Measurement Of Stellar Motions The Stars example essay topic

Star, a glowing body of gases that also emits heat and other forms of energy that derive ultimately from thermonuclear reactions taking place in its interior. Stars and the vast collections of stars known as galaxies are the building blocks of the universe. Although the characteristics of individual stars vary greatly, our own sun may be described as a fairly typical star. This article deals with the nature of stars and the ways in which their properties are determined, the source of stellar energy, and the birth and death of stars. Related articles in The Encyclopedia Americana include Astronomy, Astrophysics, Cosmology, Galaxy, and Universe. In ancient times the stars were an unresolvable mystery, because no means existed for estimating or even guessing at their true nature.

It is not surprising that stars were once considered to be lights on a crystal sphere surrounding the earth, or to be holes on a dark surface through which shone the brilliance of a celestial realm. The first solid foundation for the hypothesis that the stars are in fact distant suns did not exist until the 16th century and the establishment of the Copernican concept that the earth revolves around the sun. Toward the end of that century, astronomers such as Tycho Brahe made measurements of the stars that revealed no observable parallax effects. That is, a given star was observed first from one side of the earth's orbital path and then, half a year later, from the opposite side of the path.

When this was done, no shift in the star's position relative to other stars could be observed. The implication was that the star lay at a very great distance from the solar system, just as the most distant objects in a landscape on earth seem to remain fixed relative to small changes in the position of an observer. It was not until the 19th century that more precise instruments enabled the shift in position of a relatively nearby star to be measured for the first time 1. Basic Facts about the Stars On a clear and moonless night, away from the lights of cities, it may seem as though the number of stars shining in the sky is infinite.

In fact the number is surprisingly low. No more than about 6,000 individual stars are visible to the naked eye on the entire celestial sphere, and no more than half of that sphere is seen by an observer at one time. Even with the aid of a good pair of binoculars, no more than about 100,000 stars could be counted, and if the entire sky were photographed by means of powerful telescopes, the number appearing on the photographs would amount to about one billion. All the stars seen with the naked eye and practically all those observed through telescopes belong to our own collection of stars, known as the Milky Way galaxy. There are many other galaxies in the universe, but except for the nearest of these the stars they contain are too distant to be distinguished as individual points of light. Our galaxy contains about 100 billion stars, and 100 million galaxies are visible.

The Twinkling of Stars One visual characteristic of stars distinguishes them from the five planets of the solar system Mercury, Venus, Mars, Jupiter, and Saturn that can be seen with the naked eye. The stars twinkle, whereas the planets shine with a steady light except when they are viewed close to the horizon. The twinkling is a combined effect of the great distance of the stars and the turbulence of the earth's atmosphere. That is, the stars are so far away that even though they are large they act as point sources of light rather than as disks, whereas the smaller planets are relatively close to the earth and are tiny disks in the sky, although this is not discernible to the naked eye. The light coming from the stars and planets fluctuates rapidly in apparent brightness because changes of density in the earth's atmosphere refract the light and produce twinkling effects.

Because the stars are point sources of light, they appear to twinkle. Because the planets are disks, however, the twinkling produced by individual points on the disks is averaged out, and the planets shine with a steady light. Near the horizon, however, the disturbances caused by looking through a greater thickness of atmosphere are sufficient to cause the planets to twinkle as well. Stellar Distances The stars are indeed very far from the earth, but astronomers have developed methods for estimating these distances. Some sense of stellar distances may be gained by comparing them to the greatest distances in the solar system. Light moves at a velocity of about 186,282 miles (299,776 km) per second.

At this rate it takes light reflected from Pluto, the outermost planet, about five hours to reach the earth. So vast is space, however, that the time light takes to travel from the stars is spoken of not in terms of hours or days but of years. The light even from the nearest known star, Alpha Centauri, takes a little longer than four years to reach our solar system. It would take a ray of light approximately 100,000 years to pass from one side of our Milky Way galaxy to the other, and distances to other galaxies must be measured in millions of light-years.

Range of Stellar Characteristics Although stars appear as point sources of light because they are so distant, man has learned that they are in fact large bodies of glowing gases like our sun. The stars vary greatly in color, depending on their temperatures. Some of them shine steadily, while others change periodically in brightness. Many stars are solitary, like the sun, but many are double stars two stars that revolve around each other and there are also complex systems of three, four, or more stars bound together gravitationally. The sun is an average star in brightness, but many stars would shine much more brightly than the sun does if they were as close as it is to the earth. The most brilliant stars radiate at between 10,000 to 1,000,000 times the rate of the sun, while the faintest stars are equivalently less brilliant than the sun is.

However, the range in stellar masses is much more restricted. The brightest stars have masses that are probably no greater than about 70 times the mass of the sun, whereas the masses of the faintest stars are still on the order of 1/20 of the sun's mass. Thus the least massive star is nevertheless much more massive than the giant planets of our solar system, such as Jupiter, which has a mass only about 1/1,000 that of the sun. 2. Measurement of Stellar Motions The stars are so far away that their positions relative to one another in the sky do not seem to change. For this reason they are sometimes referred to as the "fixed stars", in contrast to the "wandering stars", or planets, whose positions relative to the fixed stars change noticeably over a period of days.

The constellations, or patterns formed in the sky by brighter stars, were known since ancient times and are still being used by stargazers and in catalogs of celestial objects. However, the stars in fact do move relative to one another and to our own sun with its system of planets. If the Greek astronomer Ptolemy of the 2d century were to return today, he would notice that certain stars including Sirius, the brightest star in the sky had shifted their positions by an amount greater than the width of the moon's disk since his time. As the relative positions of the stars continue to change, the constellations of the far distant future will become quite different from those of today. Proper Motions The observatories of the major nations of the world have telescopes with which it is possible to fix the positions of the stars on the celestial sphere very precisely. The positions are then listed in extensive catalogs, and by comparing these catalogs with those from previous years, it is possible to find measurable shifts in the positions of thousands of stars.

These shifts, measured in terms of angular degrees on the celestial sphere, are called proper motions. A star may at the same time be moving toward or away from the solar system, but the term proper motion refers only to the component of motion across the line of sight from the earth. Other aspects of motion are determined from studies of stellar spectra. Sirius has a proper motion of 1.3 seconds of arc per year, which means that over 2,000 years it shifts in position by about one and a half lunar diameters.

The largest proper motion known is that of a faint object called Barnard's star, which shifts more than ten seconds of arc per year, or one full lunar diameter in less than 200 years. However, on the average, stars show annual proper motions of only a few thousandths of a second of arc and will not shift by more than one second of arc in two centuries, and it will take 10,000 to 100,000 years for proper motions of even the nearest galaxies of stars to become measurable. Parallax Measurements It is extremely difficult to separate proper motion from parallax effects, since both represent angular measurements of shifts in a star's position. As already described, the basic technique for determining the distance of a sufficiently nearby star is to measure the star's displacement on the celestial sphere as it is viewed a half-year apart from opposite ends of the earth's orbit. Parallax is defined as the greatest angular distance between the direction of the star as seen from the earth and as if from the sun, so the total displacement observed from the opposite ends of the earth's orbit is twice the star's parallax. The technique is basically the same as that used by surveyors on earth.

The problem of separating proper motion and parallax can be resolved by making measurements of a star's position exactly one year apart, so that the parallax displacement is identical each time and any observed shift should represent only proper motion. With this quantity known, the star's parallax can be calculated after making further positional observations. However, parallax measurements themselves are exceedingly difficult to carry out. The uncertainty of a high-quality determination amounts to about 0.005 second of arc, which means that a star with a true parallax of 0.010 second may have a measured parallax of anywhere between 0.005 and 0.015 second. Such measurements therefore cannot be reliable for distances much beyond about 65 light-years, or 20 parsecs one parsec being the distance at which a star would lie that showed a parallax of one second of arc, or about 3.26 light-years. There are many other methods for estimating distances of more remote stars.

Some of these other methods will be indicated in the course of this article. 3. Measurement of Stellar Brightness The brightness of a star in the sky is only its apparent brightness. The star may appear bright only because it is relatively close to the solar system, while another star may appear dim only because it lies at a great distance. The brightness scale in use today is a modification of the scale established by the ancient Greek astronomers. The Greeks defined the very brightest stars as being of the "first magnitude" and the faintest observable stars as of the sixth magnitude, with gradations of brightness in between.

The word "magnitude", meaning "size", came from the natural but inaccurate assumption that the brightest stars were necessarily the biggest stars as well. The word is now a convention, with no reference to size intended. In the early 19th century it was determined that the magnitude scale was actually a scale of brightness ratios. That is, a star of the first magnitude was very nearly 2.5 times as bright as a star of the second magnitude, the latter was about 2.5 times as bright as a star of the third magnitude, and so forth. Thus a difference of two magnitudes in brightness would represent a brightness ratio of (2.5) 2, or a little more than 6, and a difference of five magnitudes, or (2.5) 5, would be very nearly equal to 100, so that a first magnitude star is about 100 times as bright as a sixth magnitude star. The latter in turn is about 100 times as bright as an 11th magnitude star.

The faintest stars within the reach of large reflecting telescopes have an apparent magnitude of about 23.5, or 22.5 magnitudes fainter than a first magnitude star, which means that they are about one billion times less bright than the brightest stars seen in the earth's sky. Determination of Apparent Magnitudes The determination of precise apparent magnitudes of stars is a major undertaking for observational astronomers. The instrument most commonly used for this task is the photoelectric photometer. Attached close to the focus of a telescope, the instrument has a diaphragm that permits the light of only one selected star to enter it for a given measurement.

The light falls on a light-sensitive surface of a photoelectric tube, which produces a small electric current directly proportional to the intensity of the light. The resulting current is amplified in the tube and then in an electronic amplifier, so that a readily measurable current is finally recorded. A network of standard photoelectric magnitudes has been established for the brighter stars of the entire celestial sphere. The ratio in brightness between any given star and one of the standard stars of this network can readily be established with the aid of the photometer, and the ratio is then converted by simple mathematics into the difference between the observed star and the standard star.

Color Index Another important aspect of measuring brightness is the color of the star in question. Differences in color among the bright stars are easily observed with the naked eye, but it becomes difficult to distinguish the color of faint objects, which simply look rather grayish. However, using a large telescope, one can detect differences in the colors of stars to within about three or four magnitudes of the limiting stellar visibility of that particular telescope. In making determinations of photoelectric magnitudes, the astronomer must consider the range of color sensitivity to be included in each measurement. This is done by means of small color filters inserted in the path of the stellar light entering the photometer, so that the phototube receives only the portion of the light that is transmitted by the chosen filter. Separate magnitude scales have been established for different colors.

By international agreement, astronomers decided to set the reference standard for these scales as the blue-white stars such as Sirius and Altair. Thus the apparent magnitudes, V, and the "blue" magnitudes, B, of such stars are said to be equal. On the other hand, for a reddish star such as Betelgeuse or Antares, the magnitude B measured with a blue filter is fainter than the apparent magnitude V of the star in the sky. The difference between these two values, or B V, is known as the color index of a star.

Thus in a table of data on stars, the color index is an indication of a star's color. Sirius is set as the zero point, where B and V are exactly equal. A star bluer than Sirius has a negative color index, whereas more reddish stars have positive color indexes. Thus Antares has a color index of +1.80 and Betelgeuse a color index of +1.87. Absolute Magnitudes The absolute magnitude of a star is the brightness, or luminosity, that the star would have if it lay at a certain standard distance from the earth.

The distance chosen as the standard is 10 parsecs, or 32.6 light-years, so that the apparent magnitude and the absolute magnitude of a star lying at this precise distance would be the same. If the parallax of a given star is measurable and its apparent magnitude is known, then the absolute magnitude is easily established. For example, the parallax of Altair is 0.196, which means that the star lies 16.6 light-years, or 5.1 parsecs, away. The star's apparent magnitude is nearly +0.8, so at the distance of 10 parsecs it would obviously appear much fainter than +0.8, by a matter of about 1.5 magnitudes. Thus the absolute magnitude of Altair turns out to be +2.3. The absolute magnitude of our own sun is only +4.7.

A simple logarithmic formula relates the absolute and apparent magnitudes of a star with its distance from the earth, as follows: absolute magnitude = V + 5 5 (log d). In the formula, the distance d is in parsecs. 4. Information from Stellar Spectra Thus far the stars have been considered more or less as points of differently colored light to be observed and measured. However, when the light coming from a star is dispersed into its component wavelengths by means of a prism or a ruled grating, study of the resulting spectrum tells the astronomer a great deal about the actual physical properties of the star. Compositions of Stars When the spectra of stars are examined, most of them show a background of continuous radiation, including the familiar color band that stretches from ultraviolet light through blue, green, yellow, orange, and red into the infrared region.

In a typical stellar spectrum, this background of continuous radiation is crossed by many dark lines. The lines are wavelengths of light that have been absorbed by materials in the upper atmospheric regions of the star. From these lines astrophysicists are able to identify the chemical elements that are absorbing those particular wavelengths and to learn a great deal about the physical state of the elements. The lines also provide information on stellar motions, in that the line-of-sight motions of stars receding from us shift these lines slightly to the red and, for stars approaching us, slightly to the violet. The relative abundances of the chemical elements appear to be much the same in the atmospheres of most stars. Thus in a typical star such as our sun, approximately 92.5% of the atoms are hydrogen atoms, a little more than 7% are helium atoms, and all the rest of the chemical elements that may be present make up the remaining fraction of a percent.

In terms of weight, it is found that for every 1,000 unit weights of hydrogen there are 300 unit weights of helium and about 25 unit weights of all the heavier atoms combined, including such elements as carbon, nitrogen, oxygen, sodium, magnesium, silicon, and iron. For the great majority of visible stars, differences in the appearances of spectra can be interpreted as the result of widely differing physical conditions in the stellar atmospheres rather than of any major differences in the chemical compositions of the atmospheres. There are several varieties of stars having unusual distributions of elements, such as an overabundance of helium as compared to hydrogen, or an under abundance of helium, but such peculiar stars are the exceptions. Spectral Classifications In the 19th century it was discovered that the spectra of bluish white stars such as Sirius and Rigel are very different from those of reddish stars such as Betelgeuse and Antares. As a result, several basic spectral classes were established and were identified by letters of the alphabet. The letters were retained as scientific understanding increased, with the result that the sequence of the letters is by now quite arbitrary.

Thus the principal classes have narrowed to the following order of spectral types: O, B, A, F, G, K, and M stars. There are some minor classes as well, besides the stars classified simply as peculiar, but the majority of stars fit beautifully into the O-to-M sequence. There is a fairly good relationship between the spectral class of a star, its color index, and its surface temperature. The general characteristics of the classes are given below. O Stars A typical O star has a color index of -0.3, making this the bluest of the different classes of stars.

The surface temperature of an O star is in the range of 25,000 Kelvin, or 45,000 F. (The Kelvin temperature scale begins at absolute zero, or -273 Celsius, but at higher temperatures the Kelvin and Celsius scales can be considered approximately equivalent.) The spectrum of a typical O star shows strong and rather sharp lines that are attributed mainly to ionized helium, oxygen, and nitrogen. Also present are lines for neutral hydrogen that form one of three principal series of lines of the hydrogen spectrum and are known as the Balmer series. The continuous background spectrum indicates that so much ultraviolet radiation exists in an O star that it has stripped the atmospheric helium, oxygen, and nitrogen atoms of their outer electrons to produce the ionized forms. B Stars The color indexes of B stars range from -0.25 to -0.05, and surface temperatures correspondingly range from 23,000 to 12,000 K (41, 50021,500 F).

The lines of neutral helium are quite conspicuous in the hottest B stars, but with increasing coolness the helium lines fade out and hydrogen lines increase markedly in strength. Obviously not all stars classified as B are identical, and it is customary to subdivide the class into a sequence ranging from B 0 to B 9, B 0 being the hottest and B 9 the coolest of the B stars. A Stars The color indexes of the more whitish A stars range from about -0.05 to +0.2, and the surface temperatures range from about 11,000 K (20,000 F) for A 0 stars down to a little less than 8,000 K (14,500 F) for the A 8 or A 9 stars. Sirius, the brightest star in the sky, is classified as either A 0 or A 2. The spectra of A stars typically have very strong Balmer lines for hydrogen. In the spectra of cooler A stars, lines of ionized metals begin to appear, and lines of ionized calcium are already quite conspicuous in an A 8 spectrum.

F Stars The color indexes of the yellowish F stars range from +0.2 for F 0 spectra to +0.4 for F 8 or F 9 spectra. The hottest F stars have surface temperatures of about 7500 K (13,500 F), whereas the coolest are close to 6000 K (10,000 F). The Balmer hydrogen lines are still visible in the spectra but are definitely weaker than for A stars, while metal lines continue to increase in strength. Lines of neutral iron become visible in cool F stars. G Stars Our own sun and the bright star Capella are typical G stars. Color indexes of the yellowish red stars are mostly in the range of +0.5 to +0.8, while surface temperatures range from 6000 K (10,000 F) for G 0 to G 2 stars such as the sun, to about 5000 K (8500 F) for G 8 to G 9 stars.

Two particular lines of ionized calcium are very conspicuous in the spectra, and lines from ionized and neutral metals are also prominent. The Balmer series of hydrogen lines, on the other hand, has become quite faint. The first molecular absorption bands begin to suggest their presence in the spectra of cooler G stars. K Stars The orange-red K stars have color indexes ranging from +0.8 to +1.0, and their surface temperatures drop from 4000 K (7000 F) to 3200 K (5300 F). The ionized calcium lines have decreased in intensity in K spectra, and the Balmer hydrogen lines have faded away, but there is a strong neutral calcium line.

Molecular bands begin to make their presence increasingly evident in the progression from K 0 to K 9 stars. M Stars The reddish M stars are the coolest stars in the major spectral sequence, with color indexes of +2.0 to +3.0 or higher. Their surface temperatures range from 3000 K (5000 F) downward, and their spectra show strong bands that are attributed to the presence of titanium oxide in the stars. The Hertzsprung-Russell Diagram It took many years for astronomers to sort out the stars according to their spectral characteristics, absolute magnitudes, and surface temperatures. The names of two 20th century astronomers in particular, Einar Hertzsprung of Denmark and Henry Norris Russell of the United States, remain associated with this work in the form of the Hertzsprung-Russell, or H-R, diagram.

The diagram plots the absolute magnitudes of stars against their spectral class. When many stars are plotted on an H-R diagram, it is found that by far the largest number of visible stars fall along a smoothly curved arc from the upper left-hand corner to the lower right-hand corner of the diagram. Since they represent the most common stellar forms, the stars along this arc are known as the main sequence. Stars not on the main sequence fall into a variety of special categories. From the information contained on an H-R diagram it is not difficult for astronomers to make fairly precise estimates of average stellar diameters.

The following is a very rough example of the basic technique. Suppose a main sequence star with a B spectrum has a surface temperature of 18,000 K (32,000 F), which is about three times the temperature of our sun. The star is also about 10,000 times more luminous than our sun. According to the law formulated by the 19th century Austrian physicist Josef Stefan, the total amount of radiation emitted per unit area of a surface increases as the fourth power of the temperature. Thus every unit area of the surface of the B star should radiate about 34, or 81, times as strongly as the same unit area of the sun's surface. Since the B star is 10,000 times brighter than the sun, its total surface area should be roughly equal to 10,000 divided by 81, or about 125 times the surface area of the sun.

This means that the radius of the theoretical B star is approximately 11 times greater than the sun's radius. 5. Giant and Dwarf Stars From comparisons of stellar spectra it was found that there can be great differences in absolute magnitude between stars of roughly comparable spectral appearance. For example, both our sun and Capella are G 0 or G 2 stars, but the absolute magnitude of our sun is +4.7, whereas that of Capella is 0.6. Thus Capella is some 200 times more luminous than our sun. Such differences among stars of the same spectral class are accounted for by actual differences in size.

The stars are classified accordingly as giants or dwarfs. Hertzsprung and Russell were the first to make this firm distinction. Luminosities and Spectral Classes In modern spectral classification, astronomers list stars not only by their spectral class but also by their luminosity and hence size differences. Roman numerals are used, ranging from I for supergiant stars to V for dwarf stars, with still fainter sub dwarfs sometimes listed as VI. Astronomers may also distinguish between super-supergiants and normal supergiants, designating the former as Ia and the latter as Ib.

In the O, B, and A spectral classes, giant and dwarf stars all are members of the main sequence on the H-R diagram. However, some supergiants in these classes lie above the main sequence of stars. Among the F stars, giants and supergiants can be sorted from the main sequence by the sharpness of their spectral absorption lines, an effect probably resulting from the fact that the atmospheres of the giants are much more rarefied than those of the dwarf stars. In the G, K, and M classes the separation between giants and dwarfs is very clear, with all of the main sequence stars in these classes belonging to luminosity class V, or dwarf stars. Thus the sun, a main sequence star, is classified as a dwarf. For very cool M stars, the difference in luminosity between a giant and a dwarf may amount to 10,000 times or greater.

Range in Size and Mass It is clear that giant and dwarf stars of the same spectral class must be very different kinds of objects. For example, a red supergiant with an intrinsic brightness 10,000 times that of our sun and a surface temperature of 3000 K (5000 F) has a surface area 160,000 times that of the sun. This means that the star is 400 times as wide, and if it were to replace the sun in the solar system it would encompass the orbit of Mars. For several reasons such very large diameters are hard to believe, but astronomers cannot check their results directly even with the best of telescopes in the best of climates. However, the diameters of the red supergiants Betelgeuse and Antares were checked by ingenious indirect methods at Mt. Wilson Observatory in California, and the great sizes of the stars were confirmed.

Similar checks were made in Australia of supergiant O, B, and A stars. It is to be observed that the most luminous supergiants are estimated to have masses only 50 to 75 times the mass of our sun, whereas the faintest dwarf stars seem to have masses no lower than 0.05 times the sun's mass. Thus a range in luminosity from the brightest to the faintest stars that amounts to a factor of about 100 million must be compared to a corresponding range in mass that amounts to a factor of only 2,000. This is a startling result, because it means that supergiants are greatly rarefied objects perhaps with an average density as little as 0.0000002 that of our sun that must somehow produce the tremendous energies that they do, in fact, emit. Simple calculations show that one unit of matter inside a supergiant star must manage to produce 50,000 times as much energy as an equivalent amount of matter inside a very faint dwarf star. This indicates, as later discussions will confirm, that supergiant stars must exhaust their available supplies of energy much more quickly than do dwarfs.

6. Special Kinds of Stars Thus far the main sequence of stars and the supergiant and sub dwarf variations of these common stars have been described. On a comprehensive H-R diagram, a number of special kinds of stars are also observed. 311.