Milky Way Galaxy

Large spiral galaxy (roughly 150,000 light-years in diameter) that contains Earth's solar system.

It includes the multitude of stars whose light is seen as the Milky Way, the irregular luminous band that encircles the sky defining the plane of the galactic disk. The Milky Way system contains hundreds of billions of stars and large amounts of interstellar gas and dust. Because the dust obscures astronomers' view of many of its stars, large areas could not be studied before the development of infrared astronomy and radio astronomy (see radio and radar astronomy). Its precise constituents, shape, and true size and mass are still not known; it is believed to contain large amounts of dark matter and a massive black hole at its core. The Sun lies in one of the Galaxy's spiral arms, about 27,000 light-years from the centre.

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▪ astronomy

Introduction

      large spiral system consisting of several billion stars (star), one of which is the Sun. It takes its name from the Milky Way, the irregular luminous band of stars and gas clouds that stretches across the sky as seen from Earth. Although Earth lies well within the Milky Way Galaxy (sometimes simply called the Galaxy), astronomers do not have as complete an understanding of its nature as they do of some external star systems. A thick layer of interstellar dust obscures much of the Galaxy from scrutiny by optical telescopes (telescope), and astronomers can determine its large-scale structure only with the aid of radio and infrared telescopes, which can detect the forms of radiation that penetrate the obscuring matter.

      This article discusses the structure, properties, and component parts of the Milky Way Galaxy. For a full-length discussion of the cosmic universe of which the Galaxy is only a small part, see Cosmos. For the star system within the Galaxy that is the home of Earth, see solar system.

Major components of the Galaxy

Star clusters (star cluster) and stellar associations

      Although most stars (star) in the Galaxy exist either as single stars like the Sun or as double stars, there are many conspicuous groups and clusters of stars that contain tens to thousands of members. These objects can be subdivided into three types: globular clusters (star cluster), open clusters (star cluster), and stellar associations. They differ primarily in age and in the number of member stars.

Globular clusters (globular cluster)

      The largest and most massive star clusters are the globular clusters, so called because of their roughly spherical appearance. The Galaxy contains approximately 140 globular clusters (the exact number is uncertain because of obscuration by dust in the Milky Way band, which probably prevents some globular clusters from being seen). They are arranged in a nearly spherical halo around the Milky Way, with relatively few toward the galactic plane but a heavy concentration toward the centre. The radial distribution, when plotted as a function of distance from the galactic centre, fits a mathematical expression of a form identical to the one describing the star distribution in elliptical galaxies (galaxy), though there is an anomalous peak in the distribution at distances of about 40,000 light-years (light-year) from the centre.

      Globular clusters are extremely luminous objects. Their mean luminosity is the equivalent of approximately 25,000 Suns (Sun). The most luminous are 50 times brighter. The masses of globular clusters, measured by determining the dispersion in the velocities of individual stars, range from a few thousand to more than 1,000,000 solar masses. The clusters are very large, with diameters measuring from 10 to as much as 300 light-years. Most globular clusters are highly concentrated at their centres, having stellar distributions that resemble isothermal gas spheres with a cutoff that corresponds to the tidal effects of the Galaxy. A precise model of star distribution within a cluster can be derived from stellar dynamics, which takes into account the kinds of orbits that stars have in the cluster, encounters between these member stars, and the effects of exterior influences. The American astronomer Ivan R. King, for instance, has derived dynamical models that fit observed stellar distributions very closely. He finds that a cluster's structure can be described in terms of two numbers: (1) the core radius, which measures the degree of concentration at the centre, and (2) the tidal radius, which measures the cutoff of star densities at the edge of the cluster.

      A key distinguishing feature of globular clusters in the Galaxy is their uniformly old age. Determined by comparing the stellar population of globular clusters with stellar evolutionary models, the ages of all those so far measured range from 11 billion to 13 billion years. They are the oldest objects in the Galaxy and so must have been among the first formed. That this was the case is also indicated by the fact that the globular clusters tend to have much smaller amounts of heavy elements than do the stars in the plane of the Galaxy, e.g., the Sun. Composed of stars belonging to the extreme Population II (see below Stars and stellar populations (Milky Way Galaxy)), as well as the high-latitude halo stars, these nearly spherical assemblages apparently formed before the material of the Galaxy flattened into the present thin disk. As their component stars evolved, they gave up some of their gas to interstellar space. This gas was enriched in the heavy elements produced in stars during the later stages of their evolution, so that the interstellar gas in the Galaxy is continually being changed. Hydrogen and helium have always been the major constituents, but heavy elements have gradually grown in importance. The present interstellar gas contains elements heavier than helium at a level of about 2 percent by mass, while the globular clusters contain as little as 0.02 percent of the same elements.

Open clusters (open cluster)

      Clusters smaller and less massive than the globular clusters are found in the plane of the Galaxy intermixed with the majority of the system's stars, including the Sun. These objects are the open clusters, so called because they generally have a more open, loose appearance than typical globular clusters.

      Open clusters are distributed in the Galaxy very similarly to young stars. They are highly concentrated along the plane of the Galaxy and slowly decrease in number outward from its centre. The large-scale distribution of these clusters cannot be learned directly because their existence in the Milky Way plane means that dust obscures those that are more than a few thousand light-years from the Sun. By analogy with open clusters in external galaxies similar to the Galaxy, it is surmised that they follow the general distribution of integrated light in the Galaxy, except that there are probably fewer of them in the central areas. There is some evidence that the younger open clusters are more densely concentrated in the Galaxy's spiral arms, at least in the neighbourhood of the Sun where these arms can be discerned.

      The brightest open clusters are considerably fainter than the brightest globular clusters. The peak absolute luminosity appears to be about 50,000 times the luminosity of the Sun, but the largest percentage of known open clusters has a brightness equivalent to 500 solar luminosities. Masses can be determined from the dispersion in the measured velocities of individual stellar members of clusters. Most open clusters have small masses on the order of 50 solar masses. Their total populations of stars are small, ranging from tens to a few thousand.

      Open clusters have diameters of only 2 or 3 to about 20 light-years, with the majority being less than 5 light-years across. In structure they look very different from globular clusters, though they can be understood in terms of similar dynamical models. The most important structural difference is their small total mass and relative looseness, which result from their comparatively large core radii. These two features have disastrous consequences as far as their ultimate fate is concerned, because open clusters are not sufficiently gravitationally bound to be able to withstand the disruptive tidal effects in the Galaxy (see star cluster: Open clusters (star cluster)). Judging from the sample of open clusters within 3,000 light-years of the Sun, only half of them can withstand such tidal forces for more than 200,000,000 years, while a mere 2 percent have life expectancies as high as 1,000,000,000 years.

      Measured ages of open clusters agree with the conclusions that have been reached about their life expectancies. They tend to be young objects; only a few are known to exceed 1,000,000,000 years in age. Most are younger than 200,000,000 years, and some are 1,000,000 or 2,000,000 years old. Ages of open clusters are determined by comparing their stellar membership with theoretical models of stellar evolution. Because all the stars in a cluster have very nearly the same age and chemical composition, the differences between the member stars are entirely the result of their different masses. As time progresses after the formation of a cluster, the massive stars, which evolve the fastest, gradually disappear from the cluster, becoming white dwarf stars (white dwarf star) or other underluminous stellar remnants. Theoretical models of clusters show how this effect changes the stellar content with time, and direct comparisons with real clusters give reliable ages for them. To make this comparison, astronomers use a diagram (the colour-magnitude diagram) that plots the temperatures of the stars against their luminosities. Colour-magnitude diagrams have been obtained for more than 1,000 open clusters, and ages are thus known for this large sample.

      Because open clusters are mostly young objects, they have chemical compositions that correspond to the enriched environment from which they formed. Most of them are like the Sun in their abundance of the heavy elements, and some are even richer. For instance, the Hyades, which compose one of the nearest clusters, have almost twice the abundance of heavy elements as the Sun. It became possible in the 1990s to discover very young open clusters that previously had been entirely hidden in deep, dusty regions. Using infrared array detectors, astronomers found that many molecular clouds contained very young groups of stars that had just formed and, in some cases, were still forming.

Stellar associations (stellar association)

      Even younger than open clusters, stellar associations are very loose groupings of young stars that share a common place and time of origin but that are not generally tied closely enough together gravitationally to form a stable cluster. Stellar associations are limited strictly to the plane of the Galaxy and appear only in regions of the system where star formation is occurring, notably in the spiral arms. They are very luminous objects. The brightest are even brighter than the brightest globular clusters, but this is not because they contain more stars; instead it is the result of the fact that their constituent stars are very much brighter than the stars constituting globular clusters. The most luminous stars in stellar associations are very young stars of spectral types O and B. They have absolute luminosities as bright as any star in the Galaxy—on the order of one million times the luminosity of the Sun. Such stars have very short lifetimes, only lasting a few million years. With luminous stars of this type there need not be very many to make up a highly luminous and conspicuous grouping. The total masses of stellar associations amount to only a few hundred solar masses, with the population of stars being in the hundreds or, in a few cases, thousands.

      The sizes of stellar associations are large; the average diameter of those in the Galaxy is about 250 light-years. They are so large and loosely structured that their self-gravitation is insufficient to hold them together, and in a matter of a few million years the members disperse into surrounding space, becoming separate and unconnected stars in the galactic field.

Moving groups

 These objects are remote organizations of stars that share common measurable motions but do not form a noticeable cluster. This definition allows the term to be applied to a range of objects from the nearest gravitationally bound clusters to groups of widely spread stars with no apparent gravitational identity, which are discovered only by searching the catalogs for stars of common motion. Among the best-known of the moving groups is the Hyades in the constellation Taurus. Also known as the Taurus moving cluster or the Taurus stream, this system comprises the relatively dense Hyades cluster along with a few very distant members. It contains a total of about 350 stars, including several white dwarfs. Its centre lies about 150 light-years away. Other notable moving stellar groups include the Ursa Major, Scorpius-Centaurus, and Pleiades groups. Besides these remote organizations, investigators have observed what appear to be groups of high-velocity stars near the Sun. One of these, called the Groombridge 1830 group, consists of a number of subdwarfs and the star RR Lyrae (RR Lyrae star), after which the RR Lyrae variables were named.

      Recent advances in the study of moving groups have had an impact on the investigation of the kinematic history of stars and on the absolute calibration of the distance scale of the Galaxy. Moving groups have proved particularly useful with respect to the latter because their commonality of motion enables astronomers to determine accurately (for the nearer examples) the distance of each individual member. Together with nearby parallax stars, moving-group parallaxes provide the basis for the galactic distance scale. Astronomers have found the Hyades moving cluster well suited for their purpose: it is close enough to permit the reliable application of the method, and it has enough members for deducing an accurate main-sequence position.

      One of the basic problems of using moving groups for distance determination is the selection of members. In the case of the Hyades, this has been done very carefully but not without considerable dispute. The members of a moving group (and its actual existence) are established by the degree to which their motions define a common convergent point in the sky. One technique is to determine the coordinates of the poles of the great circles defined by the proper motions and positions of individual stars. The positions of the poles will define a great circle, and one of its poles will be the convergent point for the moving group. Membership of stars can be established by criteria applied to the distances of proper-motion poles of individual stars from the mean great circle. The reliability of the existence of the group itself can be measured by the dispersion of the great circle points about their mean.

      As radial velocities will not have been used for the preliminary selection of members, they can be subsequently examined to eliminate further nonmembers. The final list of members should contain only a very few nonmembers—either those that appear to agree with the group motion because of observational errors or those that happen to share the group's motion at the present time but are not related to the group historically.

      The distances of individual stars in a moving group may be determined if their radial velocities and proper motions are known (see below Stellar motions (Milky Way Galaxy)) and if the exact position of the radiant is determined. If the angular distance of a star from the radiant is λ and if the velocity of the cluster as a whole with respect to the Sun is V, then the radial velocity of the star, V_r, is

V_r= V cos λ .

The transverse (or tangential) velocity, T, is given by

T = V sin λ = 4.74 μ/p

where p is the star's parallax in arc seconds. Thus, the parallax of a star is given by

p = 4.74 μ cot λ/V_r.

      The key to achieving reliable distances by this method is to locate the convergent point of the group as accurately as possible. The various techniques used (e.g., Charlier's method) are capable of high accuracy, provided that the measurements themselves are free of systematic errors. For the Taurus moving group, for example, it has been estimated that the accuracy for the best-observed stars is on the order of 3 percent in the parallax, discounting any errors due to systematic problems in the proper motions. Accuracies of this order were not possible by other means until the space-based telescope Hipparcos was able to measure highly precise stellar parallaxes for thousands of individual stars.

Emission nebulae (emission nebula)

 A conspicuous component of the Galaxy is the collection of large, bright, diffuse gaseous objects generally called nebulae (nebula). The brightest of these cloudlike objects are the emission nebulae, large complexes of interstellar gas and stars in which the gas exists in an ionized and excited state (with the electrons of the atoms excited to a higher than normal energy level). This condition is produced by the strong ultraviolet light emitted from the very luminous, hot stars embedded in the gas. Because emission nebulae consist almost entirely of ionized hydrogen, they are usually referred to as H II regions. (H II region)

      H II regions are found in the plane of the Galaxy intermixed with young stars, stellar associations, and the youngest of the open clusters. They are areas where very massive stars have recently formed, and many contain the uncondensed gas, dust, and molecular complexes commonly associated with ongoing star formation. The H II regions are concentrated in the spiral arms of the Galaxy, though some exist between the arms. Many of them are found at intermediate distances from the centre of the Milky Way Galaxy, with the largest number occurring at a distance of 10,000 light-years. This latter fact can be ascertained even though the H II regions cannot be seen clearly beyond a few thousand light-years from the Sun. They emit radio radiation of a characteristic type, with a thermal spectrum that indicates that their temperatures are about 10,000 kelvins. This thermal radio radiation enables astronomers to map the distribution of H II regions in distant parts of the Galaxy.

      The largest and brightest H II regions in the Galaxy rival the brightest star clusters in total luminosity. Even though most of the visible radiation is concentrated in a few discrete emission lines, the total apparent brightness of the brightest is the equivalent of tens of thousands of solar luminosities. These H II regions are also remarkable in size, having diameters of about 1,000 light-years. More typically, common H II regions such as the Orion Nebula are about 50 light-years across. They contain gas that has a total mass ranging from one or two solar masses up to several thousand. H II regions consist primarily of hydrogen, but they also contain measurable amounts of other gases. Helium is second in abundance, and large amounts of carbon, nitrogen, and oxygen occur as well. Preliminary evidence indicates that the ratio of the abundance of the heavier elements among the detected gases to hydrogen decreases outward from the centre of the Galaxy, a tendency that has been observed in other spiral galaxies.

Planetary nebulae (planetary nebula)

 The gaseous clouds known as planetary nebulae are only superficially similar to other types of nebulae. So called because the smaller varieties almost resemble planetary disks when viewed through a telescope, planetary nebulae represent a stage at the end of the stellar life cycle rather than one at the beginning. The distribution of such nebulae in the Galaxy is different from that of H II regions. Planetary nebulae belong to an intermediate population and are found throughout the disk and the inner halo. There are slightly more than 1,000 known planetary nebulae in the Galaxy, but many might be overlooked because of obscuration in the Milky Way region.

Supernova remnants

 Another type of nebulous object found in the Galaxy is the remnant of the gas blown out from an exploding star that forms a supernova. Occasionally these objects look something like planetary nebulae, as in the case of the Crab Nebula, but they differ from the latter in three ways: (1) the total mass of their gas (they involve a larger mass, essentially all the mass of the exploding star), (2) their kinematics (they are expanding with higher velocities), and (3) their lifetimes (they last for a shorter time as visible nebulae). The best-known supernova remnants are those resulting from three historically observed supernovae: that of 1054, which made the Crab Nebula its remnant; that of 1572, called Tycho's Nova; and that of 1604, called Kepler's Nova. These objects and the many others like them in the Galaxy are detected at radio wavelengths. They release radio energy in a nearly flat spectrum because of the emission of radiation by charged particles moving spirally at nearly the speed of light in a magnetic field enmeshed in the gaseous remnant. Radiation generated in this way is called synchrotron radiation and is associated with various types of violent cosmic (interplanetary dust particle) phenomena besides supernova remnants, as, for example, radio galaxies.

Dust clouds

 The dust clouds of the Galaxy are narrowly limited to the plane of the Milky Way, though very low-density dust can be detected even near the galactic poles. Dust clouds beyond 2,000 to 3,000 light-years from the Sun cannot be detected optically, because intervening clouds of dust and the general dust layer obscure more distant views. Based on the distribution of dust clouds in other galaxies, it can be concluded that they are often most conspicuous within the spiral arms, especially along the inner edge of well-defined ones. The best-observed dust clouds near the Sun have masses of several hundred solar masses and sizes ranging from a maximum of about 200 light-years to a fraction of a light-year. The smallest tend to be the densest, possibly partly because of evolution: as a dust complex contracts, it also becomes denser and more opaque. The very smallest dust clouds are the so-called Bok globules, named after the Dutch American astronomer Bart J. Bok (Bok, Bart J); these objects are about one light-year across and have masses of 1–20 solar masses.

      More complete information on the dust in the Galaxy comes from infrared observations. While optical instruments can detect the dust when it obscures more distant objects or when it is illuminated by very nearby stars, infrared telescopes are able to register the long-wavelength radiation that the cool dust clouds themselves emit. A complete survey of the sky at infrared wavelengths made during the early 1980s by an unmanned orbiting observatory, the Infrared Astronomical Satellite (IRAS), revealed a large number of dense dust clouds in the Milky Way. Twenty years later the Spitzer Space Telescope, with greater sensitivity, greater wavelength coverage, and better resolution, mapped many dust complexes in the Milky Way. In some it was possible to view massive star clusters still in the process of formation.

      Thick clouds of dust in the Milky Way can be studied by still another means. Many such objects contain detectable amounts of molecules that emit radio radiation at wavelengths that allow them to be identified and analyzed. More than 50 different molecules, including carbon monoxide and formaldehyde, and radicals have been detected in dust clouds.

The general interstellar medium

 The stars in the Galaxy, especially along the Milky Way, reveal the presence of a general, all-pervasive interstellar medium by the way in which they gradually fade with distance. This occurs primarily because of interstellar dust (interplanetary dust particle), which obscures and reddens starlight. On the average, stars near the Sun are dimmed by a factor of two for every 3,000 light-years. Thus, a star that is 6,000 light-years away in the plane of the Galaxy will appear four times fainter than it would otherwise were it not for the interstellar dust.

      Another way in which the effects of interstellar dust become apparent is through the polarization of background starlight. Dust is aligned in space to some extent, and this results in selective absorption such that there is a preferred plane of vibration for the light waves. The electric vectors tend to lie preferentially along the galactic plane, though there are areas where the distribution is more complicated. It is likely that the polarization arises because the dust grains are partially aligned by the galactic magnetic field. If the dust grains are paramagnetic so that they act somewhat like a magnet, then the general magnetic field, though very weak, can in time line up the grains with their short axes in the direction of the field. As a consequence, the directions of polarization for stars in different parts of the sky make it possible to plot the direction of the magnetic field in the Milky Way.

      The dust is accompanied by gas, which is thinly dispersed among the stars, filling the space between them. This interstellar gas consists mostly of hydrogen in its neutral form. Radio telescopes can detect neutral hydrogen because it emits radiation at a wavelength of 21 cm. Such radio wavelength is long enough to penetrate interstellar dust and so can be detected from all parts of the Galaxy. Most of what astronomers have learned about the large-scale structure and motions of the Galaxy has been derived from the radio waves of interstellar neutral hydrogen. The distance to the gas detected is not easily determined. Statistical arguments must be used in many cases, but the velocities of the gas, when compared with the velocities found for stars and those anticipated on the basis of the dynamics of the Galaxy, provide useful clues as to the location of the different sources of hydrogen radio emission. Near the Sun the average density of interstellar gas is 10⁻²¹ gm/cm³, which is the equivalent of about one hydrogen atom per cubic centimetre.

      Even before they first detected the emission from neutral hydrogen in 1951, astronomers were aware of interstellar gas. Minor components of the gas, such as sodium and calcium, absorb light at specific wavelengths, and they thus cause the appearance of absorption lines in the spectra of the stars that lie beyond the gas. Since the lines originating from stars are usually different, it is possible to distinguish the lines of the interstellar gas and to measure both the density and velocity of the gas. Frequently it is even possible to observe the effects of several concentrations of interstellar gas between Earth and the background stars and thereby determine the kinematics of the gas in different parts of the Galaxy.

Companion galaxies

 The Magellanic Clouds (Magellanic Cloud) were recognized early in the 20th century as companion objects to the Galaxy. When American astronomer Edwin Hubble (Hubble, Edwin Powell) established the extragalactic nature of what we now call galaxies, it became plain that the Clouds had to be separate systems, both of the irregular class and more than 100,000 light-years distant. (The current best values for their distances are 160,000 and 190,000 light-years for the Large and Small Clouds, respectively.) Additional close companions have been found, all of them small and inconspicuous objects of the dwarf elliptical class. The nearest of these is the Sagittarius dwarf, a galaxy that is falling into the Milky Way Galaxy, having been captured tidally by the Galaxy's much stronger gravity. Other close companions are the well-studied Carina, Draco, Fornax, Leo I, Leo II, Sextans, Sculptor, and Ursa Minor galaxies, as well as several very faint, less well-known objects. Distances for them range from approximately 200,000 to 800,000 light-years. The grouping of these galaxies around the Milky Way Galaxy is mimicked in the case of the Andromeda Galaxy, which is also accompanied by several dwarf companions.

Star populations and movement

Stars (star) and stellar populations

      The concept of different populations of stars has undergone considerable change over the last several decades. Before the 1940s, astronomers were aware of differences between stars and had largely accounted for most of them in terms of different masses, luminosities, and orbital characteristics around the Galaxy. Understanding of evolutionary differences, however, had not yet been achieved, and, although differences in the chemical abundances in the stars were known, their significance was not comprehended. At this juncture, chemical differences seemed exceptional and erratic and remained uncorrelated with other stellar properties. There was still no systematic division of stars even into different kinematic families, in spite of the advances in theoretical work on the dynamics of the Galaxy.

Principal population types

      In 1944 the German-born astronomer Walter Baade announced the successful resolution into stars of the centre of the Andromeda Galaxy, M31, and its two elliptical companions, M32 and NGC 205. He found that the central parts of Andromeda and the accompanying galaxies were resolved at very much fainter magnitudes than were the outer spiral arm areas of M31. Furthermore, by using plates of different spectral sensitivity and coloured filters, he discovered that the two ellipticals and the centre of the spiral had red giants as their brightest stars rather than blue main-sequence stars, as in the case of the spiral arms. This finding led Baade to suggest that these galaxies, and also the Milky Way Galaxy, are made of two populations of stars that are distinct in their physical properties as well as their locations. He applied the term Population I (Populations I and II) to the stars that constitute the spiral arms of Andromeda and to most of the stars that are visible in the Milky Way system in the neighbourhood of the Sun. He found that these Population I objects were limited to the flat disk of the spirals and suggested that they were absent from the centres of such galaxies and from the ellipticals entirely. Baade designated as Population II the bright red giant stars that he discovered in the ellipticals and in the nucleus of Andromeda. Other objects that seemed to contain the brightest stars of this class were the globular clusters of the Galaxy. Baade further suggested that the high-velocity stars near the Sun were Population II objects that happened to be passing through the disk.

      As a result of Baade's pioneering work on other galaxies in the Local Group (the cluster of star systems to which the Milky Way Galaxy belongs), astronomers immediately applied the notion of two stellar populations to the Galaxy. It is possible to segregate various components of the Galaxy into the two population types by applying both the idea of kinematics of different populations suggested by their position in the Andromeda system and the dynamical theories that relate galactic orbital properties with z distances (the distances above the plane of the Galaxy) for different stars. For many of these objects, the kinematic data on velocities are the prime source of population classification. The Population I component of the Galaxy, highly limited to the flat plane of the system, contains such objects as open star clusters (star cluster), O and B stars, Cepheid variables (Cepheid variable), emission nebulae, and neutral hydrogen. Its Population II component, spread over a more nearly spherical volume of space, includes globular clusters (star cluster), RR Lyrae (RR Lyrae star) variables, high-velocity stars, and certain other rarer objects.

      As time progressed, it was possible for astronomers to subdivide the different populations in the Galaxy further. These subdivisions ranged from the nearly spherical “halo Population II” system to the very thin “extreme Population I” system. Each subdivision was found to contain (though not exclusively) characteristic types of stars, and it was even possible to divide some of the variable-star types into subgroups according to their population subdivision. The RR Lyrae variables of type ab, for example, could be separated into different groups by their spectral classifications and their mean periods. Those with mean periods longer than 0.4 days were classified as halo Population II, while those with periods less than 0.4 days were placed in the “disk population.” Similarly, long-period variables were divided into different subgroups, such that those with periods of less than 250 days and of relatively early spectral type (earlier than M5e) were considered “intermediate Population II,” whereas the longer period variables fell into the “older Population I” category. As dynamical properties were more thoroughly investigated, many astronomers divided the Galaxy's stellar populations into a "thin disk," a "thick disk," and a "halo."

      An understanding of the physical differences in the stellar populations became increasingly clearer during the 1950s with improved calculations of stellar evolution. Evolving-star models showed that giants and supergiants are evolved objects recently derived from the main sequence after the exhaustion of hydrogen in the stellar core. As this became better understood, it was found that the luminosity of such giants was not only a function of the masses of the initial main-sequence stars from which they evolved but was also dependent on the chemical composition of the stellar atmosphere. Therefore, not only was the existence of giants in the different stellar populations understood, but differences between the giants with relation to the main sequence of star groups came to be understood in terms of the chemistry of the stars.

      At the same time, progress was made in determining the abundances of stars of the different population types by means of high-dispersion spectra obtained with large reflecting telescopes having a coudé focus arrangement. A curve of growth analysis demonstrated beyond a doubt that the two population types exhibited very different chemistries. In 1959 H. Lawrence Helfer, George Wallerstein, and Jesse L. Greenstein of the United States showed that the giant stars in globular clusters have chemical abundances quite different from those of Population I (Populations I and II) stars such as typified by the Sun. Population II stars have considerably lower abundances of the heavy elements—by amounts ranging from a factor of 5 or 10 up to a factor of several hundred. The total abundance of heavy elements, Z, for typical Population I stars is 0.04 (given in terms of the mass percent for all elements with atomic weights heavier than helium, a common practice in calculating stellar models). The values of Z for halo population globular clusters, on the other hand, were typically as small as 0.003.

      A further difference between the two populations became clear as the study of stellar evolution advanced. It was found that Population II was exclusively made up of stars that are very old. Estimates of the age of Population II stars have varied over the years, depending on the degree of sophistication of the calculated models and the manner in which observations for globular clusters (globular cluster) are fitted to these models. They have ranged from 10⁹ years up to 2 × 10¹⁰ years. Recent comparisons of these data suggest that the halo globular clusters have ages of approximately 1.1–1.3 × 10¹⁰ years. The work of American astronomer Allan Sandage (Sandage, Allan Rex) and his collaborators proved without a doubt that the range in age for globular clusters was relatively small and that the detailed characteristics of the giant branches of their colour-magnitude diagrams (colour–magnitude diagram) were correlated with age and small differences in chemical abundances. On the other hand, stars of Population I were found to have a wide range of ages. Stellar associations (stellar association) and galactic clusters with bright blue main-sequence stars have ages of a few million years (stars are still in the process of forming in some of them) to a few hundred million years. Studies of the stars nearest the Sun indicate a mixture of ages with a considerable number of stars of great age—on the order of 10⁹ years. Careful searches, however, have shown that there are no stars in the solar neighbourhood and no galactic clusters whatsoever that are older than the globular clusters. This is an indication that globular clusters, and thus Population II objects, formed first in the Galaxy and that Population I stars have been forming since.

      In short, as the understanding of stellar populations grew, the division into Population I and Population II became understood in terms of three parameters: age, chemical composition, and kinematics. A fourth parameter, spatial distribution, appeared to be clearly another manifestation of kinematics. The correlations between these three parameters were not perfect but seemed to be reasonably good for the Galaxy, even though it was not yet known whether these correlations were applicable to other galaxies. As various types of galaxies were explored more completely, it became clear that the mix of populations in galaxies was correlated with Hubble type. Spiral galaxies such as the Milky Way Galaxy have Population I concentrated in the spiral disk and Population II spread out in a thick disk and/or a spherical halo. Elliptical galaxies are nearly pure Population II, while irregular galaxies are dominated by a thick disk of Population I, with only a small number of Population II stars. Furthermore, the populations vary with galaxy mass; while the Milky Way Galaxy, a massive example of a spiral galaxy, contains no stars of young age and a low heavy-metal abundance, low-mass galaxies, such as the dwarf irregulars, contain young, low heavy-element stars, as the buildup of heavy elements in stars has not proceeded far in such small galaxies.

 Astronomers have devised a graphic way to explain the evolution of the stellar population in the Milky Way Galaxy, using a three-dimensional plot in which the age, the abundance of heavy elements, and the rate of star formation are all taken into account. The graph—> shows an example of such a three-dimensional plot. The volume shown in the figure indicates that the rate of star formation about the time the Galaxy originated was somewhat greater than at present but that it has not yet reached zero. As stars formed, the heavy elements were produced in the hot centres of the stars and in supernovae (supernova); thus, the volume moves forward in the box until the present is reached, and the majority of stars that are now forming have heavy elements in approximately the same amount as the Sun. At any time, τ, there is a spread in the abundances of the stars formed, depending on the history of the interstellar material in the region.

The stellar luminosity function

      The stellar luminosity function is a description of the relative number of stars of different absolute luminosities. It is often used to describe the stellar content of various parts of the Galaxy or other groups of stars, but it most commonly refers to the absolute number of stars of different absolute magnitudes in the solar neighbourhood. In this form it is usually called the van Rhijn function, named after the Dutch astronomer Pieter J. van Rhijn. The van Rhijn function is a basic datum for the local portion of the Galaxy, but it is not necessarily representative for an area larger than the immediate solar neighbourhood. Investigators have found that elsewhere in the Galaxy, and in the external galaxies (as well as in star clusters), the form of the luminosity function differs in various respects from the van Rhijn function.

      The detailed determination of the luminosity function of the solar neighbourhood is an extremely complicated process. Difficulties arise because of (1) the incompleteness of existing surveys of stars of all luminosities in any sample of space and (2) the uncertainties in the basic data (distances and magnitudes). In determining the van Rhijn function, it is normally preferable to specify exactly what volume of space is being sampled and to state explicitly the way in which problems of incompleteness and data uncertainties are handled.

      In general there are four different methods for determining the local luminosity function. Most commonly, trigonometric parallaxes (parallax) are employed as the basic sample. Alternative but somewhat less certain methods include the use of spectroscopic parallaxes, which can involve much larger volumes of space. A third method entails the use of mean parallaxes of a star of a given proper motion and apparent magnitude; this yields a statistical sample of stars of approximately known and uniform distance. The fourth method involves examining the distribution of proper motions and tangential velocities (the speeds at which stellar objects move at right angles to the line of sight) of stars near the Sun.

      Because the solar neighbourhood is a mixture of stars of various ages and different types, it is difficult to interpret the van Rhijn function in physical terms without recourse to other sources of information, such as the study of star clusters of various types, ages, and dynamical families. Globular clusters are the best samples to use for determining the luminosity function of old stars having a low abundance of heavy elements (Population II stars).

 Globular-cluster luminosity functions show a conspicuous peak at absolute magnitude M_V = 0.5, and this is clearly due to the enrichment of stars at that magnitude from the horizontal branch of the cluster. The height of this peak in the data is related to the richness of the horizontal branch, which is in turn related to the age and chemical composition of the stars in the cluster. A comparison of the observed M3 luminosity function with the van Rhijn function shows a depletion of stars, relative to fainter stars, for absolute magnitudes brighter than roughly M_V = 3.5. This discrepancy is important in the discussion of the physical significance of the van Rhijn function and luminosity functions for clusters of different ages and so will be dealt with more fully below.

      Many studies of the component stars of open clusters (open cluster) have shown that the luminosity functions of these objects vary widely. The two most conspicuous differences are the overabundance of stars of brighter absolute luminosities and the underabundance or absence of stars of faint absolute luminosities. The overabundance at the bright end is clearly related to the age of the cluster (as determined from the main-sequence turnoff point) in the sense that younger star clusters have more of the highly luminous stars. This is completely understandable in terms of the evolution of the clusters and can be accounted for in detail by calculations of the rate of evolution of stars of different absolute magnitudes and mass. For example, the luminosity function for the young clusters and χ Persei, when compared with the van Rhijn function, clearly shows a large overabundance of bright stars due to the extremely young age of the cluster, which is on the order of 10⁶ years. Calculations of stellar evolution indicate that in an additional 10⁹ or 10¹⁰ years all of these stars will have evolved away and disappeared from the bright end of the luminosity function.

      In 1955 the first detailed attempt to interpret the shape of the general van Rhijn luminosity function was made by the Austrian-born American astronomer Edwin E. Salpeter, who pointed out that the change in slope of this function near M_V = +3.5 is most likely the result of the depletion of the stars brighter than this limit. Salpeter noted that this particular absolute luminosity is very close to the turnoff point of the main sequence for stars of an age equal to the oldest in the solar neighbourhood—approximately 10¹⁰ years. Thus, all stars of the luminosity function with fainter absolute magnitudes have not suffered depletion of their numbers because of stellar evolution, as there has not been enough time for them to have evolved from the main sequence. On the other hand, the ranks of stars of brighter absolute luminosity have been variously depleted by evolution, and so the form of the luminosity function in this range is a composite curve contributed by stars of ages ranging from 0 to 10¹⁰ years. Salpeter hypothesized that there might exist a time-independent function, the so-called formation function, which would describe the general initial distribution of luminosities, taking into account all stars at the time of formation. Then, by assuming that the rate of star formation in the solar neighbourhood has been uniform since the beginning of this process and by using available calculations of the rate of evolution of stars of different masses and luminosities, he showed that it is possible to apply a correction to the van Rhijn function in order to obtain the form of the initial luminosity function. Comparisons of open clusters of various ages have shown that these clusters agree much more closely with the initial formation function than with the van Rhijn function; this is especially true for the very young clusters. Consequently, investigators believe that the formation function, as derived by Salpeter, is a reasonable representation of the distribution of star luminosities at the time of formation, even though they are not certain that the assumption of a uniform rate of formation of stars can be precisely true or that the rate is uniform throughout a galaxy.

      It was stated above that open-cluster luminosity functions show two discrepancies when compared with the van Rhijn function. The first is due to the evolution of stars from the bright end of the luminosity function such that young clusters have too many stars of high luminosity, as compared with the solar neighbourhood. The second discrepancy is that very old clusters such as the globular clusters have too few high-luminosity stars, as compared with the van Rhijn function, and this is clearly the result of stellar evolution away from the main sequence. Stars do not, however, disappear completely from the luminosity function; most become white dwarfs (white dwarf star) and reappear at the faint end. In his early comparisons of formation functions with luminosity functions of galactic clusters, Sandage calculated the number of white dwarfs expected in various clusters; present searches for these objects in a few of the clusters (e.g., the Hyades) have supported his conclusions.

      Open clusters also disagree with the van Rhijn function at the faint end—i.e., for absolute magnitudes fainter than approximately M_V = +6. In all likelihood this is mainly due to a depletion of another sort, the result of dynamical effects on the clusters that arise because of internal and external forces. Stars of low mass in such clusters escape from the system under certain common conditions. The formation functions for these clusters may be different from the Salpeter function and may exclude faint stars. A further effect is the result of the finite amount of time it takes for stars to condense; very young clusters have few faint stars partly because there has not been sufficient time for them to have reached their main-sequence luminosity.

Density distribution

The stellar density near the Sun

      The density distribution of stars near the Sun can be used to calculate the mass density of material (in the form of stars) at the Sun's distance within the Galaxy. It is therefore of interest not only from the point of view of stellar statistics but also in relation to galactic dynamics. In principle, the density distribution can be calculated by integrating the stellar luminosity function. In practice, because of uncertainties in the luminosity function at the faint end and because of variations at the bright end, the local density distribution is not simply derived nor is there agreement between different studies in the final result.

      In the vicinity of the Sun, stellar density can be determined from the various surveys of nearby stars and from estimates of their completeness. For example, Wilhelm Gliese's catalog of nearby stars (star catalog), a commonly used resourcecontains 1,049 stars in a volume within a radius of 65 light-years. This is a density of about 0.001 stars per cubic light-year. However, even this catalog is incomplete, and its incompleteness is probably attributable to the fact that it is difficult to detect the faintest stars and faint companions, especially extremely faint stars such as brown dwarfs.

      In short, the true density of stars in the solar neighbourhood is difficult to establish. The value most commonly quoted is 0.003 stars per cubic light-year, a value obtained by integrating the van Rhijn luminosity function with a cutoff taken M = 14.3. This is, however, distinctly smaller than the true density as calculated for the most complete sampling volume discussed above and is therefore an underestimate. Gliese has estimated that when incompleteness of the catalogs is taken into account, the true stellar density is on the order of 0.004 stars per cubic light-year, which includes the probable number of unseen companions of multiple systems.

      The density distribution of stars can be combined with the luminosity-mass relationship to obtain the mass density in the solar neighbourhood, which includes only stars and not interstellar material. This mass density is 4 × 10⁻²⁴g/cm³.

Density distribution of various types of stars

       Space densities of starsTo examine what kinds of stars contribute to the overall density distribution in the solar neighbourhood, various statistical sampling arguments can be applied to catalogs and lists of stars. The result of such a procedure is summarized in the table (Space densities of stars), which lists some of the kinds of objects and gives the calculated mean density over an appropriate volume centred on the Sun. For rare objects such as globular clusters, the volume of the sample must of course be rather large compared with that required to calculate the density for more common stars.

      The most common stars and those that contribute the most to the local stellar mass density are the dwarf (dwarf star) M (dM) stars, which provide a total of 0.0008 solar masses per cubic light-year. It is interesting to note that RR Lyrae variables and planetary nebulae (planetary nebula)—though many are known and thoroughly studied—contribute almost imperceptibly to the local star density. At the same time, white dwarf stars (white dwarf star), which are difficult to observe and of which very few are known, are among the more significant contributors.

Variations in the stellar density

      The star density in the solar neighbourhood is not perfectly uniform. The most conspicuous variations occur in the z direction, above and below the plane of the Galaxy, where the number density falls off rapidly. This will be considered separately below. The more difficult problem of variations within the plane is dealt with here.

      Density variations are conspicuous for early type stars (i.e., stars of higher temperatures) even after allowance has been made for interstellar absorption. For the stars earlier than type B3, for example, large stellar groupings in which the density is abnormally high are conspicuous in several galactic longitudes. The Sun in fact appears to be in a somewhat lower density region than the immediate surroundings, where early B stars are relatively scarce. There is a conspicuous grouping of stars, sometimes called the Cassiopeia-Taurus Group, that has a centroid at approximately 600 light-years distance. A deficiency of early type stars is readily noticeable, for instance, in the direction of the constellation Perseus at distances beyond 600 light-years. Of course, the nearby stellar associations are striking density anomalies for early type stars in the solar neighbourhood. The early type stars within 2,000 light-years are significantly concentrated at negative galactic latitudes. This is a manifestation of a phenomenon referred to as “the Gould Belt,” a tilt of the nearby bright stars in this direction with respect to the galactic plane, which was first noted by the English astronomer John Herschel (Herschel, Sir John, 1st Baronet) in 1847. Such anomalous behaviour is true only for the immediate neighbourhood of the Sun; faint B stars are strictly concentrated along the galactic equator.

      Generally speaking, the large variations in stellar density near the Sun are less conspicuous for the late type dwarf stars (those of lower temperatures) than for the earlier types. This fact is explained as the result of the mixing of stellar orbits over long time intervals available for the older stars, which are primarily those stars of later spectral types. The young stars (O, B, and A types) are still close to the areas of star formation and show a common motion and common concentration due to initial formation distributions. In this connection it is interesting to note that the concentration of A-type stars at galactic longitudes 160° to 210° is coincident with a similar concentration of hydrogen detected by means of 21-cm line radiation. Correlations between densities of early type stars on the one hand and interstellar hydrogen on the other are conspicuous but not fixed; there are areas where neutral-hydrogen concentrations exist but for which no anomalous star density is found.

      The variations discussed above are primarily small-scale fluctuations in star density rather than the large-scale phenomena so strikingly apparent in the structure of other galaxies. Sampling is too difficult and too limited to detect the spiral structure from the variations in the star densities for normal stars, although a hint of the spiral structure can be seen in the distribution in the earliest type stars and stellar associations. In order to determine the true extent in the star-density variations corresponding to these large-scale structural features, it is necessary to turn either to theoretical representations of the spiral structures or to other galaxies. From the former it is possible to find estimates of the ratio of star densities in the centre of spiral arms and in the interarm regions. The most commonly accepted theoretical representation of spiral structure, that of the density-wave theory, suggests that this ratio is on the order of 0.6, but, for a complicated and distorted spiral structure such as apparently occurs in the Galaxy, there is no confidence that this figure corresponds very accurately with reality. On the other hand, fluctuations in other galaxies can be estimated from photometry of the spiral arms and the interarm regions, provided that some indication of the nature of this stellar luminosity function at each position is available from colours or spectrophotometry. Estimates of the star density measured across the arms of spiral galaxies and into the interarm regions show that the large-scale spiral structure of a galaxy of this type is, at least in many cases, represented by only a relatively small fluctuation in star density.

      It is clear from studies of the external galaxies that the range in star densities existing in nature is immense. For example, the density of stars at the centre of the nearby Andromeda (Andromeda Galaxy) spiral galaxy has been determined to equal 100,000 solar masses per cubic light-year, while the density at the centre of the Ursa Minor dwarf elliptical galaxy is only 0.00003 solar masses per cubic light-year.

Variation of star density with z distances

       Stellar populationsFor all stars, variation of star density above and below the galactic plane rapidly decreases with height. Stars of different types, however, exhibit widely differing behaviour in this respect, and this tendency is one of the important clues as to the kinds of stars that occur in different stellar populations (see table (Stellar populations)).

      The luminosity function of stars is different at different galactic latitudes, and this is still another phenomenon connected with the z distribution of stars of different types. At a height of z = 3,000 light-years, stars of absolute magnitude 13 and fainter are nearly as abundant as at the galactic plane, while stars with absolute magnitude 0 are depleted by a factor of 100.

       Stellar populationsThe values of the scale height for various kinds of objects given in the table (Stellar populations) form the basis for the segregation of these objects into different population types. Such objects as open clusters and Cepheid variables that have very small values of the scale height are the objects most restricted to the plane of the Galaxy, while globular clusters and other extreme Population II objects have scale heights of thousands of parsecs, indicating little or no concentration at the plane. Such data and the variation of star density with z distance bear on the mixture of stellar orbit types. They show the range from those stars having nearly circular orbits that are strictly limited to a very flat volume centred at the galactic plane to stars with highly elliptical orbits that are not restricted to the plane.

Stellar motions

      A complete knowledge of a star's motion in space is possible only when both its proper motion and radial velocity can be measured. Proper motion is the motion of a star across an observer's line of sight and constitutes the rate at which the direction of the star changes in the celestial sphere. It is usually measured in seconds of arc per year. Radial velocity is the motion of a star along the line of sight and as such is the speed with which the star approaches or recedes from the observer. It is expressed in kilometres per second and is given as either a positive or negative figure, depending on whether the star is moving away from or toward the observer.

      Astronomers are able to measure both the proper motions and radial velocities of stars lying near the Sun. They can, however, determine only the radial velocities of stellar objects in more distant parts of the Galaxy and so must use these data, along with the information gleaned from the local sample of nearby stars, to ascertain the large-scale motions of stars in the Milky Way system.

Proper motions

      The proper motions of the stars in the immediate neighbourhood of the Sun are usually very large, as compared with those of most other stars. Those of stars within 17 light-years of the Sun, for instance, range from 0.49 to 10.31 arc seconds per year. The latter value is that of Barnard's star, which is the star with the largest known proper motion. The tangential velocity of Barnard's star is 90 km/sec, and, from its radial velocity (−108 km/sec) and distance (6 light-years), astronomers have found that its space velocity (total velocity with respect to the Sun) is 140 km/sec. The distance to this star is rapidly decreasing; it will reach a minimum value of 3.5 light-years in about the year 11,800.

Radial velocities

      Radial velocities, measured along the line of sight spectroscopically using the Doppler effect, are not known for all of the recognized stars near the Sun. Of the 45 systems within 17 light-years, only 40 have well-determined radial velocities. The radial velocities of the rest are not known, either because of faintness or because of problems resulting from the nature of their spectrum. For example, radial velocities of white dwarfs are often very difficult to obtain because of the extremely broad and faint spectral lines in some of these objects. Moreover, the radial velocities that are determined for such stars are subject to further complication because a gravitational redshift generally affects the positions of their spectral lines. The average gravitational redshift for white dwarfs has been shown to be the equivalent of a velocity of −51 km/sec. To study the true motions of these objects, it is necessary to make such a correction to the observed shifts of their spectral lines.

      For nearby stars, radial velocities are with very few exceptions rather small. For stars (star) closer than 17 light-years, radial velocities range from −119 km/sec to +245 km/sec. Most values are on the order of ±20 km/sec, with a mean value of −6 km/sec.

Space motions

      Space motions comprise a three-dimensional determination of stellar motion. They may be divided into a set of components related to directions in the Galaxy: U, directed away from the galactic centre; V, in the direction of galactic rotation; and W, toward the north galactic pole. For the nearby stars the average values for these galactic components are as follows: U = −8 km/sec, V = −28 km/sec, and W = −12 km/sec. These values are fairly similar to those for the galactic circular velocity components, which give U = −9 km/sec, V = −12 km/sec, and W = −7 km/sec. Note that the largest difference between these two sets of values is for the average V, which shows an excess of 16 km/sec for the nearby stars as compared with the circular velocity. Since V is the velocity in the direction of galactic rotation, this can be understood as resulting from the presence of stars in the local neighbourhood that have significantly elliptical orbits for which the apparent velocity in this direction is much less than the circular velocity. This fact was noted long before the kinematics of the Galaxy was understood and is referred to as the asymmetry of stellar motion.

      The average components of the velocities of the local stellar neighbourhood also can be used to demonstrate the so-called stream motion. Calculations based on the Dutch-born American astronomer Peter van de Kamp's table of stars within 17 light-years, excluding the star of greatest anomalous velocity, reveal that dispersions in the V direction and the W direction are approximately half the size of the dispersion in the U direction. This is an indication of a commonality of motion for the nearby stars; i.e., these stars are not moving entirely at random but show a preferential direction of motion—the stream motion—confined somewhat to the galactic plane and to the direction of galactic rotation.

High-velocity stars

      One of the nearest 45 stars, called Kapteyn's star, is an example of the high-velocity stars that lie near the Sun. Its observed radial velocity is −245 km/sec, and the components of its space velocity are U = 19 km/sec, V = −288 km/sec, and W = −52 km/sec. The very large value for V indicates that, with respect to circular velocity, this star has practically no motion in the direction of galactic rotation at all. As the Sun's motion in its orbit around the Galaxy is estimated to be approximately 250 km/sec in this direction, the value V of −288 km/sec is primarily just a reflection of the solar orbital motion.

Solar motion

      Solar motion is defined as the calculated motion of the Sun with respect to a specified reference frame. In practice, calculations of solar motion provide information not only on the Sun's motion with respect to its neighbours in the Galaxy but also on the kinematic properties of various kinds of stars within the system. These properties in turn can be used to deduce information on the dynamical history of the Galaxy and of its stellar components. Because accurate space motions can be obtained only for individual stars in the immediate vicinity of the Sun (within about 100 light-years), solutions for solar motion involving many stars of a given class are the prime source of information on the patterns of motion for that class. Furthermore, astronomers obtain information on the large-scale motions of galaxies in the neighbourhood of the Galaxy from solar motion solutions because it is necessary to know the space motion of the Sun with respect to the centre of the Galaxy (its orbital motion) before such velocities can be calculated.

      The Sun's motion can be calculated by reference to any of three stellar motion elements: (1) the radial velocities of stars, (2) the proper motions of stars, or (3) the space motions of stars.

Solar motion calculations from radial velocities

      For objects beyond the immediate neighbourhood of the Sun, only radial velocities can be measured. Initially it is necessary to choose a standard of rest (the reference frame) from which the solar motion is to be calculated. This is usually done by selecting a particular kind of star or a portion of space. To solve for solar motion, two assumptions are made. The first is that the stars that form the standard of rest are symmetrically distributed over the sky, and the second is that the peculiar motions—the motions of individual stars with respect to that standard of rest—are randomly distributed. Considering the geometry then provides a mathematical solution for the motion of the Sun through the average rest frame of the stars being considered.

      In astronomical literature where solar motion solutions are published, there is often employed a “K-term,” a term that is added to the equations to account for systematic errors, the stream motions of stars, or the expansion or contraction of the member stars of the reference frame. Recent determinations of solar motion from high-dispersion radial velocities have suggested that most previous K-terms (which averaged a few kilometres per second) were the result of systematic errors in stellar spectra caused by blends of spectral lines. Of course, the K-term that arises when a solution for solar motions is calculated for galaxies results from the expansion of the system of galaxies and is very large if galaxies at great distances from the Milky Way Galaxy are included.

Solar motion calculations from proper motions (proper motion)

      Solutions for solar motion based on the proper motions of the stars in proper motion catalogs can be carried out even when the distances are not known and the radial velocities are not given. It is necessary to consider groups of stars of limited dispersion in distance so as to have a well-defined and reasonably spatially-uniform reference frame. This can be accomplished by limiting the selection of stars according to their apparent magnitudes. The procedure is the same as the above except that the proper motion components are used instead of the radial velocities. The average distance of the stars of the reference frame enters into the solution of these equations and is related to the term often referred to as the secular parallax. The secular parallax is defined as 0.24h/r, where h is the solar motion in astronomical units per year and r is the mean distance for the solar motion solution.

Solar motion calculations from space motions

      For nearby well-observed stars, it is possible to determine complete space motions and to use these for calculating the solar motion. One must have six quantities: α (the right ascension of the star); δ (the declination of the star); μ_α (the proper motion in right ascension); μ_δ (the proper motion in declination); ρ (the radial velocity as reduced to the Sun); and r (the distance of the star). To find the solar motion, one calculates the velocity components of each star of the sample and the averages of all of these.

      Solar motion solutions give values for the Sun's motion in terms of velocity components, which are normally reduced to a single velocity and a direction. The direction in which the Sun is apparently moving with respect to the reference frame is called the apex of solar motion. In addition, the calculation of the solar motion provides dispersion in velocity. Such dispersions are as intrinsically interesting as the solar motions themselves because a dispersion is an indication of the integrity of the selection of stars used as a reference frame and of its uniformity of kinematic properties. It is found, for example, that dispersions are very small for certain kinds of stars (e.g., A-type stars, all of which apparently have nearly similar, almost circular orbits in the Galaxy) and are very large for some other kinds of objects (e.g., the RR Lyrae variables, which show a dispersion of almost 100 km/sec due to the wide variation in the shapes and orientations of orbits for these stars).

Solar motion solutions

      The motion of the Sun with respect to the nearest common stars is of primary interest. If stars within about 80 light-years of the Sun are used exclusively, the result is often called the standard solar motion. This average, taken for all kinds of stars, leads to a velocity V_ȯ = 19.5 km/sec. The apex of this solar motion is in the direction of α = 270°, δ = +30°. The exact values depend on the selection of data and method of solution. These values suggest that the Sun's motion with respect to its neighbours is moderate but certainly not zero. The velocity difference is larger than the velocity dispersions for common stars of the earlier spectral types, but it is very similar in value to the dispersion for stars of a spectral type similar to the Sun. The solar velocity for, say, G5 stars is 10 km/sec, and the dispersion is 21 km/sec. Thus, the Sun's motion can be considered fairly typical for its class in its neighbourhood. The peculiar motion of the Sun is a result of its relatively large age and a somewhat noncircular orbit. It is generally true that stars of later spectral types show both greater dispersions and greater values for solar motion, and this characteristic is interpreted to be the result of a mixture of orbital properties for the later spectral types, with increasingly large numbers of stars having more highly elliptical orbits.

      The term basic solar motion has been used by some astronomers to define the motion of the Sun relative to stars moving in its neighbourhood in perfectly circular orbits around the galactic centre. The basic solar motion differs from the standard solar motion because of the noncircular motion of the Sun and because of the contamination of the local population of stars by the presence of older stars in noncircular orbits within the limits of the reference frame. The most commonly quoted value for the basic solar motion is a velocity of 16.5 km/sec toward an apex with a position α = 265°, δ = 25°.

       Adopted components of the solar motion and velocity dispersionsWhen the solutions for solar motion are determined according to the spectral class of the stars, there is a correlation between the result and the spectral class. The table (Adopted components of the solar motion and velocity dispersions) summarizes values obtained from various sources and illustrates this fact. The apex of the solar motion, the solar motion velocity, and its dispersion are all correlated with spectral type. Generally speaking (with the exception of the very early type stars), the solar motion velocity increases with decreasing temperature of the stars, ranging from 16 km/sec for late B-type and early A-type stars to 24 km/sec for late K-type and early M-type stars. The dispersion similarly increases from a value near 10 km/sec to a value of 22 km/sec. The reason for this is related to the dynamical history of the Galaxy and the mean age and mixture of ages for stars of the different spectral types. It is quite clear, for example, that stars of early spectral type are all young, whereas stars of late spectral type are a mixture of young and old. Connected with this is the fact that the solar motion apex shows a trend for the latitude to decrease and the longitude to increase with later spectral types.

      The solar motion can be based on reference frames defined by various kinds of stars and clusters of astrophysical interest. Data of this sort are interesting because of the way in which they make it possible to distinguish between objects with different kinematic properties in the Galaxy. For example, it is clear that interstellar calcium lines have relatively small solar motion and extremely small dispersion because they are primarily connected with the dust that is limited to the galactic plane and with objects that are decidedly of the Population I class. On the other hand, RR Lyrae variables and globular clusters have very large values of solar motion and very large dispersions, indicating that they are extreme Population II objects that do not all equally share in the rotational motion of the Galaxy. The solar motion of these various objects is an important consideration in determining to what population the objects belong and what their kinematic history has been.

      When some of these classes of objects are examined in greater detail, it is possible to separate them into subgroups and find correlations with other astrophysical properties. Take, for example, globular clusters (globular cluster), for which the solar motion is correlated with the spectral type of the clusters. The clusters of spectral types G0–G5 (the more metal-rich clusters) have a mean solar motion of 80 ± 82 km/sec (corrected for the standard solar motion). The earlier type globular clusters of types F2–F9, on the other hand, have a mean velocity of 162 ± 36 km/sec, suggesting that they partake much less extensively in the general rotation of the Galaxy. Similarly, the most distant globular clusters have a larger solar motion than the ones closer to the galactic centre. Studies of RR Lyrae variables (RR Lyrae star) also show correlations of this sort. The period of an RR Lyrae (RR Lyrae star) variable, for example, is correlated with its motion with respect to the Sun. For type ab RR Lyrae variables, periods frequently vary from 0.3 to 0.7 days, and the range of solar motion for this range of period extends from 30 to 205 km/sec, respectively. This condition is believed to be primarily the result of the effects of the spread in age and composition for the RR Lyrae variables in the field, which is similar to, but larger than, the spread in the properties of the globular clusters.

      Since the direction of the centre of the Galaxy is well established by radio measurements and since the galactic plane is clearly established by both radio and optical studies, it is possible to determine the motion of the Sun with respect to a fixed frame of reference centred at the Galaxy and not rotating (i.e., tied to the external galaxies). The value for this motion is generally accepted to be 225 km/sec in the direction ℓ^II = 90°. It is not a firmly established number, but it is used by convention in most studies.

      In order to arrive at a clear idea of the Sun's motion in the Galaxy as well as of the motion of the Galaxy with respect to neighbouring systems, solar motion has been studied with respect to the Local Group galaxies and those in nearby space. Hubble determined the Sun's motion with respect to the galaxies beyond the Local Group and found the value of 300 km/sec in the direction toward galactic longitude 120°, latitude +35°. This velocity includes the Sun's motion in relation to its proper circular velocity, its circular velocity around the galactic centre, the motion of the Galaxy with respect to the Local Group, and the latter's motion with respect to its neighbours.

      One further question can be considered: What is the solar motion with respect to the universe? In the 1990s the Cosmic Background Explorer first determined a reliable value for the velocity and direction of solar motion with respect to the nearby universe. The solar system is headed toward the constellation Leo with a velocity of 370 km/sec. This value was confirmed in the 2000s by an even more sensitive space telescope, the Wilkinson Microwave Anisotropy Probe (Wilkinson Microwave Anisotropy Probe (WMAP)).

Paul W. Hodge

The structure and dynamics of the Milky Way Galaxy

Size

      The first reliable measurement of the size of the Galaxy was made in 1917 by American astronomer Harlow Shapley (Shapley, Harlow). He arrived at his size determination by establishing the spatial distribution of globular clusters (star cluster). Shapley found that, instead of a relatively small system with the Sun near its centre, as had previously been thought, the Galaxy is immense, with the Sun nearer the edge than the centre. Assuming that the globular clusters outlined the Galaxy, he determined that it has a diameter of about 100,000 light-years (light-year) and that the Sun lies about 30,000 light-years from the centre. (A light-year is the distance traveled by light in one year and is roughly 9,460,000,000,000 km [5,880,000,000,000 miles].) His values have held up remarkably well over the years. Depending in part on the particular component being discussed, the stellar disk of the Milky Way system is just about as large as Shapley's model predicted, with neutral hydrogen somewhat more widely dispersed and dark (i.e., unobservable) matter perhaps filling an even larger volume than expected. The most distant stars (star) and gas clouds of the system that have had their distance reliably determined lie roughly 72,000 light-years from the galactic centre, while the distance of the Sun from the centre has been found to be approximately 25,000 light-years.

Structure of the spiral system

 The Milky Way Galaxy's structure is fairly typical of a large spiral system. (Spiral galaxies and other types of galaxies are described in the article galaxy.) This structure can be viewed as consisting of six separate parts: (1) a nucleus, (2) a central bulge, (3) a disk (both a thin and a thick disk), (4) spiral arms, (5) a spherical component, and (6) a massive halo. Some of these components blend into each other.

The nucleus

      At the very centre of the Galaxy lies a remarkable object—in all likelihood a massive black hole surrounded by an accretion disk of high-temperature gas. Neither the central object nor any of the material immediately around it can be observed at optical wavelengths because of the thick screen of intervening dust in the Milky Way. The object, however, is readily detectable at radio wavelengths and has been dubbed Sagittarius A* (Sagittarius A) by radio astronomers. Somewhat similar to the centres of active galaxies (see below), though on a lesser scale, the galactic nucleus is the site of a wide range of activity apparently powered by the black hole. Infrared radiation and X-rays (X-ray) are emitted from the area, and rapidly moving gas clouds can be observed there. Data strongly indicate that material is being pulled into the black hole from outside the nuclear region, including some gas from the z direction (i.e., perpendicular to the galactic plane). As the gas nears the black hole, its strong gravitational force squeezes the gas into a rapidly rotating disk, which extends outward about 5–30 light-years from the central object. Rotation measurements of the disk and the orbital motions of stars (seen at infrared wavelengths) indicate that the black hole has a mass 3,600,000 times that of the Sun.

The central bulge

 Surrounding the nucleus is an extended bulge of stars that is nearly spherical in shape and that consists primarily of Population II stars, though they are comparatively rich in heavy elements. (For an explanation of Population II stars, see below Stars and stellar populations (Milky Way Galaxy).) Mixed with the stars are several globular clusters of similar stars, and both the stars and clusters have nearly radial orbits around the nucleus. The bulge stars can be seen optically where they stick up above the obscuring dust of the galactic plane.

The disk

      From a distance the most conspicuous part of the Galaxy would be the disk, which extends from the nucleus out to approximately 75,000 light-years. The Galaxy resembles other spiral systems, featuring as it does a bright, flat arrangement of stars and gas clouds that is spread out over its entirety and marked by a spiral structure. The disk can be thought of as being the underlying body of stars upon which the arms are superimposed. This body has a thickness that is roughly one-fifth its diameter, but different components have different characteristic thicknesses. The thinnest component, often called the "thin disk," includes the dust and gas and the youngest stars, while a thicker component, the "thick disk,” includes somewhat older stars.

The spiral arms

      Astronomers did not know that the Galaxy had a spiral structure until 1953, when the distances to stellar associations were first obtained reliably. Because of the obscuring interstellar dust and the interior location of the solar system, the spiral structure is very difficult to detect optically. This structure is easier to discern from radio maps of either neutral hydrogen or molecular clouds, since both can be detected through the dust. Distances to the observed neutral hydrogen atoms must be estimated on the basis of measured velocities used in conjunction with a rotation curve for the Galaxy, which can be built up from measurements made at different galactic longitudes.

      From studies of other galaxies it can be shown that spiral arms generally follow a logarithmic spiral form such that

log r = a − bϕ,

where ϕ is a position angle measured from the centre to the outermost part of the arm, r is the distance from the centre of the galaxy, and a and b are constants. The range in pitch angles for galaxies is from about 50° to approximately 85°. The pitch angle is constant for any given galaxy if it follows a true logarithmic spiral. The pitch angle for the spiral arms of the Galaxy is difficult to determine from the limited optical data, but most measurements indicate a value of about 75°. There are five optically identified spiral arms in the part of the Milky Way Galaxy wherein the solar system is located.

      Theoretical understanding of the Galaxy's spiral arms has progressed greatly since the 1950s, but there is still no complete understanding of the relative importance of the various effects thought to determine their structure. The overall pattern is almost certainly the result of a general dynamical effect known as a density-wave pattern. The American astronomers Chia-Chiao Lin and Frank H. Shu showed that a spiral shape is a natural result of any large-scale disturbance of the density distribution of stars in a galactic disk. When the interaction of the stars with one another is calculated, it is found that the resulting density distribution takes on a spiral pattern that does not rotate with the stars but rather moves around the nucleus more slowly as a fixed pattern. Individual stars in their orbits pass in and out of the spiral arms, slowing down in the arms temporarily and thereby causing the density enhancement. For the Galaxy, comparison of neutral hydrogen data with the calculations of Lin and Shu have shown that the pattern speed is 4 km/sec per 1,000 light-years.

      Other effects that can influence a galaxy's spiral shape have been explored. It has been demonstrated, for example, that a general spiral pattern will result simply from the fact that the galaxy has differential rotation; i.e., the rotation speed is different at different distances from the galactic centre. Any disturbance, such as a sequence of stellar formation events that are sometimes found drawn out in a near-linear pattern, will eventually take on a spiral shape simply because of the differential rotation. For example, the outer spiral structure in some galaxies may be the result of tidal encounters with other galaxies or galactic cannibalism. Distortions that also can be included are the results of massive explosions such as supernova events. These, however, tend to have only fairly local effects.

The spherical component

      The space above and below the disk of the Galaxy is occupied by a thinly populated extension of the central bulge. Nearly spherical in shape, this region is populated by the outer globular clusters, but it also contains many individual field stars of extreme Population II, such as RR Lyrae (RR Lyrae star) variables and dwarf stars deficient in the heavy elements. Structurally, the spherical component resembles an elliptical galaxy, following the same simple mathematical law of how density varies with distance from the centre.

The massive halo (galactic halo)

      The least-understood component of the Galaxy is the giant massive halo that is exterior to the entire visible part. The existence of the massive halo is demonstrated by its effect on the outer rotation curve of the Galaxy (see below Mass (Milky Way Galaxy)). All that can be said with any certainty is that the halo extends considerably beyond a distance of 100,000 light-years from the centre and that its mass is several times greater than the mass of the rest of the Galaxy taken together. It is not known what its shape is, what its constituents are, or how far into intergalactic space it extends.

magnetic field

      It was once thought that the spiral structure of galaxies might be controlled by a strong magnetic field. However, when the general magnetic field was detected by radio techniques, it was found to be too weak to have large-scale effects on galactic structure. The strength of the galactic field is only about 0.000001 times the strength of Earth's field at its surface, a value that is much too low to have dynamical effects on the interstellar gas that could account for the order represented by the spiral-arm structure. This is, however, sufficient strength to cause a general alignment of the dust grains in interstellar space, a feature that is detected by measurements of the polarization of starlight. In the prevailing model of interstellar dust grains, the particles are shown to be rapidly spinning and to contain small amounts of metal (probably iron), though the primary constituents are ice and carbon. The magnetic field of the Galaxy can gradually act on the dust particles and cause their rotational axes to line up in such a way that their short axes are parallel to the direction of the field. The field itself is aligned along the Milky Way band, so that the short axes of the particles also become aligned along the galactic plane. Polarization measurements of stars at low galactic latitudes confirm this pattern.

Rotation

      The motions of stars in the local stellar neighbourhood can be understood in terms of a general population of stars that have circular orbits of rotation around the distant galactic nucleus, with an admixture of stars that have more highly elliptical orbits and that appear to be high-velocity stars to a terrestrial observer as Earth moves with the Sun in its circular orbit. The general rotation of the disk stars was first detected through studies made in the 1920s, notably those of the Swedish astronomer Bertil Lindblad (Lindblad, Bertil), who correctly interpreted the apparent asymmetries in stellar motions as the result of this multiple nature of stellar orbital characteristics.

      The disk component of the Galaxy rotates around the nucleus in a manner similar to the pattern for the planets (planet) of the solar system, which have nearly circular orbits around the Sun. Because the rotation rate is different at different distances from the centre of the Galaxy, the measured velocities of disk stars in different directions along the Milky Way exhibit different patterns. The Dutch astronomer Jan H. Oort (Oort, Jan Hendrik) first interpreted this effect in terms of galactic rotation motions, employing the radial velocities and proper motions of stars. He demonstrated that differential rotation leads to a systematic variation of the radial velocities of stars with galactic longitude following the mathematical expression:

radial velocity = Ar sin 2l ,

where A is called Oort's constant and is approximately 15 km/sec/kiloparsec (1 kiloparsec is 3,260 light-years), r is the distance to the star, and l is the galactic longitude.

      A similar expression can be derived for measured proper motions of stars. The agreement of observed data with Oort's formulas was a landmark demonstration of the correctness of Lindblad's ideas about stellar motions. It led to the modern understanding of the Galaxy as consisting of a giant rotating disk with other, more spherical, and more slowly rotating components superimposed.

mass

      The total mass of the Galaxy, which had seemed reasonably well established during the 1960s, has become a matter of considerable uncertainty. Measuring the mass out to the distance of the farthest large hydrogen clouds is a relatively straightforward procedure. The measurements required are the velocities and positions of neutral hydrogen gas, combined with the approximation that the gas is rotating in nearly circular orbits around the centre of the Galaxy. A rotation curve, which relates the circular velocity of the gas to its distance from the galactic centre, is constructed. The shape of this curve and its values are determined by the amount of gravitational pull that the Galaxy exerts on the gas. Velocities are low in the central parts of the system because not much mass is interior to the orbit of the gas; most of the Galaxy is exterior to it and does not exert an inward gravitational pull. Velocities are high at intermediate distances because most of the mass in that case is inside the orbit of the gas clouds and the gravitational pull inward is at a maximum. At the farthest distances, the velocities decrease because nearly all the mass is interior to the clouds. This portion of the Galaxy is said to have Keplerian orbits, since the material should move in the same manner that the German astronomer Johannes Kepler (Kepler, Johannes) discovered the planets to move within the solar system, where virtually all the mass is concentrated inside the orbits of the orbiting bodies. The total mass of the Galaxy is then found by constructing mathematical models of the system with different amounts of material distributed in various ways and by comparing the resulting velocity curves with the observed one. As applied in the 1960s, this procedure indicated that the total mass of the Galaxy was approximately 200 billion times the mass of the Sun.

      During the 1980s, however, refinements in the determination of the velocity curve began to cast doubts on the earlier results. The downward trend to lower velocities in the outer parts of the Galaxy was found to have been in error. Instead, the curve remained almost constant, indicating that there continue to be substantial amounts of matter exterior to the measured hydrogen gas. This in turn indicates that there must be some undetected material out there that is completely unexpected. It must extend considerably beyond the previously accepted positions of the edge of the Galaxy, and it must be dark at virtually all wavelengths, as it remains undetected even when searched for with radio, X-ray, ultraviolet, infrared, and optical telescopes. Until the dark matter is identified and its distribution determined, it will be impossible to measure the total mass of the Galaxy, and so all that can be said is that the mass is several times larger than thought earlier.

      The nature of the dark matter in the Galaxy remains one of the major questions of galactic astronomy. Many other galaxies also appear to have such undetected matter. The possible kinds of material that are consistent with the nondetections are few in number. Planets and rocks would be impossible to detect, but it is extremely difficult to understand how they could materialize in sufficient numbers, especially in the outer parts of galaxies where there are no stars or even interstellar gas and dust from which they could be formed. Low-luminosity stars, called brown dwarfs (brown dwarf), are so faint that only a few have been detected directly. In the 1990s, astronomers carried out exhaustive lensing experiments involving the study of millions of stars in the galactic central areas and in the Magellanic Clouds (Magellanic Cloud) to search for dark objects whose masses would cause lensed brightenings of background stars. Some lensing events were detected, but the number of dark objects inferred is not enough to explain completely the dark matter in galaxies and galaxy clusters. It appears likely that there is more than one form of dark matter, perhaps including brown dwarf stars, massive neutrinos (neutrino), and possibly hypothetical types of objects, such as WIMPs (weakly interacting massive particles).

Additional Reading

Leila Belkora, Minding the Heavens: The Story of Our Discovery of the Milky Way (2003), is an interesting mix of history, biography, and science that describes how astronomers gradually uncovered the nature of the Milky Way. Linda S. Sparke and John S. Gallagher, Galaxies in the Universe (2000), gives a good basic introduction to galactic dynamics. Debra M. Elmegreen, Galaxies and Galactic Structure (1998), is an elementary text with an excellent chapter on galactic structure and kinematics. Dimitri Mihalas and James Binney, Galactic Astronomy: Structure and Kinematics, 2nd ed. (1981), is a thorough, mathematically replete textbook on the Milky Way Galaxy and other galaxies, with emphasis on structure and dynamics.Paul W. Hodge

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