Abstract
A program has been developed to evaluated the gravitational binding energy of a clumpy cluster composed ofN particles with a given mass dispersion, a given abundance of binaries and a given massive binary system at the centre. In application to clusters of galaxies nucleated by massivecD binaries, it is found that the gravitational binding energy is typically greater than the equivalent smooth distribution by a factor in the range 2–12. This suggests that the ‘missing’ mass problem in clusters of galaxies can be reduced by an order of magnitude if the correct binding energy is used in the virial theorem.
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