The Milky Way and Beyond (7 page)

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
^−24
g/cm
³
.

To 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. 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 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—though many are known and thoroughly studied—contribute almost imperceptibly to the local star density. At the same time, white dwarf stars, which are difficult to observe and of which very few are known, are among the more significant contributors.

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 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-cm (8-inch) 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 masses per cubic light-year.

For 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.

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 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.

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.

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 (56 miles/sec), and, from its radial
velocity (−108 km/sec [-67 miles/sec]) and distance (6 light-years), astronomers have found that its space velocity (total velocity with respect to the Sun) is 140 km/sec (87 miles/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, 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 55 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 (-32 miles/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 closer than 17 light-years, radial velocities range from −119 km/sec (-74 miles/sec) to +245 km/sec (+152 miles/sec). Most values are on the order of ±20 km/sec (±12 miles/sec), with a mean value of −6 km/sec (-4 miles/sec).

Space motions are made up of 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 (
U
= -5 miles/sec,
V
= −17 miles/sec, and
W
= -7 miles/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 (
U
= −5 miles/sec,
V
= -7 miles/sec, and
W
= -4 miles/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 (10 miles/second) 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.

One of the nearest 55 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 (152 miles/sec), and the components of its space velocity are

U
= 19 km/sec,
V
= −288 km/sec, and
W
= −52 km/sec (
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 (155 miles/sec) in this direction, the value
V
of −288 km/sec (-179 miles/sec) is primarily just a reflection of the solar orbital motion.