The Milky Way Galaxy

SIZE AND 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 discovered the planets to move within the solar system, where virtually all the mass is concentrated inside 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 200,000,000,000 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 from the rotation curve, and so all that can be said is that the mass is perhaps five or 10 times larger than thought earlier. That is to say, the mass, including the dark matter, must be about 1,000,000,000,000 times the mass of the Sun, with considerable uncertainty.

The nature of the dark matter in the Galaxy remains one of the major questions of galactic astronomy. Other galaxies also appear to have such matter in their outer parts. The only possible kinds of material that are consistent with the nondetections are all rather unlikely, at least according to present understanding in physics and astronomy. Planets and rocks would be impossible to detect, but it is extremely difficult to understand how they could materialize in sufficient numbers in the outer parts of galaxies where there are no stars or even interstellar gas and dust from which they could be formed. Massive neutrinos and other exotic, hypothetical subatomic particles also might be difficult to detect, but there is no good evidence that they even exist, and therefore they can only be considered a highly conjectural solution to the puzzle. It will take considerable effort to identify the dark matter with any degree of certainty. In the meantime it must be said that astronomy does not know what makes up much of the universe. 

MAJOR COMPONENTS

Stars and stellar populations.

Principal population types.

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, O and B stars, Cepheid variables, emission nebulas, and neutral hydrogen. Its Population II component, spread over a more nearly spherical volume of space, includes globular clusters, RR Lyrae 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. Table 3 summarizes the properties and membership of the five subdivisions that were accepted at the time of the Vatican Conference on stellar populations in 1957. These subdivisions ranged from the nearly spherical "halo Population II" system to the very thin "extreme Population I" system, and each of the subgroups was found to contain (though not exclusively) characteristic types of stars. It was even possible to divide some of the variable-star types into subgroups according to their population subtype. 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 M 5e) were considered "intermediate Population II," whereas the longer period variables fell into the "older Population I" category.

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 among 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 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 five 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 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 1.6 10¹⁰ years. The work of Sandage 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 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 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 10¹⁰ years or more. 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 or even quite as old as the globular clusters. This is an indication that globulars, 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. Table 3 illustrates the close correlations, as formulated in the early 1960s, for the stars in the Galaxy and shows that there are many different combinations of these three parameters that seem to be excluded in nature. The many different physical manifestations of these parameters were gradually building up. Methods of determining the abundance of metals in objects by means other than laborious high-dispersion coudé spectroscopy became possible. For example, it was found that stars having a low abundance of heavy elements exhibited an easily measurable ultraviolet excess. This is demonstrated when the three colours U, B, and V of the Yerkes system are plotted in a three-colour diagram where the Population II stars all lie distinctly to the left of the normal star, three-colour relationship. 

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 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 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 h and Persei, when compared to 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 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 to the solar neighbourhood. The second discrepancy is that very old clusters such as the globulars have too few high-luminosity stars, as compared to 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 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. 

Star clusters and stellar associations.

Globular clusters.

Globular clusters are extremely luminous objects. Their mean luminosity is the equivalent of approximately 25,000 suns. 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 globulars with stellar evolutionary models, the ages of all those so far measured range from 12 billion to 18 billion years. They are the oldest objects in the Galaxy and so must have been among the first formed when the system condensed out of the pregalactic gas. That this was the case is also indicated by the fact that the globulars 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, 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 globulars contain as little as 0.02 percent of the same elements.

Open clusters.

Clusters smaller and less massive than the globulars 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 globulars.

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 two or three to about 20 light-years, with the majority being less than five 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 of the Galaxy . 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 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. Astronomers use a diagram (the colour-magnitude diagram) that plots the temperatures of the stars against their luminosities to make this comparison. Colour-magnitude diagrams have been obtained for about 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.

Stellar associations.

The sizes of stellar associations are large; the average diameter of those in the Galaxy is about 700 light-years. Many are smaller, especially near the Sun, where they measure about 200 light-years across. In any case, stellar associations 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.

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  and if the exact position of the radiant is determined. If the angular distance of a star from the radiant is , 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

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

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

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 providing 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. By comparison, the trigonometric parallaxes of the same stars have errors of about 30 percent. 

Emission nebulas.

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 do exist between the arms. Many of them are found at intermediate distances from the centre of the Milky Way, 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 (K). 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 nebulas.

Supernova remnants.

Dust clouds.

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 Astronomy Satellite (IRAS), revealed a large number of dense dust clouds in the Milky Way.

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.

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 centimetres. 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 the Earth and the background stars and thereby determine the kinematics of the gas in different parts of the Galaxy.

STRUCTURE AND DYNAMICS

The structure of the Galaxy.

The nucleus.

The central bulge.

The disk.

The spiral arms.

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

where 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 wherein the solar system is located.

Theoretical understanding of the Galaxy's spiral arms has progressed greatly in the 1980s, 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 Chinese-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. 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 massive halo.

Density distribution.

The stellar density near the Sun.

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, Peter van de Kamp's investigation of stars within 17 light-years can be used to determine the density of stars in this volume of space. Similarly, Wilhelm Gliese's catalog of stars closer than 65 light-years can be used for a larger volume of space and a larger sampling of stars.

The result of van de Kamp's determination of star density shows that even in his extremely close sample, incompleteness remains a problem in the surveys. The 60 stars that he includes fill a volume of space equal to 20,000 cubic light-years. Therefore, it is possible to calculate that the stellar density is 0.003 stars per cubic light-year. This figure, however, includes double and multiple star systems in addition to single stars, and if only the number of the systems is used stellar density is reduced to 0.002 objects per cubic light-year. 

From Gliese's catalog, which contains 1,049 stars in a volume with a radius of 65 light-years, the average calculated density is less than one-third the calculated density for stars within 17 light-years. Thus, this catalog is incomplete, and its incompleteness is probably attributable to the fact that it is more difficult to detect the faintest stars and faint companions in the more distant systems.

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.

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

Variations in the stellar density.

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 "Gould's Belt," a tilt of the nearby bright stars in this direction with respect to the galactic plane. First noted by the English astronomer John Herschel 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-centimetre 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 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 mass per cubic light-year.  

Variation of star density with z distances.

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.

The values of the scale height for various kinds of objects given in Table 3 forms 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.

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.

Radial velocities.

For nearby stars, radial velocities are with very few exceptions rather small. For stars 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.

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 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.

Solar motion.

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.

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.

Solar motion calculations from space motions.

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 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 = 265 , = 25 .

When 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. Table 7 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, 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 also show correlations of this sort. The period of an RR Lyrae 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 day, 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 {script 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 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. 

The magnetic field of the Galaxy.

The rotation of the Galaxy.

The disk component of the Galaxy rotates around the nucleus in a manner similar to the pattern for the planets 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 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: 

where A is called Oort's constant and is approximately 15 km/sec/kpc, 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 a giant rotating disk.