Star

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Star

The nature of the stars

Energy generation

Stellar models

Mass: The fundamental stellar property

A star, in astronomy, is a roughly spherical massive ball of hot gas that shines as a result of nuclear fusion reactions in its core. Stars are the fundamental objects in the universe. They are the factories where elements heavier than hydrogen are formed. The radiation from a typical star like the Sun provides temperate conditions on planets like Earth where life can arise. Since the Sun is obviously the central source of energy for Earth and its many ecosystems, understanding how the Earth’s star works is an important area of research. Only in the past 80 years or so has the answer “Why does the Sun shine?” been partially answered, and many aspects of solar and stellar behavior are still poorly understood. Research on the physics of the Sun and stars will remain fresh and challenging for many years.

About 4,000 to 6,000 stars can be seen by the naked eye at any one time in the night sky. Hundreds of thousands of stars can be seen with a small telescope. The largest of telescopes on the Earth can observe millions of galaxies, which may contain over 200 billion stars. Astronomers estimate that there are over 1× 10²² stars in the entire universe.

Stars have been objects of human curiosity since the earliest human ancestors looked skyward. Throughout history humans have told stories about the stars, formed

bright stars into pictures in the sky, and, in just the past 80 years, begun to understand how stars work.

It is natural that scientists, and people in general, should be so fascinated by the stars, for humans are tightly linked to them. Stars—and indeed the entire universe—are made mostly of hydrogen, the simplest and lightest element. However, human bodies, and other living things, are comprised of many more complex elements including carbon, nitrogen, calcium, and iron. These elements are created in the cores of stars, and the final act in many stars” lives is a massive explosion that distributes the elements it has created into the galaxy, where eventually they may form another star, or a planet, or life on that planet. Understanding stars, therefore, is part of understanding human beings.

The nature of the stars

Internal structure

The Sun is a relatively stable star when compared to other stars. Its energy output is almost constant, with only tiny variations. This energy streams out into the solar system, where it is sufficient to heat the Earth, an entire planet nearly 93,000,000 mi (150,000,000 km) away. How does a ball of gas with the mass of the Sun (two million trillion kilograms) remain in a stable state like this for millions or billions of years?

Stars like the Sun exist in hydrostatic equilibrium, which means that at every point within the star, there is a balance between the weight of the material overlying that point and the gas pressure at that point. Figure 1 makes this a little clearer. suppose a person is halfway between the surface and the center of a star. Gravity attracts the star’s material towards its center, so the gas between the person and the surface tends to push one downward (arrow #1 in Figure 1). However, the gas where the person is positioned also exerts a pressure. The gas is being heated by the energy-producing reactions going on in the star’s core, and the hotter gas is, the more pressure it exerts. Trying to compress the gas is like trying to squeeze a balloon. One cannot just crush a balloon down to a point, because the air inside exerts a pressure on the sides of the balloon that resists the squeezing. In just the same way, the hot gas inside a star resists the weight of the overlying material, preventing it from falling inward under the influence of gravity (arrow 2 in Figure 1).

A stable star has to have this balance between gravity and gas pressure at every point in its interior. However, the closer one goes to the star’s center, the greater is the weight of the overlying material, in the same way that when one swims closer to the bottom of a swimming pool, the pressure on the ears becomes progressively greater.

Therefore, the gas nearer the center of the star has to be hotter, to exert a greater pressure that just counteracts the weight of all the gas above it. This is illustrated in Figure 2, where the size of the arrows shows the amount of gravity and gas pressure at different points within a star. The Sun and all other stable stars exist in this condition.

Energy generation

To remain in hydrostatic equilibrium, a star has to keep its gas very hot. The gas near the Sun’s surface is about 6,000 K (Kelvin) (10,292°F; 5,700°C), while deeper in its interior the temperature reaches millions of degrees Kelvin (K). Clearly, a star needs a potent power source to keep all this gas so hot. And, if one continued the imaginary trip from Figure 1 still deeper

into the star, one would eventually find this power source, the star’s core.

Stars generate energy in their cores, their central and hottest part. The Sun’s core has a temperature of about 15,000,000 K (15,000,000°C), and this is hot enough for thermonuclear fusion reactions to take place. Many different kinds of reactions are possible, but for stable stars, including the Sun, the primary reaction is one in which four hydrogen atoms are converted into one helium atom. Accompanying this transformation is an enormous release of energy, which streams out from the star’s core and supplies the energy needed to heat the star’s gas. (This is the same reaction, by the way, that occurs in a modern-day warhead of an ICBM (intercontinental ballistic missile), the so-called H-bomb. The ultimate human weapon of destruction is, for a very brief instant, a tiny star.) The Sun converts about six hundred million tons of hydrogen into helium every second, yet it is so massive that it has been maintaining this rate of fuel consumption for five billion years, and will continue to do so for another five.

Stellar models

The facts discussed above are the products of one of the great achievements of twentieth-century astronomy: the construction of stellar models that describe the internal structure of a star.

The mechanisms at work in a stellar interior can be described by four mathematical formulae known collectively as the laws of stellar structure. These equations describe how important quantities such as the temperature and pressure change with varying distances from the star’s center. A stellar model calculation involves choosing starting values for the important stellar parameters and running the model to see if a self-consistent solution emerges. If one does not, the parameters are repeatedly adjusted and the model rerun until a consistent solution is achieved. A successful model must reproduce the observed quantities at the stellar surface—i.e., the surface temperature of the model star should be the same as the temperature actually observed for a real star of the same mass and size.

In the first part of the twentieth century, astronomers calculated stellar models laboriously by hand. More recently, since the last quarter of the twentieth century, computers have enabled astronomers to construct increasingly detailed models. The work of stellar astronomers has, in just the past several decades, given humankind the essential answer to the ancient question, “Why does a star shine?”

Mass: The fundamental stellar property

Mass is the most important stellar property. This is because a star’s life is a continuous fight against gravity, and gravity is directly related to mass. The more massive a star is, the stronger its gravity. Mass therefore determines how strong the gravitational force is at every point within the star. This in turn dictates how fast the star has to consume its fuel to keep its gas hot enough to maintain hydrostatic equilibrium every where inside it. This controls the temperature structure of the star and the methods by which energy is transported from the core to the surface. It even controls the star’s lifetime, since the rate of fuel consumption determines lifetime.

The smallest stars are about 0.08 times the mass of the Sun. If a ball of gas is any smaller than that, it cannot raise its internal temperature high enough while it is forming to ignite the necessary fusion reactions in its core. The largest stars are about 50 times more massive than the Sun. A star more massive than that would shine so intensely that its radiation would start to overcome gravity—the star would shed mass from its surface so quickly that it could never be stable. Virtually everything about a star is related to its mass, and in the next section, how this works will be discussed in four case histories.

Four stars

In this section, an examination will be held about four stars in detail. At the high end of the mass scale is Alnilam, the central star in Orion’s belt, whose radius is 50 times that of the Sun. Next comes Regulus, the brightest star in the constellation Leo (the Lion). Regulus has a radius five times the Sun and a lifetime of 300,000,000 years. Next is the Sun, with a lifetime of 10,000,000,000 years, and finally Proxima Centauri, the nearest star beyond the Sun to the Earth, but so tiny, at one tenth the radius of the Sun, and faint that it is invisible to the unaided eye. These four stars are representative of the different properties and life cycles that stars can have.

Luminosity. Although Regulus is only 4.5 times more massive than the Sun, its luminosity, or rate of energy output, is 200 times greater. Stable stars obey a mass-luminosity relation, which can be expressed as an equation of the form L = 3.5 M, where L is the luminosity in solar units, and M is the mass in solar units. Since luminosity is related to fuel consumption rate, more massive stars have to burn their fuel much more rapidly than less massive ones to remain in hydrostatic equilibrium.

Lifetime. The mass-luminosity relation spells trouble for Regulus. Although Regulus has nearly five times as much fuel as the Sun does, it fuses it into helium 200 times faster. Astronomers, therefore, expect that Alnilam will live as a healthy star only about 0.025 (5/200) times as long as the Sun. By the same argument, tiny Proxima Centauri should live for an enormously long time. Long after the Sun, Regulus, and Alnilam have gone out, Proxima will still be glowing.

Energy transport. Energy flows from hot regions to cool regions. If one lets a cup of hot chocolate sit for a while, it gradually gets cold as its heat dissipates into the surroundings. Therefore, energy flows from a star’s intensely hot core outward to its surface, and it does so in two ways. One is called radiation, which is the normal flow of electromagnetic radiation through a medium such as a star’s gas. The other is called convection, and occurs when large, hot bubbles of gas rise, deposit their heat into a cooler, higher layer of the star, and then sink back down where they are reheated to begin the cycle anew. Convection is the phenomenon that builds cumulus clouds into towering thunderstorms on a hot summer day. Massive stars like Alnilam and Regulus have convective cores and radiative envelopes (envelope is the term used to describe the layers outside the core). Less massive stars like the Sun have radiative interiors with a convective zone just below their surface. Proxima Centauri is convective throughout. The type of transport mechanism a star uses at any point in its interior is determined by the local temperature structure, which in turn is governed by the star’s mass.

Surface temperature. When one speaks of a star’s surface, the photosphere is usually meant, which is the thin layer from which the star emits most of the visible light that reaches human eyes. The photosphere is not a surface as onee usually think of it, since it is thousands of times less dense than air. Below the photo-sphere, however, there is still enough stellar material between a ray of light and empty space that the light cannot escape. Above the photosphere, light can escape without interacting with any of the star’s matter, and this defines the boundary between the star’s interior and its atmosphere. More massive stars are hotter than less massive ones, because their gravity is stronger and their gas pressure (which is related to temperature) has to be higher to counteract this strong gravity. Regulus’s photosphere is about 12,000 K (21,092°F; 11,700°C), and at this temperature it blazes with a brilliant, white light. Proxima Centauri, if one could see it, would be a dull red, with a photosphere of only about 3,000 K (4,892°F; 2,700°C).

Atmosphere. The photosphere is the innermost layer of the star’s atmosphere. The Sun’s photosphere is only 300 mi (500 km) thick—minuscule when compared with its radius of almost 210,000 mi (350,000 km). One might expect the temperature to keep dropping as one moves outward though the atmosphere, but this is not the case. In the Sun, the temperature rises sharply a few thousand kilometers above the photosphere. This region, which in the Sun is about 10,000 K (17,492°F; 9,700°C), is called the chromosphere. Further out, the temperature rises even further, culminating in a corona of perhaps 2,000,000 K (2,000,000°C). Finally, beyond the corona, the temperature drops off and one has reached empty spaceand theend of thestar. The existenceof chromospheres and coronae baffled the scientists who discovered them and no one yet fully understands the nature of these regions.

Circumstellar environment. Most stars lose mass in a stellar wind. In stars like the Sun, the wind is an insignificant portion of the total mass, but many stars have enhanced winds that carry off an important part of their mass. Because mass is the property that governs a star’s evolution, mass loss can play an important role in altering the star’s evolution. The star Betelgeuse, for example, is an enormous, cool, red star that may end its life in a catastrophic supernova explosion—unless its strong wind carries off enough to prevent it. Additionally, stellar winds are a contributor to the replenishment and enrichment of the interstellar medium, the thin gas between the stars. During its life, therefore, a star contributes to the evolution of the galaxy it belongs to, as well as to future generations of stars.

Variable stars

Not all stars are as stable as the four discussed above. Many stars show periodic changes in brightness

that are greater than the tiny variations a star like the Sun exhibits. Stellar variability has many causes.

Some stars pulsate, expanding and contracting repeatedly. As they get larger, they brighten, and as they contract they get dimmer. They produce a light curve such as the one in Figure 3. This is the record of luminosity variations in the star Mira, a cool, red star that shows pronounced pulsation with a period of about 330 days.

Stars may also be variable if they belong to a binary or multiple system, in which two or more stars are in orbit around one other. (Most stars belong to multiple systems; the Sun is in a minority in this respect.) An important class of stars is the eclipsing binaries, which produce a light curve as one star passes in front of the other, blocking out its light and causing the whole system to appear dimmer. It is possible to determine the radii and masses of stars in eclipsing binaries—a very difficult or impossible task with single stars. Figure 4 shows the light curve of the famous eclipsing binary Algol.

Star deaths

All stars, whether variable or single and stable like Regulus, the Sun, and Proxima Centauri, eventually exhaust their hydrogen fuel. At this point, gravity begins to dominate as the star’s energy output drops. The gas pressure goes down and the star contracts under its own gravity. However, contraction raises the core temperature even more, and stars like Alnilam, Regulus, and the Sun will all be able to eventually begin new fusion reactions involving helium, rather than hydrogen, as the fuel. The ashes of the previous reactions are now used as the fuel for the new ones. This process of finding progressively heavier elements to burn causes the stars” radii to increase dramatically, at which point they are called giant or supergiant stars. Alnilam is one of these; it is a blazing supergiant, fusing elements heavier than hydrogen in its core, and shining with the light of 30,000 Suns. If one were suddenly to replace the Sun with Alnilam, the Earth would become a broiling wasteland in very little time.

Eventually the star fuses the last element it can use as a fuel source (for massive stars, this element is iron), and the result, as usual, depends on the mass: Alnilam will blow itself to bits in a supernova, and the dead remnant will be a neutron star or a black hole. The Sun will eject its outer layers more gently, in an expanding cloud of gas called a planetary nebula, leaving behind its carbon-and-oxygen core as a small, glowing object called a white dwarf. Proxima Centauri will do none of this. As its hydrogen runs low, an unimaginably long time in the future, it will slowly cool off as a slowly dying red dwarf.

The fate of the Sun

Our four stars illustrate the four possible fates of the stars: black holes, neutron stars, white dwarfs, and red dwarfs. The Sun will end its life as a hot-but-faint white dwarf, an object no larger than the Earth, and like a dying ember in a campfire it will gradually cool off and fade into blackness. Space is littered with such dead stars.

In its death throes, five billion years from now, the Sun will engulf Mercury, broil Venus, and wipe every vestige of life off the Earth. Alnilam will go much more violently; if it has planets, they will be vaporized by the supernova. In both cases, though, an expanding cloud of gas will be flung into space. This cloud will be rich in heavy elements, and there would be no such thing as iron atoms floating through space were it not for stars like Alnilam that create them in their central furnaces.

Stars form from these cold, dark clouds, and so do any planets that form around the stars. The Sun and its planets are second-generation products of the

KEY TERMS

Core —The central region of a star, where thermonuclear fusion reactions take place that produce the energy necessary for the star to support itself against its own gravity.

End state —One of the four possible ways in which a star can end its life. Stellar end states include black holes, neutron stars, white dwarfs, and red dwarfs.

Hydrostatic equilibrium —The condition in which the gas pressure at a given place within a star exactly counterbalances the weight of the overlying material. Such a star is stable, neither expanding nor contracting significantly.

Laws of stellar structure —The four mathematical formulae that describe the internal structure of a star. Using these laws, an astronomer can construct a stellar model that reproduces the observed properties of the star and that describes the temperature, pressure, and thermonuclear reactions, among other things, taking place inside the star.

Luminosity —The rate at which a star radiates energy (i.e., the star’s brightness). The brightest stars are 50,000 times more luminous than the Sun, while the faintest may be only a few thousandths as luminous.

Mass-luminosity relation —Describes the dependence of a star’s brightness (luminosity) on its mass, and expressed in the form L= 3.5 M. More massive stars have stronger gravity, and therefore must produce and radiate energy more intensely to counteract it, than less massive stars.

Photosphere —The thin layer at the base of a star’s atmosphere where most of the visible light escapes. Light below the photosphere is absorbed and scattered by the overlying material before it can escape to space.

Milky Way galaxy, and much of the material that went into making the Sun, the Earth, and humans was once in the center of some distant and long-dead Alnilam-like star. The theme begun by those distant stars has been picked up by the present generation, and five billion years from now, the Sun in turn will return some of its products to space. Sometime after that, the cycle will begin anew.