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Adetailed understanding of the structure and evolution of stars (the goal of Part II) requires knowledge of their physical characteristics. We have seen that knowledge of blackbody radiation curves, spectra, and parallax enables us to determine a star's effective temperature, luminosity, radius, composition, and other parameters. However, the only direct way to determine the mass of a star is by studying its gravitational interaction with other objects.
In Chapter 2 Kepler's laws were used to calculate the masses of members of our Solar System. However, the universality of the gravitational force allows Kepler's laws to be generalized to include the orbits of stars about one another and even the orbital interactions of galaxies, as long as proper care is taken to refer all orbits to the center of mass of the system.
Fortunately, nature has provided ample opportunity for astronomers to observe binary star systems. At least half of all “stars” in the sky are actually multiple systems, two or more stars in orbit about a common center of mass. Analysis of the orbital parameters of these systems provides vital information about a variety of stellar characteristics, including mass.
The methods used to analyze the orbital data vary somewhat depending on the geometry of the system, its distance from the observer, and the relative masses and luminosities of the components. Consequently, binary star systems are classified according to their specific observational characteristics.
• Optical double. These systems are not actually binaries at all but simply two stars that lie along the same line of sight (i.e., they have similar right ascensions and declinations). As a consequence of their large physical separations, the stars are not gravitationally bound, and hence the system is not useful in determining stellar masses.
• Visual binary. Both stars in the binary can be resolved independently, and if the orbital period is not prohibitively long, it is possible to monitor the motion of each member of the system. These systems provide important information about the angular separation of the stars from their mutual center of mass. If the distance to the binary is also known, the linear separations of the stars can then be calculated.
Most galaxies are not isolated in space, but rather form groups. Galaxy clusters are the largest structures visible in wide-angle images of the universe. These galactic groups are challenging subjects for astrophotographers.
THE CLASSIFICATION AND MORPHOLOGY OF GALAXY GROUPS AND GALAXY CLUSTERS
Independent of the focal length, when studying images of galaxies one notes that galaxies are not solitary objects. This does not necessarily imply spatial proximity, since even if the angular distance of two suspected neighbours is small, their true separation can be much larger. Since the third dimension, the distance of the individual galaxies from the Milky Way, is not obvious from the photograph, there is room for speculation. It is thus a logical assumption that galaxies which appear about the same size and display a similar amount of detail are located at similar distances and are thus neighbours in space. However, sizes are just a rough estimate since the appearances and thus relative sizes of galaxies in a group can be greatly changed by interactions. Redshift - derived galaxy distances in astronomical databases, by contrast, allow firmer statements to be made concerning which galaxies have a high probability of being part of a pair or group. Collections of up to 50 galaxies are deemed to be a group if the diameter is in the range three to five million light years. Due to the common gravitational potential, the members of the group differ only slightly in redshift. The so-called virial theorem implies that the mass of a bound group is always less than 2–3 × 1013 solar masses. The Milky Way is itself part of such a group – the Local Group. It consists of about 35 galaxies, although the number is increasing as further members have been discovered in the last few years. These new members are usually dwarf galaxies in the surroundings of large group members. Apart from the Milky Way, M 31 and M 33 are the largest and brightest members of the Local Group. Looking beyond the Local Group, nearby galaxies in our Galactic neighbourhood are also arranged in groups.