The Milky Way and Beyond (8 page)

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.

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.

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 0.24
h
/
r
, where
h
is the solar motion in astronomical units per year and
r
is the mean distance for the solar motion solution.

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 [62 miles/sec] due to the wide variation in the shapes and orientations of orbits for these stars).

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 (12 miles/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 (6 miles/sec), and the dispersion is 21 km/sec (13 miles/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 (10 miles/sec) toward an apex with a position

α = 265°, δ = 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. 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 (10 miles/sec) for late B-type and early A-type stars to 24 km/sec (15 miles/sec) for late K-type and early M-type stars. The dispersion similarly increases from a value near 10 km/sec (6 miles/sec) to a value of 22 km/sec (14 miles/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 (50 ± 51 miles/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 (101 ± 22 miles/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 days, and the range of solar motion for this range of period extends from 30 to 205 km/sec (18 ± 127 miles/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 (140 miles/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 (186 miles/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 (230 miles/sec). This value was confirmed in the 2000s by an even more sensitive space telescope, the Wilkinson Microwave Anisotropy Probe.

T
he Milky Way Galaxy is made up of one hundred billion of those tantalizing points of light called stars, the massive, self-luminous celestial bodies of gas that shine by radiation derived from their internal energy sources. Our Sun is a star. Of the tens of billions of trillions of stars composing the observable universe, only a very small percentage are visible to the naked eye. Many stars occur in pairs, multiple systems, and star clusters. Members of such stellar groups are physically related through common origin and bound by mutual gravitational attraction. Somewhat related to star clusters are stellar associations, which consist of loose groups of physically similar stars insufficient mass as a group to remain together as an organization.