A mass, chemical composition, and temperature. Some stars

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A star is a large ball of hot gas, thousands to millions of kilometers
in diameter, emitting large amounts of radiant energy from nuclear
reactions in its interior. Stars differ fundamentally from planets in that
they are self-luminous, whereas planets shine by reflected sunlight. Except
for the SUN, which is the nearest star, stars appear only as points of
light, even in the largest telescopes, because of their distance.

The brightest stars have long been given names. Most of the familiar
names originated with the ancient Greeks or with later Arab astronomers; an
entirely different system was used by the Chinese, starting hundreds of
years earlier, about 1000 BC. Polaris, the North Star, has a Greek name;
Betelgeuse, a bright red star, has an Arabic name. Modern astronomers
designate the bright stars according to the CONSTELLATIONS they are in.

Thus, the brightest star in the Big Dipper (part of the constellation Ursa
Major) is called alpha Ursa Majoris. Polaris, in the Little Dipper (Ursa
Minor), is gamma (designated by the Greek lower-case letter gamma) Ursa
Minoris, and Betelgeuse, in Orion, is gamma Orionis. VARIABLE STARS (those
which periodically change in brightness) have lettered names, such as RR
Lyrae in the constellation Lyra. Fainter stars are known by their numbers
in a catalog; HD 12938 is the 12,938th star in the Henry Draper Catalogue.

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Each star in the universe has its own position, motion, size, mass,
chemical composition, and temperature. Some stars are grouped into
clusters, and stars and star clusters are collected in the larger groupings
called galaxies. Our GALAXY, the Milky Way, contains more than 100 billion
stars. Because tens of millions of other galaxies are known to exist, the
total number of stars in the universe exceeds a billion billion.

Positions, Motions, and Distances
Stars are seen in the same relative positions, night after night, year
after year. They provided early astronomers with a reference system for
measuring the motions of planets (“wandering stars”), the Moon, and the
Sun. The westward rotation of the celestial sphere simply reflects the
daily eastward rotation of the Earth, and the Sun’s apparent motion among
the stars reflects the Earth’s annual orbit around the Sun.

As the construction of larger telescopes during the 19th century
improved the accuracy of determining stellar positions, it was found that
some stars are not precisely “fixed.” They move at various speeds, measured
as changes of direction in fractions of a second of arc per year, where one
second of arc is the angular size of a pinhead 183 m (200 yd) away. Most of
the faint stars are truly fixed as viewed from Earth and are used as a
reference frame for the minute motions of nearby stars, known as PROPER

PARALLAX is another apparent motion of nearby stars. It is caused by
the Earth’s orbit around the Sun: the star seems to shift, first one way,
then the other, as the Earth moves from 150 million km (93 million mi) on
one side of the Sun to 150 million km on the other side. Stellar parallax
can be used to determine astronomical DISTANCE. If the shift is 1 second of
arc each way, the star is about 32 million million km (20 million million
mi) from an observer. This distance is called the parsec and is equal to
3.26 light-years. The parallaxes of several thousand stars have been
measured during the past several decades. The nearest star is Proxima
Centauri, at about 1 parsec (3.3 light-years). Most of the measured
distances are greater than 20 parsecs (65 light-years), which shows why the
average star in the sky is so much fainter than the nearby Sun.

Brightness and Luminosity
Star brightness was first estimated by eye, and the brightest stars in
the sky were described as “stars of the first magnitude.” Later, the
magnitude scale was defined more accurately: 6th magnitude stars are just
1/100 as bright as 1st magnitude stars; 11th magnitude stars are 1/100 as
bright as 6th magnitude, and so on. The magnitude scale is logarithmic;
that is, each magnitude corresponds to a factor of 1/2.54, because (1/2.54)
to the power of 5 =1/100 (see MAGNITUDE).

Photographs are also used to measure star brightness from the size and
blackness of images on a photographic plate exposed in a telescope-camera.

With the photographic emulsions available in the early 1900s, a blue star
that appeared to the eye to have the same brightness as a red star
photographed much brighter. This discrepancy occurred because emulsions at
that time were much more sensitive to blue light than to red. Because of
this variation, two magnitude scales came into use: visual magnitude and
photographic magnitude. The difference for any one star, photographic
magnitude minus visual magnitude, measures the color of that star–positive
for red stars, negative for blue (see COLOR INDEX). By using filters and
special emulsions, astronomers soon had several other magnitude scales,
including ultraviolet and infrared. When photoelectric detectors were
introduced, the brightnesses of stars were measured with a photoelectric
photometer at the focus of a telescope. Standard colors (wavelengths) of
light were adopted, and the symbols were changed to V and B, with U for the
ultraviolet scale, and several other letters for infrared scales.

Measuring the brightness of a star on any of these scales is
complicated by factors related to the Earth’s atmosphere, which absorbs
more light when a star is near the horizon than when it is overhead. The
atmosphere also absorbs different amounts of the different colors and can
change during the night because of changing dust or moisture in the air.

Nevertheless, by comparing a star with a standard at the same height above
the horizon, astronomers using photoelectric photometers can measure U, B,
and V magnitudes with an accuracy of 0.01 magnitude (see PHOTOMETRY,

Such photometry has provided a great deal of information regarding the
temperatures and energy output of stars, but it does not give the total
energy output. Each measurement (U, B, V) gives only a fraction of the
star’s light reaching the Earth; even if the measurements are combined,
they give only the part that is not absorbed as it passes through the
Earth’s atmosphere. The atmosphere absorbs all light of short wavelengths
below ultraviolet and many of the long wavelengths above red. A theoretical
correction can be made, based on the star’s temperature, to give a
“bolometric” magnitude, m(b), adding the energy absorbed by the atmosphere.

True bolometric magnitudes, however, are measured only from rockets and
spacecraft outside the Earth’s atmosphere.

From parallax-distance measurements it is possible to calculate the
absolute bolometric magnitude, or luminosity, of a star, which is a measure
of its brightness relative to the Sun if it were at the Sun’s distance from
an observer on Earth. During the 1920s it was found that some stars
(giants) are 100,000 times as luminous as the Sun; others (white dwarfs)
are 1,000 times less luminous.

During ancient times and the Middle Ages stars were thought to be made
of an ethereal element different from matter on Earth. Their actual
composition did not become known until the invention of the SPECTROSCOPE in
the 19th century. Through the refraction of light by a prism (see PRISM,
physics) or through its diffraction by a DIFFRACTION GRATING, the light
from a source is spread out into its different visual wavelengths, from red
to blue; this is known as its SPECTRUM. The spectra of the Sun and stars
exhibited bright and dark lines, which were shown to be caused by elements
emitting or absorbing light at specific wavelengths. Because each element
emits or absorbs light only at specific wavelengths, the chemical
composition of stars can be determined. In this way the spectroscope
demonstrated that the gases in the Sun and stars are those of common
elements such as hydrogen, helium, iron, and calcium at temperatures of
several thousand degrees. It was found that the average star’s atmosphere
consists mostly of hydrogen (87%) and helium (10%), an element discovered
from spectra of the Sun, with all other elements making up about 3%. Helium
actually was first discovered in the Sun’s spectrum.

At first, visual estimates of the strengths of spectral lines were
used to estimate the amounts of the elements present in the Sun and a few
stars, based on an analysis of the lines produced by a laboratory light
source. When photographic emulsions came into use, the spectroscope became
the spectrograph, with a photographic film or plate replacing the human
eye. During the first half of the 20th century, spectrographs were used on
telescopes to observe thousands of stars. On the spectrogram, the
intensities of the lines are measured from the blackness of the film or
plate. Most recently, photoelectric detectors are used to scan the spectrum
in a spectrophotometer. Stellar spectra can also be measured by
interferometer techniques.

Although the ultraviolet, visual, and infrared parts of a star’s
spectrum can be measured in this way, other techniques must be used, above
the atmosphere, to measure the shorter wavelength spectra of X-ray stars
and gamma-ray stars. Instead of gratings and prisms, various combinations
of filters and detectors are used to measure portions of the X-ray and
gamma-ray spectra. At the other extreme (long wavelengths), radio spectra
of stars and other radio sources are measured by “tuning” a radio telescope
to different frequencies. A radio telescope–the largest is more than 305 m
(1,000 ft) across–is like a giant optical reflector with a radio amplifier
at the focus. Radio spectra are much more accurate than optical spectra.

Multiple radio telescopes, placed thousands of kilometers apart, can
determine the position of a radio-emitting star as accurately as an optical
telescope can, to better than 0.1 second of arc (see RADIO ASTRONOMY).

Spectral Type and Surface Temperature
During the early decades of the 20th century, Annie J. Cannon at
Harvard University examined thousands of stellar spectra. Without concern
for the actual atmospheric gases or temperatures, Cannon classified each
spectrum as A, B, C, . . .S, depending on the number of absorption lines.

Class A has few strong lines, class F has more, and classes M to S have
bands, which are many lines close together, produced by molecules (see
HARVARD CLASSIFICATION OF STARS). Later studies showed that Cannon’s
classes are a measure of surface temperature in the sequence O, B, A, F, G,
K, M, R, N, S. This measurement is based partly on physicist Max Planck’s
formula, which gives the relative emissions of various colors from a hot
body. A cool star emits most of its light in the red; a hot star emits most
of its light in the blue. A measurement of the ratio of blue to red light
coming from a star (its color index) determines its temperature. O stars
are hot (surface temperature =30,000 K); A stars have surface temperature =
10,000 K; G stars, such as the Sun, have surface temperature =6,000 K; and
M stars have surface temperature =3,000 K. Other spectrographic
measurements of absorption lines and emission lines help to confirm or
modify this so-called color temperature.

From 1911 to 1913, Einar Hertzsprung and H. N. Russell first plotted
the luminosity (L) versus the surface temperature (Ts) of stars, using as a
measure of temperature the spectral types determined by Cannon. The
HERTZSPRUNG-RUSSELL DIAGRAM first showed that highly luminous stars are
mostly of classes O and B, with helium lines and surface temperature
=25,000 K, whereas low-luminosity stars are mostly of class M and surface
temperature =3,000 K.

Once the temperature and the bolometric luminosity of a star are known,
its size can easily be calculated. Planck’s formula gives the total
emission of radiant energy per unit area of a hot body’s surface at each
temperature. From the bolometric luminosity, the total energy emitted is
known; from the temperature, the radiant energy emitted per square
centimeter is known. The ratio gives the number of square centimeters, from
which the radius of the star can be calculated. This rough calculation
shows that the radii of stars vary from 1/100 of that of the Sun for WHITE
DWARFS to 400 times that of the Sun for SUPERGIANTS. The radius of a nearby
star can also be measured directly with an interferometer on a telescope.

Astronomers theorize that 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).

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 (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
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

Bibliography: Barrow, J. D., and Silk, Joseph, The Left Hand of Creation
(1983); Abell, G., Exploration of the Universe (1969); Baade, Walter,
Evolution of Stars and Galaxies (1975); Evans Martin, Martha, The Friendly
Stars, rev. ed. (1982); Goldberg, H. S., and Scadron, M. D., Physics of
Stellar Evolution and Cosmology (1982); Hall, Douglas, “Starspots,”
Astronomy, February 1983; Kruse, W., and Dieckvoss, W., The Stars (1957);
Kyselka, Will, and Lanterman, Ray, North Star to Southern Cross (1976);
Meadows, A. J., Stellar Evolution (1978); Page, Thornton, and Page, L. W.,
Starlight (1967) and Stars and Clouds of the Milky Way (1968); Shklovskii,
Iosif S., Stars: Their Birth, Life and Death, trans. by Richard Rodman

DistanceApparent Brightness
Sun – -26.8
Centauri A4.3 -0.01
Centauri B4.3 1.33
Centauri C4.3 11.05
Barnard’s Star 5.9 9.54
Wolf 359 7.6 13.53
Lalande 21185 8.1 7.50
Sirius A 8.7 -1.47
Sirius B 8.7 8.68
Luyten 726-8A 8.9 12.45
Luyten 726-8B 8.9 12.95
Ross 154 9.4 10.6
Ross 24810.3 12.29
Eridani 10.7 3.73
Luyten 789-6 10.8 12.18
Ross 12810.8 11.10
61 Cygni A11.2 5.22
61 Cygni B11.2 6.03
Indi11.2 4.68
Procyon A11.3 0.37
Procyon B11.3 10.7
SOURCE: Adapted from a table compiled by Alan H. Batten in The Observer’s
Handbook 1976 of the Royal Astronomical Society of Canada and a table Drama
of the Universe (1978) by George O. Abell (reprinted by permission of Holt,
Rinehart and Winston).

NameConstellation (magnitude)(light-year)
Sun–26.8 –
Sirius ACanis Major -1.47 8.7
Canopus Carina-0.7298
Centauri ACentaurus-0.01 4.3
Capella Auriga 0.0545
RigelOrion 0.14900
Procyon ACanis Minor 0.3711.3
BetelgeuseOrion 0.41520
Altair Aquila 0.7716.5
Crucis Crux0.87400
AldebaranTaurus 0.8668
SpicaVirgo 0.91220
Antares Scorpius0.92520
FomalhautPiscis Austrinus1.1522.6
Pollux Gemini 1.1635
DenebCygnus 1.261,600
Crucis Crux1.28490
SOURCE: Adapted from a table compiled by Donald A. MacRae in The Observer’s
Handbook 1976 of the Royal Astronomical Society of Canada and a table in
Contemporary Astronomy, 2d., by Jay m. Pasachoff, Holt/Saunders, 1980.

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