energy could power the sun’s output at its current rate for about 100 million years.
But when it started to become clear that the earth was much older (geological evidence showed that it was at least 3.5 billion years old), scientists went back to the drawing board. The nineteenth century ended without an understanding of the source of energy in the sun.

Understanding Sun

An evening spent looking up under dark skies will convince you that stars can be breathtaking in their loveliness. We can appreciate why, for thousands of years, human beings thought that the stars were embedded in a perfect sphere, spinning and changeless. Yet, because of their great distance, theirs is a remote beauty. Many amateur astronomers are disappointed to discover that stars (other than the sun) look pretty much the same through even the best telescope. Our common sense sees little similarity between the distant, featureless points of light against a sable sky and the great yellow disk of daytime, whose brilliance overwhelms our vision and warms our world. Yet, of course, our sun is a star—and, as stars go, not a particularly remarkable one. We now turn our attention to the very center of our solar system, the parent of the terrestrial and jovian planets and their rings and moons. We have spent the last three chapters discussing the planets and their moons. But taken together, these objects represent only 0.1 percent of the mass of the solar system. The other 99.9 percent of the mass is found in the sun. Peoples of many times and cultures have worshipped the sun as the source of all life, and in some sense, they were right. The sun is our furnace and our light bulb: the ultimate source of most energy and light here on the earth. And because it contains almost all of the mass, it is the gravitational anchor of the solar system. Indeed, its very matter is ours. The early sun was the hot center of a swirling disk of gas and dust from which the solar system formed some 4.6 billion years ago. If the sun were a cake, the earth and the rest of the planets would be some flour left on the counter. But the sun is only one star in a galaxy containing hundreds of billions of stars. Astronomers feel fortunate that the sun is so nondescript a citizen of the galaxy. It is, of course, the star closest to us and its very averageness lets us generalize about the many stars that lie far beyond our reach. In this chapter we examine our own star, and begin to explore how the sun (and stars in general) generate the enormous energies that they do.