Objects with a starlike composition but too small to initiate nuclear reactions may also exist in the universe, helping to account for the “missing mass” of COSMOLOGY theories (see BROWN DWARF). Mass More than half of all stars are BINARY STARS–two or more stars that orbit one another. About 100 orbits have been measured accurately. These measurements provide perhaps the most important characteristic of a star: its mass. From Newton’s Laws of gravitation and motion, it is known that two highly massive stars must orbit (one around the other) faster than two stars of lesser mass at the same distance apart; thus the masses can be calculated from the orbit size and the period of the orbit.
If the binary stars eclipse each other, this situation also gives estimates of each star’s diameter. Orbits of the planets show that the Sun’s mass is 2 X (10 to the power of 33) g (2 billion billion billion tons, or about 333,000 times the Earth’s mass). Orbits of binary stars show that some stars (giants) are 40 times the mass of the Sun, and others (dwarfs) only 1/10 the mass of the Sun. The mass of a star is also related to its luminosity; a high-mass star has high luminosity, and a low-mass star has low luminosity. The MASS-LUMINOSITY RELATION states that the luminosity is approximately proportional to (mass) to the power of 3.5.
A star twice the mass of the Sun will have luminosity 2 to the power of 3.5, or 11.3 times the Sun’s. This fact, together with the temperatures and compositions of stars, is closely related to theories of stellar structure. In addition to luminosity and binary-star orbits, two systematic features in the motions of stars relate to their masses. In many groups and clusters of stars, the stars have similar motions and similar Doppler shifts in the lines of their spectra (see RED SHIFT); these similarities are easy to pick out from the random motions of single stars. The smaller motions of stars within a cluster show the cluster’s total mass–the sum of the masses of all the stars bound together in it by their gravitation.
These internal motions can also be used statistically to determine the distance from Earth to the cluster. More dramatic are the general motions of all the stars in the Sun’s vicinity, showing a circulation around the center of the Milky Way Galaxy. Again, Newton’s laws apply, and from the average orbits of stars around the center, the mass of this GALAXY is found to be 100 billion times the Sun’s mass. Because the orbital motions are faster near the center and slower farther away, individual motions can also be used to determine the distances to individual stars.
Since interstellar dust obscures more than half of the stars in the Milky Way Galaxy, mass measurements give the only reliable estimate of the total number of stars in the Galaxy, 100 billion, each with a mass between (10 to the power of 32)g and 2 X (10 to the power of 35)g. Starspots Starspots (cooler regions on the surface of stars, similar to the familiar SUNSPOTS) are now known to exist on a number of relatively nearby stars. The disks of such stars can be mapped to some degree to show areas of differing temperature, using the technique known as speckle interferometry (see INTERFEROMETER). The giant star Betelgeuse was observed in this manner as long ago as the mid-1970s. By means of spectral studies, astronomers have also been able to detect apparent granulation patterns on some stars.
Such patterns on the Sun are produced by convection, or the rising and falling of hotter and cooler currents just below the visible surface. Analysis of stellar spectra to yield this kind of detail requires the use of supercomputers. A larger, different kind of surface variation on stars has been reported by some astronomers, who call these variations “starpatches.” STRUCTURE OF STARS The structure of a typical star was worked out by astrophysicists after 1920, largely based on observations of the Sun. The photosphere is the visible surface of a star and is the layer to which the surface temperature and radius apply.
Above the photosphere is an atmosphere, mostly transparent, where gases absorb characteristic lines in the spectrum and reveal the chemical composition of the star. The temperature of the stellar atmosphere is lower than the temperature of the photosphere. Above the atmosphere is a transparent CORONA of diffuse gas at high temperature. For reasons as yet uncertain, outgoing energy from the Sun or star heats the corona to temperatures over 1,000,000 K (1,800,000 deg F), so that it emits X rays of much shorter wavelength than visible light. The solar corona also has emission lines in visible light which give it the greenish glow visible during a total solar eclipse. In the atmosphere and corona of a star, explosions known as flares occur in regions several thousand kilometers across, shooting out high-speed protons and electrons and causing plumes of higher temperature in the corona.
At a fairly constant rate, high-speed protons and electrons are also shot out in all directions to form the solar or stellar wind. The SOLAR WIND has been detected by the two VOYAGER spacecraft and PIONEERS 10 and 11 on their way out of the solar system.Eventually they are expected to cross the outer boundary of the solar wind, the heliopause, where interstellar gas pressure stops the outflow of the wind. The knowledge of a star’s internal structure is almost entirely theoretical, based on laboratory measurements of gases. Beneath the photosphere are several layers, some where the hot, ionized gas is turbulent, and some where it is almost at rest. Calculations of structure are based on two principles: convective equilibrium, in which turbulence brings the energy outward, and radiative equilibrium, in which radiation brings the energy outward. The temperature and density are calculated for each depth, using the characteristics of the mix of gases (hydrogen, helium, and heavier elements) derived from the spectrum of the atmosphere.
The pressure is calculated from the weight of the gases overhead. Eventually, deep in the interior the temperature and density are high enough (10,000,000 K and 30 g/cu cm) for a nuclear reaction to occur, converting four hydrogen atoms to one helium atom, with a 0.7% loss of mass. Because the conversion of this mass (m) to energy (E) follows Einstein’s equation E = mcc (where c is the velocity of light), such a reaction releases 6.4 X (10 to the power of 18) ergs of energy per gram of hydrogen, 60 million times more than chemical reactions such as the burning of hydrogen in oxygen. It is this enormous energy source that makes long-lasting, self-luminous stars possible. In an attempt to determine the precise mechanism providing the energy for stars, physicists in the early 1930s measured the rates of several nuclear reactions in the laboratory.
In 1938, Hans Bethe showed that the carbon-nitrogen cycle could account for a star’s long-lasting luminosity (see CARBON CYCLE, astronomy). In Bethe’s theory, carbon acts as a catalyst in the conversion of hydrogen to helium. The small amount needed is converted to nitrogen, then converted back to carbon to be used again. The reaction rates at the temperature and density in the core of the Sun are fast enough to produce (10 to the power of 33) ergs/sec, the luminosity of the Sun. Later it was shown that the PROTON-PROTON REACTION could also produce the Sun’s luminosity.
More recent studies show that in the Sun and smaller stars, where temperature and density in the core are lower than in larger stars, the proton-proton reaction beats out the Bethe cycle and can occur with no carbon or nitrogen present, if the temperature is about 10,000,000 K. In equations for the proton-proton reaction, the rates increase with the fourth power of the temperature, so that at a temperature of 20,000,000 K the rate is 16 times faster than at 10,000,000 K. Lithium and beryllium are probably also involved. The NEUTRINO is a very-low-mass particle that is produced in the Sun’s core and can pass through its outer regions to enter space. One of the great mysteries of modern astrophysics is the failure of experiments to detect the neutrinos expected from nuclear reactions in the Sun.
Whether by the Bethe cycle or by the proton-proton reaction, the Sun and other stars are converting hydrogen to helium in their cores at a considerable rate (600,000,000 tons/sec in the Sun). Because helium has different characteristics, this conversion changes the structure of the star. During the process there is a central core composed entirely of helium, a spherical shell around it in which hydrogen is being converted to helium, and the rest of the star, composed mostly of hydrogen. When a large core of helium has been created, the core may collapse, and new nuclear reactions may start as the temperature and density jump to very high values. When the temperature exceeds 100,000,000 K, helium is converted to carbon by the triple-alpha (ionized helium) process.
Astrophysicists make use of the Hertzsprung-Russell diagram and large computers to calculate how stars evolve in this way. They find that stars of different masses evolve in different ways and at different rates. The most massive stars (ten times the Sun’s mass) rapidly change from blue giants to red giants and may become unstable and pulsate as variable stars during this stage. Stars of lesser mass, such as the Sun, spend a large fraction of their lives on the main sequence of the Hertzsprung-Russell diagram while they convert hydrogen to helium. After several billion years, these stars become white dwarfs.
Depending on mass and other circumstances, a star may evolve to a NOVA or SUPERNOVA, PULSAR, NEUTRON STAR, or BLACK HOLE (see STELLAR EVOLUTION).
