The Milky Way and Beyond (10 page)

Even the basic measurement of where a star is in the sky can yield much useful information. Such observations can tell if a star is related to its neighbours and how it moves through the Galaxy.

Accurate observations of stellar positions are essential to many problems of astronomy. Positions of the brighter stars can be measured very accurately in the equatorial system (the coordinates of which are called right ascension [α, or RA] and declination [δ, or DEC] and are given for some epoch—for example, 1950.0 or, currently, 2000.0). Fainter stars are measured by using photographic plates or electronic imaging devices (e.g., a charge-coupled device, or CCD) with respect to the brighter stars, and finally the entire group is referred to the positions of known external galaxies. These distant galaxies are far enough away to define an essentially fixed, or immovable, system, whereas positions of both the bright and faint stars are affected over relatively short periods of time by galactic rotation and by their own motions through the Galaxy.

Accurate measurements of position make it possible to determine the movement of a star across the line of sight (i.e., perpendicular to the observer)—its proper motion. The amount of proper motion, denoted by μ (in arc seconds per year), divided by the parallax of the star and multiplied by a factor of 4.74 equals the tangential velocity,
V
_T
, in kilometres per second in the plane of the celestial sphere.

The motion along the line of sight (i.e., toward the observer), called radial velocity, is obtained directly from spectroscopic observations. If λ is the wavelength of a characteristic spectral line of some atom or ion present in the star, and λ
_L
the wavelength of the same line measured in the laboratory, then the difference Δλ, or λ − λ
_L
, divided by λ
_L
equals the radial velocity,
V
_R
, divided by the velocity of light,
c
—namely,

Δλ/λ
_L
=
V
_R
/
c
.

Shifts of a spectral line toward the red end of the electromagnetic spectrum (i.e., positive
V
_R
) indicate recession, and those toward the blue end (negative
V
_R
) indicate approach. If the parallax is known, measurements of μ and
V
_R
enable a determination of the space motion of the star. Normally, radial velocities are corrected for Earth's rotation and for its motion around the Sun, so that they refer to the line-of-sight motion of the star with respect to the Sun.

Consider a pertinent example. The proper motion of Alpha Centauri is about 3.5 arc seconds, which, at a distance of 4.4 light-years, means that this star moves 0.00007 light-year in one year. It thus has a projected velocity in the plane of the sky of 22 km per second (14 miles per second). As for motion along the line of sight, Alpha Centauri's spectral lines are slightly blue-shifted, implying a velocity of approach of about 20 km per second. The true space motion, equal to (22
²
+ 20
²
)
^½
or about 30 km per second (19 miles per second), suggests that this star will make its closest approach to the Sun (at three light-years' distance) some 280 centuries from now.

The light that stars emit does more than beautify the night sky. It tells us much about the stars themselves. All we know about what the stars are made of, how massive they are, and the temperatures of their surfaces all comes from starlight.

Stellar brightnesses are usually expressed by means of their magnitudes, a usage inherited from classical times. A star of the first magnitude is about 2.5 times as bright as one of the second magnitude, which in turn is some 2.5 times as bright as one of the third magnitude, and so on. A star of the first magnitude is therefore 2.5
⁵
or 100 times as bright as one of the sixth magnitude. The magnitude of Sirius, which appears to an observer on Earth as the brightest star in the sky (save the Sun), is −1.4. Canopus, the second brightest, has a magnitude of −0.7, while the faintest star normally seen without the aid of a telescope is of the sixth magnitude. Stars as faint as the 30th magnitude have been measured with modern telescopes, meaning that these instruments can detect stars about four billion times fainter than can the human eye alone.

The scale of magnitudes comprises a geometric progression of brightness. Magnitudes can be converted to light ratios by letting
l
_n
and
l
_m
be the brightnesses of stars of magnitudes
n
and
m
; the logarithm of the ratio of the two brightnesses then equals 0.4 times the difference between them—i.e.,

log(
l
_m
/
l
_n
) = 0.4(
n
−
m
).

Magnitudes are actually defined in terms of observed brightness, a quantity that depends on the light-detecting device employed. Visual magnitudes were originally measured with the eye, which is most sensitive to yellow-green light, while photographic magnitudes were obtained from images on old photographic plates, which were most sensitive to blue light.

Today, magnitudes are measured electronically, using detectors such as CCDs equipped with yellow-green or blue filters to create conditions that roughly correspond to those under which the original visual and photographic magnitudes were measured. Yellow-green magnitudes are still often designated
V
magnitudes, but
blue magnitudes are now designated
B
. The scheme has been extended to other magnitudes, such as ultraviolet (
U
), red (
R
), and near-infrared (
I
). Other systems vary the details of this scheme. All magnitude systems must have a reference, or zero, point. In practice, this is fixed arbitrarily by agreed-upon magnitudes measured for a variety of standard stars.

The actually measured brightnesses of stars give apparent magnitudes. These cannot be converted to intrinsic brightnesses until the distances of the objects concerned are known. The absolute magnitude of a star is defined as the magnitude it would have if it were viewed at a standard distance of 10 parsecs (32.6 light-years). Since the apparent visual magnitude of the Sun is −26.75, its absolute magnitude corresponds to a diminution in brightness by a factor of (2,062,650)
²
and is, using logarithms,

−26.75 + 2.5 × log(2,062,650)
²
, or −26.75 + 31.57 = 4.82.

This is the magnitude that the Sun would have if it were at a distance of 10 parsecs—an object still visible to the naked eye, though not a very conspicuous one and certainly not the brightest in the sky. Very luminous stars, such as Deneb, Rigel, and Betelgeuse, have absolute magnitudes of −7 to −9, while an extremely faint star, such as the companion to the star with the catalog name BD + 4°4048, has an absolute visual magnitude of +19, which is about a million times fainter than the Sun. Many astronomers suspect that large numbers of such faint stars exist, but most of these objects have so far eluded detection.

Stars differ in colour. Most of the stars in the constellation Orion visible to the naked eye are blue-white, most notably Rigel (Beta Orionis), but Betelgeuse (Alpha Orionis) is a deep red. In the telescope, Albireo (Beta Cygni) is seen as two stars, one blue and the other orange. One quantitative means of measuring stellar colours involves a comparison of the yellow (visual) magnitude of the star with its magnitude measured through a blue filter. Hot, blue stars appear brighter through the blue filter, while the opposite is true for cooler, red stars.

In all magnitude scales, one magnitude step corresponds to a brightness ratio of 2.512. The zero point is chosen so that white stars with surface temperatures of about 10,000 K have the same visual and blue magnitudes. The conventional colour index is defined as the blue magnitude,
B
, minus the visual magnitude,
V
; the colour index,
B
−
V
, of the Sun is thus

+5.47 − 4.82 = 0.65.

Problems arise when only one colour index is observed. If, for instance, a star is found to have, say, a
B
−
V
colour index of 1.0 (i.e., a reddish colour), it is impossible
without further information to decide whether the star is red because it is cool or whether it is really a hot star whose colour has been reddened by the passage of light through interstellar dust. Astronomers have overcome these difficulties by measuring the magnitudes of the same stars through three or more filters, often
U
(ultraviolet),
B
, and
V
.

Observations of stellar infrared light also have assumed considerable importance. In addition, photometric observations of individual stars from spacecraft and rockets have made possible the measurement of stellar colours over a large range of wavelengths. These data are important for hot stars and for assessing the effects of interstellar attenuation.

The measured total of all radiation at all wavelengths from a star is called a bolometric magnitude. The corrections required to reduce visual magnitudes to bolometric magnitudes are large for very cool stars and for very hot ones, but they are relatively small for stars such as the Sun. A determination of the true total luminosity of a star affords a measure of its actual energy output. When the energy radiated by a star is observed from Earth's surface, only that portion to which the energy detector is sensitive and that can be transmitted through the atmosphere is recorded. Most of the energy of stars like the Sun is emitted in spectral regions that can be observed from Earth's surface. On the other hand, a cool dwarf star with a surface temperature of 3,000 K has an energy maximum on a wavelength scale at 10000 angstroms (Å) in the far-infrared, and most of its energy cannot therefore be measured as visible light. (One angstrom equals 10
^−10
metre, or 0.1 nanometre.) Bright, cool stars can be observed at infrared wavelengths, however, with special instruments that measure the amount of heat radiated by the star. Corrections for the heavy absorption of the infrared waves by water and other molecules in Earth's air must be made unless the measurements are made from above the atmosphere.

The hotter stars pose more difficult problems, since Earth's atmosphere extinguishes all radiation at wavelengths shorter than 2900 Å. A star whose surface temperature is 20,000 K or higher radiates most of its energy in the inaccessible ultraviolet part of the electromagnetic spectrum. Measurements made with detectors flown in rockets or spacecraft extend the observable wavelength region down to 1000 Å or lower, though most radiation of distant stars is extinguished below 912 Å—a region in which absorption by neutral hydrogen atoms in intervening space becomes effective.

To compare the true luminosities of two stars, the appropriate bolometric corrections must first be added to each of their absolute magnitudes. The ratio of the luminosities can then be calculated.

A star's spectrum contains information about its temperature, chemical
composition, and intrinsic luminosity. Spectrograms secured with a slit spectrograph consist of a sequence of images of the slit in the light of the star at successive wavelengths. Adequate spectral resolution (or dispersion) might show the star to be a member of a close binary system, in rapid rotation, or to have an extended atmosphere. Quantitative determination of its chemical composition then becomes possible. Inspection of a high-resolution spectrum of the star may reveal evidence of a strong magnetic field.

Spectral lines are produced by transitions of electrons within atoms or ions. As the electrons move closer to or farther from the nucleus of an atom (or of an ion), energy in the form of light (or other radiation) is emitted or absorbed. The yellow “D” lines of sodium or the “H” and “K” lines of ionized calcium (seen as dark absorption lines) are produced by discrete quantum jumps from the lowest energy levels (ground states) of these atoms. The visible hydrogen lines (the so-called Balmer series), however, are produced by electron transitions within atoms in the second energy level (or first excited state), which lies well above the ground level in energy. Only at high temperatures are sufficient numbers of atoms maintained in this state by collisions, radiations, and so forth to permit an appreciable number of absorptions to occur. At the low surface temperatures of a red dwarf star, few electrons populate the second level of hydrogen, and thus the hydrogen lines are dim. By contrast, at very high temperatures—for instance, that of the surface of a blue giant star—the hydrogen atoms are nearly all ionized and therefore cannot absorb or emit any line radiation. Consequently, only faint dark hydrogen lines are observed. The characteristic features of ionized metals such as iron are often weak in such hotter stars because the appropriate electron transitions involve higher energy levels that tend to be more sparsely populated than the lower levels. Another factor is that the general “fogginess,” or opacity, of the atmospheres of these hotter stars is greatly increased, resulting in fewer atoms in the visible stellar layers capable of producing the observed lines.