So far, we have limited ourselves to a consideration of the outward appearance of galaxies, somewhat like a taxonomist classifying the shapes of plants and animals. A taxonomist knows that his subjects are part of a large chain of evolution, allowing the recognition of order in the living diversity; also, he probably recognizes the function of many of his subjects’ features. But anyone studying galaxies knows that although they evolve, they have no parents or offspring, and their shapes are certainly not due to adaptation to their environment. Thus it is difficult to find the causes underlying the diversity of galaxies.

Little progress can be made in this respect unless, like the biologist, we also consider behaviour: the motions of the various components of the galaxies, or their dynamics. Before turning to the more complicated systems, let us consider elliptical galaxies. Motion is observed by means of the Doppler shift of a spectrum. As its bulk consists of stars only, the study of an elliptical’s dynamics requires the observation of the stellar velocities. Unfortunately only a few nearby ellipticals can be resolved into individual stars, and even in these cases the stars are too fault to allow detailed spectra to be made; these are necessary to determine the Doppler shift of spectral lines. One is therefore reduced to trying to obtain velocity information from an entire section of the galaxy, so that the spectrum observed is a composite of the spectra of all stars along the line of sight. This has four major disadvantages.Firstly, not all stars in the galaxy are of the same spectral type, so that a wide variety of stellar line shapes are blended together. Secondly, one looks right through the galaxy, which means that it is impossible to determine the velocity of a small region. Thirdly, not all stars are in perfectly circular orbits; most of them have a certain random velocity which usually is of the same order of magnitude as the systematic velocity due to galactic rotation. Finally, not every volume along the line of sight contains the same amount of stars, and consequently the central parts of the galaxy contribute; much more to the light than do the outskirts. These four disadvantages show that we are effectively looking at some¬thing which is a mixed, if not muddled, bag of material. It is there-Core not surprising that there is practically no information about the rotation curves of ellipticals; only a couple are known with Home, confidence . We see therefore that the masses of elliptical galaxies cannot be found by the method of integrating the rotation curve.

Fortunately, the systematic motions are not the sole source of information about a galaxy’s dynamics: the random motions can be used too. These are measured by observing the width of the absorption lines in a section of a galaxy . The random velocities of the stars in such a section cause a broadening of the absorption profile, because of the random superposition of Doppler shifts. The random velocities are of the order of 100 or 200 km s”1. Such a measurement can be translated into a mass by using the fact that virtually the only influence on the motion of a star is gravity, and that in a not-too-flattened system a star is on the average influenced only by the mass encompassed by its orbit. Thus one expects the stars in the outskirts of an elliptical galaxy to have a velocity corresponding to that of a Keplerian orbit about a central mass equal to the mass of the galaxy. By the laws of classical mechanics, this implies that the square of the velocity dispersion (i.e. spread in random velocities) is proportional to the galaxy’s mass divided by a typical orbital radius. Since the average orbit is about as large as the galaxy itself, it follows that the square of the velocity dispersion is proportional to the mass of the galaxy divided by its radius. Therefore, measurement of the radius (five kiloparsecs, say) and the velocity dispersion (l00kms-1 or so) yields an estimate of the mass (1010 solar masses in this example). By use of masses so determined, astronomers have found that the mass-to-luminosity ratio of an elliptical galaxy is typically 50. Since the M/L ratio of a spiral galaxy is about 5, an elliptical that is as luminous as a spiral contains 10 times as much mass. For example the companion of M 51 is almost as massive as the spiral galaxy itself!

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