The radius-dependence of velocity dispersion in elliptical galaxies

The equations of stellar hydrodynamics are used to derive the radial variation of velocity dispersion in glaxies whose mass-to-light ratios are constant and whose brightness profiles obey the r1/4-law. One finds that the projected central velocity dispersion in such a system should be about 40 per cent lower than the peak velocity dispersion. The observability and physical interpretation of this phenomenon is discussed. There is some evidence that a similar effect has been observed in the structure of rich clusters of galaxies.